text:
## Introduction

During a Raman scattering process, phonons are coupled to photo-excited electrons that relax to the ground state by the emission of scattered photons1,2,3. The frequency of a Raman mode is given by the energy difference between the incident and scattered photons4, and reveals structural information of materials5,6. On the other hand, the intensity is more sophisticated to estimate, and is majorly determined by the electron–photon and electron–phonon interactions7,8. More importantly, quantum interference can occur between different elementary pathways of Raman scattering, resulting in the modulation of inelastic scattering efficiencies9,10,11. So far, the quantum interference effect in Raman scattering have only been reported for few two-dimensional (2D) layered materials, such as electrostatically doped graphene12 and few-layer MoTe213,14. The observation of the quantum interference is challenging, yet essential for understanding the fundamental light-matter interaction, and for possible manipulation of light scattering in materials.

Rhenium dichalcogenide (ReX2, X = S or Se) is a layered transitional metal dichalcogenide (TMDC) material with triclinic symmetry15. The Re atoms in ReX2 (X = S, Se) crystals move away from metal sites in 2H phase to form Re4 parallelograms, leading to a distorted crystal structure and giving rise to anisotropic in-plane properties, such as anisotropic carrier mobility16,17,18, photoluminescence7,19,20 and Raman scattering21,22. It has been reported that chiral Raman scattering arose in ReS2 flakes of tens of nanometers in thickness, where the anisotropic optical effects play a prominent role23. However, the underlying fundamental interactions between photons/electrons/phonons during the chiral Raman scattering process, apart from the optical effects, have remained unexplored.

Herein, we report that chiral Raman scattering can be observed in monolayer ReS2 and ReSe2 excited by circularly polarized light, and large circular intensity difference (CID) is induced by the quantum interference between first-order Raman processes occurred at different k-points in the Brillouin zone. Our calculations show that although the amplitudes of induced electric dipoles are the same at each k-point, a phase difference exists for left- and right-handed circular polarization excitations, which results in the circular polarization differentiated Raman scattered intensities for all Raman modes due to quantum interference effect. The calculated chiral Raman spectra based on the quantum interference effect agree well with the experimental ones.

## Results

### Circular intensity difference in 2D ReS2 enantiomers

The optical setup for chiral Raman scattering measurements is shown in Fig. 1a. A quarter wave plate (QWP) is used to produce right-handed (RCP) or left-handed (LCP) circular polarization for excitation. The scattered light passes through the same QWP, and is collected without any analyzer. Single-layer (1L) ReS2 was mechanically exfoliated on a fused silica substrate (170 μm in thickness). The optical and atomic force microscopy (AFM) images are shown in Supplementary Fig. 2. The thickness of monolayer ReS2 was measured to be 1.1 nm.

The eigenvectors of the Raman-active vibrational modes (marked as mode I–VI) were calculated using density functional theory (DFT) and are shown in Fig. 1b24,25. In Fig. 1c, d, we show the experimental Raman spectra of 1L ReS2 below 250 cm1, excited by RCP and LCP of 1.96 eV and 2.33 eV, respectively. The helicity-dependent Raman intensities of 1L ReS2 can be clearly seen, and the intensity differences (IR − IL) are depicted in the insets. When excited by 1.96 eV photon energy, both mode III (153 cm1) and mode VI (235 cm−1) exhibit obvious chiral response but with opposite signs. For 2.33 eV excitation photon energy, the Raman scattering efficiencies by RCP are higher than that by LCP for I (132 cm1), II (143 cm1), III (153 cm1), and V (212 cm1) Raman modes, while mode IV at 162 cm1 and mode VI at 235 cm1 show opposite chiral Raman response. The circular intensity differential (CID, ) values, defined as (IR − IL)/(IR + IL), are obtained to be 0.49, 0.33, 0.18, −0.05, 0.27 and −0.16 for modes I–VI, respectively, for 2.33 eV excitation. While with 1.96 eV excitation photon energy, the CID values are −0.43 for 153 cm1 mode and 0.34 for 235 cm1 mode. The CID values are distinctly correlated to the phonon modes with certain excitation photon energy. This indicates that the helicity-dependence does not originate from circular dichroism26. It should also be noted that owing to the monolayer thickness (~1 nm), the optical birefringence can be negligible27.

Owing to the triclinic symmetry, layered ReX2 has two vertical orientations23,28. The chiral Raman scattering spectra of monolayer ReS2 with two different orientations were also measured and depicted in Fig. 2. To distinguish the two orientations, the atomic structures of 1L ReS2 were characterized by annular dark-field (ADF) scanning transmission electron microscopy (STEM) and the results are shown in Fig. 2a, e, where the Re4 parallelograms are highlighted. The vertical orientation in Fig. 2a is defined as ReS2 (+), and the angle between the a-axis ([100]) and b-axis ([010]) is 119.8° (anticlockwise), while for ReS2 (−) in Fig. 2e, the angle is −119.8° (clockwise).

To further investigate the chiral Raman scattering, the scattering efficiencies of ReS2 (+) and ReS2 (−) were measured as a function of rotation angle of the QWP. The Jones matrix of the electric field can be described as $$\left(\begin{array}{cc}1-{{{{{\rm{icos}}}}}}2\theta & -{{{{{\rm{isin}}}}}}2\theta \\ -{{{{{\rm{isin}}}}}}2\theta & 1+{{{{{\rm{icos}}}}}}2\theta \end{array}\right)$$. The Raman scattering intensities excited by 1.96 eV (Fig. 2b) and 2.33 eV (Fig. 2c) photon energy vary periodically. The intensities of all the Raman modes with different rotation angles θ are extracted and the polar plots are depicted in Supplementary Tables 3, 4. Figure 2d shows the polar plots of mode 132 cm−1. For 1.96 eV excitation, the Raman scattering intensity of RCP (IR) is almost identical to that of LCP (IL). While for 2.33 eV excitation, the 132 cm−1 Raman peak shows the maximum IR and the minimum IL. These results imply that the chiral Raman response is dependent on the excitation photon energy. For ReS2 (−), the intensity maps (Fig. 2f, g) and the polar plots of the 132 cm−1 mode in Fig. 2h show opposite trends to that of 1L ReS2 (+).

It has been reported that chirality in two-dimensions arises when distinct enantiomers are confined to a plane, that can be interconverted by space inversion but owing to the inaccessible third dimension, can not be interconverted by any rotation about the axis perpendicular to the plane29,30. Considering the spatial operation in three dimensions, ReS2 is an achiral material. However, layered ReS2 confined to a substrate exhibits planer chirality, owing to that the mirror reflection of Re4 parallelogram can not be superposed on its original one by rotation (Supplementary Fig. 1). Indeed, the lack of inversion center in the 2D plane leads to the two distinct 2D ReS2 enantiomers. However, it is still not clear how the chiral Raman response arises from the microcosmic view of electron/photon and electron/phonon interactions.

### Theoretical calculations

In order to understand the physical origin of large CID observed in 1L ReS2, the intensity of the first-order Raman scattering is calculated by third-order perturbation theory. The Raman intensity and Raman tensor can be both calculated according to the electronic band structure and the phonon dispersion (Supplementary Fig. 3) of 1L ReS2, and the expressions are given in Eqs. (1) and (2) in the Method section, respectively. The calculated band gap (~1.50 eV) is indirect in the vicinity of Brillouin zone center and the direct one is around 1.55 eV, which is almost coincident with the experimental fundamental optical absorption edge in literature31. The calculated phonon dispersion relation shows dispersive phonon bands below 250 cm−1 and relatively flat bands above 250 cm1. The phonon modes of interest here lie below 250 cm−1, as marked in yellow. There are 9 optical phonon modes in this region in which all the 6 gerade modes (Ag) are Raman-active while the other 3 ungerade modes (Au) are infrared-active according to the character table of Ci point group. Raman frequencies of the 6 Raman modes agree quantitatively between the experiment and calculation. More importantly, the calculated Raman spectra reveals that the chiral Raman scattering of 1L ReS2 arises from the interference effect between all possible quantum pathways of elementary transitions as discussed below.

Figure 3 shows the dependence of the calculated Raman spectra on laser energy and helicity. In Fig. 3a, b, the Raman spectra within three different interference patterns excited by both RCP and LCP at two laser energies are given. The three interference patterns include no interference, intra-k interference, and full interference, as demonstrated in Fig. 3c. In the simplest scenario, 4 electrons at two k-points are assumed to be involved in the Raman scattering process, for each scattering channel Tn = es*Rn*ei, in which Rn is the Raman tensor, ei and es is Jones vector of incident and scattering polarization, respectively. No interference refers to the case that Raman intensity consists of simple superposition of each independent Raman process, namely, |T1|2 + |T2|2 + |T3|2 + |T4|2; intra-k interference to |T1 + T2|2 + |T3 + T4|2, and full interference to |T1 + T2 + T3 + T4|2 (consistent with the third-order perturbation theory in Eq. (1)). From top to bottom panel of Fig. 3a, b, Raman spectra excited by two circularly polarized lasers show no difference between RCP and LCP for no interference case; the intra-k interference shows very slight difference but CID values do not agree with the experimental data; when the full interference effect is concerned, not only the CID sign but also the relative values agree well with experimental observations. The calculated CID spectra for 1.96 eV and 2.33 eV lasers are given in Fig. 3d, e. To have a direct impression, the calculated values of CID for the 6 Raman modes at two photon energies in the three interference patterns are listed in Fig. 3f. The agreement between the calculated CID spectra in Fig. 3d, e and our experimental measurement in Fig. 1c, d reveals the essential role played by the full interference between all possible quantum pathways of elementary transitions. The microscopic picture of the full interference effect and its relevance to the phase coherent dipole vector D are discussed in more details in Supplementary Material 4. Briefly, the amplitudes of induced dipole vectors are the same for LCP and RCP excitations, so that the optical absorption is helicity-independent (Supplementary Fig. 4a, b). This confirms that no circular dichroism is expected in ReS2. Further, the phase angles of Raman tensors $${{{{{{\bf{R}}}}}}}_{{{{{{\bf{i}}}}}},{{{{{\bf{f}}}}}},{{{{{\bf{n}}}}}},{{{{{{\bf{n}}}}}}}^{\prime}} ({{{{{\bf{k}}}}}})$$ involving one electron are found to be either parallel or antiparallel to each other (Supplementary Fig. 5), indicating that the Raman intensity would not depend on helicity if no inter-k interference effect considered. However, the k-resolved phase distribution of complex $${{{{{{\bf{T}}}}}}}_{{{{{{\bf{i}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{f}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{n}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{{\bf{n}}}}}}}^{{{{\prime} }}}}\left({{{{{\bf{k}}}}}}\right)={{{{{{\bf{e}}}}}}}_{{{{{{\bf{s}}}}}}}\cdot {{{{{{\bf{R}}}}}}}_{{{{{{\bf{i}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{f}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{n}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{{\bf{n}}}}}}}^{{{{\prime} }}}}{{{{{\boldsymbol{(}}}}}}{{{{{\bf{k}}}}}}{{{{{\boldsymbol{)}}}}}}\cdot {{{{{{\bf{e}}}}}}}_{{{{{{\bf{i}}}}}}}$$ is different between LCP and RCP excitations, leading to different interference between k points, and hence distinctive Raman intensities as observed in Fig. 1c, d and calculated in Fig. 3d, e.

The Raman tensor of ReS2 for a given excitation photon energy, defined as $$\left(\begin{array}{cc}{a{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{a}} & {b{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}}\\ {b{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}} & {c{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{c}}\end{array}\right)$$ for 2D ReS2 (+), is the result of the quantum interference between all k-points. The tensor elements are calculated by considering full interference and are listed in Supplementary Tables 1, 2. The 2D ReS2 (−) is the mirror reflection of ReS2 (+), and the first Brillouin zone is the primitive cell of the reciprocal lattice, hence it can not be interconverted with its mirror reflection, resulting in enantiomorphous electronic band structure and phonon dispersion. Therefore, the Raman tensor for ReS2 (−) is represented as $$\left(\begin{array}{cc}{a{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{a}} & -{b{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}}\\ -{b{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}} & {c{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{c}}\end{array}\right)$$. The Raman intensity of 2D ReS2 (+) for LCP and RCP excitations can be evaluated by the Raman selection rules as:

$${I}_{L}\propto {{{{{\rm{\pi }}}}}}\left({a}^{2}+{2b}^{2}+{c}^{2}\right)-2{{{{{\rm{\pi }}}}}}\left({ab}\,{{\sin }}\left({\varphi }_{b}-{\varphi }_{a}\right)-{bc}\,{{\sin }}\left({\varphi }_{c}-{\varphi }_{b}\right)\right),$$
$${I}_{R}\propto {{{{{\rm{\pi }}}}}}\left({a}^{2}+{2b}^{2}+{c}^{2}\right)+2{{{{{\rm{\pi }}}}}}\left({ab}\,{{\sin }}\left({\varphi }_{b}-{\varphi }_{a}\right)-{bc}\,{{\sin }}\left({\varphi }_{c}-{\varphi }_{b}\right)\right).$$

However, for ReS2 (−), $$b{{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}}$$ is replaced by $$-b{{{{{{\rm{e}}}}}}}^{{{{{{\rm{i}}}}}}{\varphi }_{b}}$$, leading to opposite chiral Raman responses Δ(+) = −Δ(−).

### Chiral Raman response of ReSe2

Although the quantum interference effect in Raman scattering has been reported in other 2D materials11,12,13,14, this is the first observation of quantum interference leading to pronounced chiral Raman response. Furthermore, it can be expected that quantum interference exists in Raman scattering of a broader frame of materials. Here, we show that the chiral Raman scattering can also be observed in other triclinic 2D layered materials such as ReSe2. The crystal structure of ReSe2 is similar to ReS2, and there are 18 Raman active modes (Ag modes) in the center of Brillouin zone32. The optical and AFM images of mechanically exfoliated 1L ReSe2(±) samples are shown in Supplementary Fig. 2e–h. Figure 4a show the chiral Raman scattering spectra (EL = 2.33 eV) of mechanically exfoliated 1L ReSe2 (+). The corresponding ADF-STEM image is given in Fig. 4b, where the Re4 structure is indicated by white parallelogram. The Raman intensities of the four modes at 110 cm−1, 119 cm−1, 125 cm−1, and 162 cm−1 are extracted for different excitation photon energies and plotted in Supplementary Tables 5, 6, respectively. The modes at 119 cm−1 and 162 cm−1 are shown in Fig. 4c, d with 2.33 eV in blue and 1.96 eV in red color. From Fig. 4c, it can be seen that for 2.33 eV excitation, IR of 119 cm−1 mode is larger than IL, while for 1.96 eV, IL is larger than IR. These results also indicate the occurrence of quantum interference in Raman scattering. For the 162 cm−1 mode shown in Fig. 4d, IR is larger than IL for 2.33 eV, but almost the same for 1.96 eV. The results for ReSe2(−) are given in Fig. 4e–h. The 119 cm1 mode (Fig. 4g) shows larger IL for 2.33 eV, and larger IR for 1.96 eV, and the fitting profiles of the polar plots are opposite to that of ReSe2 (+). As for the 162 cm−1 mode, the chiral Raman response is also orientation-dependent (Fig. 4h). For 2.33 eV excitation, the 162 cm−1 mode has the lowest IR and significantly larger IL, but IR is larger than IL.

## Discussions

In summary, we reported that the quantum interference in Raman scattering can result in strong chiral response in 2D enantiomers of single-layer triclinic ReX2. The Raman scattering efficiencies for LCP and RCP excitations are observed to be clearly different and depend on the Raman modes and excitation photon energies. Our calculations reveal that the optical absorption intensities are exactly the same in the whole k-space for photons of LCP and RCP, however, the k-resolved phases of complex $${{{{{{\bf{T}}}}}}}_{{{{{{\bf{i}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{f}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{n}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{{\bf{n}}}}}}}^{{{{\prime} }}}}\left({{{{{\bf{k}}}}}}\right)={{{{{{\bf{e}}}}}}}_{{{{{{\bf{s}}}}}}}\cdot {{{{{{\bf{R}}}}}}}_{{{{{{\bf{i}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{f}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{\bf{n}}}}}}{{{{{\boldsymbol{,}}}}}}{{{{{{\bf{n}}}}}}}^{{{{\prime} }}}}{{{{{\boldsymbol{(}}}}}}{{{{{\bf{k}}}}}}{{{{{\boldsymbol{)}}}}}}\cdot {{{{{{\bf{e}}}}}}}_{{{{{{\bf{i}}}}}}}$$ show different patterns, resulting in distinct Raman scattering intensities as a result of different quantum interference.

Our findings reveal that quantum interference can lead to pronounced chiral response of Raman scattering in materials and indicate that quantum interference can be a generic effect in inelastic optical scattering, which becomes evident when either constructive or destructive interference between all the inelastic scattering pathways dominates, in the condition that the excitation photon energy is larger than the band gap of the materials. This effect is also applicable to the bulk triclinic crystals (ReS2 and ReSe2), but additional anisotropic optical environment should be taken into consideration for a complete analysis of chiral response.

## Methods

### Specimen preparation and Raman scattering measurement

The ReS2 and ReSe2 flakes were mechanically exfoliated on fused silica substrates. Single-layer ReS2 and ReSe2 were located by an optical microscope (Olympus BX51), and the thicknesses were measured by atomic force microscope (AFM, Bruker ICON). Raman spectra were measured using JY Horiba HR800 with 2.33 eV and 1.96 eV excitation energy at room temperature. A 100× objective lens (NA0.9) and 1800 lines/mm grating were chosen for spectra acquisition.

### STEM measurement

A PPC/PDMS stamp was used to pick the ReS2 flakes from the substrates, and was covered onto the SiNx grids using a transfer stage. The temperature was raised to 110 °C until the stamps and the grids were well contacted, and then the grids and the stamps were placed in acetone for 24 h at room temperature to remove the PPC. STEM-ADF images were taken using FEI Titan Cubed Themis G2 300 operated at 300 kV. The convergence semi-angle was 21.3 mrad while the collection angle of ADF detector was 39–200 mrad. While acquiring images, the probe current was ~8 pA, and the dwell time was 2 μs/pixel. For this condition, the radiation damages can be avoided and images with high signal-to-noise ratio were obtained.

### Computation method

First-order Raman intensity and Raman tensor as a function of phonon energy $${\hslash \omega }_{\nu }$$ and of the incident laser energy EL can be described by third-order perturbation theory as

$${I}^{\nu }\left({E}_{L}\right)\propto {\left|\mathop{\sum}\limits_{{{{{{\bf{k}}}}}}}\mathop{\sum}\limits_{i=f,m,{m}^{{\prime} }}\frac{{{{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{f}}}}}}{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{s}}}}}}}}\left({{{{{\bf{k}}}}}}\right){\cdot {{{{{\bf{M}}}}}}}_{{{{{{\bf{ep}}}}}}}^{{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{m}}}}}}}_{{{{{{\boldsymbol{\upsilon }}}}}}}}\left({{{{{\bf{k}}}}}}\right){\cdot {{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{mi}}}}}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{i}}}}}}}}\left({{{{{\bf{k}}}}}}\right)}{\left({E}_{L}-{\Delta E}_{{mi}}-{{{{{\rm{i}}}}}}\gamma \right)\left({E}_{L}-{{\hslash }}{\omega }_{\nu }-{\Delta E}_{{m}^{{\prime} }i}-{{{{{\rm{i}}}}}}\gamma \right)}\right|}^{2}$$
(1)
$$R\left(\nu \right)=\mathop{\sum}\limits_{{{{{{\rm{k}}}}}}}\mathop{\sum}\limits_{i=f,\,m,{m}^{{\prime} }}\frac{{{{{{{\bf{D}}}}}}}^{{{{{{\bf{f}}}}}}{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}}\left({{{{{\bf{k}}}}}}\right)\cdot {{{{{{\bf{M}}}}}}}_{{{{{{\bf{ep}}}}}}}^{{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{m}}}}}}}_{{{{{{\boldsymbol{\upsilon }}}}}}}}\left({{{{{\bf{k}}}}}}\right)\cdot {{{{{{{\bf{D}}}}}}}^{{{{{{\bf{mi}}}}}}}\left({{{{{\bf{k}}}}}}\right)}^{* }}{\left({E}_{L}-{\Delta E}_{{mi}}-{{{{{\rm{i}}}}}}\gamma \right)\left({E}_{L}-{{\hslash }}{\omega }_{\nu }-{\Delta E}_{{m}^{{\prime} }i}-{{{{{\rm{i}}}}}}\gamma \right)}$$
(2)

where $${{{{{{\bf{D}}}}}}}^{{{{{{\bf{fm}}}}}}{{{\prime} }}}\left({{{{{\bf{k}}}}}}\right)$$ and $${{{{{{{\bf{D}}}}}}}^{{{{{{\bf{mi}}}}}}}\left({{{{{\bf{k}}}}}}\right)}^{{{{{{\boldsymbol{* }}}}}}}$$ are the dipole vectors for photon emission and absorption in the electron-photon interactions, respectively.

To single out the interference effect, we use Eq. (1) for the full interferences between all possible quantum pathways. To compare, Eq. (3), is used for considering the interference only between different excited states at the same k point not between different k points, and Eq. (4) for the case of no interference at all.

$${I}^{\nu }\left({E}_{L}\right)\propto \mathop{\sum}\limits_{k}{\left|\mathop{\sum}\limits_{i=f,m,{m}^{{\prime} }}\frac{{{{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{f}}}}}}{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{s}}}}}}}}\left({{{{{\bf{k}}}}}}\right){\cdot {{{{{\bf{M}}}}}}}_{{{{{{\bf{ep}}}}}}}^{{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{m}}}}}}}_{{{{{{\boldsymbol{\upsilon }}}}}}}}\left({{{{{\bf{k}}}}}}\right){\cdot {{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{mi}}}}}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{i}}}}}}}}\left({{{{{\bf{k}}}}}}\right)}{\left({E}_{L}-{\Delta E}_{{mi}}-{{{{{\rm{i}}}}}}\gamma \right)\left({E}_{L}-{{{\hslash }}\omega }_{\nu }-{\Delta E}_{{m}^{{\prime} }i}-{{{{{\rm{i}}}}}}\gamma \right)}\right|}^{2}$$
(3)
$${I}^{\nu }\left({E}_{L}\right)\propto \mathop{\sum}\limits_{k}\mathop{\sum}\limits_{i=f,\,m,{m}^{{\prime} }}{\left|\frac{{{{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{f}}}}}}{{{{{{\bf{m}}}}}}}^{{\prime}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{s}}}}}}}}\left({{{{{\bf{k}}}}}}\right){{{\cdot }}{{{{{\bf{M}}}}}}}_{{{{{{\bf{ep}}}}}}}^{{{{{{{\bf{m}}}}}}}^{{{{\prime} }}}{{{{{{\bf{m}}}}}}}_{{{{{{\boldsymbol{\upsilon }}}}}}}}\left({{{{{\bf{k}}}}}}\right){{{\cdot }}{{{{{\bf{M}}}}}}}_{{{{{{\bf{opt}}}}}}}^{{{{{{\bf{mi}}}}}}{{{{{{\bf{e}}}}}}}_{{{{{{\bf{i}}}}}}}}\left({{{{{\bf{k}}}}}}\right)}{\left({E}_{L}-{\Delta E}_{{mi}}-{{{{{\rm{i}}}}}}\gamma \right)\left({E}_{L}-{{{\hslash }}\omega }_{\nu }-{\Delta E}_{{m}^{{\prime} }i}-{{{{{\rm{i}}}}}}\gamma \right)}\right|}^{2}$$
(4)

All the required matrix elements are calculated by using a modified version of the QUANTUM-ESPRESSO code, and especially, the electron-phonon coupling is computed by means of the Wannier interpolation schemes in the standard Electron–Phonon Wannier (EPW) package as implemented in QUANTUM-ESPRESSO. The electron and phonon bands are calculated in the local density approximation with norm-conserving pseudopotentials. A fine Monkhorst-Pack grid of 9 × 9 × 1 and 5 × 5 × 1 is used to sample the first Brillouin zone, respectively. We use the energy cut-off of 150 Ry to expand the wave functions with 10−13 Ry energy convergence threshold for self-consistency. A vacuum region of 20 Angstroms in the z-direction is used to avoid spurious interactions between two monolayers. The geometry is optimized using the quasi-newton algorithm, until none of the residual Hellmann–Feynman forces exceeds 10−5 Ry/Bohr and all components of stress tensor are less than 0.01 kbar. At last, we get the matrix elements on a much fine grid of 45 × 45 × 1 which is dense enough to achieve satisfactory results.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.


text:
Journal article Open Access

Does Reviewer Recommendation Help Developers?

Vladimir Kovalenko; Nava Tintarev; Evgeny Pasynkov; Christian Bird; Alberto Bacchelli

Citation Style Language JSON Export

{
"DOI": "10.5281/zenodo.1404814",
"abstract": "
Selecting reviewers for code changes is a critical step for an efficient code review process. Recent studies propose automated reviewer recommendation algorithms to support developers in this task. However, the evaluation of recommendation algorithms, when done apart from their target systems and users (i.e., code review tools and change authors), leaves out important aspects: perception of recommendations, influence of recommendations on human choices, and their effect on user experience.
\n\n
This study is the first to evaluate a reviewer recommender in vivo. We compare historical reviewers and recommendations for over 21,000 code reviews performed with a deployed recommender in a company environment and set out to measure the influence of recommendations on users' choices, along with other performance metrics.
\n\n
Having found no evidence of influence, we turn to the users of the recommender. Through interviews and a survey we find that, though perceived as relevant, reviewer recommendations rarely provide additional value for the respondents. We confirm this finding with a larger study at another company. The confirmation of this finding brings up a case for more user-centric approaches to designing and evaluating the recommenders.
\n\n
Finally, we investigate information needs of developers during reviewer selection and discuss promising directions for the next generation of reviewer recommendation tools.
\n\n
Preprint: https://doi.org/10.5281/zenodo.1404814
",
"author": [
{
},
{
"family": "Nava Tintarev"
},
{
"family": "Evgeny Pasynkov"
},
{
"family": "Christian Bird"
},
{
"family": "Alberto Bacchelli"
}
],
"container_title": "IEEE Transactions on Software Engineering",
"id": "1404814",
"issued": {
"date-parts": [
[
2018,
8,
28
]
]
},
"publisher": "Zenodo",
"title": "Does Reviewer Recommendation Help Developers?",
"type": "article-journal"
}
510
314
views

format: plain


text:
💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# To prove that sine is continuous, we need to show that $\lim_{x \to a} \sin x = \sin a$ for every real number $a$. By Exercise 63 an equivalent statement is that $$\lim_{h \to 0} \sin (a + h) = \sin a$$.Use (6) to show that this is true.

Check back soon!

Limits

Derivatives

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

this problem Number sixty four of the Stuart Calculus eighth edition, section two point five. To prove the sinus continuous, we need to show that the limit is expert is a The function sign of X is equal to sign of A for every real number, eh? I exercised sixty three, and a cool and statement is that the limit is a H bridge. Zero of sign of the quantity April's age is equal to sign of a ah use six to show that this is true. So we will be using an identity to confirm that this isn't true. Identities Sign of experts Why is equal to cynics cosign y plus cosign x sanely that we will pry it here directly if we take this limit and sage approaches zero of the function given sign of the quality of those h, we can separate this into sign of a Kosanovic plus AH co sign a V sign of age. And little by little, we will separate the limit out. H approaches zero. This is a sum inside that would limit. We can use a limit law to separate this into, ah, two different limits. So the first limited sign echoes and h the second limit Each approaches zero of co sign a sign h what we will see in this The great limit is that h approaching zero for this term Sign of age Coast to zero since sign of H Senat zero is equal to zero. So we're left with this first limit. And if we approach zero for H, well, we have the first part, which is a sign of a and then we're multiplying this by the limiters h broke Ziro cosign of each. What is this limit? The second limit equal to well as HBO zero cosign of h approaches one. So this limit is actually equal to one. And what were left over with his the limit as they H bridges are a sign of E and in this case, Santa is independent of H. It is a constant value no matter what age approaches this values equal to their This limit is equal to Santa Fe, and what we've done here is what we have confirmed exactly. This limit this definition for the continuity of sign for any value they on this confirms that this is a D true and sign is continuous

Limits

Derivatives

Lectures

Join Bootcamp


text:
HOME

PHOTOS

VENEZUELA ECON

ONLINE

Instagram
AngelList
Keybase
GitHub
IFTTT

BY COUNTRY

Afghanistan
Brazil
Colombia
Cuba
Egypt
Guyana
Iraq
Jordan
Lebanon
Mexico
United Kingdom
Venezuela

BY MEDIUM

Text
Photo
TV/Video

BY PUBLISHER

Al Jazeera
BBC
BuzzFeed
CBC
Christian Science Monitor
CNN
Daily Mail
Data Driven Journalism (EJC)
Datum
Ecologist
Economist Intelligence Unit
Emerging Markets
Financial Times
Foreign Policy
France 24
Fusion
GlobalPost
Guardian
Independent
La Prensa (Panama)
LatinFinance
Mancunion
Monocle
National (Abu Dhabi)
New Internationalist
New Statesman
New York Times
New Yorker
NPR
PBS
PRI
Reuters
RTE
Sky News
Sun
Sunday Times
Telegraph
TIME
Times of London
USA Today
Vice
WLRN

 Chávez Wins New Term in Venezuela, Holding Off Surge by OppositionOct. 8, 2012 — Caracas, Venezuela Published by New York Times [PDF] President Hugo Chávez, long a fiery foe of Washington, won re-election on Sunday, facing down cancer and the strongest electoral challenge of his nearly 14 years in office and gaining a new mandate to deepen his socialist revolution. Though his margin of victory was much narrower than in past elections, he still won handily. With 90 percent of the votes tallied, Mr. Chávez received 54 percent, to 45 percent for his opponent, Henrique Capriles Radonski, the national election council said. Fireworks erupted in Caracas after the news, and Chávez supporters celebrated in the streets. Shortly before 11:30 p.m. local time, Mr. Chávez stepped out onto the balcony of the presidential palace in Caracas and waved to a sea of jubilant supporters. “My words of recognition go out from here to all who voted against us, a recognition for their democratic temperament,” he said. A former soldier, he called the election a “perfect battle.” Still, after a spirited campaign, the polarizing Mr. Chávez finds himself governing a changed country. He is an ailing and politically weakened winner facing an emboldened opposition that grew stronger and more confident as the voting neared, and held out hope that an upset victory was within reach. Mr. Chávez has said that he would move forward even more aggressively to create his version of socialism in Venezuela in a new six-year term, although his pledges were short on specifics. His health, though, remains a question mark. He has undergone several rounds of treatment for cancer in the last 15 months, but has refused to make public essential details of his illness. If he overcomes the disease and serves out his new term to its end in 2019, he will have been in power for two full decades. Toward the end of the campaign, facing pressure from Mr. Capriles, he pledged to make his government more efficient and to pay more attention to the quality of government programs like education. He even made appeals for the middle class and the opposition to join in his revolution. But Mr. Chávez spent much of the year insulting and trying to provoke Mr. Capriles and his followers. And on Sunday night, he had to face the fact that the people he taunted as squalid good-for-nothings, little Yankees and fascists, turned out to be nearly half the electorate. As the opposition’s momentum grew, Mr. Chávez’s insults seemed to lose their sting. By the end of the campaign, young people in Caracas were wearing colorful T-shirts that said “majunche” or good-for-nothing, Mr. Chávez’s favorite taunt. Mr. Capriles was subdued on Sunday night, congratulating Mr. Chávez and saying he hoped the president would see the result as “the expression today of a country with two visions, and to be president means working to solve the problems of all Venezuelans.” He appeared poised to carry on his fight in the elections for state governors in December. “You should all feel proud, do not feel defeated,” he told supporters. Michael Shifter, president of the Inter-American Dialogue, a research institute in Washington, called the presidential election “a fundamental turning point.” He said Mr. Chávez was “going to have to deal with a very different society than he dealt with in his last term, a society that’s awakened and more organized and more confident.” Even so, the opposition is a fragile coalition with a history of destructive infighting, especially after an election defeat. Mr. Capriles will have to keep this fractious amalgam of parties from the left, right and center together in order to take advantage of the new ground they have gained. “The opposition has more power, it feels more support,” said Elsi Fernandes, a schoolteacher, who voted for Mr. Capriles on Sunday morning in Catia, a poor neighborhood in Caracas. “The difference is that we’re not going to stay with our arms crossed.” The turnout was more than 80 percent, the highest in decades, the election council said. People stood in line for hours, although the voting appeared in most cases to run smoothly. Venezuela uses a touch-screen electronic voting system, and voters are identified with a digital thumbprint reader; technical problems at some polling places caused long delays and, in some, a resort to backup paper ballots. Polling places were told to keep working until everyone in line at closing time had a chance to vote. Venezuela is mired in problems, including out-of-control violent crime, crumbling roads and bridges, and power blackouts that regularly plague much of the country outside the capital. Oil production, the country’s mainstay, has plateaued in recent years, and other exports have not picked up the slack. The overall economy grew this year, largely because of a huge pre-election boost in government spending, but clouds loom. A devaluation of the Venezuelan currency, the bolívar, is widely seen as inevitable, and inflation remains stubbornly high. Mr. Chávez has trumpeted his programs to help the poor, and has pointed to a sharp reduction in the number of people living in poverty. But he has governed during a phenomenal rise in oil prices, which have soared from $10 in 1998, the year before he took office, to more than$100 in recent years and the high \$80s now, pouring huge amounts of revenue into Venezuela. Mr. Capriles, who has served as a legislator, mayor and governor, campaigned almost nonstop, seeking to contrast his energetic style with the reduced schedule of Mr. Chávez, who received a diagnosis of cancer in 2011. Mr. Chávez has kept most details of his condition secret, refusing to say exactly what kind of cancer he has or where in his body it is. He received chemotherapy last summer after an operation to remove a tumor, but the cancer returned and he had another operation in February, followed by radiation therapy. The operations and treatments were performed in Cuba, taking Mr. Chávez out of Venezuela for extended periods. His health, and whether he was well enough to serve a new six-year term, always loomed over the campaign, but it receded as an issue as Mr. Chávez gradually increased his public appearances. Still, he never threw himself into campaigning at the frenzied pace of Mr. Capriles. Opposition to Mr. Chávez has long been divided and easily manipulated by Mr. Chávez, a master politician who kept his rivals off balance. Mr. Capriles changed that. He crisscrossed the country, campaigning in places long considered bastions of support for Mr. Chávez, including urban slums and poor rural areas. He told voters that he was the future and Mr. Chávez the past. Mr. Chávez dismissed Mr. Capriles as an unworthy opponent, accusing him of lying about wanting to continue Mr. Chávez’s social programs. He called Mr. Capriles a right-wing oligarch in disguise who sought to bring back the bad old days of rule by the rich. In Catia, María Elena Severine, 59, who works as a cleaner in a bank, said that Mr. Chávez was still as fresh a candidate as when he first ran in 1998. She lives in a rental apartment but hopes someday to be given a new home government-built home. “I like my president,” she said. “He is the revolution. He is change.” Reporting was contributed by María Eugenia Díaz, Jonathan Gilbert, Girish Gupta and Andrew Rosati from Caracas, and María Iguarán from Cumaná, Sucre State.


text:
randomise items mode 1 doesnt work on bgee (install fail)

Recommended Posts

hi I got a bgee in steam version

and whenever I try to install randomise item mode 1 or 2, it fails

it copies/patches a lot of files but eventually it shows error message

though mode 3 or 4 works fine.

Randomise items: Mode 1: Randomise with in-game scripts. No items are lost

my debug list is like this

~~~~ copying a lot of things

Copied [ar0506.are] to [override/ar0506.are]

Copying and patching 1 file ...

Copying and patching 1 file ...

Copied [...blank] to [randomiser/baf/compile/flset15.baf]

Copying and patching 1 file ...

Copied [randomiser/copy/flrandom.cre] to [override/flset15.cre]

Copying and patching 1 file ...

Copied [ar3100.are] to [override/ar3100.are]

Compiling 218 scripts ...

Processing 1 dialogues/scripts ...

Creating 1 directory

Copying 1 file ...

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

ERROR Installing [Mode 1: Randomise with in-game scripts. No items are lost], rolling back to previous state

Will uninstall 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

Uninstalled 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

RANDOMISER/RANDOMISER.TP2 0 500 Installed ~Randomly replace the WIS tome normally found in TotSC with one of the 6 available types~

RANDOMISER/RANDOMISER.TP2 0 530 Installed ~Randomise scrolls~

ERROR: Unix.Unix_error(20, "stat", "randomiser/ssl/ssl_out/fltier.baf")

PLEASE report the error message in the file SETUP-RANDOMISER.DEBUG to Wisp, www.forums.gibberlings3.net

Using Language [English]

[English] has 2 top-level TRA files

[randomiser/languages/english/setup.tra] has 50 translation strings

[randomiser/languages/english/in-game.tra] has 408 translation strings

Install Component [Randomise items]?

[N]o, [Q]uit or choose one:

1] Mode 1: Randomise with in-game scripts. No items are lost

2] Mode 1: Randomise with in-game scripts. Some items are lost

3] Mode 2: Randomise with WeiDU. No items are lost

4] Mode 2: Randomise with WeiDU. Some items are lost

Saving This Log:

btw there is no other weidu mod at all

I just had deleted the existing bgee folder and installed bgee freshly

and then I have installed randomise mod

all options works fine except that only randomise items mode 1 or 2 doesn't work during install

...
Can you find the: randomiser/ssl/ssl_out/fltier.baf -file ? I suspect a coding spelling error or the like ...
...
Can you find the: randomiser/ssl/ssl_out/fltier.baf -file ? I suspect a coding spelling error or the like ...

well I know nothing at programming/coding

anyhow you are right

I got a folder: bgee/randomiser/ssl/ssl_out

but there is no file; No fitier bat-file or something

its completely void in ssl_out folder

hi I got a bgee in steam version

and whenever I try to install randomise item mode 1 or 2, it fails

Looks like SSL is failing to produce output for some reason. What operating system are you using? When you install the mod, do you see any lines like

This is Stratagems Scripting Language
before the installation fails? (They won't show up in the debug file, just in the terminal.)

hi I got a bgee in steam version

and whenever I try to install randomise item mode 1 or 2, it fails

Looks like SSL is failing to produce output for some reason. What operating system are you using? When you install the mod, do you see any lines like

This is Stratagems Scripting Language
before the installation fails? (They won't show up in the debug file, just in the terminal.)

Hi I cannot access the computer right now

Cos its in workplace and I am home now

I believe its operation is win7 and

I guess I havent seen such message

But I may be wrong

I will check and confirm it tomorrow

Thanks !

And could you elaborate

how I can check the message in detail?

I am not sure what is the terminal you mentioned

and how to check the message since

you say they wont show up in the debug file

and how to check the message since

you say they wont show up in the debug file

Erhm Wisp said: "Did you see... ?" So you open the .debug file with Notepad and go look.

Erhm Wisp said: "Did you see... ?" So you open the .debug file with Notepad and go look.

I also said it does not show up in the debug file.

Hi I cannot access the computer right now

Cos its in workplace and I am home now

I believe its operation is win7 and

I guess I havent seen such message

But I may be wrong

I will check and confirm it tomorrow

Thanks !

And could you elaborate

how I can check the message in detail?

I am not sure what is the terminal you mentioned

and how to check the message since

you say they wont show up in the debug file

If you are on Windows, your terminal is called "the command prompt". Try to install the mod. Messages from SSL, if any, will be printed to the command prompt. If you scroll up a bit from where the installation fails, you should be able to see if there are any. There might also be something helpful printed by Windows up there, so keep your eyes open for error messages.

hi I have checked my commander window (command program of black screen with white alphabet right lol?)

there is NO sentence of "This is Stratagems Scripting Language"

btw my computer is laptop let me know if you got any more questions on this error

hi I have checked my commander window (command program of black screen with white alphabet right lol?) there is NO sentence of "This is Stratagems Scripting Language" btw my computer is laptop let me know if you got any more questions on this error

Is there anything else printed or does the text in the command prompt exactly match the text in the debug file?

You can also try opening a command prompt yourself and using the two commands

cd /d driveletter:\path\to\your\game\folder

randomiser\ssl\ssl.exe

If SSL complains about not getting any input files, at least you know the program itself can run on your system.

Here are whole messages from install command program

I type them myself

---------------------------------------

copying and patching 1 file....

~~

compiling 218 scripts

creating 1 directory

'randomiser/ssl/ssl.exe' is not recognized as an internal or external command,

operable program or batch file.

copying 1 file...

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

Error installating [Mode 1: Randomise with in-game scripts. No items are lost]

rolling back to previous state

Will uninstall 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

uninstalled 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

ERROR: Unix.Unix_error<20, "start", "randomiser/ssl/ssl_out/filter.baf">

PLEASE report the error message in the file SETUP-RANDOMISER.DEBUG to Wisp,

www.forums.gibeerling3.net

Using Language [English]

-----------------------------------------

if you got any more questions or requests

plz let me know

I am eager to fix this error so that I can use your mods with random 1 option

Stopping installation because of error

these four same sentence appears without space

my type-error

---------------------------------------------

copying and patching 1 file....

~~

compiling 218 scripts

creating 1 directory

'randomiser/ssl/ssl.exe' is not recognized as an internal or external command,

operable program or batch file.

copying 1 file...

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

Stopping installation because of error.

Error installating [Mode 1: Randomise with in-game scripts. No items are lost]

rolling back to previous state

Will uninstall 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

uninstalled 1031 files for [RANDOMISER/RANDOMISER.TP2] component 1100.

ERROR: Unix.Unix_error<20, "start", "randomiser/ssl/ssl_out/filter.baf">

PLEASE report the error message in the file SETUP-RANDOMISER.DEBUG to Wisp,

www.forums.gibeerling3.net

Using Language [English]

---------------------------------------

one more, my bgee folder is in program files(x86)/steam/steamapps/common/baldur's gate enhanced edition

and I dont know how to I apply your request to mine

I have tried but message says

"the file name, directory name, or volume label syntax is incorrect"

cd /d driveletter:\path\to\your\game\folder

randomiser\ssl\ssl.exe

'randomiser/ssl/ssl.exe' is not recognized as an internal or external command,

operable program or batch file.

Additionally, having your game installed to C:\Program Files(x86) has been known to cause strange problems with WeiDU mods. It's advisable to install your game to another location.

I don't know why you are unable to run SSL, but chances are it's due to some local factor, like having the game installed to C:\Program Files(x86). You mentioned it was a work computer, so if your workplace has an IT department or something, I guess it is also possible they have locked the computer down in some manner that interferes with the installation.

'randomiser/ssl/ssl.exe' is not recognized as an internal or external command,

operable program or batch file.

Additionally, having your game installed to C:\Program Files(x86) has been known to cause strange problems with WeiDU mods. It's advisable to install your game to another location.

I don't know why you are unable to run SSL, but chances are it's due to some local factor, like having the game installed to C:\Program Files(x86). You mentioned it was a work computer, so if your workplace has an IT department or something, I guess it is also possible they have locked the computer down in some manner that interferes with the installation.

sadly it is my personal computer and there is no regulation on computer uses at all

btw.. I have changed steam installation basic folder from program x86 to c:\steam by your feed

brand new bgee folder has made in c:/steam/bg

and I run your mod but well...

it doesnt work

same error message appears

Archived

This topic is now archived and is closed to further replies.

×
• Website


text: CARMA SEMINAR Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 1:00 pm, Thu, 24th Sep 2015 Practice talks for the 2015 AustMS Meeting. Speaker: Mr Matthew Tam, School of Mathematical and Physical Sciences, The University of Newcastle Title: Reconstruction Algorithms for Blind Ptychographic Imaging      In scanning ptychography, an unknown specimen is illuminated by a localised illumination function resulting in an exit-wave whose intensity is observed in the far-field. A ptychography dataset is a series of these observations, each of which is obtained by shifting the illumination function to a different position relative to the specimen with neighbouring illumination regions overlapping. Given a ptychographic data set, the blind ptychography problem is to simultaneously reconstruct the specimen, illumination function, and relative phase of the exit-wave. In this talk I will discuss an optimisation framework which reveals current state-of-the-art reconstruction methods in ptychography as (non-convex) alternating minimization-type algorithms. Within this framework, we provide a proof of global convergence to critical points using the Kurdyka-Łojasiewicz property. Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle Title: Using random walks to detect amenability in finitely generated groups      We use random walks to experimentally compute the first few terms of the cogrowth series for a finitely presented group. We propose candidates for the amenable radical of any non-amenable group, and a Følner sequence for any amenable group, based on convergence properties of random walks. Speaker: David Franklin, School of Mathematical and Physical Sciences, The University of Newcastle Title: Hardy Spaces and Paley-Wiener Spaces for Clifford-valued functions      The Hardy and Paley-Wiener Spaces are defined due to important structural theorems relating the support of a function's Fourier transform to the growth rate of the analytic extension of a function. In this talk we show that analogues of these spaces exist for Clifford-valued functions in n dimensions, using the Clifford-Fourier Transform of Brackx et al and the monogenic ($n+1$ dimensional) extension of these functions. [Permanent link]


text:
# 1.5. Formal and Natural Languages¶

Natural languages are the languages that people speak, like English, Spanish, and French. They were not designed by people (although people try to impose some order on them); they evolved naturally.

Formal languages are languages that are designed by people for specific applications. For example, the notation that mathematicians use is a formal language that is particularly good at denoting relationships among numbers and symbols. Chemists use a formal language to represent the chemical structure of molecules. And most importantly:

Note

Programming languages are formal languages that have been designed to express computations.

As I mentioned before, formal languages tend to have strict rules about syntax. For example, $$3+3=6$$ is a syntactically correct mathematical statement, but $$3=+6\$$ is not. Also, $$H_2O$$ is a syntactically correct chemical name, but $$_2Zz$$ is not.

Syntax rules come in two flavors, pertaining to tokens and structure. Tokens are the basic elements of the language, like words and numbers and chemical elements. One of the problems with 3=+6$is that$ is not a legal token in mathematics (at least as far as I know). Similarly, $$_2Zz$$ is not legal because there is no element with the abbreviation $$Zz$$.

The second type of syntax error pertains to the structure of a statement; that is, the way the tokens are arranged. The statement 3=+6\$ is structurally illegal, because you can’t have a plus sign immediately after an equals sign. Similarly, molecular formulas have to have subscripts after the element name, not before.

When you read a sentence in English or a statement in a formal language, you have to figure out what the structure of the sentence is (although in a natural language you do this unconsciously).

Note

The process of examining a program and analysing the syntactic structure is called parsing.

For example, when you hear the sentence, “The other shoe fell,” you understand that “the other shoe” is the subject and “fell” is the verb. Once you have parsed a sentence, you can figure out what it means, that is, the semantics of the sentence. Assuming that you know what a shoe is, and what it means to fall, you will understand the general implication of this sentence.

Although formal and natural languages have many features in common—tokens, structure, syntax and semantics—there are many differences.

ambiguity:

Natural languages are full of ambiguity, which people deal with by using contextual clues and other information. Formal languages are designed to be nearly or completely unambiguous, which means that any statement has exactly one meaning, regardless of context.

redundancy:

In order to make up for ambiguity and reduce misunderstandings, natural languages employ lots of redundancy. As a result, they are often verbose. Formal languages are less redundant and more concise.

literalness:

Natural languages are full of idiom and metaphor. If I say, “The other shoe fell,” there is probably no shoe and nothing falling. Formal languages mean exactly what they say.

People who grow up speaking a natural language (everyone) often have a hard time adjusting to formal languages. In some ways the difference between formal and natural language is like the difference between poetry and prose, but more so:

poetry:

Words are used for their sounds as well as for their meaning, and the whole poem together creates an effect or emotional response. Ambiguity is not only common but often deliberate.

prose:

The literal meaning of words is more important and the structure contributes more meaning. Prose is more amenable to analysis than poetry, but still often ambiguous.

programs:

The meaning of a computer program is unambiguous and literal, and can be understood entirely by analysis of the tokens and structure.

Here are some suggestions for reading programs (and other formal languages). First, remember that formal languages are much more dense than natural languages, so it takes longer to read them. Also, the structure is very important, so it is usually not a good idea to read from top to bottom, left to right. Instead, learn to parse the program in your head, identifying the tokens and interpreting the structure. Finally, remember that the details matter. Little things like spelling errors and bad punctuation, which you can get away with in natural languages, can make a big difference in a formal language.


text:
# Do electron really experience any repulsive force while attracted by proton compared to positron?

I read up that the reason 2 electrons with same energy states can be binded to the first orbital of a necleus is due to one electron having positive spin half and another having negative spin half allowed by Pauli exclusion principle, then I wonder how do an electron tell the difference between a proton and positron? Also I am not exactly sure why electrons don't repel each other while in the first orbital and can I safely rule out that the electrogmatic force is cancelled out in the first orbital since one or two electrons don't make any difference?

• There are no positrons in normal atoms. Do you consider something exotic like positronium en.wikipedia.org/wiki/Positronium? – atarasenko Jan 29 '19 at 6:21
• @atarasenko: no, I am comparing electron-positron annihilation and hydrogen atom. Because electron in both case experiences an attractive forces but in the case of hydrogen atom something is acting like a force to prevent the electron from colliding with the proton... I like to know more about this force. – user6760 Jan 29 '19 at 6:35
• Electron cannot fall on a proton because of uncertainty principle: if it is confined in a ball of radius $r$, its momentum is $\sim\hbar/r$, and kinetic energy is $\sim \hbar^2/mr^2$. The potential energy grows slower (as $1/r$). More info here physics.stackexchange.com/questions/20003/… – atarasenko Jan 29 '19 at 6:46
• It is not clear what you are asking. What do you mean by electrons "telling the difference between a proton and positron"? It is possible for an electron and a positron to not annihilate and form positronium – ACuriousMind Jan 29 '19 at 18:46

This is only approximately true. Heuristically, each electron is distributed spherically symmetrically, and so has apprx' vanishing electric field inside the sphere, so it's felt by the other electron less then the nucleus is. This sounds very strange, but it kinda works. If it was exact, then we would expect the ionization energy of Helium to be twice that of Hydrogen. In reality it's $$\frac{24.6 \, \rm{eV}}{13.6 \, \rm{eV}}\approx 1.8$$.


text:
# How to use CMYK-Colors in the whole document

I found out, that my color laser printer prints graphics with gray color in RGB-Representation instead of using black (they are more red then gray). So it seems, that PDFLaTeX is creating RGB-PDF-Files.

I only use pstricks-graphics like this one:

\documentclass[letterpaper,dvips]{article}

\usepackage[utf8]{inputenc}
\usepackage{textcomp}

\usepackage{pst-all}

\usepackage{color}

\begin{document}

\pagestyle{empty}
\begin{TeXtoEPS}
\psset{xunit=1cm,yunit=1cm,runit=1cm}
\begin{pspicture}(2,2)
\psset{linewidth=1pt}

\psframe[fillstyle=solid, linewidth=1pt, fillcolor=lightgray](2,2)

\end{pspicture}

\end{TeXtoEPS}

\end{document}

I'm creating eps-files with this steps:

• latex Grafik1.tex
• dvips Grafik1.dvi -o Grafik1.ps
• ps2eps --ignoreBB Grafik1.ps

and include the eps-file with \includegraphics

So is there a way to tell the whole document only create CMYK-Colors or an other way to create a document with the wright colors?

EDIT: The basic Problem is solved, but when creating a gradient, colors are used instead of black

\documentclass[letterpaper,dvips]{article}

\usepackage[utf8]{inputenc}
\usepackage{textcomp}

\PassOptionsToPackage{cmyk}{xcolor}% NB: put this *before* \usepackage{pst-all}
\usepackage{pst-all}

\begin{document}

\pagestyle{empty}
\begin{TeXtoEPS}
\psset{xunit=1cm,yunit=1cm,runit=1cm}
\begin{pspicture}(2,2)
\psset{linewidth=1pt}

\end{pspicture}

\end{TeXtoEPS}

\end{document}

-
The xcolor package provides the package option cmyk. Also related: PDF colour model and LaTeX –  Qrrbrbirlbel Oct 2 '12 at 14:25
Does including \selectcolormodel{gray} help? –  percusse Oct 2 '12 at 17:59
I edited your second example to put the \PassOptionsToPackage line in the correct place. –  Lev Bishop Oct 2 '12 at 21:57

Drop the \usepackage{color} and load pstricks this way (because pstricks loads xcolor for you already, at the proper moment):

\PassOptionsToPackage{cmyk}{xcolor}
\usepackage{pst-all}

-
Works great - with one exception: gradients. a \psframe with gradient from white to black is created with color instead of black - even if I pass gray'' as xcolor option. –  PascalTurbo Oct 2 '12 at 16:19
@PascalTurbo, edit an example showing the gradient problem into the question and maybe someone can help.... –  Lev Bishop Oct 2 '12 at 17:25
@LevBisop Hi, excuse me for posting this in here (this would be no proper SX question) but...can i do the same with TikZ (seen PGFManual ctan.mirror.garr.it/mirrors/CTAN/graphics/pgf/base/doc/…, pag. 36, lines -8 and -7)? Can I say \PassOptionsToPackage{cmyk}{xcolor} \usepackage{tikz}? –  MattAllegro Nov 9 '14 at 16:55


text:
# What is the derivative of y = [(x-2)/k]^(1/2) where k is a constant?

Oct 20, 2017

Look below.

#### Explanation:

where $k \ne 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} {\left[\frac{x - 2}{k}\right]}^{- \frac{1}{2}} \cdot \frac{d}{\mathrm{dx}} \left(\frac{x - 2}{k}\right)$

$= \frac{1}{2} {\left[\frac{x - 2}{k}\right]}^{- \frac{1}{2}} \cdot \left(\frac{1}{k}\right)$

=1/(2sqrt(k(x-2))


text:
# How can I correctly change page size to a non-letter size in pdflatex?

The following example, based on this answer, creates a pdf that is letter size.

\documentclass{report}

\usepackage[pass,paperwidth=2.5in,paperheight=7in]{geometry}

\begin{document}
Hello World
\end{document}

I also tried the following.

\documentclass{report}

%\usepackage[pass,paperwidth=2.5in,paperheight=7in]{geometry}
\pdfpaperheight=7in
\pdfpaperwidth=2.5in

\begin{document}
Hello World
\end{document}

But it gives the following error

! Undefined control sequence.
l.4 \pdfpaperheight
=7in
?
! Emergency stop.
l.4 \pdfpaperheight
=7in

What is the correct way to control page size for pdflatex?

• it is called \pdfpageheight, I'd suggest using the geometry interface, then you don't got get adjusting other stuff. – daleif Nov 25 '16 at 9:03
• @daleif, any hints on how to make the geometry interface work? – merlin2011 Nov 25 '16 at 20:15
• Geometry has an excellent manual and sets the pdfpage... variables automatically – daleif Nov 25 '16 at 20:19


text:
# Source code description in LaTeX

I have a problem concerning the creation of the name below a "Source code" (Listing) in LaTeX. When I have a figure I use:

       \begin{figure}[t]
\centering
\includegraphics{Figures/drawing.pdf}
\caption{Spoken Dialogue System}

\label{fig:SLDS2}
\end{figure}

I see

Figure 4.5.: Spoken Dialog System

on the screen. However, when I could not figure out how to print

Listing.4.5 Java Code

below this framed code on the screen. What should I add to this code? The source code is as shown in the following:

     \begin{framed}
\begin{lstlisting}[frame=single, backgroundcolor=\color{light-gray}, basicstyle=\footnotesize\ttfamily, language=Java, numbers=left, numberstyle=\tiny
\color{black}]

[HERE IS THE JAVA CODE]

\end{lstlisting}

\end{framed}

-
Before you copy-paste the question, though, call over some moderator help to see if you can get this migrated. Or, search over there first and see if your question's been answered. –  Makoto May 25 '13 at 18:55
Welcome to TeX.SX! Your post was migrated here from another Stack Exchange site. Please register on this site, too, and make sure that both accounts are associated with each other (by using the same OpenID), otherwise you won't be able to comment on or accept answers or edit your question. –  texenthusiast May 26 '13 at 0:45

## migrated from stackoverflow.comMay 25 '13 at 19:41

This question came from our site for professional and enthusiast programmers.

You can use the caption=<caption text> option for lstlisting:

\documentclass{article}
\usepackage{xcolor}
\usepackage{listings}

\colorlet{light-gray}{gray!20}

\begin{document}

\begin{lstlisting}[frame=single, backgroundcolor=\color{light-gray}, basicstyle=\footnotesize\ttfamily, language=Java, numbers=left, numberstyle=\tiny\color{black},caption= {A desciption of the listing}]
[HERE IS THE JAVA CODE]
\end{lstlisting}

\end{document}

Since you didn't provide your definition for light-gray I used a temporary one in my example.

Initially I overlooked the requirement about the caption position to be on the bottom; this can be a chieved using the captionpos=b option (although for listings I would suggest to have the caption on top, as in the default settings):

\documentclass{article}
\usepackage{xcolor}
\usepackage{listings}

\colorlet{light-gray}{gray!20}

\begin{document}

\begin{lstlisting}[frame=single, backgroundcolor=\color{light-gray}, basicstyle=\footnotesize\ttfamily, language=Java, numbers=left, numberstyle=\tiny\color{black},caption= {A desciption of the listing},captionpos=b]
[HERE IS THE JAVA CODE]
\end{lstlisting}

\end{document}

If the same settings are going to be used for various listings, it's better to use \lstset instead of having to repeat them for each lstlisting environment:

\documentclass{article}
\usepackage{xcolor}
\usepackage{listings}

\colorlet{light-gray}{gray!20}

\lstset{
frame=single,
backgroundcolor=\color{light-gray},
basicstyle=\footnotesize\ttfamily,
language=Java,
numbers=left,
numberstyle=\tiny\color{black},
captionpos=b
}

\begin{document}

\begin{lstlisting}[,caption= {A desciption of the listing}]
[HERE IS THE JAVA CODE]
\end{lstlisting}

\end{document}

-


text:
## Doctoral Dissertations

Spring 1998

Dissertation

Mathematics

#### Degree Name

Doctor of Philosophy

Eric Nordgren

#### Abstract

Banach spaces of analytic functions are defined by norming a collection of these functions defined on a set X. Among the most studied are the Hardy and Bergman spaces of analytic functions on the unit disc in the complex plane. This is likely due to the richness of these spaces.

An analytic self-map of the unit disc induces a composition operator on these spaces in the natural way. Beginning with independent papers by E. Nordgren and J. V. Ryff in the 1960's, much work has been done to relate the properties of the composition operator to the characteristics of the inducing map. Every composition operator induced by an analytic self-map of the unit disc is bounded on the Hardy and Bergman spaces.

Differentiation is another linear operation which is natural on spaces of analytic functions. Unlike the composition operator, the differentiation operator is poorly behaved on the Hardy and Bergman spaces; that is, it is not a bounded operator.

We define a linear operator, possibly unbounded, by applying composition followed by differentiation; that is, for f in a Hardy or Bergman space and an analytic self-map of the disk, $\phi$,$$DC\sb\phi(f)=(f\circ\phi)\prime.$$We have found a characterization for the boundedness of this operator on the Hardy space in terms of the inducing map. The operator is bounded exactly when the image of the self-map of the disc is contained in a compact subset of the disc.

In contrast, we have found a self-map of the disc with supremum norm equal to one that induces a bounded operator on the Bergman spaces. In this setting we have found conditions necessary for boundedness, and conditions sufficient to imply boundedness. These conditions are closely related.

The techniques used involve Carleson-type measures on the unit disc. A very general question arising out of this work involves relating boundedness of the differentiation operator to characteristics of these measures.

COinS


text:
# Math Help - Arccot series and Arithmetic progressions?

1. ## Arccot series and Arithmetic progressions?

If $x_1,x_2,x_3,\mbox{...}$ are in arithmetic progression with common difference $d$, show that:

$\mbox{arccot}\left(\frac{1 + x_{1}x_{2}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{2}x_{3}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{3}x_{4}}{d}\right) + \mbox{...}$ $+\ \mbox{arccot}\left(\frac{1 + x_{n}x_{n + 1}}{d}\right) = \mbox{arccot}\left(\frac{1 + x_{1}x_{n + 1}}{d}\right)$, where $x_1 > 0$ and $d > 0$

2. ## This statement is false.

Letting $x=\{2,4,6,8,10,12\}$ ,

$\sum_{k=1}^5 \arctan(\frac{2}{1+x_kx_{k+1}}) = .381$

but $\arctan(\frac{2}{1+x_1x_{6}}) = .0798$

3. Originally Posted by fardeen_gen
If $x_1,x_2,x_3,\mbox{...}$ are in arithmetic progression with common difference $d$, show that:

$\mbox{arccot}\left(\frac{1 + x_{1}x_{2}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{2}x_{3}}{d}\right) + \mbox{arccot}\left(\frac{1 + x_{3}x_{4}}{d}\right) + \mbox{...}$ $+\ \mbox{arccot}\left(\frac{1 + x_{n}x_{n + 1}}{d}\right) = \mbox{arccot}\left(\frac{1 + x_{1}x_{n + 1}}{d}\right)$, where $x_1 > 0$ and $d > 0$
Since they are in A.P with common difference 'd', $x_2 - x_1 = x_3 - x_2 = x_4 - x_3 = \cdots = d$

$\sum_{k=1}^{k=n}\mbox{arccot}\left(\frac{1 + x_{k}x_{k+1}}{d}\right) =$ $\sum_{k=1}^{k=n}\mbox{arccot}\left(\frac{1 + x_{k}x_{k+1}}{x_{k+1} - x_k}\right)$ $= \sum_{k=1}^{k=n}\mbox{arccot}(x_{k+1}) - \mbox{arccot}(x_{k}) = \mbox{arccot}(x_{n+1}) - \mbox{arccot}(x_1)$ $=\mbox{arccot}\left(\frac{1 + x_{1}x_{n+1}}{nd}\right)$

4. ## Slight Correction

Isomorphism:

$\mbox{arccot}(x_{n+1}) - \mbox{arccot}(x_1)$ = $\mbox{arccot}\left(\frac{1 + x_{1}x_{n+1}}{x_{n+1}-x_{1}}\right)$ = $\mbox{arccot}\left(\frac{1 + x_{1}x_{n+1}}{nd}\right)$

This slight correction will make the theorem true.


text:
## Introductory Algebra for College Students (7th Edition)

$x^2-2x+1$
Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the square of the given expression, $\left( x-1 \right)^2,$ is \begin{array}{l}\require{cancel} (x)^2-2(x)(1)+(1)^2 \\\\= x^2-2x+1 .\end{array}


text:
# HowTo: Method of Conjugate Distributions

I'm trying to understand the usage of this method.

What i mean: (maybe i named this method in wrong way)

Let $\xi$ be a random variable with distribution function $F(x)$

Add condition: $\mathbb{E}e^{t\xi}\lt \infty$

Denote $S(x) = \int\limits_{-\infty}^x e^{ts}dF(s)$

After all, let $G(x) = \frac{S(x)}{\mathbb{E}e^{t\xi}}$

If $\eta$ is a random variable with distribution function $G(x)$, we can say, that $\eta$ and $\xi$ have conjugate distributions.

Can anybody help me with this interesting method? (usage and features) (Or good books about it)

-


text:
## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.7 - Probability - Exercise Set - Page 1118: 16

#### Answer

The required solution of probability is, $0$

#### Work Step by Step

We know that when the die is rolled then the sample space of equally likely outcomes given below is $S=\left\{ 1,2,3,4,5,6 \right\}$ As there are six outcomes in the sample space, thus, $n\left( S \right)=6$ Also, the event of getting a number greater than 7 can be represented as $E=\phi$ Since there is only one outcome in this event, therefore, $n\left( E \right)=0$ Thus, the probability of obtaining a number greater than 4 is: \begin{align} & P\left( E \right)=\frac{n\left( E \right)}{n\left( S \right)} \\ & =\frac{0}{6} \\ & =0 \end{align}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Convention History by Jan Polish

## OrigamiUSA Convention History

By Jan Polish

When I look back on my first few years as a member of The Friends of The Origami Center of America, they seem to be sort of fuzzy. I joined in 1986, and started attending monthly folding sessions right away. I was a very beginning folder, and knew no one else in the organization. I remember sitting in the back of the room trying my best to follow the instructions of Michael Shall and Alice Gray, among others. They (those brave enough to teach) seemed quite intimidating. How did they know what to say? And those who followed the instructions easily were even more intimidating. How did they know what to do? People were very helpful, but I felt that I'd wandered into the middle of a movie, while everyone else in the audience had been there since the opening credits.

When they talked about the coming convention, they emphasized that you should be careful not to get in over your head. I took that very, very seriously because I was determined to graduate to intermediate models. I remember how much I practiced preliminary and waterbomb bases so that I could do them quickly from memory, and how often I tried the bird base, sometimes getting it right, sometimes sitting in frustration.

At the last monthly folding session before that first convention, which was to be held in the children's lunchrooms at the American Museum of Natural History, Michael announced that they needed volunteers to come in the day before to help with collating papers, etc. I took the day off from work, and showed up at the Museum, eager to help, and perhaps even more eager to find out how I could learn the beginning of the movie. Michael and Alice greeted me kindly, and quickly assigned me to a collating table. The Friends office was then in the space that had been Alice's until she retired, in the corner circular turret on 77th Street and Central Park West. You had to go through an unmarked door, then through a rather deserted and poorly lit storage area, and then into the office, which was a wonderland. It was a circular office, with high ceilings and huge windows on all sides, and an amazing view of Central Park. The cooling breezes from the park helped to make the temperature tolerable during the hot summers - the office was not air-conditioned, along with most of the Museum in those days. The most intriguing part of the office was bug-land, a dark section in the back of the office. Alice was an entomologist, and had a collection of such exotic pets as tarantulas and hissing cockroaches. (I can remember a guard taking me aside as I entered the Museum and whispering to me, "Watch out when you go into the office ... Alice says that there's a tarantula loose." And of course we all knew that Alice had spread the warning not because she was afraid that the tarantula would harm us, but that we might inadvertently hurt one of her pets.)

There were tables set up outside the office, and I worked with a couple of other volunteers sorting the attendee lists that were to be included in the survival kits. One of the highlights of my volunteering session was following Michael to what we now call Support Services at the Museum. Michael was extremely hyperactive. He did not walk - he strode. And he did not stride moderately - he strode fast. He brought me through the labyrinth that was the Museum basement, racing past carpentry shops and electrical closets, around mail rooms and locker rooms, until we arrived at the copy machines. He set me up to make copies, and then left. I had no idea where I was - I wasn't even yet sure where the office was! But everyone at the Museum knew Alice and Michael, and kind guards and behind-scenes workers sent me from milestone to milestone ("go right at the elephants, then left at the Indians, and then ask the next guard") until I found my way back.

When the convention started I helped Martha Landy with registration, an excellent introduction to volunteering. Martha was a gentle and articulate guide, and registration was a great way to meet new people as they picked up their nametags. But I have to admit that I have no real idea of how many classes there were, or how many people attended, although I've been told there were 200-250 people. I remember that they were crammed into a dozen or so small classrooms, but what I recall most are a few snippets. I remember a man named Terrell Hayes, a lawyer/professional clown/paperfolder, entertaining the people who waited on line by juggling and telling jokes. I remember that in order to take a complex class you had to get past questioning by Michael Shall and Ron Levy. I remember watching David and Don Shall help Ted Bond build the ‘Big Board,' the oversized schedule that would hang on the wall, using brown wrapping paper and handwritten sheets with class names. They, like the other volunteers, seemed to be having a wonderful time, with much muttering, and as much laughter. I also recall a mountain of shoe boxes, which Alice and a few others collected from shoe stores all year and then brought to convention so that attendees would have something to put their models in. (There were lots of stories about the difficulties in corralling a carload of loose shoe boxes, and one year a member's car was broken into when a thief thought the expensively-named boxes still contained the expensive shoes.)

I don't remember what models I learned, and I don't remember which people I met that year. I do remember starting to feel more comfortable with origami, and with origami people.

Lillian Oppenheimer started having gatherings at her home (first on Gramercy Park, then 11th Street, then Union Square) very soon after she discovered origami. When she founded The Origami Center in 1958 the gatherings gradually became meetings, and soon regularly scheduled monthly occurrences. Larger gatherings were held periodically, especially when Fred Rohm could make it into New York from Pennsylvania. The Origamian refers to the first ever American origami "conference" on November 6, 1962. A second gathering, now called a convention, was held on October 31 - November 1, 1964, and attracted 17 people. Conventions continued, each year getting larger. By 1978 there was an official listing of the 50 attendees. Everyone learned each model together - there was one large room, and a teacher in front.

By the late 1970's the conventions were getting too large for Lillian's home. At the same time, Lillian was getting older and concerned about a permanent home for her library. Michael Shall, Alice Gray and others started working to establish a formal non-profit, to be called The Friends of The Origami Center of America. Because of Alice Gray's connection to the American Museum of Natural History (she was a recently retired entomologist), they had access to the Museum's meeting rooms.

The first convention at the American Museum of Natural History was held April 12 - 13, 1980. The attorney working towards our non-profit status gave a progress report, and there were two full days of folding. There was an Open House at Lillian Oppenheimer's on Friday and Saturday evenings, where people could get together informally and also shop, since the Museum did not permit sales of origami materials. For the first time, there were multiple simultaneous classes. By the following year, 1981, The Friends of The Origami Center of America was a legal non-profit corporation, and we held our first ‘official' convention at the Museum. Four years later, The Friends signed a contract with the Museum, and gradually moved the contents of Lillian's library and collection of step-folds and models. Two years after that, Lillian sold the origami book and paper business to The Friends, and the transition was complete.

By my next convention, in 1988, I had become an active year-round volunteer, typing and editing articles for The Newsletter. Michael asked me to coordinate volunteers for the convention, which entailed taking names of people who had checked a box on their forms, and calling them to figure out where and when they could be assigned. Again, it was a great way to meet people; after talking to them on the phone, they were already buddies by the time I met them in person. I remember trying to call one man, the father of a folder in Ohio, to ask him about volunteering. He had offered to be in our most valuable volunteer category ... what we called a ‘green boat,' or non-folding, full-time volunteer. But each time I called and asked for him, the person who picked up the phone would curse at me, and then hang up! After this happened four or five times, with the curses escalating in volume and creativity, Michael called him. When the person on the other end heard a male voice he stayed on the phone. It turned out that he had just broken up with a woman who was harassing him, and apparently my voice was similar to hers. He was so embarrassed that he was more than willing to do anything we wanted that convention, and for years to follow!

The biggest change was that we had moved to a new venue. The prior convention, the last at the Museum of Natural History, had been cramped, and we had found new space at IS 44, a middle school down the block. It was a very major change: we had to pay for the rental of the gym and classrooms, rent tables and chairs, and move all our materials to the school just prior to the convention. Many meetings were held as we volunteers tried to figure out how to handle this move. I remember one meeting where we spent (literally!) hours trying to decide between providing water and seltzer, and another where we tried to figure out how we could coordinate a ‘pot luck' Saturday night dinner for several hundred people. We had gotten to the point of deciding who would man the telephone hot line to coordinate the 200 tuna noodle casseroles when sanity returned. We realized that we would have to purchase main courses from an outside source - but we still encouraged people to bring ‘finger foods' to share. People's interpretation of the term ‘finger foods' was a bit loose - I can remember things like pasta salad and roast beef! Each year we were at IS 44 the ‘snack table' was an asset - people truly enjoyed contributing the food, and it was a remembrance of our mom-and-pop days. But it was also a major hassle to keep the area stocked and clean, and it used up too large a percentage of our too small space. Each year at our meetings we fought about whether to eliminate the snack tables - some of the discussions matching the old seltzer/water debates. We did some other seriously strange things that we look back on and laugh at, such as renting lots of coffee urns, and hiring a teenager to make coffee in them. Imagine our shock when plugging in half-a-dozen urns in one room blew the fuses! So our teen had to move the urns to locations all over the school, and then lug them back when the coffee perked.

For the new venue more volunteers were needed - we had to move the tables and chairs up three flights of stairs to the gym, and then cover the unfinished wood tables with white butcher paper so that people could fold on them. The paper had to be replaced each evening ... folding wasn't hard on the covering, but a day's worth of sodas, chicken and ‘finger foods' left them seriously grotty by nightfall. And speaking of grotty ... IS 44 was not exactly white-glove sparkling. This was in the days when NYC public school custodians had a rather lucrative union contract. They had lots of rights, such as the ability to rent out the school off-hours and pocket a large percentage of the money, but very few responsibilities. Floors only had to be washed once or twice a month, and bathrooms did not have to be cleaned except on schedule, an interesting concept when you have a school filled with pre-teens. In short, the school smelled; the floors were filthy; half the bathrooms didn't work and those that did had no toilet paper; and origami paper (and elbows) stuck to the unknown (or maybe we just didn't want to know!) substances on the classroom desks. We had to send over an army of volunteers with Ajax and paper towels, to clean the classrooms the afternoon before the convention, and we had to purchase a case of toilet paper.

The survival kits were prepared at the Museum, in shopping bags, and had to be taken over to the school. We thought of many alternatives - a small van, carts, etc. - but Michael came up with the best answer. He procured a bunch of broom sticks, and gathered a group of volunteers. He placed a broom stick across each volunteer's shoulders, and then loaded shopping bags on the sides of the stick. They walked in a caravan over to the school, looking like a giggling parade of little Dutch children.

Michael was a wonderful teacher and leader, but he was not a planner. Things were purchased as needed, not ordered in advance. For example, he had indeed arranged for coffee urns, but forgot to order the coffee. When we realized that, just hours before the convention was to begin, someone had to run over to Zabar's, the local gourmet shop, and purchase very expensive coffee. In the beginning, Michael did almost everything, with help on tasks as he could find people willing and able. As the conventions grew, and the number of volunteers willing to take on areas of responsibility increased, Michael was persuaded to give up some of his jobs to others. I eventually became the coordinator, with Tony Cheng and Jean Baden-Gillette. Those first few years, though, it seemed that my primary job was to corner Michael and pull information from him about what needed to be done, which could then be passed on.

Gradually people came forward to take on specific areas. Kathleen O'Regan, whose full-time job was as a graphic artist, was the visual ‘eye' of the organization. She had been working on many things that required artistic input, such as the Annual Collection and Newsletter, and she developed convention logos each year that were creative and unique. Now we needed to determine where to locate signs to identify areas and guide people to and from, so Kathleen took charge of signage. This prompted long discussions on whether signage was actually a word. (It is.) Jean arranged for equipment rental and food, and Tony set up the gym. deg farrelly used garbage can stands and foam-core shelves to create a model menu. Phyliss Meth brought over the contents of the Supply Center, and a team helped her set up her area. Michael emptied his closets, and created the first Gold Mine. Michael also sought teachers and figured out the schedule, using large sheets of foam-core and post-it notes, and Kathleen and I put it onto paper.

The registration forms were put into books, and Michael attached tabs on various locations of the sheets. He knew that a tab in the upper right corner of the sheet, for example, meant that the person had volunteered to teach, while a tab in the upper left corner meant that the person was looking for housing. This ingenious pre-computer method of multiple keys worked well until the number of attendees made it too cumbersome for anyone to handle, especially when many people needed information. I loaded the information onto a computer database, which expanded in functionality every year.

One area that remained Michael's until his death, however, was hospitality. The Michael Shall New York Tours for overseas visitors were famous, and justly so. People around the world still talk about their visit to New York, and the time that Michael ran them around all the tourist spots. He also arranged for housing ... in those days most people attending the convention were local, and those people who came in from out-of-town stayed at inexpensive hotels in the neighborhood or in members' spare rooms, sofa beds, and sleeping bags, all arranged by Michael. He was relentless in begging for sleeping space - people who were known to have guest rooms knew that they could not avoid him, and that it was much easier to just say yes.

We stayed at IS 44 for five years. It was wonderful to have unlimited classrooms, but they were middle school rooms, with small desks, and, oh, did I mention, lots of dirt. Working with the custodian was difficult, to say the least. His rules (and prices) changed with his mood. The year that we misplaced one of the walkie-talkies we'd borrowed, and got billed a huge amount, was the last straw. In any case, we were outgrowing the school's gymnasium, and needed more space for sales areas and exhibition.

We started looking aggressively for another venue. Someone mentioned FIT - the Fashion Institute of Technology, and we sent an advance team over to tour it. Michael went, of course, along with Wendy Zeichner and Jean Baden-Gillette. The head of facilities, Bette LeVine, took them around, showing them the cafeterias that could be our main hospitality area, the classrooms, and other locations that were potential sites for exhibition, sales and dinner. The team was dazzled. The cafeteria already had smooth-top tables and chairs, so no rentals and no white butcher paper. The classrooms had desks and chairs built for adults. There was a spacious area on the top floor for exhibition and/or sales. Meals could be catered by the on-site firm. And if we scheduled the convention for the summer, we could use the dormitories for housing out-of-town attendees. And best of all ... it was clean. Michael stood in the middle of a hallway, opposite a bathroom, and gave an exaggerated sniff. "Smell that," he said to the team, grinning. "What do you mean, smell that," Bette said, indignantly. "My school doesn't smell." "Exactly," confirmed Michael, "your school doesn't smell." We signed a contract immediately.

When we started at FIT we felt that we were growing up. Planning became critical - you no longer could just run down the block to get some forgotten essential. Logistics (the art of moving things from point A to point B) was also critical - we needed to rent a van, and find volunteers to load and unload (something that was always very difficult - several years ago we switched to hiring a moving company, although volunteers still do much of the loading, unloading, staging and set-up). We had to design each area from scratch, figuring out where to put each component. Tony was in charge of designing and setting up the cafeteria/Hospitality Area. Jean worked on the 8th floor, which was the Supply Center, Exhibition and Gold Mine for the first year, and Supply Center, Gold Mine and Vendor areas in subsequent years. In later years they switched stations.

The space had expanded again, and signage changed too. Wendy took that area over eventually, with new helpers each year for assistance in hanging her signs. We soon discovered that volunteers from outside New York could handle many of the areas of responsibility for the convention. deg farrelly, first from Pennsylvania and now from Arizona, has handled model menu for years. With the larger exhibition space, V'Ann Cornelius from California took over design and display, and drastically increased the sophistication. She designed plinths, shelves and stands, and other amazingly ingenious ways to effectively display exhibition origami. That first Gold Mine from Michael's closet was expanded by Tony and Maria Velazquez to include items specially purchased for the convention. Eventually Michael turned the teacher schedule over to Tony, Maria and me. Tony continues to use manual scheduling methods, until this year using Michael's original foam-core boards, but I've put the rest onto the computer. Mike Hamilton, Janet Hamilton's non-folding husband, started working with Phyliss. He came up with a user-friendly layout, and stays all weekend as the ‘foreman' of her team of volunteers.

Wendy Zeichner became our ‘efficiency expert,' using her wonderful analytical and creative mind to re-engineer different areas each year - for example, she and deg designed folding shelf units that could be easily stored and then expanded into the Model Menu frame each year. Then she came up with her ‘ticket id' concept, which assigned a single-digit number to each class that enabled us to determine number of periods, and starting and ending times, without having to record the specific information for each class. With that one number we could sort for ticketing, for big board, for schedules, etc., and typing into the database was drastically reduced while accuracy increased. Wendy continues to be in charge of ticketing, with an experienced team that returns each year. Volunteer coordination has gone through many hands, from Michael to me to Lin Balinsky to Scott Cramer to MaryJane Kettler to MaryAnn Scheblein-Dawson and now Toby Schwartz. Housing is handled by Martha Winslow-Cole in Atlanta, who receives, records, and juggles requests for housing from over 250 people.

We get a lot of first-time attendees each year, and we soon realized that they presented a unique problem. Showing up in a room full of 600-700 people, most of whom seem to know each other, can be daunting. One year I overheard a first-timer on the phone, calling home in tears saying that she was baffled, and was having an awful time. We realized that most first-timers adjusted quickly, and were thrilled by the experience, but a small percentage needed more assistance. We had used yellow ribbons on their nametags since Michael's time, we had a special first-timer fact sheet, and we had someone in charge of answering questions, etc., but we needed to do more. We tried setting up ‘buddies' for them, but that didn't work because it was so hard to arrange meetings. Our first-timer coordinator (first Lin Balinsky, now Delrosa Marshall) initiated special orientation meetings, and we started putting blue Convention Pro ribbons on the badges of those who had agreed to make themselves available for help. Delrosa designed maps that explained the school's confusing layout. This year we initiated special ‘express' and ‘local' paths through Registration, so that experienced attendees can get their convention packages quickly, and with limited conversation, while the registration volunteers spend more time with the first-timers.

I handle office registration, and for a while I also supervised on-site registration, until I realized that the area was too important for part-time attention. Rachel Katz took it over, and has done an extraordinary job, processing hundreds of people in an amazingly short time. Her volunteers set the tone for the convention, welcoming people and keeping everyone calm. (This was a more difficult task some years than others. I can remember one year when FIT decided to arrange a fire drill just as we were starting to process registration. It was scheduled, but no one bothered to let us know in advance. And then there was 2004, when we were an hour late getting from the Home-Office with the registration envelopes, and Rachel taught t-shirt folding to keep the anxious attendees amused!). Our administrator, Joy Low, is involved with everything, especially the survival kits, and making certain that everyone's requirements, from volunteers to attendees, are met. Mette Pederson, Cynthia Fulbright and Ben Reed from Raleigh fold over 900 sailboats to put on nametags, which I generate (along with labels, meal, t-shirt and Origami Collection tickets) from my computer programs for the wonderful office volunteers to attach. June Sakamoto organizes a "collating party" where 40-50 people collate all the paper and materials in one day. Jean, Kathryn Wagner, Mike Montebello (Susan Dugan's non-folding husband) and Mike Hamilton now handle logistics, and Jean and I are the liaisons with the staff at FIT.

In August or September following each convention we hold a de-briefing meeting, where we discuss what worked and didn't, and review the suggestion forms from attendees. We make notes of changes we want to make the following year. Then in January or February we start to plan, including deciding who will be our special guest and sending a formal invitation.

When Bette LeVine retired just before last year's convention, along with her Administrative Assistant, FIT hired someone brand-new for the job, Christine Ryan, and we were concerned that someone new would have difficulty wrestling FIT's academic bureaucracy. There were a few glitches, but eventually things were resolved. The staff for the Housing group has changed several times, although the current Summer Housing Coordinator, Nicole Martin-Lewis, has been there for many years now. Their staff adores our conventions and our conventioneers - not only do we do virtually all the paperwork for them, but they love the origami gifts they get. They also enjoy the demographic variety of our attendees. The facilities, however, at times present a challenge - there are occasional problems with cleanliness or locks, and summer construction schedules have caused limitations. Generally, though, they're a bargain for New York, and the convenience of having housing across the street is wonderful.

The biggest change for 2005 was the destruction of the cafeteria we'd been using for our Hospitality Area. Originally there were two cafeterias, and we used one for convention and the other for Saturday night dinner. One had been converted to classrooms a few years ago, and since then construction had continued on new spaces - rumored to be a food court and a conference center. Hard facts were hard to find - configurations were stated, then changed; dates were absolute, then missed. Finally we were told that the construction was complete, but was the new space larger or smaller than the old? Don't know yet. Could we rent the food court, with its convenient tables and chairs? Don't know yet. How many tables would the new space fit? Don't know yet. Finally we were able to see the new spaces. Wendy, Tony, Kathryn, Delrosa and I visited the school many times, and discovered the good news / bad news of the new configuration. Good news: the space was modern and (marginally) large enough. Bad news: there were no tables or chairs (the food court is still unavailable); it was at the opposite end of the block-long campus from our sales areas and exhibition; and because of window walls and poor planning in locating electrical outlets, the layout design would be difficult. Wendy came up with an acceptable design, moving ticketing to the building lobby, and retaining the Model Menu and Information Desk in Hospitality. We found a rental company that could provide finished-top tables rather than rough wood ones (we really didn't want to go back to butcher paper!), and came up with new signage to direct people through the maze of buildings.

Another problem this year was that the in-house catering firm decided that they ‘needed' to raise their prices. Our reasonably-priced (and mediocre) box lunches were going to double in price, and so would the cost of almost all food services. We decided that we couldn't live with these prices - there was no way that we could recommend that people buy a sandwich with a few slices of meat, plus a soda and cookie, for over $15. We cancelled all food arrangements except for coffee, tea and juice in the morning (absurdly priced, but necessary), and asked Bob and Eunice Stack to compile a restaurant map and collection of menus. We also found a local Chinese restaurant willing to provide a 10-course meal for$25 - an arrangement that quickly sold-out.

This year the movers showed up at Phyliss' on time, and quickly loaded The Source into the truck. On to the Museum, where Kathryn and Joy had pre-staged the materials to be added. We'd arranged for an additional van to move some of the awkward-sized materials, and both trucks left on time and arrived at FIT as planned. Christine had warned us that the Fire Marshal might be involved in our layout this year, something new in our experience with FIT, and, indeed, he showed up early in our set-up. Jean, Tony and the two Mikes negotiated changes in the planned layouts, cutting the available number of tables. Toby's volunteer schedule was a smash hit - we had enough people where and when we needed - and everything was done on time. The new methods we'd incorporated in our office registration process after last year's problems meant that we actually showed up at FIT hours early, and I was able to trouble-shoot problems with our cash registers (who remembered that we needed special thermal paper for the Gold Mine register?). Our talented photographer, Susan Dugan, was already on-scene, recording the process when she wasn't helping with the un-loading and set-up (or running to Staples to buy the special thermal paper!).

By the time the 800+ people arrived for the convention (over 628 paid attendees, plus guardians and staff), all was smooth. Hundreds of volunteers had copied materials, collated paper, glued sailboats, added tickets to envelopes and alphabetized forms. 270 people had checked into FIT housing. The rented tables and AV equipment were set-up. 125 teachers were prepared to teach 243 classes. Volunteers were scheduled to monitor the model menu and exhibition, greet and teach the public, and sell materials. The model menu sparkled with the samples of models to be taught. 5,000 class tickets waited. Phyliss and her staff were ready in The Source, as were Tony and Maria in the Gold Mine. The vendors had their materials ready for sale. V'Ann put some final touches on the amazing Exhibition. Delrosa had her maps sorted for the First-Timers' Orientation.

Did the attendees who stood in line waiting for Rachel to open registration have any idea of all the work that had prepared this convention for them? Probably not ... we work hard to make it all look easy. When the doors finally opened, the effort was forgotten, and on both sides of the door we were ready to greet old friends and make new ones. We were united in enjoying this art and craft that we love, and that has brought us together. We'd made another origami convention.

Thanks to Jean Baden-Gillette, Tony Cheng, Gay Merrill Gross, Kyoko Kondo, Martha Landy, Ron Levy, David Lister and David Shall for sharing their memories and materials with me for this article.