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• ### LOFAR discovery of the fastest-spinning millisecond pulsar in the Galactic field(1709.01453)

Sept. 5, 2017 astro-ph.HE
We report the discovery of PSR J0952$-$0607, a 707-Hz binary millisecond pulsar which is now the fastest-spinning neutron star known in the Galactic field (i.e., outside of a globular cluster). PSR J0952$-$0607 was found using LOFAR at a central observing frequency of 135 MHz, well below the 300 MHz to 3 GHz frequencies typically used in pulsar searches. The discovery is part of an ongoing LOFAR survey targeting unassociated Fermi Large Area Telescope $\gamma$-ray sources. PSR J0952$-$0607 is in a 6.42-hr orbit around a very low-mass companion ($M_\mathrm{c}\gtrsim0.02$ M$_\odot$) and we identify a strongly variable optical source, modulated at the orbital period of the pulsar, as the binary companion. The light curve of the companion varies by 1.6 mag from $r^\prime=22.2$ at maximum to $r^\prime>23.8$, indicating that it is irradiated by the pulsar wind. Swift observations place a 3-$\sigma$ upper limit on the $0.3-10$ keV X-ray luminosity of $L_X < 1.1 \times 10^{31}$ erg s$^{-1}$ (using the 0.97 kpc distance inferred from the dispersion measure). Though no eclipses of the radio pulsar are observed, the properties of the system classify it as a black widow binary. The radio pulsed spectrum of PSR J0952$-$0607, as determined through flux density measurements at 150 and 350 MHz, is extremely steep with $\alpha\sim-3$ (where $S \propto \nu^{\alpha}$). We discuss the growing evidence that the fastest-spinning radio pulsars have exceptionally steep radio spectra, as well as the prospects for finding more sources like PSR J0952$-$0607.
• We present a measurement of the helicity of the W boson produced in top quark decays using ttbar decays in the l+jets and dilepton final states selected from a sample of 5.4 fb^-1 of collisions recorded using the D0 detector at the Fermilab Tevatron ppbar collider. We measure the fractions of longitudinal and right-handed W bosons to be f_0 = 0.669 +- 0.102 [ +- 0.078 (stat.) +- 0.065 (syst.)] and f_+ = 0.023 +- 0.053 [+- 0.041 (stat.) +- 0.034 (syst.)], respectively. This result is consistent at the 98% level with the standard model. A measurement with f_0 fixed to the value from the standard model yields f_+ = 0.010 +- 0.037 [+- 0.022 (stat.) +- 0.030 (syst.) ].
• We present a search for the pair production of scalar top quarks ($\tilde{t}_{1}$), the lightest supersymmetric partners of the top quarks, in $p\bar{p}$ collisions at a center-of-mass energy of 1.96 TeV, using data corresponding to an integrated luminosity of {7.3 $fb^{-1}$} collected with the \dzero experiment at the Fermilab Tevatron Collider. Each scalar top quark is assumed to decay into a $b$ quark, a charged lepton, and a scalar neutrino ($\tilde{\nu}$). We investigate final states arising from $\tilde{t}_{1} \bar{\tilde{t}_{1}} \rightarrow b\bar{b}\mu\tau \tilde{\nu} \tilde{\nu}$ and $\tilde{t}_{1} \bar{\tilde{t}_{1}} \rightarrow b\bar{b}\tau\tau \tilde{\nu} \tilde{\nu}$. With no significant excess of events observed above the background expected from the standard model, we set exclusion limits on this production process in the ($m_{\tilde{t}_{1}}$,$m_{\tilde{\nu}}$) plane.
• ### Identification of gamma-ray emission from 3C345 and NRAO512(1107.2926)

July 14, 2011 astro-ph.CO, astro-ph.HE
For more than 15 years, since the days of the Energetic Gamma-Ray Experiment Telescope (EGRET) on board the Compton Gamma-Ray Observatory (CGRO; 1991-2000), it has remained an open question why the prominent blazar 3C 345 was not reliably detected at gamma-ray energies <=20 MeV. Recently a bright gamma-ray source (0FGL J1641.4+3939/1FGL J1642.5+3947), potentially associated with 3C 345, was detected by the Large Area Telescope (LAT) on Fermi. Multiwavelength observations from radio bands to X-rays (mainly GASP-WEBT and Swift) of possible counterparts (3C 345, NRAO 512, B3 1640+396) were combined with 20 months of Fermi-LAT monitoring data (August 2008 - April 2010) to associate and identify the dominating gamma-ray emitting counterpart of 1FGL J1642.5+3947. The source 3C 345 is identified as the main contributor for this gamma-ray emitting region. However, after November 2009 (15 months), a significant excess of photons from the nearby quasar NRAO 512 started to contribute and thereafter was detected with increasing gamma-ray activity, possibly adding flux to 1FGL J1642.5+3947. For the same time period and during the summer of 2010, an increase of radio, optical and X-ray activity of NRAO 512 was observed. No gamma-ray emission from B3 1640+396 was detected.
• We report the result of a search for the pair production of the lightest supersymmetric partner of the top quark ($\tilde{t}_1$) in $p\bar{p}$ collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider corresponding to an integrated luminosity of 5.4 fb$^{-1}$. The scalar top quarks are assumed to decay into a $b$ quark, a charged lepton, and a scalar neutrino ($\tilde{\nu}$), and the search is performed in the electron plus muon final state. No significant excess of events above the standard model prediction is detected, and improved exclusion limits at the 95% C.L. are set in the the ($M_{\tilde{t}_1}$,$M_{\tilde{\nu}}$) mass plane.
• We extract the total width of the top quark, Gamma_t, from the partial decay width Gamma(t -> W b) measured using the t-channel cross section for single top quark production and from the branching fraction B(t -> W b) measured in ttbar events using up to 2.3 fb^-1 of integrated luminosity collected by the D0 Collaboration at the Tevatron ppbar Collider. The result is Gamma_t = 1.99 +0.69 -0.55 GeV, which translates to a top-quark lifetime of tau_t = (3.3 +1.3 -0.9) x 10^-25 s. Assuming a high mass fourth generation b' quark and unitarity of the four-generation quark-mixing matrix, we set the first upper limit on |Vtb'| < 0.63 at 95% C.L.
• ### Eight gamma-ray pulsars discovered in blind frequency searches of Fermi LAT data(1006.2134)

We report the discovery of eight gamma-ray pulsars in blind frequency searches using the LAT, onboard the Fermi Gamma-ray Space Telescope. Five of the eight pulsars are young (tau_c<100 kyr), energetic (Edot>10^36 erg/s), and located within the Galactic plane (|b|<3 deg). The remaining three are older, less energetic, and located off the plane. Five pulsars are associated with sources included in the LAT bright gamma-ray source list, but only one, PSR J1413-6205, is clearly associated with an EGRET source. PSR J1023-5746 has the smallest characteristic age (tau_c=4.6 kyr) and is the most energetic (Edot=1.1E37 erg/s) of all gamma-ray pulsars discovered so far in blind searches. PSRs J1957+5033 and J2055+25 have the largest characteristic ages (tau_c~1 Myr) and are the least energetic (Edot~5E33 erg/s) of the newly-discovered pulsars. We present the timing models, light curves, and detailed spectral parameters of the new pulsars. We used recent XMM observations to identify the counterpart of PSR J2055+25 as XMMU J205549.4+253959. In addition, publicly available archival Chandra X-ray data allowed us to identify the likely counterpart of PSR J1023-5746 as a faint, highly absorbed source, CXOU J102302.8-574606. The large X-ray absorption indicates that this could be among the most distant gamma-ray pulsars detected so far. PSR J1023-5746 is positionally coincident with the TeV source HESS J1023-575, located near the young stellar cluster Westerlund 2, while PSR J1954+2836 is coincident with a 4.3 sigma excess reported by Milagro at a median energy of 35 TeV. Deep radio follow-up observations of the eight pulsars resulted in no detections of pulsations and upper limits comparable to the faintest known radio pulsars, indicating that these can be included among the growing population of radio-quiet pulsars in our Galaxy being uncovered by the LAT, and currently numbering more than 20.
• ### Observations of Milky Way Dwarf Spheroidal galaxies with the Fermi-LAT detector and constraints on Dark Matter models(1001.4531)

Jan. 25, 2010 hep-ph, astro-ph.CO, astro-ph.HE
We report on the observations of 14 dwarf spheroidal galaxies with the Fermi Gamma-Ray Space Telescope taken during the first 11 months of survey mode operations. The Fermi telescope provides a new opportunity to test particle dark matter models through the expected gamma-ray emission produced by pair annihilation of weakly interacting massive particles (WIMPs). Local Group dwarf spheroidal galaxies, the largest galactic substructures predicted by the cold dark matter scenario, are attractive targets for such indirect searches for dark matter because they are nearby and among the most extreme dark matter dominated environments. No significant gamma-ray emission was detected above 100 MeV from the candidate dwarf galaxies. We determine upper limits to the gamma-ray flux assuming both power-law spectra and representative spectra from WIMP annihilation. The resulting integral flux above 100 MeV is constrained to be at a level below around 10^-9 photons cm^-2 s^-1. Using recent stellar kinematic data, the gamma-ray flux limits are combined with improved determinations of the dark matter density profile in 8 of the 14 candidate dwarfs to place limits on the pair annihilation cross-section of WIMPs in several widely studied extensions of the standard model. With the present data, we are able to rule out large parts of the parameter space where the thermal relic density is below the observed cosmological dark matter density and WIMPs (neutralinos here) are dominantly produced non-thermally, e.g. in models where supersymmetry breaking occurs via anomaly mediation. The gamma-ray limits presented here also constrain some WIMP models proposed to explain the Fermi and PAMELA e^+e^- data, including low-mass wino-like neutralinos and models with TeV masses pair-annihilating into muon-antimuon pairs. (Abridged)
• ### Measurement of the Fermi-LAT Localization Performance(0912.3855)

Dec. 19, 2009 astro-ph.IM, astro-ph.HE
We present results of a study of the localization capability of Fermi-LAT, using a large set of blazars with precise radio locations. Since the width of the PSF decreases with energy, the performance is typically dominated by a few high energy photons, so it is important to properly characterize the high-energy PSF. Using such data, we have found a need to modify the pre-launch high-energy (greater than a few GeV) PSF derived from extensive Monte Carlo simulations of particle interactions in the LAT; the resulting data-based PSF is shown

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Show Question
Math and science::Topology

# Compactness

Compact sets can be thought of as a generalization of closed sets. See the reverse side for a justification.

There are multiple ways of formulating compactness, with some being more intuitive than others.

There are 3 formulations that are particularly important.

### 1. Compactness, in terms of sequences in $$\mathbb{R}$$.

A set $$K \subset \mathbb{R}$$ is compact iff every sequence in $$K$$ has a subsequences that converges to a limit that is also in $$K$$.

What is the topological generalization of this definition?

The most basic example of such a closed set in $$\mathbb{R}$$ is a closed interval.

Bolzano-Weierstrass's theorem connects the first and second formulations.

### 2. Compactness, in terms of closed, bounded sets.

A set $$K \subset \mathbb{R}^n$$ is compact iff it is closed and bounded.

The next formulation is the most general of the three, graduating to the topic of topology. It uses the idea of a cover and a subcover.

#### Cover

Let $$X$$ be a topological space. A cover of $$X$$ is a family $$(U_i)_{i \in I}$$ of subsets of $$X$$ such that $$\bigcup_{i \in I} U_i = X$$. It is finite iff the indexing set $$I$$ is finite, and open iff $$U_i$$ is open for each $$i \in I$$.

Given a cover $$(U_i)_{i \in I}$$ and $$J \subseteq I$$, we say that $$(U_j)_{j \in J}$$ is a subcover of $$(U_i)_{i \in I}$$ if it is itself a cover of $$X$$.

### 3. Compactness, in terms of covers.

A topological space $$X$$ is compact iff every open cover of $$X$$ has a finite subcover.

What is the theorem that connects these three formulations of compactness?

### Heine-Borel theorem

The Heine-Borel theorem is precicely the statement that ties these three notions of compactness together. [Hmm... actually, I think the Heine-Borel theorem might only cover the equivalence of the first two].

### Heine-Borel theorem

Let $$K$$ be a subset of $$\mathbb{R}$$. The following three statements are equivalent:

1. $$K$$ is compact.
2. $$K$$ is closed and bounded.
3. Every open cover of $$K$$ has a finite subcover.

### Proof 1: #2 $$\implies$$ #3

A MathExchange answer does a good job of motivating intuition as to why a closed interval must always have a finite subcover. Below is a screenshot of the proof (that any cover of $$[0, 1]$$ has a finite subcover).

#### Proof 1 essence

If prooving by contradiction, we must be able to zoom in on an ever narrower closed sub-interval of $$[0, 1]$$ that requires an infinite cover. As the intervals are closed, their intersection is not empty, but a point. This point must be in an open set of the cover, but this open set must cover at least some of the intervals that we zoomed in on.

Infinite open covers can occur when covering next to and edge. But if we need to cover the edge, then the open set that covers the edge will also cover the tail of our infinite cover.

### The essence of compactness

Abbott on p97 mentions this about compact sets and closed intervals:

There may be a temptation to consider closed intervals as being a kind of standard archetype for compact sets, but this is misleading. The structure of compact sets can be much more intricate and interesting. For instance, one implication of Theorem 3.3.4 is that the Cantor set is compact. It is more useful to think of compact sets as generalizations of closed intervals. When ever a fact involving closed intervals is true, it is often the case that the same result holds when we replace “closed interval” with “compact set.” As an example, let’s experiment with the Nested Interval Property proved in the first chapter...

He then goes on to prove a version of the nested closed interval property, but with compact sets replacing closed intervals:

If $$K_1 \supseteq K_2 \supseteq K_3 \supseteq K_4 \supseteq ...$$ is a nested sequence of nonempty compact sets, then the intersection $$\cap_{n=1}^{\infty} K_n$$ is not empty.

Even more content...this whole section from Abbott is good to re-read.

#### Some phrasing that might help reading the above excerpt

The watershed case is covering a sequence of points in a set of reals (or rationals) with ever smaller open sets. Think of a sequence from the set that approaches some limit. What if the set (and thus the sequence) is bounded? What if the sequence approaches a limit within the set (i.e. think closed sets)? All points of the sequence has some wriggle-room; in other words, can be covered by an open subset. If a finite-cover is possible, then the sequence can't approach a limit outside of the set.


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• Volume 80, Issue 1

January 2013,   pages  1-185

• General editorial on publication ethics

• Quantum effects at low-energy atom–molecule interface

The effects of quantum interference in inter-conversion between cold atoms and diatomic molecules are analysed in this study. Within the framework of Fano’s theory, continuum bound anisotropic dressed state formalism of atom–molecule quantum dynamics is presented. This formalism is applicable in photo- and magneto-associative strong-coupling regimes. The significance of Fano effect in ultracold atom–molecule transitions is discussed. Quantum effects at low-energy atom–molecule interface are important for exploring coherent phenomena in hitherto unexplored parameter regimes.

• SUSY formalism for the symmetric double well potential

Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.

• Exact solutions of Feinberg–Horodecki equation for time-dependent anharmonic oscillator

In this work, an alternative treatment known as Nikiforov–Uvarov (NU) method is proposed to find the exact solutions of the Feinberg–Horodecki equation for the time-dependent potentials. The present procedure is illustrated with two examples: (1) time-dependent Wei Hua oscillator, (2) time-dependent Manning–Rosen potential.

• Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).

• Unpolarized coupled DGLAP evolution equation at small-𝑥

In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small-𝑥 limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated 𝑡-evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-$Q^{2}$ region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when $Q^{2}$ increases for fixed values of 𝑥.

• Candidate of the member of three-phonon multiplet observed in the $\beta^{+}$ +EC decay of 76Br

The decay scheme of 76Br is established by the 76Br($T1/2 = 16.2$ h) $\bate^{+}$/EC study. The 1791.31 keV level, which was identified initially by Müller $\mathit{et al}$ with 76Se($p, p'$) reaction more than three decades ago, is reconfirmed. However, the spin and parity have not been assigned by Müller $\mathit{et al}$. Now we consider it reasonable to assign the 1791.31 keV level as a new candidate of the three-phonon multiplet in 76Se. In addition, in order to study the deformation of 76Se which lies in transitional region between strongly deformed and spherical nuclei, we calculate the total Routhian surfaces (TRS) of positive-parity states by cranking shell model formalism.

• Role of energy cost in the yield of cold ternary fission of 252Cf

The energy costs in the cold ternary fission of 252Cf for various light charged particle emission are calculated by includingWong's correction for Coulomb potential. Energy cost is found to be higher in cold fission than in normal fission. It is found that energy cost always increases with decrease in experimental yield in all the light charged particle emissions. The higher ground state deformation of the fragments, the odd–even effect and the enhanced yield in the octupole region observed in cold fission are found to be consistent with the concept of energy cost.

• Thermal-hydraulic analysis of LBE spallation target for accelerator-driven systems

In an accelerator-driven subcritical system (ADS), a high-performance spallation neutron source is used to feed the subcritical reactor. Neutron generation depends on the proton beam intensity. If the beam intensity is increased by a given factor, the number of generated neutrons will increase. The mechanism yielding a high rate of neutron production per energy is the spallation process, and this mechanism produces very high-energy deposition in the spallation target material. Producing a high rate of neutrons is accompanied by creation of problems of decay heat cooling and radiological protection. As a first step in designing a full-scale industrial ADS, a small-scale experimental ADS, which is similar to the European experimental ADS (XADS) is analysed. The analysis presented in this paper is based on lead–bismuth eutectic (LBE) cooled XADS-type experimental reactors, designed during the European experimental (PDS-XADS) project. Computational fluid dynamics analysis has been carried out for the spallation target. Steady-state behaviour and shear stress transport turbulence model with the automatic wall treatment were applied in the present analysis.

• Neutronic simulation of a research reactor core of (232Th, ${}^{235}$U)O2 fuel using MCNPX2.6 code

The small reactor design for the remote and less developed areas of the user countries should have simple features in view of the lack of infra-structure and resources. Many researchers consider long core life with no on-site refuelling activity as a primary feature for the small reactor design. Long core life can be achieved by enhancing internal conversion rate of fertile to fissile materials. For that purpose, thorium cycle can be adopted because a high fissile production rate of 233U converted from 232Th can be expected in the thermal energy region. A simple nuclear reactor core arranged 19 assemblies in hexagonal structure, using thorium-based fuel and heavy water as coolant and moderator was simulated using MCNPX2.6 code, aiming an optimized critical assembly. Optimized reflector thickness and gap between assemblies were determined to achieve minimum neutron leakage and void reactivity. The result was a more compact core, where assemblies were designed having 19-fuel pins in 1.25 pitch-to-diameter ratio. Optimum reflector thickness of 15 cm resulted in minimal neutron leakage in view of economic limitations. A 0.5 cm gap between assembles achieved more safety and $2.2$% enrichment requirements. The present feasibility study suggests a thermal core of acceptable neutronic parameters to achieve a simple and safe core.

• Antenna coupling study for ICWC plasma characterization in TEXTOR

Ion cyclotron wall conditioning (ICWC) discharges, in pulsed-mode operation, were carried out in the limiter tokamak TEXTOR to explore safe operational regimes for the experimental parameters for possible ICWC-discharge cleaning in International Thermonuclear Experimental Reactor (ITER) at half field. Antenna coupling properties obtained during the ion cyclotron range of frequencies (ICRF) wall conditioning experiments performed in helium–hydrogen mixture in TEXTOR were analysed in relation to the obtained ICWC-plasma characterization results. Satisfactory antenna coupling in the mode conversion scenario along with reproducible generation of ICRF plasmas for wall conditioning, were achieved by coupling radio frequency (RF) power from one or two ICRF antennas. The plasma breakdown results obtained in the TEXTOR tokamak have been compared with the predictions of a zero-dimensional RF plasma production model. The present study of ICWC emphasizes the beneficial effect of application of an additional (along with toroidal magnetic field) stationary vertical ($B_{V} \ll B_{T}$) or oscillating poloidal magnetic field ($B_{P} \ll B_{T}$) on antenna coupling and relevant plasma parameters.

• Influence of argon plasma treatment on polyethersulphone surface

Polyethersulphone (PES) was modified to improve the hydrophilicity of its surface, which in turn helps in improving its adhesive property. The modified PES surface was characterized by contact angle measurement, X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and Vicker’s microhardness measurement. The contact angles of the modified PES reduces from $49^{\circ}$ to $10^{\circ}$ for water. The surface free energy (SFE) calculated from measured contact angles increases from 66.3 to 79.5 mJ/m2 with the increase in plasma treatment time. The increase in SFE after plasma treatment is attributed to the functionalization of the polymer surface with hydrophilic groups. The XPS analysis shows that the ratio of O/C increases from 0.177 to 0.277 for modified PES polymer. AFM shows that the average surface roughness increases from 6.9 nm to 23.7 nm due to the increase in plasma treatment time. The microhardness of the film also increases with plasma treatment.

• A model for the occurrence and analysis of ionic thermocurrent spectrum involving different orders of kinetics

Ionic thermocurrent (ITC) spectrum is much similar to a thermoluminescence (TL) glow curve involving monomolecular kinetics. It has already been reported that different orders of kinetics are involved in TL processes, which depend specifically on the extent of recombination and simultaneous retrapping. It is found that the involvement of different orders of kinetics in ITC spectrum depends on the experimental conditions of polarization and rate of rapid cooling. Consequently, order of kinetics involved in the ITC spectrum does not represent any specific feature of the system under investigation. An equation is developed which explains the occurrence of ITC spectrum involving any order of kinetics. Dielectric relaxation parameters, order of kinetics and approximate number of dipoles per unit volume are evaluated conveniently and easily following the proposed model.

• A comparative study of the spectra recorded at RRCAT synchrotron BL-8 dispersive EXAFS beamline with other beamlines

The aim of the present work is to make a comparative study of the EXAFS spectra recorded at the BL-8 dispersive EXAFS beamline at 2 GeV Indus-2 synchrotron source at RRCAT, Indore (India) with those recorded at other synchrotron EXAFS beamlines, viz., X-19A at NSLS, BNL (USA), EXAFS wiggler beamline 4-1 at the SSRL (USA) and beamline 11.1 at ELETTRA (Italy). For this purpose, EXAFS spectra at Cu K-edge in copper metal have been recorded at these four beamlines. Further, EXAFS spectra at Cu K-edge in a copper complex have also been recorded at BL-8 beamline and beamline 11.1 at ELETTRA (Italy). The obtained experimental $\mu(E)$ data have been background-subtracted and then normalized. The normalized data have been then converted to $\chi(k)$ data, which have been Fourier-transformed and then fitted with the theoretical model, thereby yielding different structural parameters. It has been shown that the results obtained from the EXAFS spectra recorded at the BL-8 beamline are comparable with those obtained from other synchrotron EXAFS beamlines and also with the crystallographic results reported by earlier workers. The reliability, usefulness and data quality of the BL-8 beamline have been discussed.

• Community detection using global and local structural information

Community detection is of considerable importance for understanding both the structure and function of complex networks. In this paper, we introduced the general procedure of the community detection algorithms using global and local structural information, where the edge betweenness and the local similarity measures respectively based on local random walk dynamics and local cyclic structures were used. The algorithms were tested on artificial and real-world networks. The results clearly show that all the algorithms have excellent performance in the tests and the local similarity measure based on local random walk dynamics is superior to that based on local cyclic structures.

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 6
December 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.


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Why this works for proving ZF axioms system is free of Russell's paradox?

In a book on mathematical logic, the author explains why ZF axioms avoid universal set like this:

We may also now show that no universal set exists. Suppose $$u$$ is a set containing all sets. By comprehension, we may form the set $$\{x\in u\,:\,x\notin x\}$$, which yields Russell's paradox, a contradiction. Thus, not every collection of sets is itself a set.

The author is using reductio ad absurdum. If a set of axiom $$\Sigma$$ plus a proposition $$\alpha$$ produce a paradox, then we know that $$\alpha$$ is inconsistent with $$\Sigma$$. In our case, $$\Sigma$$ is the ZF, while $$\alpha$$ is "universal set exists".

Here comes my confusion, if we don't assume the consistence of ZF, how do we know that the paradox comes from $$\alpha$$ rather than the dubious ZF? But we can't presume the consistence of ZF, because what we are doing is exactly to prove it free from Russell's paradox.

• We can only prove that Russel's paradox does not occur. The consistency of ZFC remains an open question. Dec 28, 2021 at 13:02

This doesn't show that ZF is free from Russel paradox, or consistency of ZF (it's imaginable, though extremely unlikely, that ZF is in fact inconsistent).

This shows that ZF proves that no universal set exists. Reductio ad absurdum works with all theories, even inconsistent: if by adding hypothesis $$H$$ to theory $$T$$ we can get inconsistency, then $$T$$ can prove $$\neg H$$. Of course it's not interesting if $$T$$ is itself inconsistent (because then it can prove anything), but it's still correct.

• Why do you think is it extremely likely for ZF to be consistent? Also, do you think it is likely or unlikely for ZF to be arithmetically sound? Jan 7 at 14:16
• There are a lot of open problems that can be formulated in ZF, and they seem hard. As proving something in consistent theory is harder than in inconsistent one, it is evidence in favor of consistency of ZF. I think it's likely that ZF is arithmetically sound, but I don't actually trust my intuition about it. Jan 7 at 15:12
• I agree that proving things in a consistent theory is harder, but most people are unable to actually think beyond a certain strength level, roughly around that of bounded Replacement. Though I do think ZF is consistent. Would you like to have a more in-depth discussion in chat? I think it might be a very interesting one. Jan 7 at 15:32

Russell's Paradox arose from an inconsistency in an early attempt to axiomatize set theory by G. Frege. In his system, it was possible to both prove and disprove:

$$~~~~\exists x: \forall y: [y\in x \iff y\notin y]$$

In ZFC theory, it seems to be impossible to derive this result. You can, of course, derive its negation in ZFC theory.


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How closely related two or more separate strands of DNA are to each other, based on their base sequences. For more information, see homology. From the B...
I will describe a spectral sequence that starts at reduced odd Khovanov homology and converges to a version of instanton homology for double branched covers.. ...
Tätä artikkelia/julkaisua ei ole tallennettu Julkariin. Julkaisun tiedoissa voi kuitenkin olla linkki toisaalle tallennettuun artikkeliin/julkaisuun. ...
A review of the literature on homology indicates that the theory does not provide evidence for evolutionary naturalism, and that the common examples of homology can be better explained by Creation.
Please call it sequence SIMILARITY In a search you may find many sequence similarities but only few of the matches may represent homologies. See Reeck et al. (1987) Homology in proteins and nucleic acids: A terminology muddle and a way out of it. Cell 60, 667 ...
Opens the Highlight Feature Bar and highlights feature annotations from the FEATURES table of the record. The Highlight Feature Bar can be used to navigate to and highlight other features and provides links to display the highlighted region separately. Links in the FEATURES table will also highlight the corresponding region of the sequence. More... ...
Page 1 of 4 - Vestigial Organs - posted in Best all time threads.: Most of the obvious anatomical homologies are between anatomical structures which are in active use by the species in question, but some anatomical homologies involve structures which are no longer needed but which also havent disappeared entirely. A vestigial organ or structure is any organ or structure found in a species which is not being used as it is in other species. Contrary to popular belief, vestigial organs a...
We will study the l1-homology of the 2-class in one relator groups. We will see that there are many qualitative and quantitive similarities between the l1-norm of the top dimensional class and the stable commutator length of the defining relation. As an application we construct manifolds with small simplicial volume.. This work in progress is joint with Clara Loeh.. ...
Considerable insights into important cis regulatory elements in a gene can be gleaned from the identification of sequence homologies among different species. To extend and optimize the sequence comparison between human and mouse erythropoietin (Epo) genes, we have obtained new human sequence from 5,547 to 385 bp upstream of the cap site and extended the 3 flank by 489 bp. In addition, we have obtained new sequence information on the mouse Epo gene extending from within the 3 untranslated region (UTR) to 1,001 bp downstream of the polyadenylation site. Analysis of these additional sequences shows considerable homology between human and mouse Epo genes as far as 4 kb (human) or 3 kb (mouse) upstream of the cap sites, as well as far more homology at the 3 end than was previously realized. In addition, both species were found to have a high frequency of short interspersed (SINE) repetitive sequences that interrupt homologies in both the 5 flank and within the transcription unit.
Knowledge of the sequence of a DNA segment has many uses, and some examples follow. First, it can be used to find genes, segments of DNA that code for a specific protein or phenotype. If a region of DNA has been sequenced, it can be screened for characteristic features of genes. For example, open reading frames (ORFs)-long sequences that begin with a start codon (three adjacent nucleotides; the sequence of a codon dictates amino acid production) and are uninterrupted by stop codons (except for one at their termination)-suggest a protein-coding region. Also, human genes are generally adjacent to so-called CpG islands-clusters of cytosine and guanine, two of the nucleotides that make up DNA. If a gene with a known phenotype (such as a disease gene in humans) is known to be in the chromosomal region sequenced, then unassigned genes in the region will become candidates for that function. Second, homologous DNA sequences of different organisms can be compared in order to plot evolutionary ...
NPC1s amino acid sequence homology to PATCHED, human HMG-CoA reductase and SCAP. Credit: Reprinted with permission from AAAS / Carstea et al., Science 277:228, 1997. />NPC1s amino acid sequence homology to PATCHED, human HMG-CoA reductase and SCAP. Credit: Reprinted with permission from AAAS / Carstea et al., Science 277:228, 1997. In the 1990s, the Ara Parseghian Foundation donated money to the National I. 0 Comments. ...
Marvin5.2 introduced the enumeration of homology groups. Homology groups are R-groups represented as pseudo atoms - with the names covering a set of R-groups either built-in or user-defined.. ...
package transeq import ( bufio bytes context encoding/binary fmt io runtime sync ) var ( letterCode = map[byte]uint8{ A: aCode, C: cCode, T: tCode, G: gCode, N: nCode, U: uCode, } standard = map[string]byte{ TTT: F, TCT: S, TAT: Y, TGT: C, TTC: F, TCC: S, TAC: Y, TGC: C, TTA: L, TCA: S, TAA: *, TGA: *, TTG: L, TCG: S, TAG: *, TGG: W, CTT: L, CCT: P, CAT: H, CGT: R, CTC: L, CCC: P, CAC: H, CGC: R, CTA: L, CCA: P, CAA: Q, CGA: R, CTG: L, CCG: P, CAG: Q, CGG: R, ATT: I, ACT: T, AAT: N, AGT: S, ATC: I, ACC: T, AAC: N, AGC: S, ATA: I, ACA: T, AAA: K, AGA: R, ATG: M, ACG: T, AAG: K, AGG: R, GTT: V, GCT: A, GAT: D, GGT: G, GTC: V, GCC: A, GAC: D, GGC: G, GTA: V, GCA: A, GAA: E, GGA: G, GTG: V, GCG: A, GAG: E, GGG: G, } ) ...
Definition of homologies in the Legal Dictionary - by Free online English dictionary and encyclopedia. What is homologies? Meaning of homologies as a legal term. What does homologies mean in law?
Sequencing: is the process of determining the nucleic acid sequence - the order of nucleotides in DNA. It includes any method or technology that is used
The OT-XL is an open top tool bag. Its the perfect king-sized, all-purpose tool storage bag for those fill ´em up and go situations.
37 CFR 1.822(c)(5) provides that nucleotide sequences shall only be represented by a single strand, in the 5′ to 3′ direction, from left to right. That is, double stranded nucleotides shall not be represented in the sequence listing. A double stranded nucleotide may be represented as two single stranded nucleotides, and any relationship between the two may be shown in the drawings. The procedures for presenting and numbering amino acid sequences are set forth in 37 CFR 1.822(d). Two alternatives are presented for numbering amino acid sequences. Amino acid sequences may be numbered with respect to the identification of the first amino acid of the first mature protein or with respect to the first amino acid appearing at the amino terminal. The numbering procedure for nucleotides is set forth in 37 CFR 1.822(c)(6). Sequences that are circular in configuration are intended to be encompassed by these rules, and the numbering procedures described above remain applicable with the exception that the ...
The degree of similarity between sequences of Amino Acids. This information is useful for the analyzing genetic relatedness of Proteins and species ...
The observed gene overlays in the viruses ФX174 and SV40 show a surprising economy of information storage; two different amino acid sequences are read in different frames from the same stretch of DNA.
LOC FOR DETECTION OF HYBRIDIZATION OF NUCLEIC ACID SEQUENCES WITH PRIMER-LINKED STEM-AND-LOOP PROBES - diagram, schematic, and image 20 ...
In article ,36nmhcINN2ng at bigbird.cc.williams.edu, writes: , Hello, , Does anyone have any experience producing a very crude , structural hypothesis from sequence data? We have Sybyl, but Ive , been unable to get the Homology modeler to produce adequate results. , The situation is this: I have a sequence-structure coordinate file of , a protein with , 85 % homology to the protein I want to make a , structure for, but Sybyl complains about not having enough short , regions of homology! Are there any free programs that can do this? , Ive tried Sybyls built in structure-seq database, and constructed my , own database with many similar proteins and just the resolved protein , with homology. Any suggestions or references would be appreciated, , , Max Nanao , 95mhn at cc.williams.edu , nanao at ochre.mgh.harvard.edu Depends on what exactly is meant by , 85% homology (% sequence identity?), but, by most definitions of homology in most situations like this, you should not have a problem to calculate ...
M.P.E.P. Section 1823.02: Nucleotide and/or Amino Acid Sequence Listings, and Tables Related to Sequence Listings. Taken from the 9th Edition of the MPEP, Revision 08.2017, (Last Revised Jan. 2018). Updated in BitLaw in February 2018
No matter what the length of A and B are, A and B (the aligned sequences) will be of the same length. This simply comes from the definition of an alignment. The characters (representing base pairs) from the two sequences are arranged as to minimize the differences between them, and then the empty spaces (if any) are filled in with gaps (dash characters). These gaps are typically interpreted as evolutionary events between two homologous sequences, i.e. an insertion of nucleotides to one sequence or a deletion of nucleotides from the other (indels).. ...
Ordinary homology and cohomology factor through chain complexes via singular homology and cohomology. What about other (co)homology theories?. That is, for each spectrum $E$, do we have a lift in the following diagram?. $\begin{array}[ccc] & \mathsf{HoTop} & \overset{E}{\to} & \mathsf{GrAb} \\ & \underset{?}{\searrow} & \uparrow \\ & & \mathcal{D}(\mathsf{Ch}_{\mathbb{Z}}) \end{array}$. Where $\mathsf{HoTop}$ is the homotopy category, $E$ is $E$-homology or $E$-cohomology (in which case its contravariant, of course), $\mathsf{GrAb}$ is graded abelian groups, $\mathcal{D}(\mathsf{Ch}_{\mathbb{Z}})$ is the derived category of chain complexes in abelian groups, the functor $\mathcal{D}(\mathsf{Ch}_{\mathbb{Z}}) \to \mathsf{GrAb}$ is homology, and the functor labeled ? is the desired lifting.. It would just about suffice to do this in the universal example of stable homotopy (just about only because we have to do this for all spectra now), because we have a factorization:. \$\begin{array}[ccc] & ...
Amino acid sequences of SsCOMT, SbCOMT, OsCOMT, TaCOMT, AtCOMT, and ZmCOMT were initially aligned by DNAMAN6.0 using default parameters, and followed by manual
The FASTA programs provide a comprehensive set of rapid similarity searching tools (fasta36, fastx36, tfastx36, fasty36, tfasty36), similar to those provided by the BLAST package, as well as programs for slower, optimal, local, and global similarity searches (ssearch36, ggsearch36), and for searching with short peptides and oligonucleotides (fasts36, fastm36)
CACCTAAATT GTAAGCGTTA ATATTTTGTT AAAATTCGCG TTAAATTTTT GTTAAATCAG CTCATTTTTT AACCAATAGG CCGAAATCGG CAAAATCCCT TATAAATCAA AAGAATAGAC CGAGATAGGG TTGAGTGTTG TTCCAGTTTG GAACAAGAGT CCACTATTAA AGAACGTGGA CTCCAACGTC AAAGGGCGAA AAACCGTCTA TCAGGGCGAT GGCCCACTAC GTGAACCATC ACCCTAATCA AGTTTTTTGG GGTCGAGGTG CCGTAAAGCA CTAAATCGGA ACCCTAAAGG GAGCCCCCGA TTTAGAGCTT GACGGGGAAA GCCGGCGAAC GTGGCGAGAA AGGAAGGGAA GAAAGCGAAA GGAGCGGGCG CTAGGGCGCT GGCAAGTGTA GCGGTCACGC TGCGCGTAAC CACCACACCC GCCGCGCTTA ATGCGCCGCT ACAGGGCGCG TCCCATTCGC CATTCAGGCT GCGCAACTGT TGGGAAGGGC GATCGGTGCG GGCCTCTTCG CTATTACGCC AGCTGGCGAA AGGGGGATGT GCTGCAAGGC GATTAAGTTG GGTAACGCCA GGGTTTTCCC AGTCACGACG TTGTAAAACG ACGGCCAGTG AATTGTAATA CGACTCACTA TAGGGCGAAT TGGAGCTCCA CCGCGGTGGC GGCCGCTCTA GAACTAGTGG ATCCCCCGGG CTGCAGGAAT TCGGCACGAG AAAACCTTCA CTACTCTTGA CCCTGCGTCC CTAGCTTGGC TGACAGAGGA GCCAGGGCCA ACAGAGGTCA CACGCACATC CCAAAGCCCT CGCTCTCCAG ATTCCAGTCA GAGTTCTATG GCCCAGGAGG AAGAGGAGGA AGAGCAAGGA AGAACTAGGA AACGGAAACA GAGTGGTCAG TGCCCAGCCC ...
7800gccttctctg ccctgagggt cgaaggtcga gcaggccggg ggtgtccggg aggtctttgg 7860gcatcgcggt ctggggttgg gacgtgtaag cgcctgggag agcctagacc aggctccggg 7920ctgccaataa agaagtgaaa tgcgtatctg gtctcctgtc gtgggagagt gtgaggtgta 7980acggattcaa gtctgaaccc agagcctgga aaaggctgac cgcccagatt gacgttgcta 8040ggcaactccg gaggcgggcc cagcgccaaa agaacagggc gaggcgtcgt ccccgcatcc 8100cattggccgt tctctgcggg gccccgccct cgggggccgg agctagaagc tctacgcttc 8160cgaggcgcac ctcctggcct gcacgctttg acgt 8194162526DNAHomo sapiens 16atgctgctct gcacggctcg cctggtcggc ctgcagcttc tcatttcctg ctgctgggcc 60tttgcctgcc atagcacgga gtcttctcct gacttcaccc tccccggaga ttacctcctg 120gcaggcctgt tccctctcca ttctggctgt ctgcaggtga ggcacagacc cgaggtgacc 180ctgtgtgaca ggtcttgtag cttcaatgag catggctacc acctcttcca ggctatgcgg 240cttggggttg aggagataaa caactccacg gccctgctgc ccaacatcac cctggggtac 300cagctgtatg atgtgtgttc tgactctgcc aatgtgtatg ccacgctgag agtgctctcc 360ctgccagggc aacaccacat agagctccaa ggagaccttc tccactattc ccctacggtg 420ctggcagtga ttgggcctga cagcaccaac ...
Chalmers R, Sewitz S, Lipkow K, Crellin P. Complete nucleotide sequence of Tn10. J Bacteriol. 2000 May;182(10):2970-2. doi: 10.1128/jb.182.10.2970-2972.2000. PubMed ID: 10781570 ...
Anyway, if you get some proteins, you identify them with mass spec (either MALDI or digest on LC-MS) and this information you use for the identification ...
human CSDE1 protein: amino acid sequence in first source; unr gene located close to N-ras locus and may interact with it; RefSeq NM_007158
Gentaur molecular products has all kinds of products like :search , Biolin \ Mouse Gene, RPL13A \ QT12X-MS-07 for more molecular products just contact us
We have conducted a human cDNA project to predict protein-coding sequences (CDSs) in large cDNAs (, 4 kb) since 1994, and the number of newly identified genes, known as KIAA genes, already exceeds 2000. The ultimate goal of this project is to clarify the physiological functions of the proteins encoded by KIAA genes. To this end, the project has recently been expanded to include isolation and characterization of mouse KIAA-counterpart genes. We herein present the entire sequences and the chromosome loci of 500 mKIAA cDNA clones and 13 novel cDNA clones that were incidentally identified during this project. The average size of the 513 cDNA sequences reached 4.3 kb and that of the deduced amino acid sequences from these cDNAs was 816 amino acid residues. By comparison of the predicted CDSs between mouse and human KIAAs, 12 mKIAA cDNA clones were assumed to be differently spliced isoforms of the human cDNA clones. The comparison of mouse and human sequences also revealed that four pairs of human ...
For the Predefined groups, the R-group definitions specify the enumerable library as User-defined groups. I.e. these groups definitions can be customized. These structures are characteristic to the Homology group and encompass simple and large structures as well.. We have to emphasize, that these definitions are used only for enumeration and do not affect searching. As noted earlier, arbitrary structures fulfilling the requirements for the Homology group will match such a target.. Enumeration definitions contain two attachment points as default. After enumeration these are the atoms which connect to the first two neighbors of the group. If the enumerated Homology groups Pseudo atom has more than two connections, then further attachment points are added. These are put on atoms that have free valence and comply the requirements for externally connecting atoms of the given group. E.g. for aryl only aromatic ring atoms can be the connection points. The atoms of the definition are investigated in ...
cloning of non-coding region for protein expression - posted in Protein Expression and Purification: Hi! I am trying to see the function of my non-coding region in protein expression. I have clone my gene and its non-coding region upstream of 5UTR to find if non-coding region plays any role in expression of cloned protein. I have other clones with no non-coding region just 5UTR and coding region. Has anybody cloned these type construct in mammalian expression vector and does...
Purchase Molecular Evolution: Computer Analysis of Protein and Nucleic Acid Sequences, Volume 183 - 1st Edition. Print Book & E-Book. ISBN 9780121820848, 9780080883007
Genomic organization, chromosomal mapping, nucleotide sequence, and predicted amino acid sequence of the murine MCP-5 gene. (A) Partial restriction map and ge
Eiglmeier, K., W. Boos, S.T. Cole 1987. Nucleotide sequence and transcriptional startpoint of the glpT gene of Escherichia coli: extensive sequence homology of the glycerol-3-phos transport protein with components of the hexose-6-phos transport system ...
develop a new model summarizing the entire process of transcription and translation with your lab group you will be asked to communicate share amino acid sequence chart dna.. ...
This MATLAB function cuts SeqAA, an amino acid sequence, into parts at the cleavage sites specific for Enzyme, a character vector specifying a name or abbreviation code for an enzyme or compound for which the literature specifies a cleavage rule.
I was wondering if I did something wrong with the deletion, it seems pretty self explanatory but I just want to make sure I did this right. The filled in answers are in bold And Im completely lost with the Amino Acid sequence, my TA did this in class and I still dont get it ...
The next few posts are presented to help you prepare for the AP exam. This first post addresses the homologies between humans and chimps. Recall that homologies are traits that are derived from the same ancestral form - they have a shared ancestry ...
lets assume that i fould a valuable gene fragment ex. dna sequence homology with one of the human myosin ii genes1., Hire Biology Expert, Ask Academics Expert, Assignment Help, Homework Help, Textbooks Solutions
Gentaur molecular products has all kinds of products like :search , Gene Link \ Lambda gt10 reverse primer 24mer \ 26-3000-11 for more molecular products just contact us
Extensive nucleotide sequence data is new known for six small isometric phages, ([o with diagonal slash]Xl 74, G4, St-1, Sl3, [lowercase alpha]3 and [phi]K).Comparison of these sequences allows us to observe the role of ...
Tsou, C.H., Li, L. & Vijayan, K. 2016. The Intra-familial Relationships of Pentaphylacaceae sl as Revealed by DNA Sequence Analysis. Biochemical Genetics pp.1-13. doi: 10.1007/s10528-016-9717-1 ...
Forex Strategies - Come here to share or discuss any forex strategy that you have invented, developed, modified, enhanced, or somehow used in order to
Mc kean, D J.; Potter, M; and Hood, L, Amino acid sequence comparison of three new balb/c mouse kappa chains. Abstr. (1972). Subject Strain Bibliography 1972. 679 ...
TY - JOUR. T1 - Deduced primary structure of rat tryptophan-2,3-dioxygenase. AU - Maezono, Katsumi. AU - Tashiro, Kosuke. AU - Nakamura, Toshikazu. PY - 1990/7/16. Y1 - 1990/7/16. N2 - The complete amino acid sequence of the tryptophan 2, 3-dioxygenase (TO) of rat liver was determined from the nucleotide sequence of a full length TO cDNA isolated from a rat liver cDNA library and determined its primary structure. TO was encoded in a mRNA of about 1.7 kb containing an open reading frame of 1218 bp. According to the deduced amino acid sequence, the monomeric polypeptide of TO consisted of 406 amino acid residues with a calculated molecular weight of 47,796 daltons. It has twelve histidine residues around its hydrophobic region, which has homology with some heme proteins and oxygenase, suggesting that this hydrophobic region might to be the core of TO for the activity.. AB - The complete amino acid sequence of the tryptophan 2, 3-dioxygenase (TO) of rat liver was determined from the nucleotide ...
The full-length ORF clone contains only the coding sequence of the full-length protein, while the other full-length cDNA clones contain some untranslated sequences, such as the 5side or 3′ side non translation. It is well known that these untranslated sequences may have a negative effect on the transcription and translation processes of the encoded proteins in the host.. If it is the ORF expressed clone, it can be transfected into cells and expressed in cells.. In the general situation, the carrier of cDNA clone is not the expression vector, so it can not be directly used for transfection of cells.. The difference between ORF, cDNA and CDS:. 1.what is a full-length ORF clone?. A full-length ORF clone is a plasmid inserted into a DNA fragment encoding a full-length protein. The inserted DNA fragment only contains sequence incoding a full-length protein, and does not contain the untranslated region of 5 or 3 end (UTRs) or intron.. 2.why should the full length ORF cDNA clones are used instead ...
Read Hop mosaic virus: complete nucleotide sequence and relationship to other carlaviruses, Archives of Virology on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Chang, E., et al. N-Terminal Amino Acid Sequence Determination of Proteins by N-Terminal Dimethyl Labeling: Pitfalls and Advantages When Compared with Edman Degradation Sequence Analysis. Journal of Biomolecular Technology. 27(2). 07/03/2016.. ...
I) instructions for representing the set of sequence elements on a display, each sequence element representing an amino acid sequence segment or a nucleic acid sequence segment, wherein the set of sequence elements collectively encode the design nucleic acid sequence, wherein said instructions for representing said set of sequence elements comprise instructions for displaying a plurality of icons in a linear or a near linear arrangement on a display, each respective icon in said plurality of icons uniquely representing a corresponding sequence element in said set of sequence elements such that neighboring icons in said plurality of icons represent neighboring sequence elements in said plurality of sequence elements in said design nucleic acid sequence, and each said respective icon in said plurality of icons depicts a directional property for the corresponding sequence element in said set of sequence elements; and ...
Stanniocalcins (STCs) represent small glycoprotein hormones, found in all vertebrates, which have been functionally implicated in Calcium homeostasis. However, recent data from mammalian systems indicated that they may be also involved in embryogenesis, tumorigenesis and in the context of the latter especially in angiogenesis. Human STC1 is a 247 amino acids protein with a predicted molecular mass of 27 kDa, but preliminary data suggested its di- or multimerization. The latter in conjunction with alternative splicing and/or post-translational modification gives rise to forms described as STC50 and big STC, which molecular weights range from 56 to 135 kDa. In this study we performed a biochemical and structural analysis of STC1 with the aim of obtaining low resolution structural information about the human STC1, since structural information in this protein family is scarce. We expressed STC1 in both E. coli and insect cells using the baculo virus system with a C-terminal 6 × His fusion tag. From the
We previously reported the isolation and characterization of a cDNA clone, I-309, that encodes a small secreted protein produced by activated human T lymphocytes. This protein is structurally related to a large number of recently identified proteins that are secreted upon cellular activation. In this report we describe the isolation and characterization of the gene encoding I-309. The genomic organization is essentially identical to that found in the genes encoding the structurally similar proteins TCA-3, hJE/MCP-1, and mJE, strengthening the hypothesis that these genes are evolutionarily related. The region of the I-309 gene 5 of the mRNA cap site exhibits extensive nucleotide sequence homology with the same region of the murine gene TCA-3, providing additional evidence that I-309 and TCA-3 are likely to be homologs. Finally, panels of rodent-human somatic cell hybrids were used to map the I-309 gene to human chromosome 17. In conjunction with recent mapping data from other laboratories, this ...
Maloy W.L.; Nathenson S.G.; Coligan J.E., 1981: Primary structure of murine major histo compatibility complex allo antigens amino acid sequence of the amino terminal 98 residues of the h 2d b glyco protein
The distinct subcellular redistribution of p53 and p73 in MDM2-expressing cells suggests the existence of structural differences between the proteins. Whereas the oligermerization domain of p53 and p73 share 33% identity, the extreme CT (outside of the oligermerization domain) of the two proteins is much less conserved. Inspection of the primary amino acid sequence reveals that the p53 CT contains five lysine residues that are not conserved in p73. In addition, we showed recently that under conditions where p53 is highly ubiquitinated, p73 exhibits a much lower tendency for ubiquitination (10) . According to the current model of p53 nuclear export, the p53 NES is inactive when p53 is in tetramer. Ubiquitination of the p53 CT lysine residues by MDM2 results in the revealing of the NES that then permits p53 to be nuclear-exported (5, 6, 7) . It is therefore possible that the NES of p73 is unable to be activated because of its lack of the corresponding lysine residues available for ubiquitination. ...
Patenting around nuisance prior art. Patenting gene sequences. Patenting nucleotide and amino acid sequences in view of electronic sequence database searches
A RecA-single-stranded DNA (RecA-ssDNA) filament searches a genome for sequence homology by rapidly binding and unbinding double-stranded DNA (dsDNA) until homology is found. We demonstrate that pulling on the opposite termini (3′ and 5′) of one of the two DNA strands in a dsDNA molecule stabilizes the normally unstable binding of that dsDNA to non-homologous RecA-ssDNA filaments, whereas pulling on the two 3′, the two 5′, or all four termini does not. We propose that the outgoing strand in the dsDNA is extended by strong DNA-protein contacts, whereas the complementary strand is extended by the tension on the base pairs that connect the complementary strand to the outgoing strand. The stress resulting from different levels of tension on its constitutive strands causes rapid dsDNA unbinding unless sufficient homology is present ...
Ben Hanelt, D. Van Schyndel, C. M. Adema, L. A. Lewis, E. S. Loker. The Phylogenetic Position of Rhopaluva ophiocomae (Orthonectida) Based on 18s Ribosomal DNA Sequence Analysis. -Molecular Biology and Evolution, 1996,. 13 (9), lk 1187-1191. Veebiversioon. ...
Every protein in a cell is created through the transcription of a specific sequence, that is part of the DNA. This transcription provides the sequence in which amino acids are to be linked, to form a protein.
LBHD1 - C11orf48 (untagged)-Human chromosome 11 open reading frame 48 (C11orf48) available for purchase from OriGene - Your Gene Company.
Definition of primary structure - the characteristic sequence of amino acids forming a protein or polypeptide chain, considered as the most basic element of its str
Molecular Cloning, also known as Maniatis, has served as the foundation of technical expertise in labs worldwide for 30 years. No other manual has been so popular, or so influential.
GLYATL1P1 (glycine-N-acyltransferase like 1 pseudogene 1), Authors: Dessen P. Published in: Atlas Genet Cytogenet Oncol Haematol.
This page is meant to be a storage place for example data. Hopefully this example data will help people to learn how to use Mussa without going through the trouble of finding homologous regions in multiple species. ...


text:
# Changes

,  08:19, 2 June 2011
Added note on use of first bracket
Stack option is used to emulate LaTeX's marginpars (they're considered floats, hence the resulting margin notes do not overlap).

The first bracket can be used to provide different setups for different margin text types. It defines which type of text the following parameters apply to. So the following code defines that any text placed in the margin using \inright{...} will be slanted:
<texcode>
\setupinmargin[right][style=slanted]
</texcode>

The previous code does not alter the location of the \inmargin command. To do that you would use:
<texcode>
\setupinmargin[location=right,style=slanted]
</texcode>
== Example ==


text:
# Sparse structure estimation for multivariate count data with PLN-network In PLNmodels: Poisson Lognormal Models

knitr::opts_chunk$set( screenshot.force = FALSE, echo = TRUE, rows.print = 5, message = FALSE, warning = FALSE)  ## Preliminaries This vignette illustrates the basical use of the PLNnetwork function and the methods accompaning the R6 Classes PLNnetworkfamily and PLNnetworkfit. ### Requirements The packages required for the analysis are PLNmodels plus some others for data manipulation and representation: library(PLNmodels) library(ggplot2)  ### Data set We illustrate our point with the trichoptera data set, a full description of which can be found in the corresponding vignette. Data preparation is also detailed in the specific vignette. data(trichoptera) trichoptera <- prepare_data(trichoptera$Abundance, trichoptera$Covariate)  The trichoptera data frame stores a matrix of counts (trichoptera$Abundance), a matrix of offsets (trichoptera$Offset) and some vectors of covariates (trichoptera$Wind, trichoptera$Temperature, etc.) ### Mathematical background The network model for multivariate count data that we introduce in @PLNnetwork is a variant of the Poisson Lognormal model of @AiH89, see the PLN vignette as a reminder. Compare to the standard PLN model we add a sparsity constraint on the inverse covariance matrix${\boldsymbol\Sigma}^{-1}\triangleq \boldsymbol\Omega$by means of the$\ell_1$-norm, such that$\|\boldsymbol\Omega\|1 < c$. PLN-network is the equivalent of the sparse multivariate Gaussian model [@banerjee2008] in the PLN framework. It relates some$p$-dimensional observation vectors$\mathbf{Y}_i$to some$p$-dimensional vectors of Gaussian latent variables$\mathbf{Z}_i$as follows \begin{array}{rcl} \text{latent space } & \mathbf{Z}_i \sim \mathcal{N}\left({\boldsymbol\mu},\boldsymbol\Omega^{-1}\right) & \|\boldsymbol\Omega\|_1 < c \ \text{observation space } & Y{ij} | Z_{ij} \quad \text{indep.} & Y_{ij} | Z_{ij} \sim \mathcal{P}\left(\exp{Z_{ij}}\right) \end{array} The parameter${\boldsymbol\mu}$corresponds to the main effects and the latent covariance matrix$\boldsymbol\Sigma$describes the underlying structure of dependence between the$p$variables. The$\ell_1$-penalty on$\boldsymbol\Omega$induces sparsity and selection of important direct relationships between entities. Hence, the support of$\boldsymbol\Omega$correspond to a network of underlying interactions. The sparsity level ($c$in the above mathematical model), which corresponds to the number of edges in the network, is controlled by a penalty parameter in the optimization process sometimes referred to as$\lambda$. All mathematical details can be found in @PLNnetwork. #### Covariates and offsets Just like PLN, PLN-network generalizes to a formulation close to a multivariate generalized linear model where the main effect is due to a linear combination of$d$covariates$\mathbf{x}_i$and to a vector$\mathbf{o}_i$of$p$offsets in sample$i$. The latent layer then reads $$\mathbf{Z}_i \sim \mathcal{N}\left({\mathbf{o}_i + \mathbf{x}_i^\top\boldsymbol\Theta},\boldsymbol\Omega^{-1}\right), \qquad \|\boldsymbol\Omega\|_1 < c ,$$ where$\boldsymbol\Theta$is a$d\times p$matrix of regression parameters. #### Alternating optimization Regularization via sparsification of$\boldsymbol\Omega$and vizualization of the consecutive network is the main objective in PLN-network. To reach this goal, we need to first estimate the model parameters. Inference in PLN-network focuses on the regression parameters$\boldsymbol\Theta$and the inverse covariance$\boldsymbol\Omega$. Technically speaking, we adopt a variational strategy to approximate the$\ell_1$-penalized log-likelihood function and optimize the consecutive sparse variational surrogate with an optimization scheme that alternates between two step 1. a gradient-ascent-step, performed with the CCSA algorithm of @Svan02 implemented in the C++ library [@nlopt], which we link to the package. 2. a penalized log-likelihood step, performed with the graphical-Lasso of @FHT08, implemented in the package fastglasso [@glassofast]. More technical details can be found in @PLNnetwork ## Analysis of trichoptera data with a PLNnetwork model In the package, the sparse PLN-network model is adjusted with the function PLNnetwork, which we review in this section. This function adjusts the model for a series of value of the penalty parameter controling the number of edges in the network. It then provides a collection of objects with class PLNnetworkfit, corresponding to networks with different levels of density, all stored in an object with class PLNnetworkfamily. ### Adjusting a collection of network - a.k.a. a regularization path PLNnetwork finds an hopefully appropriate set of penalties on its own. This set can be controlled by the user, but use it with care and check details in ?PLNnetwork. The collection of models is fitted as follows: network_models <- PLNnetwork(Abundance ~ 1 + offset(log(Offset)), data = trichoptera)  Note the use of the formula object to specify the model, similar to the one used in the function PLN. ### Structure of PLNnetworkfamily The network_models variable is an R6 object with class PLNnetworkfamily, which comes with a couple of methods. The most basic is the show/print method, which sends a very basic summary of the estimation process: network_models  One can also easily access the successive values of the criteria in the collection network_models$criteria %>% head() %>% knitr::kable()

A diagnostic of the optimization process is available via the convergence field:

network_models$convergence %>% head() %>% knitr::kable()  An nicer view of this output comes with the option "diagnostic" in the plot method: plot(network_models, "diagnostic")  ### Exploring the path of networks By default, the plot method of PLNnetworkfamily displays evolution of the criteria mentioned above, and is a good starting point for model selection: plot(network_models)  In this case, the variational lower bound of the log-likelihood is hopefully strictly increasing with a lower level of penalty (meaning more edges in the network). The same holds true for the penalized counterpart of the variational surrogate. Generally, smoothness of these criteria is a good sanity check of optimization process. BIC and its extended-version high-dimensional version EBIC are classically used for selecting the correct amount of penalization with sparse estimator like the one used by PLN-network. However, we will consider later a more robust albeit more computationally intensive strategy to chose the appropriate number of edges in the network. To pursue the analysis, we can represent the coefficient path (i.e., value of the edges in the network according to the penalty level) to see if some edges clearly come off. An alternative and more intuitive view consists in plotting the values of the partial correlations along the path, which can be obtained with the options \texttt{corr = TRUE}. To this end, we provide the S3 function coefficient_path: coefficient_path(network_models, corr = TRUE) %>% ggplot(aes(x = Penalty, y = Coeff, group = Edge, colour = Edge)) + geom_line(show.legend = FALSE) + coord_trans(x="log10") + theme_bw()  ### Model selection issue: choosing a network To select a network with a specific level of penalty, one uses the getModel(lambda) S3 method. We can also extract the best model according to the BIC or EBIC with the method getBestModel(). model_pen <- getModel(network_models, network_models$penalties[20]) # give some sparsity
model_BIC <- getBestModel(network_models, "BIC")   # if no criteria is specified, the best BIC is used

An alternative strategy is to use StARS [@stars], which performs resampling to evaluate the robustness of the network along the path of solutions in a similar fashion as the stability selection approach of @stabilitySelection, but in a network inference context.

model_StARS <- getBestModel(network_models, "StARS") # if StARS is requested, stabiltiy selection is performed if needed

When "StARS" is requested for the first time, getBestModel automatically calls the method stability_selection with the default parameters. After the first call, the stability path is available from the plot function:

plot(network_models, "stability")

### Structure of a PLNnetworkfit

The variables model_BIC, model_StARS and model_pen are other R6Class objects with class PLNnetworkfit. They all inherits from the class PLNfit and thus own all its methods, with a couple of specific one, mostly for network vizualization purposes. Most fields and methods are recalled when such an object is printed:

model_StARS

The plot method provides a quick representation of the inferred network, with various options (either as a matrix, a graph, and always send back de plotted object invisibly if users needs to perform additional analyses).

my_graph <- plot(model_StARS, plot = FALSE)
my_graph

plot(model_StARS)
plot(model_StARS, type = "support", output = "corrplot")

We can finally check that the fitted value of the counts -- even with sparse regularization of the covariance matrix -- are close to the observed ones:

data.frame(
fitted   = as.vector(fitted(model_StARS)),
observed = as.vector(trichoptera\$Abundance)
) %>%
ggplot(aes(x = observed, y = fitted)) +
geom_point(size = .5, alpha =.25 ) +
scale_x_log10(limits = c(1,1000)) +
scale_y_log10(limits = c(1,1000)) +
theme_bw() + annotation_logticks()

## Try the PLNmodels package in your browser

Any scripts or data that you put into this service are public.

PLNmodels documentation built on Jan. 28, 2020, 1:07 a.m.


text:
# Derivation of static replication formula

I know that a way of computing the price of a derivative paying $$S^2$$ at time $$T$$ is by making use of the following strategy:

$$V=\int_{0}^{\infty} s^2 \frac{\partial^2 C}{\partial K^2}(K=s)ds$$

Where $$\frac{\partial^2 C}{\partial K^2}(K=s)$$ is simply the risk neutral distribution of $$S$$.

Now, one should apply integration by parts twice in order to get an integral of the call prices. My question is, what is the name of this strategy/formula? Where can I find a derivation of it?

EDIT: By integrating by parts once, I get:

$$V=\left[ s^2 \frac{\partial C}{\partial K}(K=s) \right]^{\infty}_{0} -\int_{0}^{\infty} 2s \frac{\partial C}{\partial K}(K=s)ds$$

The first term is zero, but I don't know why. Can you please provide an explanation? Now by integrating by parts a second time the first derivative should become simply the price of options. But as I don't know why the first term is zero I hesitate to continue the derivation. Can you please help with next steps? EDIT: By taking into account the answer provided, the first term is zero,

$$V= -\int_{0}^{\infty} 2s \frac{\partial C}{\partial K}(K=s)ds$$

then we integrate by parts a second time:

$$V= -\left(\left[2kC(k)\right]_{0}^{\infty}-\int_{0}^{\infty} 2 C(s)ds \right)$$

Now, as

$$C(k=\infty)=0$$

Then:

$$V= 2\int_{0}^{\infty}C(K=s)ds$$

Is that correct?

• I think that one way to get a static replication formula is to use the Carr-Madan-formula and set $f(S_T)=S_T^2$.
– Lars
Sep 7, 2021 at 8:18
• I cannot do the link between my question and Carr-adan formula. Maybe it is simpler if I continue the derivation. See the edit, can you help me with the next step? Sep 7, 2021 at 19:41

Proof sketch for

$$\lim_{S\rightarrow \infty} S^2 \frac{\partial C}{\partial K}(K=S) = 0.$$

We have:

$$C(K) = E\left[(S_T-K)^+\right] = \int_K^\infty (u-K)f_{S_T}(u) du$$ $$\frac{\partial C}{\partial K} = \int_K^\infty \frac{\partial }{\partial K}(u-K)f_{S_T}(u) du = -\int_K^\infty f_{S_T}(u) du =-(1-F_{S_T}(K))$$

$$\frac{\partial C}{\partial K}(K=\infty) = 0$$

Next, I think one might need to assume that the complementary cdf has a thin tail:

$$\lim_{x\rightarrow \infty} x^2 (1-F_{S_T}(x)) = 0$$

In the case of a normal distribution this is true as, according to WolframAlpha, we have: $$\lim_{x\rightarrow \infty} x^2 {\rm erfc(x)} = 0.$$

Since your payoff only depends on $$S_T$$, you could use the Carr-Madan-formula
$$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K) (S_T-K)^+ \ d K$$
to get a static replication formula. In your example you have $$f(S_T)=S_T^2$$ and therefore $$f'(F_t)=2F_t$$ and $$f''(F_t)=2$$. Then choose $$F_t=0$$ to get:
$$S_T^2=\int_0^\infty2(S_T-K)^+\mathrm{d}K=2\int_0^\infty(S_T-K)^+\mathrm{d}K$$


text:
시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 512 MB77948243562.771%

## 문제

Farmer John has received an order for exactly $$M$$ units of milk ($$1 \leq M \leq 1,000$$) that he needs to fill right away. Unfortunately, his fancy milking machine has just become broken, and all he has are three milk pails of integer sizes $$X$$, $$Y$$, and $$M$$ ($$1 \leq X < Y < M$$). All three pails are initially empty. Using these three pails, he can perform any number of the following two types of operations:

- He can fill the smallest pail (of size $$X$$) completely to the top with $$X$$ units of milk and pour it into the size-$$M$$ pail, as long as this will not cause the size-$$M$$ pail to overflow.

- He can fill the medium-sized pail (of size $$Y$$) completely to the top with $$Y$$ units of milk and pour it into the size-$$M$$ pail, as long as this will not cause the size-$$M$$ pail to overflow.

Although FJ realizes he may not be able to completely fill the size-$$M$$ pail, please help him determine the maximum amount of milk he can possibly add to this pail.

## 입력

The first, and only line of input, contains $$X$$, $$Y$$, and $$M$$, separated by spaces.

## 출력

Output the maximum amount of milk FJ can possibly add to the size-$$M$$ pail.

## 예제 입력 1

17 25 77

## 예제 출력 1

76

## 힌트

In this example, FJ fills the pail of size 17 three times and the pail of size 25 once, accumulating a total of 76 units of milk.


text:
• # question_answer When a vehicle travels on a rough road whose undulations can be assumed to be sinusoidal, the resonant conditions of the base-excited vibrations, are determined by the: A) Mass of the vehicle, stiffness of the suspension spring, speed of the vehicle, wavelength of the roughness curveB) Speed of the vehicle onlyC) Speed of the vehicle and the stillness of the suspension springD) Amplitude of the undulations

$\beta =\frac{\omega }{{{\omega }_{n}}},$ ${{\omega }_{n}}=\sqrt{\frac{k}{m}},\,\,\omega =\frac{v}{\lambda }$ Where v = vehicle speed, $\lambda \,\,=\,\,$wave length of rod undulations                         $\therefore \,\,\,\,\,\,\,\,\,\,\,\beta \,\,=\,\,f\,(m,k,v,\lambda )$


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Is Open Access

# A Compressive Sensing Based Approach to Sparse Wideband Array Design

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There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### Abstract

Sparse wideband sensor array design for sensor location optimisation is highly nonlinear and it is traditionally solved by genetic algorithms, simulated annealing or other similar optimization methods. However, this is an extremely time-consuming process and more efficient solutions are needed. In this work, this problem is studied from the viewpoint of compressive sensing and a formulation based on a modified $$l_1$$ norm is derived. As there are multiple coefficients associated with each sensor, the key is to make sure that these coefficients are simultaneously minimized in order to discard the corresponding sensor locations. Design examples are provided to verify the effectiveness of the proposed methods.

### Author and article information

###### Journal
1403.4879

Numerical methods, Information systems & theory


text:
# Tough induction

1. May 10, 2007

### shirel

tough induction!!

hey !

I'm new here...

I'm looking for a really tough induction!

I will appreaciate who will write here some inductions..

thanks...

* I JUST LOVVVVVE THOSE SMILIES ! :tongue:

2. May 10, 2007

### Office_Shredder

Staff Emeritus
Ok

Prove, by induction, that

$$log(2) = \sum_{n=1}^k \frac{(-1)^{n-1}}{n} +(-1)^k 2\int_0^1 \frac{t^{2k+1}dt}{1+t^2}$$

A hint: start by showing $$log(2) = 2\int_0^1\frac{tdt}{1+t^2}$$

EDIT: Does anyone here know why my first latex image isn't working?

EDIT: I appear to have gotten it to work.... never mind

Last edited: May 10, 2007
3. May 10, 2007

### shirel

wow! That's great!
thank you very much.

Does anyone have a trigonometric induction?

4. May 11, 2007

### VietDao29

Have you solved Office_Shredder's one?

Ok, here's a pretty good problem in trigonometry. There are many ways to go about solving it, and Induction is a way to go.

Problem:
Prove that:
$$1 + 2 \sum_{k = 1} ^ n \left( \cos (k x) \right) = \frac{\sin \left[ \left( n + \frac{1}{2} \right) x \right]}{\sin \left( \frac{x}{2} \right)}$$

5. May 11, 2007

### shirel

Thank you very much!

About Office_Shredder 's induction I think it is wrong.. It must be ln(2) instead of log(2).

Am I wrong?

6. May 11, 2007

### morphism

It's common for mathematicians to use log(x) to mean ln(x).

Here's another exercise:

Prove that
$$\sum_{i=1}^n \tan (r\theta) \tan ((r+1)\theta) = \tan ((n+1)\theta) \cot \theta \; - \, n \, - \, 1$$

Last edited: May 11, 2007
7. May 11, 2007

### Werg22

Just to point out: that is actually a really nice result and constitutes a clever proof of the integral of sin x.

8. May 12, 2007

### shirel

OK. Thanks.

9. May 22, 2007

### truewt

Thanks for the problems :) managed to solve the last 2 problems, but the one involving log2, how do you go about doing it?

10. May 22, 2007

### Office_Shredder

Staff Emeritus
Spoiler for the log 2 problem:

For the log2 problem, it's trivial for k=1. For the inductive step, multiply inside the integral by (1+t2-t2 and see what you can get (if you're at all like me, you spent an hour trying to do integration by parts before feeling stupid :p)

11. May 22, 2007

### truewt

Hmmm cos I was thinking induction is prove for all cases of n..

but i guess this usually comes up as a follow up question to an induction question? something like an inference question after the induction is done..

12. May 22, 2007

### Office_Shredder

Staff Emeritus
No truewt... prove that the relation is true for any k. So you show it's true for k=1, then show if it's true for k=r, it's true for k=r+1 via the hint I gave (or on your own of course)

13. May 23, 2007

### truewt

Hmmm I see thanks. I'll go try it now.

14. May 23, 2007

### truewt

What do you mean by trivial?

15. May 23, 2007

### truewt

Thanks. Solved the log2 problem. But it is still really ln 2 :P

16. May 24, 2007

### phoenixthoth

Here's something related to induction. Find a statement P(n) about the natural number n such that for all n, if P(n) is true then P(n+1) is true but P(n) is false for all n.

17. May 25, 2007

### mathwonk

prove by induction, the moduli space of curves of genus g has dimension 3g-3, if g > 1.

prove by induction the torelli map (taking a curve to its jacobian) from the moduli space of curves of genus g to the moduli space of abelian varieties of dimension g is generically injective, for all g.

find by induction, the volume of a sphere of dimension d, assuming the area formula for a circle.

find by induction the number of vertices of an n dimensional cube.

Last edited: May 25, 2007
18. May 26, 2007

### mathwonk

hey, at least the last one is easy. the first is an exercise in intuition about moduli of curves acquiring singularities, and the second an easy version of some research i have done in a similar case. the third one is a good calculus problem.

the point here is that induction works also in geometry, and is very powerful. these questions give the flavor of the kind of algebraic geometry research i have been involved in.
realistically, try the 4th one first, and then the third one, (perhaps this one should be called a recursive calculation).

Last edited: May 26, 2007
19. May 26, 2007

### JohnDuck

Ok, for the third one, an n-sphere is given by the equation:

$$\sum_{i=0}^{n} x_{i}^{2} = r^{2}$$

and the area of a circle (or 1-sphere) is given by pi*r2. Then the basis of induction is to find the volume of a 2-sphere in terms of the volume of a 1-sphere. Consider the equation of the 2-sphere for different values of x2 (note that |x2| cannot be greater than r):

$$x_{0}^{2} + x_{1}^{2} = r^{2} - x_{2}^{2} = R^{2}$$

It's just the equation of a 1-sphere with radius R given by

$$R = \sqrt{r^{2} - x_{2}^{2}}$$

The volume of the 2-sphere of radius r is just the sum of the volumes of 1-spheres as we range through possible values of x2, or:

$$\int_{-r}^{r} \pi(r^{2} - x_{2}^{2}) dx_{2}$$

For the step of induction we have to show that the volume of an (n+1)-sphere can be found in terms of the volume of an n-sphere. Consider the equation of an (n+1)-sphere of radius r as we range through values of xn+1. Again, it's just the equation of an n-sphere with a radius of

$$R = \sqrt{r^{2} - x_{n+1}^{2}}$$

Then the volume of the (n+1)-sphere is the sum of the volumes of the n-spheres as we range through all possible values of xn+1, or:

$$\int_{-r}^{r} V_{n}( \sqrt{r^{2} - x_{n+1}^{2}}) dx_{n+1}$$

Where Vn(x) is the volume of an n-sphere of radius x.

Last edited: May 26, 2007
20. May 27, 2007

### prasannapakkiam

Here is an easy one: Prove by induction, the Binomial Theorem.


text:
Minimum spanning tree with small set of possible edge weights

Given a undirected graph which only has two different edge weights $$x$$ and $$y$$ is it possible to make a faster algorithm than Prim's algorithm or Kruskal's algorithm?

I saw on Kruskal's algorithm that it already assumes that the edges can be sorted in linear time with count sort, so then can we gain any benefit by knowing the weights of all of the edges ahead of time?

I don't think there is any benefit, but I am not sure...

1 Answer

No, Kruskal's algorithm doesn't make any assumptions about how fast edges can be sorted. I suspect you misinterpreted what you read. Kruskal's algorithm doesn't make assumptions.

You linked to a Wikipedia article. It states:

Provided that the edges are either already sorted or can be sorted in linear time (for example with counting sort or radix sort), the algorithm can use a more sophisticated disjoint-set data structure to run in O(E α(V)) time

"Provided" means "If", not "We assume that".

If you use a standard sorting algorithm that takes $$O(E \log E)$$ time, then Kruskal's algorithm runs in $$O(E \log E)$$ time. If you are in a special situation where there is a way to sort the edges in linear time (e.g., using counting sort), then Kruskal's algorithm can be implemented in a way that takes $$O(E \alpha(V))$$ time, which is faster. But there is no assumption that you will always be in that special situation; usually, you won't.

The case where there are only two edge weights is indeed such a special situation, and thus Kruskal's algorithm can be implemented in a way that is asymptotically faster for such graphs than for general graphs.


text:
FNGR 1 | Lesson 1 | Explore (Linear vs Exponential)

1.   Consider the following problem, you will come back to it in Lesson 2.   You go to one bank who will give you 5% interest on your \$5000 for 5 years.  You go to another bank who will give you 5% interest compounded daily for 5 years.   Which one should you take and why?

What do you notice? What do you wonder?

2.  How are the two functions alike/different?

a) $$y=2x$$

b) $$y=2^x$$


text:
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text:
Record Details

Title:
Tracking Chemical Reactions with Ultrafast X-ray Spectroscopic Techniques
Affiliation(s):
XFEL.EU guest
Keyword(s):
Topic:
Scientific area:
Abstract:
Chemical reactions in transition metal complexes can be triggered with light, which results in structural and electronic changes. These changes can be visualised by measuring the geometric and electronic structure of a complex in real-time during a chemical reaction pathway. Time-resolved (TR) X-ray Absorption and Emission Spectroscopy (XAS and XES) delivers information about the geometric (via XANES and EXAFS) and electronic (via XES) transient changes when used in synchronisation with an ultrafast laser in a pump-probe scheme. Element specificity and sensitivity to the local structure of X-ray spectroscopic tools around the absorbing atom allows us to look at the photoexcited changes of transition metal complexes. We studied aqueous ferrocyanide ([$Fe^{II}(CN)_{6}]^{4-}$) following photoexcitation with UV laserlight which results in two photoproducts namely [$Fe^{II}(CN)_{5}H_{2}O]^{3-}$ and [$Fe^{III}(CN)_{6}]^{3-}$. Picosecond-resolved XANES measurements after 266 nm excitation show both photoproducts and the ratio of extracted excited state fractions is consistent with quantum yield measurements reported by Shirom et al. TR XES was used to look at the spin state and ligand environment changes with the core-to-core ($Kβ_{1,3}$) and valance-to-core (vtc) (or $Kβ_{2,5}$) emission lines of the central Fe atom. Furthermore, we investigated the ultrafast ligand dissociation of aqueous ferrocyanide ions upon irradiation of 355 nm laser light. Based on a comparison of the simulated pre-edge peaks of 1s->3d transition and the experimental data, we concluded that the reaction pathway commences via ligand detachment followed by the formation of the long-lived photoaquated complex. TR XES reveals the spin state of the intermediate complex. Combining these finding we interpret that the aquation process happens from a non-singlet potential energy surface and takes about 13 ps. Also, we characterised the molecular structure of photoexcited [$Fe^{II}(terpy)_{2}]^{2+}$ molecule via TR EXAFS. The data analysis in energy space used two structural model expansions which are the representations of DFT predicted $^{5}E$ and $^{5}B_{2}$ quintet high spin states. After statistical evaluation of the two models, $^{5}E$ high spin state model is in better agreement with experimental data. The transient EXAFS fitting implemented here can be used to characterise molecular structures of other spin crossover complexes.
Imprint:
Schenefeld, Germany, European X-Ray Free-Electron Laser Facility GmbH, 2017
External related publications:
nbn:de:gbv:18-83431 (urn)
Report number:
XFEL.EU THESIS-2017-001
Language(s):
English
Degree type:
Ph.D. Thesis
Starting date:
2012-02-01
Ending date:
2016-12-16
Year granted:
2016
University name:
Universität Hamburg
Record appears in:

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text:
MathSciNet bibliographic data MR758892 58F11 (30D05 54H20) Devaney, Robert L.; Krych, Michał Dynamics of ${\rm exp}(z)$${\rm exp}(z)$. Ergodic Theory Dynam. Systems 4 (1984), no. 1, 35–52. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
Proof that micro black holes can't exist?

1. Aug 7, 2011

zeromodz

I was playing around with some equations and I found a reason why I think micro black holes cannot exist. This proof requires a few assumptions which I have tended to find to be a scientific consensus. They are the following.

1) The smallest mass a black hole can have is the planck mass which by definition will give the schwarchilds radius of the black hole the planck length.
2) The smallest meaningful increment of time in the universe is the planck time.

ΔXΔP <= h / 4π

This can also being written as.

ΔEΔT <= h / 4π
ΔE <= h / 4πΔT

This tells us that the amount of energy uncertainty created from the vacuum is inversely proportional to the time. Now let us change our units of energy to mass by dividing the equation by c^2

Mtotal <= h / 4πΔTc^2

The maximum amount of mass that can be created from nothing out of the uncertainty of the vacuum can now be written as the following.

Mtotal = h / 4π(Tplanck)c^2
Mtotal = (6.626 * 10^-34) / ((4π)(5.39 * 10^-44)(299792458)^2)
Mtotal = 1.088 * 10^-8 kg

The planck mass is 2.17 * 10^-8 kg. So it turns out the maximum amount of mass that can be created from nothing for 10^-44 seconds is exactly half the planck mass. Am I missing a factor of two anywhere? Or is it just planck masses and micro black holes cannot be created from the uncertainty principle? Thanks

2. Aug 8, 2011

n1person

Well, what if you have a black hole moving at relativistic speeds? (so E =/= mc^2) :P

I don't know quite enough about QM to comment about anything else...

3. Aug 8, 2011

zeromodz

Well, at least you tried.

4. Aug 8, 2011

IRobot

You just go in the reference where it is at rest (which exist becausse $M_{BH} > 0$)

Well, first you need to reverse all the inequalities: It's $\Delta X \Delta P \geq \hbar$ and $\Delta E \Delta t \geq \hbar$.

Last edited: Aug 8, 2011


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SEARCH HOME
 Math Central Quandaries & Queries
 Question from ken, a student: y=ln^3x/x from x=1 to x=11

Hi Ken,

Since the derivative of $\ln x$ is $\frac{1}{x}$, to integrate $\frac{\ln^3 x}{x}$ I would try the substitution $u = \ln x.$

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.


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Volume 1 (2005) Article 8 pp. 149-176
A Non-linear Time Lower Bound for Boolean Branching Programs
Revised: May 5, 2005
Published: October 5, 2005
We give an exponential lower bound for the size of any linear-time Boolean branching program computing an explicitly given function. More precisely, we prove that for all positive integers $k$ and for all sufficiently small $\epsilon >0$, if $n$ is sufficiently large then there is no Boolean (or $2$-way) branching program of size less than $2^{\epsilon n}$ which, for all inputs $X\subseteq \lbrace 0,1,{\ldots},n-1\rbrace$, computes in time $kn$ the parity of the number of elements of the set of all pairs $\langle x,y\rangle$ with the property $x\in X$, $y\in X$, $x < y$, $x+y\in X$.
For the proof of this fact we show that if $A=(a_{i,j})_{i=0,j=0}^{n}$ is a random $n$ by $n$ matrix over the field with $2$ elements with the condition that “$A$ is constant on each minor diagonal,” then with high probability the rank of each $\delta n$ by $\delta n$ submatrix of $A$ is at least $c\delta |\log \delta |^{-2}n$, where $c>0$ is an absolute constant and $n$ is sufficiently large with respect to $\delta$.


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## Sunday, 11 December 2011

### Class 10 - Physics - Light - Numerical and Questions

Q1: When an object is placed at a distance of 60 cm from a convex mirror, the magnification produced is 1/2.
Where should the object be placed to get a magnification of 1/3?

Q2: When an object is kept at a distance of 60cm from a concave mirror, the magnification is 1/2. Where should the object be placed to get magnification of 1/3?

Answer: (Hint: steps are same as in the above question, except it is concave mirror, m = -1/2. Compute f in first case i.e. f = -20 cm and the compute u in case II i.e. u = 80 cm)

Q3(CBSE Board): A concave lens made of material of refractive index (n1) is kept in a medium of refractive index (n2). A parallel beam of light is incident on the lens. Complete the path of the rays of light emerging from a concave lens if:
(a) n1 > n2
(b) n1 = n2
(c) n1 < n2

Q4: A convex lens made of material of refractive index (n1) is kept in a medium of refractive index (n2). A parallel beam of light is incident on the lens. Complete the path of the rays of light emerging from a concave lens if:
(a) n1 > n2
(b) n1 = n2
(c) n1 < n2
Q5: Which of the two has a great power? A lens of short focal length or a lens of large focal length?
Answer: lens of short focal length.
Q6: When a convex lens and a concave lens of equal focal lengths are placed side by side, what will be the equivalent power and the combined focal length.
Answer: Equivalent Power = 0 and Combined focal length = infinity.

Q7: When a plane mirror is rotated by an angle $\theta$, what will be the angle of rotation of the reflected ray for the fixed incident ray?

Answer: The reflected ray will be rotated twice w.r.t to the angle of rotation of mirror. i.e. $2\theta$

Consider the following figure:

As shown, mirror M is rotated by an angle $\phi$. Let I be incident ray, N be normal and R is reflected ray.
Before rotation, let the incident angle be $\theta$
After rotation, normal moves by angle $\phi$,
$\therefore \text{incident angle } \angle {ION'} = \theta + \phi \newline \angle{ROR'} = \angle{IOR'} - \angle{IOR} = 2(\theta + \phi) - 2\theta = 2\phi$

Q8: With respect to air the refractive index of kerosene is 1.44 and that of diamond is 2.42. Calculate the refractive index of diamond with respect to kerosene.

1. it is much helpful

1. it's very helpful not much helpful use correct english

2. Hmmm. Even u forgot to put a comma in your sentence. Use proper punctuation.😑😑😡

3. Need to give more. Numericals

4. @TanishaSharma, a sentence always starts with a capital letter.
@HARSHVARDHANSINGHChauhan, it’s not “u” it is “you” and it’s not “even u” it’s “you even”.

5. @Food is Good, you have omitted a word. The word 'but' is missing between 'it's not u' and 'it is you.' Moreover you don't use speechmarks to quote words.

2. In Q3 the last n1<n2 should'nt be a convex lens???

1. they have said "if" so we can accept that

3. i cud hav lookd it earlier

1. This comment has been removed by the author.

4. In Q2, u cannot be (+)80.... u has to be -ive

1. this is very true but it is said that in hint apply that u is if positive so what will be the answer u should read the question nicely

5. Questions are too easy........post sumthing intresting

6. Thank you very much. Found this post very useful

7. thanks it is very useful for me!

8. It was really very helpful 😊😊.... Enough to make my concepts better and strong..Thanks a lot!!😊😊☺☺


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# zbMATH — the first resource for mathematics

Stability of functional differential equations. (English) Zbl 0593.34070
Mathematics in Science and Engineering, Vol. 180. London etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XIV, 217 p. hbk: $50.00; pbk:$ 29.95 (1986).
The book is devoted to actual problems of stability of systems with aftereffect and to various applications of these. First the foundations of the theory of the equations with aftereffect are exposed in detail. The most important classes of equations with aftereffect include equations of neutral type and stochastic equations. Further on in the book the problems of stability of these equations are investigated in detail. Various methods of investigation of their stability are comprehensively exposed. The book is particularly useful since in it a number of important applications to the theory of the nuclear reactors as well as to control theory, ecology, immunology, theory of viscoelastic media, economics, etc. are given. It can be sucessfully used by mathematicians, physicists, engineers, biologists and economists. Undoubtedly, this exclusive book will stimulate the further development of the theory of function differential equations.
Reviewer: D.Bainov

##### MSC:
 34K20 Stability theory of functional-differential equations 34D20 Stability of solutions to ordinary differential equations 34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations 34F05 Ordinary differential equations and systems with randomness