text:
# confidence interval

• July 30th 2007, 06:30 PM
mkcar
confidence interval
I'm so lost on how to do this problem,
could someone take me step by step on how to solve it pleeze.

the question is construct the indicated confidence interval for the population mean.
__
c= 0.95, x ( the line is supposed to be on top of the x)=31.39, s=0.8,n=82
if you could take me through the steps on how you do this I can maybe try to fiqure out how to do the next ones. Thank you
• July 30th 2007, 09:08 PM
CaptainBlack
Quote:

Originally Posted by mkcar
I'm so lost on how to do this problem,
could someone take me step by step on how to solve it pleeze.

the question is construct the indicated confidence interval for the population mean.
__
c= 0.95, x ( the line is supposed to be on top of the x)=31.39, s=0.8,n=82
if you could take me through the steps on how you do this I can maybe try to fiqure out how to do the next ones. Thank you

Suppose that $X$ is a normally distributed random variable, and we have a sample
$x_1, .., x_{82}$ of $X$'s, then the statistic:

$
t=\frac{\mu-\bar{x}}{s/\sqrt{n}}
$

has a t-distribution with $n-1$ degrees of freedom, and so looking this up in a
table of the t-distribution we find that a 95% interval for $t$ with 81 degrees of
freedom is $(-1.99, 1.99)$, so th corresponding interval for the population mean $\mu$ is:

$
( \bar{x}-1.99 ~s/\sqrt{n},\bar{x}+1.99 ~s/\sqrt{n})
$

Now plug in your numerical values and its done.

RonL


text:
# Help me prove

Reshma
Let $\vec A$ be an arbitrary vector and let $\hat n$ be a unit vector in some fixed direction. Show that
$$\vec A = (\vec A .\hat n)\hat n + (\hat n \times \vec A)\times \hat n.$$

$$\left( {\vec A \times \vec B} \right) \times \vec C = - \vec A\left( {\vec B \cdot \vec C} \right) + \vec B\left( {\vec A \cdot \vec C} \right)$$
The vector $$\vec A$$ is expressed as the sum of its projections on $$W= \mathcal{L} (\hat{n})$$ and $$W^\bot$$.

format: plain


text:
# A search for Ly-alpha emitters around a concentrated-region of strong Ly-alpha absorbers at z=2.3 [GA]

In order to investigate the physical relationship between strong Ly-alpha absorbers (logN_HI>20.0 cm^-2) such as damped Ly-alpha absorption systems (DLAs) and young star-forming galaxies at high redshift, we have conducted narrow-band observations of Ly-alpha emitters (LAEs) in a concentrated region of strong Ly-alpha absorbers at z= 2.3, the J1230+34 field. Using a catalog of Ly-alpha absorbers with logN_HI>20.0 cm^-2 based on the baryon oscillation spectroscopic survey (BOSS), we found 6 fields where 3 or more absorbers are concentrated within a (50 Mpc)^3 cubic box in the comoving scale. Among them, we focus on the J1230+34 field, where 2 DLAs and 2 sub-DLAs present. Our narrow-band imaging observations with Subaru/Suprime-Cam using a custom-made filter, NB400 (lambda_c=4003 A and FWHM=92 A) yield a sample of 149 LAEs in this field. In the large scale (~50 Mpc), we have found no differences between the obtained Ly-alpha luminosity function and those in the blank fields at similar redshifts. We also compare the frequency distribution of the Ly-alpha rest-frame equivalent width (EW_0) in the target field and other fields including both overdensity region and blank field, but find no differences. On the other hand, in the small scale (~10 Mpc), we have found a possible overdensity of LAEs around a DLA with the highest HI column density (N_HI=21.08 cm^-2) in the target field while there are no density excess around the other absorbers with a lower N_HI.

K. Ogura, T. Nagao, M. Imanishi, et. al.
Fri, 17 Mar 17
30/50

Comments: 15 pages, 15 figures, Accepted for publication to PASJ

# Effects of dust absorption on spectroscopic studies of turbulence [GA]

We study the effect of dust absorption on the recovery velocity and density spectra as well as on the anisotropies of magnetohydrodynamic turbulence using the Velocity Channel Analysis (VCA), Velocity Coordinate Spectrum (VCS) and Velocity Centroids. The dust limits volume up to an optical depth of unity. We show that in the case of the emissivity proportional to the density of emitters, the effects of random density get suppressed for strong dust absorption intensity variations arise from the velocity fluctuations only. However, for the emissivity proportional to squared density, both density and velocity fluctuations affect the observed intensities. We predict a new asymptotic regime for the spectrum of fluctuations for large scales exceeding the physical depths to unit optical depth. The spectrum gets shallower by unity in this regime. In addition, the dust absorption removes the degeneracy resulted in the universal $K^{-3}$ spectrum of intensity fluctuations of self-absorbing medium reported by Lazarian & Pogosyan. We show that the predicted result is consistent with the available HII region emission data. We find that for sub-Alfv\’enic and trans-Alfv\’enic turbulence one can get the information about both the magnetic field direction and the fundamental Alfv\’en, fast and slow modes that constitute MHD turbulence.

D. Kandel, A. Lazarian and D. Pogosyan
Fri, 17 Mar 17
33/50

# An X-ray/SDSS sample (I): multi-phase outflow incidence and dependence on AGN luminosity [GA]

Multi-phase fast, massive outflows have been postulated to play a crucial role in galaxy evolution. The aim of this work is to constrain the nature and the fraction of outflowing gas in AGNs, as well as the nuclear conditions possibly at the origin of such phenomena.
We present a large spectroscopic sample of X-ray detected SDSS AGNs at z <0.8. X-ray and optical flux ratio diagnostics are used to select the sample. Physical and kinematic characterisation are derived re-analysing optical (and X-ray) spectra.
We derive the incidence of ionised (~40%) and atomic (< 1%) outflows covering a wide range of AGN bolometric luminosity, from 10^42 to 10^46 erg/s. We also derive bolometric luminosities and X-ray bolometric corrections to test whether the presence of outflows is associated with an X-ray loudness, as suggested by our recent results obtained studying high-z QSOs.
We study the relations between the outflow velocity inferred from [O III] kinematic analysis and different AGN power tracers, such as black hole mass (M_BH), [O III] and X-ray luminosity. We show a well defined positive trend between outflow velocity and L_X, for the first time over a range of 5 order of magnitudes. Overall, we find that in the QSO-luminosity regime and at M_BH>10^8 Msun the fraction of AGNs with outflows becomes >50%. Finally, we discuss our results about X-ray bolometric corrections and outflow incidence in cold and ionised phases in the context of an evolutionary sequence allowing two distinct stages for the feedback phase: an initial stage characterized by X-ray/optical obscured AGNs in which the atomic gas is still present in the ISM and the outflow processes involve all the gas components, and a later stage associated with unobscured AGNs, which line of sight has been cleaned and the cold components have been heated or exhausted.

M. Perna, G. Lanzuisi, M. Brusa, et. al.
Fri, 17 Mar 17
35/50

Comments: 16 pages, 13 figures, Accepted for publication in A&A

# Dark-ages reionization and galaxy formation simulation XI: Clustering and halo masses of high redshift galaxies [GA]

We investigate the clustering properties of Lyman-break galaxies (LBGs) at $z\sim6$ – $8$. Using the semi-analytical model {\scshape Meraxes} constructed as part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation (DRAGONS) project, we predict the angular correlation function (ACF) of LBGs at $z\sim6$ – $8$. Overall, we find that the predicted ACFs are in good agreement with recent measurements at $z\sim 6$ and $z\sim 7.2$ from observations consisting of the Hubble eXtreme Deep Field (XDF), the Hubble Ultra-Deep Field (HUDF) and Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) field. We confirm the dependence of clustering on luminosity, with more massive dark matter haloes hosting brighter galaxies, remains valid at high redshift. The predicted galaxy bias at fixed luminosity is found to increase with redshift, in agreement with observations. We find that LBGs of magnitude $M_{{\rm AB(1600)}} < -19.4$ at $6\lesssim z \lesssim 8$ reside in dark matter haloes of mean mass $\sim 10^{11.0}$- $10^{11.5} M_{\rm \odot}$, and this dark matter halo mass does not evolve significantly during reionisation.

J. Park, H. Kim, C. Liu, et. al.
Fri, 17 Mar 17
36/50

Comments: 14 pages, 10 figures, submitted to MNRAS

# Optical Thickness, Spin Temperature, and Correction Factor for Density of the Galactic HI Gas [GA]

A method to determine the spin temperature of the local (Vlsr=0 km/s) HI gas using saturated brightness temperature of the 21-cm line in the radial-velocity degenerate regions (VDR) is presented. The spin temperatures is determined to be Ts= 146.2 +/- 16.1 K by measuring saturated brightness in the VDR toward the Galactic Center, 146.8 +/- 10.7 K by chi^2 fitting of expected brightness distribution to observation around the VDR, and 144.4 +/- 6.8 K toward the local arm. Assuming Ts=146 K, a correction factor Gamma for the HI density, defined by the ratio of the true HI density for finite optical thickness to that calculated by assuming optically thin HI, was obtained to be Gamma~1.2 (optical depth tau~0.3) in the local HI gas, ~1.8 (~1.3) toward the arm and anti-center, and as high as ~3.6 (~2.7) in the Galactic Center direction. It is suggested that the HI density and mass in the local arm could be ~2 times, and that in the inner Galaxy ~3.6 times, greater than the currently estimated values.

Y. Sofue
Fri, 17 Mar 17
41/50

Comments: 10 pages, 13 figures, accepted for MNRAS

# Accurate recovery of HI velocity dispersion from radio interferometers [GA]

Gas velocity dispersion measures the amount of disordered motions of a rotating disk. Accurate estimates of this parameter are of the utmost importance because it is directly linked to disk stability and star formation. A global measure of the gas velocity dispersion can be inferred from the width of the atomic hydrogen HI 21 cm line. We explore how several systematic effects involved in the production of HI cubes affect the estimate of HI velocity dispersion. We do so by comparing the HI velocity dispersion derived from different types of data cubes provided by The HI Nearby Galaxy Survey (THINGS). We find that residual-scaled cubes best recover the HI velocity dispersion, independent of the weighting scheme used and for a large range of signal-to-noise ratio. For HI observations where the dirty beam is substantially different from a Gaussian, the velocity dispersion values are overestimated unless the cubes are cleaned close to (e.g., ~1.5 times) the noise level.

R. Ianjamasimanana, W. Blok and G. Heald
Fri, 17 Mar 17
45/50

Comments: Accepted for publication in the Astronomical Journal, 14 pages, 12 Figures, 2 Tables

# The predicted luminous satellite populations around SMC and LMC-mass galaxies – A missing satellite problem around the LMC? [GA]

Recent discovery of many dwarf satellite galaxies in the direction of the Small and Large Magellanic Clouds (SMC and LMC) provokes questions of their origins, and what they can reveal about galaxy evolution theory. Here, we predict the satellite stellar mass function of Magellanic Cloud-mass host galaxies using abundance matching and reionization models applied to the Caterpillar simulations. Specifically focusing on the volume within 50 kpc of the LMC, we predict a mean of 4-8 satellites with stellar mass $M_* > 10^4 \, \mathrm{M_\odot}$, and 3-4 satellites with $80 < M_* \leq 3000 \, \mathrm{M_\odot}$. Surprisingly, all $12$ currently known satellite candidates have stellar masses of $80 < M_* \leq 3000 \, \mathrm{M_\odot}$. Reconciling the dearth of large satellites and profusion of small satellites is challenging and may require a combination of a major modification of the $M_* – M_{\rm{halo}}$ relationship (steep, but with an abrupt flattening at $10^3 \, \mathrm{M_\odot}$), late reionization for the Local Group ($z_{\rm{reion}} \lesssim 9$ preferred), and/or strong tidal stripping. We can more robustly predict that $\sim 53\%$ of satellites within this volume were accreted together with the LMC and SMC, and $\sim 47\%$ were only ever Milky Way satellites. Observing satellites of isolated LMC-sized field galaxies is essential to placing the LMC in context, and to better constrain the $M_* – M_{\rm{halo}}$ relationship. Modeling known LMC-sized galaxies within $8$ Mpc, we predict 1-6 (2-12) satellites with $M_* > 10^5 \, \mathrm{M_\odot}$ ($M_* > 10^4 \, \mathrm{M_\odot}$) within the virial volume of each, and 1-3 (1-7) within a single $1.5^{\circ}$ diameter field of view, making their discovery likely.

G. Dooley, A. Peter, J. Carlin, et. al.
Fri, 17 Mar 17
47/50

Comments: Submitted to MNRAS, 15 pages, 7 figures


text:
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 Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 7, Pages 1059–1072 (Mi zvmmf10743)

Integro-differential polynomial and trigonometrical splines and quadrature formulas

I. G. Burova, T. O. Evdokimova, O. V. Rodnikova

St. Petersburg State University, St. Petersburg, Russia

Abstract: This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following: the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed as the sum of products of the basic splines and the values of function in nodes and/or the values of its derivatives and/or the values of integrals of this function over subintervals. Basic splines are determined by using a solving system of equations which are provided by the set of functions. It is known that when integrals of the function over the intervals is equal to the integrals of the approximation of the function over the intervals then the approximation has some physical parallel. The splines which are constructed here satisfy the property of the fifth order approximation. Here, the one-dimensional polynomial and trigonometrical basic splines of the fifth order approximation are constructed when the values of the function are known in each point of interpolation. For the construction of the spline, we use the discrete analogues of the first derivative and quadrature with the appropriate order of approximation. We compare the properties of these splines with splines which are constructed when the values of the first derivative of the function are known in each point of interpolation and the values of integral over each grid interval are given. The one-dimensional case can be extended to multiple dimensions through the use of tensor product spline constructs. Numerical examples are represented.

Key words: polynomial splines, trigonometrical splines, integro-differential splines, interpolation.

DOI: https://doi.org/10.31857/S004446690000308-9

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1011–1024

Bibliographic databases:

UDC: 519.65
Received: 13.03.2017

Citation: I. G. Burova, T. O. Evdokimova, O. V. Rodnikova, “Integro-differential polynomial and trigonometrical splines and quadrature formulas”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1059–1072; Comput. Math. Math. Phys., 58:7 (2018), 1011–1024

Citation in format AMSBIB
\Bibitem{BurEvdRod18} \by I.~G.~Burova, T.~O.~Evdokimova, O.~V.~Rodnikova \paper Integro-differential polynomial and trigonometrical splines and quadrature formulas \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2018 \vol 58 \issue 7 \pages 1059--1072 \mathnet{http://mi.mathnet.ru/zvmmf10743} \crossref{https://doi.org/10.31857/S004446690000308-9} \elib{https://elibrary.ru/item.asp?id=35723859} \transl \jour Comput. Math. Math. Phys. \yr 2018 \vol 58 \issue 7 \pages 1011--1024 \crossref{https://doi.org/10.1134/S0965542518070047} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000442613300001} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052246754}

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# Comment on “Esperantism expands”

My co-authors (J. Ellenberg and C. Hall) and myself have received some interesting remarks from P. Sarnak concerning our joint work discussed a few days ago. With his permission, it follows below (with minimal editing to clean-up the list of references at the end).

One important point he makes is that the result of Abramovich, who gave a lower bound for the gonality of modular curves using Selberg’s 3/16 lower-bound for the eigenvalue of the Laplace operator on these curves and an inequality of Li-Yau, had been anticipated by P. Zograf in a little-known paper in Russian (see here for the English translation; it is Theorem 5 at the very end of that paper). We will soon update the arXiv version of our paper to add a reference to this result (the PDF from my home page is already updated).

Dear Jordan,Chris and Emmanuel,

I was pointed to your recent posting with the above
title.I particularly like the application in Corollary 4.
It would be nice if you supplemented it with a similar explicit application
which requires the full force of the blossoming number/combinatorial theory of
what I like to call “thin subgroups of SL(n,Q)”.By the latter I mean a finitely
generated such group which is not of finite index in the S-integral points of
the Zariski closure of the group.
My reason for writing is to point out a couple of papers connected to
parts of your paper,which are not commonly known and which should be.The first
is a paper of Zograf [Z] and the second
is result of Solovay ,called the Solovay-Kitaev theorem (see[ C-N ]),
which was pointed out to me some years ago by Dorit Aharonov.
Zograf’s paper should have been cited in the paper of Abramovich
that you cite as a key to your paper.I feel partially responsible for this
mistake as I communicated Abramovich’s paper.I was
aware of the results in Zograf which give a lower bound for
the genus of a curve in terms of its volume and lambda_1 ,
but I was not aware that he also gave the lower bound on the gonality.
Anyway his genus lower bound is what you use in (5) page 8 of your paper and
attribute to Kelner and the gonality lower bound is
the same as that in Abramovich. Note that his bound is based
on the earlier paper of Yang and Yau [Y-Y] rather than Li and Yau.
Since Abramovich’s paper there have been improvements in
bounds towards Selberg’s Conjecture and thus improvements
in the gonality lower bound.The recent paper of Blomer
and Brumley [B-B] gives the best such bounds in the case
of general Shimura curves.For me it is an interesting
question as to whether for modular curves,the ratio gonality/genus tends to a
limit as the genus goes to infinity? If so is this constant the same as what
one gets for the same ratio,gonality/genus,of a random curve of large genus?
Solovay’s theorem is concerned with diameter and expansion
in the group SU(2). Let A and B be members of SU(2) such that
the group generated by them is Zariski dense in SL(2,C).
The issue is how quickly can one approximate any element in
SU(2),by words in A and B.Given any g in SU(2) and e>0 there is a word w in A
and B such that d(w,g)<e [in some some fixed metric on SU(2)].Let l(e,g)
be the length of the shortest such w and let l(e) be the maximum of l(e,g) as g
varies over SU(2).If A and B form an “expander” in
the sense that the left convolution operator corresponding
to A+A^(-1)+B +B^(-1) on L^2(SU(2),haar) has a spectral gap,
then l(e)=O(log (1/e)).This “diameter” bound is optimal.
In [G-J-S] a substitute in this setting was
found for the argument exploiting the high dimension of any
nontrivial representation of G(F_p) [G a Chavelley group],that
is used in all proofs of expansion in this finite simple group setting.
This led to many examples of such expanders in SU(2) and it was
conjectured there that every such pair A,B gives an expander.
[B-G] have the best result towards this conjecture showing that
it is true if A and B have entries in Q bar.In terms of
technical difficulty this is probably the most difficult case
of expansion that is known.The proof of expansion for SL_2(F_p)
relies indirectly on the proof in [E-M] of the Erdos-Volkman
ring conjecture ,while this SU(2) case relies on the
proof in [B] of the more difficult quantitive local version
of this ring conjecture.
What Solovay proves is the analogue of your “esperante” property,
though he didnt give it any such colorful name. He shows that
l(e)=O(log(1/e)^2),for any given A and B as above.So
in this setting we have the small diameter property but
unlike your case ,where as you note a proof of the expansion property
is close to being proven,for SU(2) it remains wide open.Solovay proves this
polynomial diameter bound in an appendix
to his paper with Yao[S-Y], where it is used as one of the ingredients
to analyse how quantum computation classes can simulate classical ones up to
polynomial slowdown [whether the converse
is true or false is far from clear].For this purpose they need not
only that the diameter is small,but also that one can find a short
word quickly, and Solovay’s proof provides such a short word
in more or less the same number operations.The expansion proof
of an optimally small diameter goes via a counting argument and
it offers no means of finding a short word (or path in the
graph case).Even in the case of optimal expansion in the
graph setting,that is of Ramanujan Graphs,no fast algorithm for
finding a short path between vertices is known,and I have long
thought of this as a basic problem. In [L],Larsen resolves this
problem when one relaxes the diameter bound to something slightly bigger
than O(log) and also allowing a random element into the
algorithm,making it a probablistic algorithm.For computer science applications
what he does is surely good enough.
I know that you guys are avid bloggers,so feel free to include this letter in
your discussions if you feel it is appropriate.

Best regards
Peter

References:

[B] J. Bourgain, GAFA 13 (2003), 334-365.

[B-B] V. Blomer and F. Brumley, “On the Ramanujan Conjecture over
Number Fields”, arXiv:1003.0559.

[B-G] J.Bourgain and A.Gamburd, Invent Math. 171 (2008), 83-121.

[E-M] G.Edgar and C.Miller, Proc. AMS 131 (2003) 1121-1129.

[J-G-S] D.Jakobson, A.Gamburd and P.Sarnak, Journal European
Math. Soc. 1 (1999), 51-85.

[L] M.Larsen, International Math. Res. Notices (2003) No 27, 1455-1471.

[C-N] M. Nielsen and I. Chuang, “Quantum computation and
Quantum Information” CUP, Cambridge 2000.

[S-Y] R.Solovay and A.Yao, preprint 1996.

[Y-Y] P.Yang and S.T.Yau, Ann Scuola Norm. Super. Pisa, 7 (1980), 55-63.

[Z] P.Zograf, “Small eigenvalues of automorphic Laplacians in spaces
of cusp forms”, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov
(LOMI) 134 (1984), 157-168; translation Journal of Math. Sciences 36,
Number 1, 106-114, DOI: 10.1007/BF01104976


text: But for the 3d transition elements, the expected decrease in atomic radius is observed from Sc to V , thereafter up to Cu the atomic radius nearly remains the same. For example, the atomic radius of the metal zirconium, Zr, (a period-5 transition element) is 155 pm (empirical value) and that of hafnium, Hf, (the corresponding period-6 element) is 159 pm. d-block elements are also called as transition metals Atomic radius is the distance between the nucleus and the outermost electron So, across a period transition series on moving from left to right in the transition series the atomic size decreases And in the group, on moving from top to bottom the atomic radii increases (ii) The E° M 2+ /M, for copper is positive (+ 0.34 V). Events draw large numbers of people to them. In order to standardize the measurement of atomic radii, the distance between the nuclei of two identical atoms bonded together is measured. 8.2: Atomic Radii and Effective Nuclear Charge Thus sometime different methods are used to measure the radius while they are bonded in a molecule. There are some small exceptions, such as the oxygen radius being slightly greater than the nitrogen radius. So, as the position of electron is not certain rather they are explained as electron cloud around the nucleus, it is hard to measure an atomic radius accurately. The radii of most transition elements, however, stay roughly constant across each row. Then depending on atomic size, the atomic radius of the two atoms are calculated. As there are no physical existence of orbital in atoms, it is difficult to measure the atomic radius. The atomic radius of atoms generally increases from top to bottom within a group. So, size of elements of 4d series is larger than those of 3d series. Decreases rapidly, from column 3 to 6 2. The crowd capacity depends on the amount of space in the venue, and the amount of space depends on the size of the objects filling it. The size of an atom is defined by the edge of its orbital. All the d-block elements carry a similar number of electronsin their furthest shell. The effect of the greater number of principal energy levels outweighs the increase in nuclear charge and so atomic radius increases down a group. Ionic radius are calculated by considering the atomic size of the two atoms. The metallic radius can also be calculated by measuring the distance between the two nuclei of the two atoms in metal cluster. For ions having the same or closely similar charges, the ionic radii decrease slowly with an increase in atomic number across the period for transition elements positioned in Groups 3-12 of the modern periodic table. The size of atoms is important when trying to explain the behavior of atoms or compounds. The bigger the atomic size, the larger the atomic radius. Atomic and ionic radii of elements of all three-transition series 1. The general trend is that atomic sizes increase as one moves downwards in the Periodic Table of the Elements, as electrons fill outer electron shells. Thus the increasing number of nucleus attracts the more electrons more tightly towards it and the atomic radius decreases. The ionic radius is thus reduced than atomic radius. Transition elements (also known as transition metals) are elements that have partially filled d orbitals. As an example, the internuclear distance between the two hydrogen atoms in an $$\ce{H_2}$$ molecule is measured to be $$74 \: \text{pm}$$. Therefore, the atomic radius of a hydrogen atom is 74 2 = 37 pm. The configuration or stacking of atoms and ions affects the distance between their nuclei. There are different methods of calculating the radius by measuring the distance between two nucleus when an atom is bonded in a molecule. -The atomic radius of main group elements decreases across a period. Hence, for ions of a given charge the radius decreases gradually with an increment in atomic number. In the second- and third-row transition metals, such irregularities can be difficult to predict, particularly for the third row, which has 4f, 5d, and 6s orbitals that are very close in energy. The atomic mass of the first transition elements increases gradually with increasing their atomic number but nickel is abnormal because it has five stable isotops with average mass 58.7U, There is a little change in atomic radii as we move through first transition series, Atomic radius of the transition elements is relatively constant from (Cr) to (Cu), this â¦ ... -Across a transition series, atomic size shrinks through the first two or three elements. In the same way the anions can have lesser radius that the radius of its original neutral atom. Visit A-Level Chemistry to download comprehensive revision materials - for UK or international students! Even an outdoor event can fill up so that there is no room for more people. Atomic Volume and Densities The following diagram uses metallic radii for metallic elements, covalent radii for elements that form covalent bonds, and van der Waals radii for those (like the noble gases) which don't form bonds. The partially filled subshells of d-block elements incorporate (n-1) d subshell. The characteristics of Atomic radii of the transition elements are given below: (a) The d-block elements atomic radii and atomic volumes in any series reduce with increase in atomic number. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. The atomic radius is defined as one-half the distance between the nuclei of identical atoms that are bonded together. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Generally, the atomic radii of d-block elements in a series decrease with increase in atomic number but the decrease in atomic size is small after midway. This is because as the new electron enters a d orbital, each time the â¦ The energy required for the complete removal of 1 mol of electrons from 1 mol of gaseous atoms or ions is called _____ energy. Atomic Mass. The atomic radius in the periodic table decreases across the period and increases down the group.eval(ez_write_tag([[320,100],'chemdictionary_org-banner-1','ezslot_9',115,'0','0'])); Moving from left to right across a period, the number of protons and electrons increases while the number of energy shells stay same. Remains steady, from column 7 to 10 and 3. The units for atomic radii are picometers, equal to $$10^{-12}$$ meters. It is because of lanthanoid contraction that the atomic radii of the second row of transition elements are almost similar to those of the third row of transition elements. The atomic radius of atoms generally decreases from left to right across a period. But for the 3d transition elements, the expected decrease in atomic radius is observed from Sc to V , thereafter upto Cu the atomic radius nearly remains the same. This is because the number of electrons in the outermost principal energy level is nearly constant. The atomic size of Transition Elements are relatively the same because although the number of protons in the nucleus increase, the additional electrons are added to the 3d subshell. In this video I have explained the general characteristics of Lanthanoids. One of the ways we can express the size of atoms is with the atomic radius. The term refers to the fact that the d sublevel , which is in the process of being filled, is in a lower principal energy level than the s sublevel filled before it. High Performance Liquid Chromatography (HPLC), Hydrogen Bonding in Hydrogen Flouride (HF). Legal. The nucleus of the atom gains protons moving from left to right, which increases the positive charge of the nucleus which attracts electrons. Within a period, protons are added to the nucleus as electrons are being added to the same principal energy level. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. The atomic radii of the transition metals lie in-between those of s- and p-block elements. At the end of the period, there is a slight increase in the atomic radii. (ii) The E° value for the Mn3+/Mn2+ couple is much more positive than that for Cr3+/Cr2+ couple or Fe3+/Fe2+ couple. So why does the atomic radius decrease? However, after nickel, electrons will be added to a s-orbital (specifically 4s), making the overall compound have an additional shell, â¦ 2. The effect lessens as one moves further to the right in a period because of electron-electron repulsions that would otherwise cause the atom's size to increase. As in the transition metals the electrons are added in the inner shell, the nucleus attracts the increasing electrons towards it more and thus the radius decreased. A complete A-Z dictionary of chemistry terms. (i) The atomic radii of the metals of the third (5d) series of transition elements are virtually the same as those of the corresponding members of the second (4d) series. Atomic radii have been measured for elements. This is due to the increase in the nuclear charge that attracts the electron cloud inwards resulting in a decrease in size. The ionic radius of Zr 4+ is 79 pm and that of Hf 4+ is 78 pm [citation needed]. The I.E. The ionic radius of transition metals in a period does not, however, change very much from one atom to the next near the beginning of a series. Atomic And Ionic Radius Of Transition Elements - Duration: 17:32. sardanatutorials 32,771 views. The atomic radius is the size of the atom, typically measured by the distance from the nucleus of the atom to the electron clouds around the nucleus. Yes, atomic radius in d block initially decreases then remains constant and finally increases at the end. Thus the atomic radius also increases down the group in periodic table. The atomic radius is the size of the atom, typically measured by the distance from the nucleus of the atom to the electron clouds around the nucleus. Atomic radii: a great degree of variation is seen in the atomic radii across each transition series. Transition elements are the elements that are found in Groups 3-12 (old groups IIA-IIB) on the periodic table (salmon-colored block in the middle of the table). Here the radius of two ions are not equal and few other things need to be discussed before we calculate the ionic radius: So to calculate the atomic radius, at first the distance between the nuclei is measured. Typically, when As the atomic number increases down a group, there is again an increase in the positive nuclear charge. Again the atomic radius is different because of their ionic status of the atom. Atomic radius is determined as half the distance between the nuclei of two identical atoms bonded together. The atom can be cation or anion by losing or gaining electron. Variations in Ionic Radius Neither the atomic radius nor the ionic radius of an atom is a fixed value. Atomic radii represent the sizes of isolated, electrically-neutral atoms, unaffected by bonding topologies. When an atom (A) is covalently bonded with another homonuclear atom (A), the atomic radius of that atom can be calculated by measuring the distance between the two nucleus of those two atoms. Ionic Radii Trends of Transition Elements. IUPAC defines transition elements as an element having a d subshell that is partially filled with electrons, or an element that has the ability to form stable cations with an incompletely filled d orbital. Trends in atomic radius down a group. However, orbital boundaries are fuzzy and in fact are variable under different conditions. In general, any element which corresponds to the d-block of the modern periodic table (which consists of groups â¦ Moving down a group, the number of energy shells also increases with the increase of protons and electrons. Transition elements are those elements that have partially or incompletely filled d orbital in their ground state or the most stable oxidation state. Watch the recordings here on Youtube! Start increasing from column 11 to 12. It is generally expected a steady decrease in atomic radius along a period as the nuclear charge increases and the extra electrons are added to the same sub shell. The atomic radius of atoms generally increases from top to bottom within a group. Covalent radius can be calculated by measuring the distance between the two nucleus of two atoms in covalent compound. As an example, the internuclear distance between the two hydrogen atoms in an H 2 molecule is measured to be 74 pm. The atomic radius of atoms generally decreases from left to right across a period. Radii of atoms and ions In general, atomic radii (Table 1) of the elements show progressive decrease with increasing atomic number across a row in the transition series. CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon. Active 2 years, 11 months ago. Fig. As we move across Period 4, moving from K to Cu, we observe the graph below which shows the trend of how atomic radius changes with an equal increase in proton and a corresponding increase in electron. Have questions or comments? The metallic radius can also be calculated by measuring the distance between the two nuclei of the two atoms. Higher principal energy levels consist of orbitals which are larger in size than the orbitals from lower energy levels. The diameter of an atom is equal to the distance between two nuclei and the atomic radius will be the half of it. Ask Question Asked 5 years, 3 months ago. Atomic radii have been measured for elements. We can get more squirrels into that same space than we can people for the same reason. In general for main group elements atomic radii _____ from left to right across a period and _____ down a group of the period table. However the nucleus attract the rest of the electrons more tightly towards the nucleus. The atomic radius of a chemical element is the distance from the â¦ The metallic diameter is equal to the distance between two nuclei and the radius is just half of it.eval(ez_write_tag([[300,250],'chemdictionary_org-medrectangle-4','ezslot_10',114,'0','0']));eval(ez_write_tag([[300,250],'chemdictionary_org-medrectangle-4','ezslot_11',114,'0','1'])); Ionic radius is the radius calculated when an atom is bonded with another atom in a molecule by transferring electrons to make ionic bond. With this increase, the nuclear charge also increases, due to the addition of a proton as well; this causes the radius to decrease moving down this group. Ionic Radii. Transition Metal - Trend in atomic radius. The units for atomic radii are picometers, equal to 10 â 12 meters. The metallic radius is the radius calculated between two metal atoms bonded together in metal cluster. [ "article:topic", "showtoc:no", "license:ccbync", "program:ck12" ], information contact us at info@libretexts.org, status page at https://status.libretexts.org. We can get more people into a given space than we can elephants, because the elephants are larger than people. decreases, increases. Trends in atomic radius in Periods 2 and 3. f- block transition elements _____ transition metals noble gases lanthanides and actinides main group elements. The atomic radius is the size of the atom, typically measured by the distance from the nucleus of the atom to the electron clouds around the nucleus. Exceptions are observed in transition metal elements. Missed the LibreFest? (i) In general the atomic radii of transition elements decrease with atomic number in a given series. Variation in atomic sizes in the transition elements. For example, in the first transition series, atomic radii, the decrease is more from Sc to Cr (group 3 to 6 ), is almost same for Mn, Fe, Co, Ni (group 7,8 9 &10) and increase in cu and Zn. Since the force of attraction between nuclei and electrons increases, the size of the atoms decreases. 5: Variation in atomic radius of transition metals as a function of the periodic table group number. Hence, they possess similar chemical properties. Are you a chemistry student? Hence there is decreases in the atomic radius but the extent of variation is very small compared to s block and p block elements. The pattern of ionic radius is similar to the atomic radii pattern. The larger decrease in atomic radii, in column 3 to 6 elements is due to the increase in effective nuclear charâ¦ The decrement is not regular. The atoms of different element, they must differ in electrons and protons, sometimes number of orbitals and so on. The atomic radii of the d-block elements within a given series decrease with an increase in the atomic number. 1. However, there is also an increase in the number of occupied principal energy levels. As there are no physical existence of orbital in atoms, it is difficult to measure the atomic radius. According to the Heisenberg uncertainty principle, it is not possible to measure the momentum and the position of the electron simultaneously. It is the only metal in the first series of transition elements showing this type of behaviour. These electrons are gradually pulled closer to the nucleus because of its increased positive charge. Therefore, the atomic radius of a hydrogen atom is $$\frac{74}{2} = 37 \: \text{pm}$$. When an atom loses electron sometime it has less orbital than before. d) Ionisation enthalpy: There is slight and irregular variation in ionization energies of transition metals due to irregular variation of atomic size. The similar atomic radii of second and third transition series is due to phenomenon called lanthanoid contraction, associated with intervention of 4f-orbitais which must be filled before the 5d series of elements begin. The atomic radius of these elements shows a gradual decrease as electrons are added to the 3d block. Knowing the sizes of objects we are dealing with can be important in deciding how much space is needed. The increase in atomic radius is greater between the 3d and 4d metals than between the 4d and 5d metals because of the lanthanide contraction. The atomic radius in the periodic table decreases across the period and increases down the group. This data helps us understand why some molecules fit together and why other molecules have parts that get too crowded under certain conditions. In regards to atomic size of transition metals, there is little variation. Covalent radius is the radius calculated when an atom is bonded covalently with another atom of same element. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Block elements block elements half of it exceptions, such as the atomic radius the. More people into a given series decrease with atomic number in a given charge the radius calculated when an is! Decreases rapidly, from column 7 to 10 and 3 lower energy levels consist orbitals! Charâ¦ Fig trying to explain the behavior of atoms is with the atomic radius identical atoms bonded is. Atom can be calculated by considering the atomic radius of Zr 4+ is pm. Together is measured to be 74 pm from lower energy levels consist of orbitals which are in... 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# How do you calculate voltage drop in a series circuit?

Mar 22, 2018

Ohm's Law is $E = I \cdot R$, which tells us to then multiply $I \text{ by } R$. E is the voltage across the component also known as voltage drop.


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Lab 12: Files and Persistence

Due Date: Monday 4/11 11:59PM. Note that this lab has a different deadline than the usual Friday deadline due to Test 2.

## A. Intro

So far in this class, you have exclusively made programs whose state only persists while the program is running, and all traces of the program disappear once the program exits. For example, in Project 2, you created a game that you could play while the program was running, but there was no way to save the game state, quit the program, go do some other stuff, and then run the program again, load up your previous progress, and continue playing the game. In this lab, we will go over two methods to make the state of your program persist past the execution of your program: one through writing plain text to a file, and the other through serializing objects to a file. This will be directly applicable Project 3: Gitlet as well as any future projects you want to do where you want to be able to save state between programs.

As always, you can get the skeleton files with the following commands:

 git fetch shared
git merge shared/lab12 -m "Start Lab 12"

Here are useful links for content review for this lab:

• Lab 12 Intro Video (Though this video is from Spring 2020, the lab content stays the same. This lab intro video includes some explanations of concepts, examples of usage of methods mentioned in the spec, and an intro to the coding portion of the lab. All the information in the video is covered in the spec and timestamps for topics are in the video description.)
• Lab 12 Slides

## B. Files and Directories in Java

Before we jump into manipulating files and directories in Java, let's go through some file system basics.

### Current Working Directory

The current working directory (CWD) of a Java program is the directory from where you execute that Java program. Examples follow for Windows & Mac/Linux users - they are very similar, just different stylistically.

Windows For example, for Windows users, let's say we have this small Java program located in the folder C:/Users/Linda/example (or ~/example) named Example.java:

// file C:/Users/Linda/example/Example.java
class Example {
public static void main(String[] args) {
System.out.println(System.getProperty("user.dir"));
}
}

This is a program that prints out the CWD of that Java program.

If I ran:

cd C:/Users/Linda/example/
javac Example.java
java Example

C:\Users\Linda\example

Mac & Linux For example, for Mac & Linux users, let's say we have this small Java program located in the folder /home/Linda/example (or ~/example) named Example.java:

// file /home/Linda/example/Example.java
class Example {
public static void main(String[] args) {
System.out.println(System.getProperty("user.dir"));
}
}

This is a program that prints out the CWD of that Java program.

If I ran:

cd /home/Linda/Example
javac Example.java
java Example

/home/Linda/example

IntelliJ In IntelliJ, you can view the CWD of your program under Run > Edit Configurations > Working Directory.

Terminal In terminal / Git Bash, the command pwd will give you the CWD.

### Absolute and Relative Paths

A path is the location of a file or directory. There are two kinds of paths: absolute paths and relative paths. An absolute path is the location of a file or directory relative to the root of the file system. In the example above, the absolute path of Example.java was C:/Users/Linda/example/Example.java (Windows) or /home/Linda/example/Example.java (Mac/Linux). Notice that these paths start with the root which is C:/ for Windows and / for Mac/Linux. A relative path is the location of a file or directory relative to the CWD of your program. In the example above, if I was in the C:/Users/Linda/example/ (Windows) or /home/Linda/example/ (Mac/Linux) folders, then the relative path to Example.java would just be Example.java. If I were in C:/Users/Linda/ or /home/Linda/, then the relative path to Example.java would be example/Example.java.

Note: the root of your file system is different from your home directory. Your home directory is usually located at C:/Users/<your username> (Windows) or /home/<your username> (Mac/Linux). We use ~ as a shorthand to refer to your home directory, so when you are at ~/repo, you are actually at C:/Users/<your username>/repo (Windows) or /home/<your username>/repo (Mac/Linux).

When using paths, . refers to the CWD. Therefore, the relative path ./example/Example.java is the same as example/Example.java.

### File & Directory Manipulation in Java

The Java File class represents a file or directory in your operating system and allows you to do operations on those files and directories. In this class, you usually will want to be doing operations on files and directories by referring to them to their relative paths. You'll want any new files or directories you create to be in the same directory as where you run your program (in this lab, the ~/repo/lab12 folder) and not some random place on your computer.

#### Files

You can make a File object in Java with the File constructor and passing in the path to the file:

 File f = new File("dummy.txt");

The above path is a relative path where we are referring to the file dummy.txt in our Java program's CWD. You can think of this File object as a reference/pointer to the actual file dummy.txt - when we create the new File object, we aren't actually creating the dummy.txt file itself, we are just saying, "in the future, when I do operations with f, I want to do these operations on dummy.txt". To actually create this dummy.txt file, we could call

 f.createNewFile();

and then the file dummy.txt will actually now exist (and you could see it in File Explorer / Finder).

You can check if the file "dummy.txt" already exists or not with the exists method of the File class:

 f.exists()

We can also write to the file with the following:

 Utils.writeContents(f, "Hello World");

Now dummy.txt would now have the text "Hello World" in it. Note that Utils is a helper class provided in this lab and project 3 and is not a part of standard Java.

#### Directories

Directories in Java are also represented with File objects. For example, you can make a File object that represents a directory:

File d = new File("dummy");

Similar to files, this directory might not actually exist in your file system. To actually create the folder in your file system, you can run:

d.mkdir();

and now there should be a folder called dummy in your CWD.

#### Summary

There are many more ways to manipulate files in Java, and you can explore more by looking at the File javadocs and Googling. There are a ton of resources online and, if you Google it, doing more extensive file operations in Java can get a bit complicated. I'd recommend understanding the basics by doing this lab, and in the future if you come across a use case you don't know how to handle, then start searching or asking on Piazza. For this lab and Gitlet, we provide you with a Utils.java class that has many useful helper functions you should use for file operations.

## C. Serializable

Writing text to files is great and all, but what if we want to save some more complex state in our program? For example, what if we want to be able to save the Board object in Ataxx so we can come back to it later? We could somehow write a toString method to convert a Board to a String and then write that String to a file. If we do that though, we would also need to figure out how to load the Board by parsing that file, which can get complicated.

Luckily, we have an alternative called serialization which Java has already implemented for us. Serialization is the process of translating an object to a series of bytes that can then be stored in the file. We can then deserialize those bytes and get the original object back.

To enable this feature for a given class in Java, this simply involves implementing the java.io.Serializable interface:

import java.io.Serializable;

class Board implements Serializable {
...
}

This interface has no methods; it simply marks its subtypes for the benefit of some special Java classes for performing I/O on objects. For example,

    Board b = ....;
File outFile = new File(saveFileName);
try {
ObjectOutputStream out =
new ObjectOutputStream(new FileOutputStream(outFile));
out.writeObject(b);
out.close();
} catch (IOException excp) {
...
}

will convert b to a stream of bytes and store it in the file whose name is stored in saveFileName. The object may then be reconstructed with a code sequence such as

    Board b;
File inFile = new File(saveFileName);
try {
ObjectInputStream inp =
new ObjectInputStream(new FileInputStream(inFile));
inp.close();
} catch (IOException | ClassNotFoundException excp) {
...
b = null;
}

The Java runtime does all the work of figuring out what fields need to be converted to bytes and how to do so. We have provided helper function in Utils.java that does the above two for you and you should use them for this lab.

Note: There are some limitations to Serializable that are noted in the Project 3 spec. You will not encounter them in this lab.

## D. Exercise: Canine Capers

For this lab, you will be writing a program that will be taking advantage of file operations and serialization. We have provided you with three files:

• Main.java: The main method of your program. Run it with java capers.Main [args] to do the operations specified below. The majority of the FIXMEs in this program are in here.
• Dog.java: Represents a dog that has a name, breed, and age. Contains a few FIXMEs.
• Utils.java: Utility functions for file operations and serialization. These are a subset of those provided with Gitlet, so not all will be used.

You can change the skeleton files in any way you want as long as the spec and comment above the main method in Main.java is satisfied. You do not need to worry about error cases or invalid input. You should be able to complete this lab with just the methods provided in Utils.java and other File class methods mentioned in this spec, but feel free to experiment with other methods.

### Main

You should allow Main to run with the following three commands:

• story [text]: Appends "text" + a newline to a story file in the .capers directory. Additionally, prints out the current story.
• dog [name] [breed] [age]: Persistently creates a dog with the specified parameters; should also print the dog's toString(). Assume dog names are unique.
• birthday [name]: Advances a dog's age persistently and prints out a celebratory message.

All persistent data should be stored in a ".capers" directory in the current working directory.

Recommended file structure (you do not have to follow this):

.capers/ -- top level folder for all persistent data
- dogs/ -- folder containing all of the persistent data for dogs
- story -- file containing the current story

You should not create these manually, your program should create these folders and files.

Note: Naming a folder or file with a period in the front makes it hidden - to be able to see it in terminal, run ls -a instead of just ls. If you want to remove all saved data from your program, just remove the .capers directory (NOT the capers directory) with rm -rf .capers. (There is no space between the dot . and capers). But BE CAREFUL that you don't make a typo with the rm -rf ... command since deletion is not undoable and you can accidently delete your whole file system if ran incorrectly.

### Suggested Order of Completion

Please be sure to read the comments above each method in the skeleton for a description of what they do.

1. Fill out the main method in Main.java. This should consist mostly of calling other methods.
2. Fill out CAPERS_FOLDER in Main.java, then DOG_FOLDER in Dog.java, and then setUpPersistence in Main.java.
3. Fill out writeStory in Main.java. The story command should now work.
4. Fill out saveDog and then fromFile in Dog.java. You will also need to address the FIXME at the top of Dog.java. Remember dog names are unique!
5. Fill out makeDog and celebrateBirthday in Main.java using methods in Dog.java. You will find the haveBirthday method in the Dog class useful. The dog and birthday commands should now work.

Each FIXME should take at most around 8 lines, but many are fewer.

### Usage

The easiest way to run and test your program is to compile it in terminal with javac and then run it from there. E.g.

 cd ~/repo/lab12              # Make sure you are in your lab12 folder (NOT the lab12/capers folder)
make                         # or javac capers/*.java, make sure to recompile your program each time you make changes
java capers.Main [args]      # Run the commands you want! e.g., java story hello

For the story command, if you want to pass in a long string that includes spaces as the argument, you will want to put it in quotes, e.g.

 java capers.Main story "hello world"

If running in IntelliJ, you will need to use Run > Edit Configurations > Program Arguments to add the arguments.

### Useful Util Functions

Useful Util functions (as a start, may need more and you may not need all of them):

• writeContents - writes out strings/byte arrays to a file
• readContentsAsString - reads in a file as a string
• readContents - reads in a file as a byte array
• writeObject - writes a serializable object to a file
• readObject - reads in a serializable object from a file. You can get a Class object by using .class, e.g. Dog.class.
• join - joins together strings or files into a path. E.g. Utils.join(".capers", "dogs") would give you a File object with the path of ".capers/dogs"

### Testing

You should test your program yourself by running it in the command line. The Gradescope autograder will also run a small set of tests. The AG tests are a combination of running these commands in order:

$java capers.Main story Hello Hello$ java capers.Main story World
Hello
World

$java capers.Main dog Sammie Samoyed 5 Woof! My name is Sammie and I am a Samoyed! I am 5 years old! Woof!$ java capers.Main birthday Sammie
Woof! My name is Sammie and I am a Samoyed! I am 6 years old! Woof!
Happy birthday! Woof! Woof!
$java capers.Main dog Larry Lab 11 Woof! My name is Larry and I am a Lab! I am 11 years old! Woof!$ java capers.Main birthday Sammie
Woof! My name is Sammie and I am a Samoyed! I am 7 years old! Woof!
Happy birthday! Woof! Woof!
\$ java capers.Main birthday Larry
Woof! My name is Larry and I am a Lab! I am 12 years old! Woof!
Happy birthday! Woof! Woof!

It also ignores whitespace at the beginning and end of the output so don't worry too much about that.

Note: If you'd like to re-test your code, make sure to remove the .capers hidden directory to make sure you have a fresh new directory to start with. As noted in the previous section, to remove .capers (NOT the capers directory), you run rm -rf .capers.

## E. Submission

You should have made changes in capers/Main.java and capers/Dog.java. If you worked with a partner, please also update the partner.txt file. You should not be submitting a .capers data folder. Do not use git add . or git add -A to add your files, and git add your files one by one. Submit the lab as always:

 git commit -m "submitting lab12"
git tag lab12-0 # or the next highest submission number
git push
git push --tags

There is no style check for this lab.

## F. Tips, FAQs, Misconceptions

#### Tips

These are tips if you're stuck!

• setUpPersistence: In setUpPersistence, you should make sure that if the files and folders you need for the program to work don't exist yet that they are made.
• writeStory: You should be using readContentsAsString and writeContents. Since the story is just plain text (i.e. it's just a string), you do not need to serialize anything.
• saveDog: You should be using writeObject, since Dogs aren't Strings so we want to be able to serialize them. Make sure you're writing your dog to a File object that represents a file and not a folder!
• fromFile: You should be using readObject. This should be similar to saveDog except you're loading a Dog from your filesystem instead of writing it!

#### FAQs & Misconceptions

• writeObject: writeObject takes in (1) the File object that represents the file you want to write the object to and (2) the object you want to serialize and write into the file. The first argument should be a File object that represents a file on your filesystem, not a directory.
• File objects can represent both files and directories in your filesystem. The only way to differentiate between them is the methods you use with the File object. You can check if a File object represents a directory with .isDir(), which you shouldn't need for the lab since you should already know which File objects represent files and which represent directories.
• Creating a new File object in Java does not create the corresponding file or directory on your computer. The file is only created when you call .createNewFile() or mkdir() on that File object. You can think of File objects as pointers to files or directories - you can have multiple of them, and whenever you want to actually change the corresponding file or directory, you will need to call specific methods (usually the ones in Utils with "read" and "write" in the name).
• Utils.join(File d, String s) is shorthand for new File(File d, String s) (and Utils.join(String d, String s) is shorthand for new File(new File(d), String s)), both of which will create a new File object that represents the file or folder called s in the d directory. Again, this doesn't make the actual file/folder in your filesystem until you call appropriate methods.
• When we say "make changes persistently", that means you should make the changes in Java and then also make sure that those changes are reflected on your filesystem by writing those changes back into the appropriate files.

## G. Credits

Capers was originally written by Sean Dooher in Fall 2019. Spec and lab adaptation were written by Michelle Hwang in Spring 2020 and Linda Deng in Fall 2021 and Spring 2022.


text:
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# The difficulty, the need and the rules

Xavier Bordoy

Category

blog

Keywords

Abstract

How should we learn a fundamental identity

What is the difficulty we need to teach to our students? Sometimes we teach things in a hard way because our teachers, in the past, taught us this way. But perhaps we could think about why we need to teach that way. In general, we could teach one thing more easyly if we don’t need it afterwards and so, we don’t need rules. The rules should be simplifications or generalizations after several rutine repetitions1. I’m going to explain it with an example: how can we teach how to calculate $(x+3)^2$?2

• We could do applying the formula $(a+b)^2 = a^2 + 2ab + b^2$:

But we don’t need it. We surely have got our students confused. And we would introduce a mathematical arsenal that we will not need.

• We could do as a product: $(x+3)^2 = (x+3) \cdot (x+3)$. So we could apply distributive property.

This reminds our students the “rule” $3(x+3) = 3x + 9$ seen before, but surely most of them will have a mess after their application. And surely most of them would not understand what would be doing.

• Why not teach simply as we can: $(x+3)^2 = (x+3) \cdot (x+3)$. So let’s multiply it.

This reduces the unexpected thing to familiar and known thing: algorithm for multiplying integers.

When does we need to know the formula $(a+b)^2 = a^2 + 2ab + b^2$? In my opinion, only when our students need to expand expressions like $(x+3)^2$ many times or if they needed in order to solve a major problem (in which it is embeded) and they need not to spend their time in calculations (like they do in third way).

Note: for making this article, I used SimpleScreenRecorder for recording an specific area of my desktop while running LibreOffice Writer formula editor and Geogebra. For conversion from webm to animated gif I used ffmpeg.

Update: Fred G. Harwood (@HarMath) suggested we could calculate it also visually. It gets better understanding to students and avoid typical errors.

1. But sometimes (many more than it should be), the rules are taught before they are needed.↩

2. I need it to teach it because I want it to pass from the form $y=4(x+3)^2 -5$ to the form $y=4x^2 + 24x + 31$ for treating quadratic functions. In particular for representing that in cartesian plane. Yes I know we could represent directly (and more easyly) quadratic functions in the form $y=A(x-B)^2 + C$.↩


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18-Opal

## Sometimes multiplication is really complex ...

Every engineer, mathematician and scientist is born knowing that the vector dot product is the sum of the element-by-element multiplication of the components of the two vectors. But occasionally, when our brain isn't paying full attention, things don't work out as intended ...

Stuart

PS.  I blame Valery for this one.  If he hadn't posed that clock question, I wouldn't have tried to generalize it and spend a couple of minutes wondering why my previously fine power series expansion formula wasn't working when applied to complex number bases.

5 REPLIES 5
15-Moonstone
(To:StuartBruff)

An interesting bug!  It appears that Mathcad takes the complex conjugate of the "z" vector before multiplying!  You can avoid the problem by replacing a*z in PowerDot Mul by aT*z  (where aT is the transpose of a).  Mathcad no longer bothers to take the complex conjugate!

Alan

 AlanStevens wrote: An interesting bug!  It appears that Mathcad takes the complex conjugate of the "z" vector before multiplying!  You can avoid the problem by replacing a*z in PowerDot Mul by aT*z  (where aT is the transpose of a).  Mathcad no longer bothers to take the complex conjugate!

Interesting.  A bug?

Stuart

4-Participant
(To:AlanStevens)

Thats not a bug, thats exactly how the dot product is defined for complex vectors in math

So if you just want the summation of elementwise multiplication, you should use the matrix product a^T*z as Alan had pointed out

For real vectors there is no difference between the two (as every real is its own conjugate)

18-Opal
(To:lturek)

Leopold Turek wrote:

Thats not a bug, thats exactly how the dot product is defined for complex vectors in math

Indeed.  It even says so in the Help for the dot product:

• If x and y are vectors, returns the dot product (inner product) of x and y, a scalar formed by multiplying element-wise the entries of the first vector with the complex conjugate of the entries of the second vector, and summing the results.

However,

 Thats not a bug, thats exactly how the dot product is defined for complex vectors in math

In quantum theory, the bra-ket notation ⟨v|w⟩ defines the inner product as being the conjugate of the first term rather than the second term, ie the result is v*·w

, where * denotes the conjugate transpose.

Interestingly, and confusingly, Mathematica defines Dot[v,w] as the Hademard (element-by-element) product whilst Matlab and Maxima take the braket approach in conjugating the first vector.  Python's numpy library adopts two approaches, with dot carrying out Hademard multiplication and vdot multiplying braket style.

Stuart

4-Participant
(To:StuartBruff)
 StuartBruff wrote: In quantum theory, the bra-ket notation ⟨v|w⟩ defines the inner product as being the conjugate of the first term rather than the second term, ie the result is v*·w , where * denotes the conjugate transpose.

This would be conform with Matlab and Maxima. It serves the same purpose as if we conjugate the second vector - the inner product of a vector with itself would be always positive.

However until now I was only aware of the definition Mathcad is following (transpose the first but conjugate the second vector) - just looked it up in some books.

I always found the same definition as given by Wiki https://en.wikipedia.org/wiki/Dot_product#Complex_vectors or Wolfram http://mathworld.wolfram.com/HermitianInnerProduct.html

```Interestingly, and confusingly, Mathematica defines Dot[v,w] as the Hademard (element-by-element) product
```

I am not well versed with Mathematica, but maybe it distinguishes between the Hermitian Inner product (see reference above) and a simpler Dot Product Dot Product -- from Wolfram MathWorld

Confusing anyway.

LT

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# Event generators for two charged and neutral pions production in proton-antiproton annihilation

Abstract : In the technical reports of Panda, The Orsay hadronic physics group have proposed to measure the electromagnetic time-like form factors of the proton via the $p \bar{p}$ annihilation into $e^{+}e^{-}$ reaction. The physics interest of the two-body hadronics channels is also emphasized in order to complete a full physics program of our letter of intent. The event generators for the two-body hadronic reactions are investigated in this report
Document type :
Reports
2008, pp.14

http://hal.in2p3.fr/in2p3-00222925
Contributor : Suzanne Robert <>
Submitted on : Tuesday, January 29, 2008 - 3:50:49 PM
Last modification on : Saturday, September 17, 2016 - 1:06:18 AM
Document(s) archivé(s) le : Friday, April 30, 2010 - 5:48:53 PM

### Files

ong.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : in2p3-00222925, version 1

### Citation

S. Ong, J. Van de Wiele. Event generators for two charged and neutral pions production in proton-antiproton annihilation. 2008, pp.14. <in2p3-00222925>

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text:
# why is 1/0 undefined

## Why Is 1/0 Undefined?

1/0 is undefined as any number divided by zero is not defined in Mathematics. So, Any number / 0 = undefined.

## Is 1 0 undefined or no solution?

So we don’t assign a value to 1/0, it’s undefined because be haven’t defined a value for it, we could, but not in a way that would not break algebra, which we prize more highly than being able to assign a value to every possible result of an operation. Why are and undefined? Let’s say, 7/0=x and 0/0=y.

## Is 1 0 undefined or infinity?

In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity. Similarly, expressions like 0/0 are undefined. But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate.

## Is O over 1 undefined?

So zero divided by zero is undefined. … Just say that it equals “undefined.” In summary with all of this, we can say that zero over 1 equals zero. We can say that zero over zero equals “undefined.” And of course, last but not least, that we’re a lot of times faced with, is 1 divided by zero, which is still undefined.

## Why a number divided by zero is undefined?

The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. … r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).

## What is the value of 1 by 0?

undefined
01 is undefined. Why some people say it’s true: Dividing by 0 is not allowed.

## What is the limit when 1 0?

And, just to be clear, 1/0 is undefined as well. a limit of the type f(x)g(x), where limf(x)=1 and limg(x)=0. While writing 10 is much more convenient than writing that expression, it has the downside that many people take it to mean literary 1 divided by 0.

## Is 1 0 is a rational number?

A number is rational if it can be expressed in the form p/q, where p & q are integers & q is NOT 0. 1/0 is not rational as the denominator (q) is zero. 1/0 is also not an irrational number, as anything 0 in the denominator is undefined.

## How do you prove that 1 0 is undefined?

Like fraction of 1/0, 1/0 =2/0 =3/0 =4/0…… =n/0. When we divide any number by 0 quotient is always same is not defined mathematically and so 1/0 is undefined.

## What is the difference between 0 1 and 0?

1/0 is undefined. Any number divided by zero does not produce any real number result. Sanjay C. In very simple terms, the first one gives you Infinity (1/0) and the second gives Zero (0/1) !!!!!!!

## What is the value of 0 by 0?

Answer: 0 divided by 0 is undefined.

Thus, using both the rules given above, it is impossible to come to a conclusion when 0 is divided by 0. Hence, we give the solution as undefined.

## Is 0 undefined in slope?

Well you know that having a 0 in the denominator is a big no, no. This means the slope is undefined. As shown above, whenever you have a vertical line your slope is undefined.

## Can zero be divided by 1?

Answer: Zero divided by 1 is 0.

Let’s divide zero by 1. Explanation: Zero divided by any number is always 0. … For example, if zero is to be divided by any number, this means 0 items are to be shared or distributed among the given number of people.

## Why is anything to the zeroth power 1?

In short, 0 is the only number such that for any number x, x + 0 = x. … So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1. Answer 2: It’s exciting to me that you asked this question.

## What happens if you ask Siri 0 divided by 0?

“What is zero divided by zero?” If you ask Siri this question in the iOS 8 operating system, the iPhone’s virtual assistant will cleverly tell you that you’re making no sense. “Imagine that you have zero cookies,” Siri’s response begins, “and you split them evenly among zero friends.

## Is 0 the same as undefined?

It is a rule that anything decided by zero is an undefined value since nothing can be divided by zero. … 1.An undefined slope is characterized by a vertical line while a zero slope has a horizontal line. 2. The undefined slope has a zero as the denominator while the zero slope has a difference of zero as a numerator.

## What does undefined mean in math?

An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real numbers.

## Is undefined equal to infinity?

Undefined means, it is impossible to solve. Infinity means, it is without bound.

## What is the value of 0?

The place value of zero in any number is always zero. Zero may hold any place in a number, but its value will remain to be zero. In numbers having zeros such as 105, 350, 42017, 90218, the place value of 0 in each number is 0.

## Does the limit 0 0 exist?

Typically, zero in the denominator means it’s undefined. … When simply evaluating an equation 0/0 is undefined. However, in taking the limit, if we get 0/0 we can get a variety of answers and the only way to know which on is correct is to actually compute the limit.

## What is 0 divided anything?

Infinity is not a real number, and even if it were, it wouldn’t be the answer to dividing something by zero. There is no number that you can multiply by 0 to get a non-zero number. There is NO solution, so any non-zero number divided by 0 is undefined.

## Is infinity a real number?

Infinity is a “real” and useful concept. However, infinity is not a member of the mathematically defined set of “real numbers” and, therefore, it is not a number on the real number line. … One of the most common definitions to learn then is that the real numbers are the set of Dedekind cuts of the rational numbers.

## What type of number is 1 0?

Whole Numbers
What does it look like?
Type of Number Example
Whole Numbers W=0,1,2,3,4,…
Integers Z=…,−3,−2,−1,0,1,2,3,…
Rational Numbers Q=−12,0.33333…,52,1110,…
Irrational Numbers F=…,π,√2,0.121221222…

## Is 0 is a rational number Why or why not?

Yes, 0 is a rational number. Since we know, a rational number can be expressed as p/q, where p and q are integers and q is not equal to zero. Thus, we can express 0 as p/q, where p is equal to zero and q is an integer.

## Why is 0 a rational number?

Why Is 0 a Rational Number? This rational expression proves that 0 is a rational number because any number can be divided by 0 and equal 0. Fraction r/s shows that when 0 is divided by a whole number, it results in infinity. Infinity is not an integer because it cannot be expressed in fraction form.

## Why is 1000 Undefined?

For instance, a large number such as 1,000 multiplied by zero becomes zero. It disappears! On the other hand, a nice number such as 5 divided by zero becomes undefined. It misbehaves.

## How do you tell the difference between 0 and O?

The slashed zero glyph is often used to distinguish the digit “zero” (“0”) from the Latin script letter “O” anywhere that the distinction needs emphasis, particularly in encoding systems, scientific and engineering applications, computer programming (such as software development), and telecommunications.

## What is the difference between 0 and 1?

0 is the additive identity, that is, even if you add it to any number, there is no change to the value of the number. 1 is the multiplicative identity, that is, even if you multiply any number with it, there is no change to its value.

## What is the difference between zero and one?

The difference between zero and one is the same as that between one and two, namely one-end of analysis. … Zero, however, is less than something infinitely small, whereas one, though not infinitely great, is vastly more than an infinitely minute quantity. Two on the other hand is only twice as much as one.

## How do you explain 0 0?

0. Reply: This is true for any nonzero denominator, but dividing by 0 0 0 is not allowed no matter what the numerator is. Rebuttal: Any number divided by 0 0 0 is ∞ .

## Does 0 squared exist?

Yes. The square root of zero is zero. A square root answers what number times itself equals the target number.

## Is Infinity Infinity defined?

There is no answer to this. Since, infinity is not really a number, we cannot treat it in the same manner we treat “numbers” i.e we cannot perform mathematical calculations on Infinity. Due, to the above, what “minus” exactly means for infinity isn’t clear.

## Dividing by zero?

Related Searches

why is 0/0 undefined
is 0/1 0
what is 1/0
indeterminate vs undefined


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# The Plan

## Assumptions

• 10k base net income
• 10% net income raise every year
• 0.29% monthly inflation (~3.54% yearly)
• 0.33% monthly risk free rate (~4.03% yearly)
• 0.35% monthly multi-market rate (~4.28% yearly)
• Invest 30% of net income every month
• Conservative portfolio allocation:
• 30% on inflation protection
• 30% on risk free bonds
• 40% on multi-market funds

These assumptions should yield:

• Real returns of 0.035% monthly
• Real income increases of 6% every year

## Theoretical Performance

Using an expected monthly return of ~0.035%, the total wealth $W$ at month $n$ is given by: $$W(n+1) = W(n) \times 1.00035 • 3000 \times 1.06^{\lfloor{n/12}\rfloor}$$ Following this calculation, the expected date of Financial Independence is the end of year 2040, as show in the Wealth Expectation Calculator.

## Implementation

1. Until the Emergency Fund is enough for a year of expenses, all investment goes into risk-free assets
2. After that, investment are made to balance the conservative portfolio allocation
3. Financial Independence is reached when a year of today’s expenses equals 5% of the emergency fund, meaning the total wealth should cover about 30 years of today’s standard of living.


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# Thiol agents can influence the equilibrium between these two states (Calero and Calvo, 2008). Thus,

Thiol agents can influence the equilibrium between these two states (Calero and Calvo, 2008). Thus, within a similar manner NO can react making an Snitrosylation of thiol groups at Cysloop C177 and C191 and, in turn, this covalent modification induces protein structural rearrangements that effect on GABA binding and channel gating (Chang and Weiss, 2002). The leftward shift and the concomitant improve inside the maximal existing values, observed in D curves for GABA in the presence of NO, are compatible with this hypothesis. This interpretation is also consistent cis-ACPD Epigenetic Reader Domain together with the effects of decreasing agents that protect against Cysloop formation and behave as GABAr1 Acalabrutinib web receptor potentiators (Calero and Calvo, 2008). Interestingly, earlier studies on NMDA receptors showed that redox modulation induced by both minimizing thiol agents and NOinduced Snitrosylation is mediated via the same extracellular cysteines (Lipton et al., 2002). Apart from NMDA receptors, ryanodine receptors, TRP channels and numerous other membranesignalling proteins are physiological targets for cysteine Snitrosylation (Eu et al., 2000; Lipton et al., 2002; Yoshida et al., 2006). Nonetheless, the modulation of Cysloop receptors by Snitrosylation was still not substantiated. It was shown that the redox modulation of Cysloop receptors, including the GABAC receptors, is commonly reversible (Amato et al., 1999; Pan et al., 2000; Calero and Calvo, 2008). Similarly, we located that NO modulation of GABAr1 receptors is very easily reversible. Hence, the present benefits also suggest that other redoxsensitive amino acid residues inside the r1 subunits, like tryptophane, methionine and tyrosine, are certainly not involved, mainly simply because these residues are normally modified by reactive nitrogen species in an irreversibly manner (e.g. by peroxynitrite, which can be developed by the reaction of NO with superoxide). Nitrosothiols are usually very labile within the presence of decreasing reagents, but our experiments showed that NO effects on GABAr1 receptors may also be washed out within the absence of lowering agents. A doable explanation is that chemical modification of the extracellular redox internet site (the disulfide bond that types the Cysloop) produces a transient conformational adjust in the receptor that, inside the absence of NO, quickly relaxes to a reduced energy state by excluding the NO group. This description is compatible using the actions of MTSEA on GABAr1 receptors. Ordinarily, the effects of this cysteinespecific reagent require the presence of minimizing agents as a way to be washed out (Xu and Akabas, 1993; Choi et al., 2000). In contrast, we discovered here that MTSEA applications created a quickly potentiation of the GABAr1 receptor responses that spontaneously disappeared through bath perfusion with a typical Ringer’s answer.Pharmacological and physiological relevance of your modulation of GABAC receptors by NOGABAC receptors mediate a number of modes of inhibitory actions in the retina (Lukasiewicz et al., 2004). They’re highly expressed in retinal bipolar cells (Koulen et al., 1998) and play a crucial role inside the manage of axon terminal excitability by mediating reciprocal synapses with amacrine cells (Matthews et al., 1994; Dong and Werblin, 1998; Hartveit, 1999).Nitric oxide and GABAC receptorsBJPGABAC receptors also mediate tonic inhibitory currents, which could be persistently activated by low concentrations of ambient GABA, locally controlled by GABA transporters located on amacrine cells (Hull et al., 2006; Jones and Palmer,.


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# transitive verb \in-ˈvi-zij, en-\: to picture (something) in your mind

Full Definition of ENVISAGE
1: to view or regard in a certain way
2: to have a mental picture of especially in advance of realization
*******************************************************************

Video reel on vimeo


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# Integral of $\int \tan^4 x \, \sec^6 x dx$

I am trying to find the integral of $$\int \tan^4 x \, \sec^6 x dx$$

I tried to rewrite as trig identities using $\sec^2 - \tan^2 = 1$ but that got me nowhere so I wrote it like this.

$$\int \frac{\sin^4x}{\cos^4 x} \frac{1}{\cos^6 x} dx$$

$$\int \frac{\sin^4x}{\cos^{10} x} dx$$

Then I use the idea that making u substitutions for cos will get rid of a power of sin so I just say that the power will go $4 3 2 1 0$ and I will get a $- + - + -$ sign change. I am not sure if this is correct or really how this works exactly but I did a few steps of it and it seemed to work correctly.

$$-1\int \frac{1}{u^{10}} dx$$

$$-1\int u^{-10} dx$$

$$-1 \times \frac{u^{-9}}{-9}$$

$$\frac{u^{-9}}{9}$$

$$\frac{\cos^{-9}}{9}$$

This is wrong and I am not sure why.

-
Did you see how your previous questions were edited? Do you mind using the same format? –  Gigili Jun 3 '12 at 18:02
@Gigili What is the difference? –  user138246 Jun 3 '12 at 18:08

Your substitution is not correct. You should still still have a $\sin^3 x$ upstairs.

However when integrating a product of an even power of $\tan$ with an even power of $\sec$, you can do the following, which takes advantage of the facts that $\tan^2x+1=\sec^2 x$ and that the derivative of $\tan x$ is $\sec^2 x$:

First write \eqalign{\tan^4 x\,\sec^6 x&=\tan^4x\,\sec^4x\cdot \sec^2 x\cr &= \tan^4x \,(\sec^2x)^2\cdot \sec^2 x\cr &=\tan^4x \,(\tan^2 x+1)^2\cdot \sec^2 x.} To evaluate the integral, set $u=\tan x$ (so that $du=\sec^2 x \,dx$).

-

Here is a relatively easier way. Remember that $\sec^2(x) = 1 + \tan^2(x)$. Hence the integral $$I = \int \tan^4(x) \sec^6(x) dx = \int \tan^4(x) \sec^4(x) \sec^2(x) dx\\ = \int \tan^4(x) \left(1 + \tan^2(x) \right)^2 \sec^2(x) dx$$ Let $\tan(x) = t$. Hence, $\sec^2(x) dx = dt$. Hence, we get that $$I = \int t^4 \left( 1+t^2 \right)^2 dt = \int t^4 \left( 1+2t^2 +t^4 \right) dt = \int \left(t^4 + 2t^6 + t^8 \right) dt\\ =\dfrac{t^5}{5} + \dfrac{2t^7}{7} + \dfrac{t^9}{9} + C$$ Hence, we get that $$I = \dfrac{\tan^5(x)}{5} + \dfrac{2\tan^7(x)}{7} + \dfrac{\tan^9(x)}{9} + C$$

-

No. You haven't done it correctly. Hint

• $\tan^{4}(x) \cdot \sec^{4}(x) \cdot \sec^{2}(x)$.

• $\sec^{4}(x) = (1+\tan^{2}{x})^{2}$.

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