text:
# Exercise 5-6 The bookkeeper for Metlock Company has prepared the following balance sheet as of July...

###### Question:

Exercise 5-6 The bookkeeper for Metlock Company has prepared the following balance sheet as of July 31, 2020. Cash Accounts receivable (net) Inventory Equipment (net) Patents METLOCK COMPANY BALANCE SHEET AS OF JULY 31, 2020 $72,670 Notes and accounts payable 44,170 Long-term liabilities 63,670 Stockholders' equity 84,000 21,000$285,510 $47,670 78,670 159,170$285,510 The following additional information is provided. 1. Cash includes $1,200 in a petty cash fund and$13,020 in a bond sinking fund. 2. The net accounts receivable balance is comprised of the following two items: (a) accounts receivable $47,670 and (b) allowance for doubtful accounts$3,500. 3. Inventory costing $5,418 was shipped out on consignment on July 31, 2020. The ending inventory balance does not include the consigned goods. Receivables in the amount of$5,418 were recognized on these consigned goods. 4. Equipment had a cost of $115,670 and an accumulated depreciation balance of$31,670. 5. Income taxes payable of $6,000 were accrued on July 31. Metlock Company, however, had set up a cash fund to meet this obligation. This cash fund was not included in the cash balance but was offset against the income taxes payable amount. Prepare a corrected classified balance sheet as of July 31, 2020, from the available information, adjusting the account balances using the additional information. (List Current Assets in order of liquidity) METLOCK COMPANY Balance Sheet Assets$  Liabilities and Stockholders' Equity  Click if you would like to Show Work for this question: Open Show Work

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text:
# How to use \Cite in sidenotes without printing the URL?

I am using biblatex-chicago-notes in combination with the sidenotes package. For my current project I am using quite a lot of online articles with an URL field. The use of \Cite prints the URL not only in the bibliography but also in the text margin. In order to save space and improve the clarity I would like to omit the URL field in the margins but not in the bibliography (otherwise, I could have used url=false in the preamble). All current citation commands in biblatex-chicago do not fullfill that need. How can this be achieved?

MWE:

\documentclass{scrartcl}

\usepackage[notes]{biblatex-chicago}
\usepackage{sidenotes}
\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@article{article:poole2001,
author          = {Poole, Steven},
title           = {Trigger Happy: Videogames and the Entertainment Revolution},
date            = {2008-01-15},
abstract        = {2001 edition, with 2004 afterword},
url             = {http://stevenpoole.net/blog/trigger-happier/},
}
\end{filecontents}

\begin{document}

Lorem ipsum.\sidenote{\Cite{{article:poole2001}}

\printbibliography

\end{document}

You can use

\AtEveryCitekey{\clearfield{url}\clearfield{urlyear}}

to get rid of the URL and urldate in citations as explained in Excessive fields in biblatex could not be removed if using \fullcite.

With chicago-notes that leaves a spurious comma, however, this is due to the macro cjournal+issue+year+pages not using \setunits in certain places. To fix that we need

\renewbibmacro*{cjournal+issue+year+pages}{%
\usebibmacro{cjournal+ser+vol+num}%
\ifboolexpr{% 16th ed.
test {\iffieldundef{issue}}%
and
test {\iffieldundef{year}}%
and
not togl {cms@switchdates}%
}%
{\iffieldundef{number}%
{\ifthenelse{\iffieldundef{pagination}\AND%
\iffieldundef{bookpagination}}%
{\setunit{\postvolpunct}}%
{\ifthenelse{\iffieldundef{volume}\AND\iffieldundef{number}}% 16th ed.
{\newcunit%
\iffieldundef{issue}
{\usebibmacro{number+or+month}}%
{\printfield{issue}%
\usebibmacro{cmsyear}}%
\printtext[parens]{% parens is the default here
\iffieldundef{issue}
{\usebibmacro{number+or+month}}%
{\printfield{issue}%
\usebibmacro{cmsyear}}}}}}

Where we wrapped the \addcomma\addspace in the indicated lines in \setunits.

MWE

\documentclass{scrartcl}
\usepackage[marginparwidth=5cm,
margin=6cm,
]{geometry}

\usepackage[notes]{biblatex-chicago}
\usepackage{sidenotes}
\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@article{article:poole2001,
author          = {Poole, Steven},
title           = {Trigger Happy: Videogames and the Entertainment Revolution},
date            = {2008-01-15},
abstract        = {2001 edition, with 2004 afterword},
url             = {http://stevenpoole.net/blog/trigger-happier/},
}
\end{filecontents}

\AtEveryCitekey{\clearfield{url}\clearfield{urlyear}}

\renewbibmacro*{cjournal+issue+year+pages}{%
\usebibmacro{cjournal+ser+vol+num}%
\ifboolexpr{% 16th ed.
test {\iffieldundef{issue}}%
and
test {\iffieldundef{year}}%
and
not togl {cms@switchdates}%
}%
{\iffieldundef{number}%
{\ifthenelse{\iffieldundef{pagination}\AND%
\iffieldundef{bookpagination}}%
{\setunit{\postvolpunct}}%
{\ifthenelse{\iffieldundef{volume}\AND\iffieldundef{number}}% 16th ed.
{\newcunit%
\iffieldundef{issue}
{\usebibmacro{number+or+month}}%
{\printfield{issue}%
\usebibmacro{cmsyear}}%
\printtext[parens]{% parens is the default here
\iffieldundef{issue}
{\usebibmacro{number+or+month}}%
{\printfield{issue}%

format: plain


text:
Special relativity from different angle

1. Jul 18, 2006

exponent137

If we accelerate one body with mass m0 on a distance dx, then, we need energy dW:
dW = a m0 dx = dv/dt m dx = m0 dv v
Energy dW, which we gives weight dW= dm c^2
If we put this in differential equation, solvation is
dm/m0 = v dv /c^2
and
(m/m0)=exp(v^2/(2c^2))
But this calculation does not give that m is infinity at v = c.

What failing to my calculation?

(I know normal derivation of special relativity equation)

2. Jul 18, 2006

pervect

Staff Emeritus
You are assuming that in SR, F=ma, where m is the 'relativistic mass'.

This formula is fundmanetally wrong. See for instance

https://www.physicsforums.com/showpost.php?p=687759&postcount=71

You can also take a look at http://www.math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

in the addendum "what is the relativistic version of F=ma"

3. Jul 25, 2006

exponent137

I found another formula for relativistic mass which works:
c^2 dm = m v dv gama^-2
where
gama=(1-(v/c)^2)^-1/2

The result is m = gama m0
Where m0 is mass at v=0.
This give the same formula of relativistic mass in longitudinal direction as in horizontal direction. This gives hint that absolute explanation is possible. This means slower time-run in rocket which moves very fast is consequence of larger mass in rocket and so means that we see mans in rocket moving slow. But how to explain that peoples in rocket see us that our clock run slow?

I understand that two main postulates of relativity,
1.speed of light is the same in every inertial system
2. All system are equally valid.
But one explanation should to exist, if we suppose that our system is privileged. Suppositions are more involved than with points 1 and 2, but some explanation should to exist.

4. Jul 27, 2006

exponent137

Above mentioned relativistic mass (longitudinal = transverzal) is useful, because it is alternative explanation for time dilatation:
Because mass is larger, everything is moving slower and this gives slower time running.
But how this concept explain that someone in moving rocket see time dilatation on earth?
I suppose that that classical special relativity is only the most simple view on special relativity, but it is not the only one.

P.S
I think that this question of beginners, but thread was moved.


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1. $50 sqrt 19$
2. $-50 sqrt 19$
3. $50 sqrt 38$
4. $-50 sqrt 38$
What is $root3( 27/125)$ in simplest form?
1. $(3 root3 5)/5$
2. $(3)/(root3 5)$
3. $(root3 5)/5$
4. $(3)/5$
Solve the equation.

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1. $49$
2. $23$
3. $-13$
4. $32$
$(2x^2)^(1/3) (2x)^(1/2)$
1. $root6 (32x^5$
2. $root6 (4x^7$
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1. $4x^2$
2. $4x$
3. $5x^2 sqrt3$
4. $5x sqrt3$
5. none of these are correct
Which expression is equivalent to $(sqrt(3x^2))^4$?
1. $3x^4$
2. $9x^4$
3. $9x^8$
4. $12x^8$
Simplify: $sqrt63-3sqrt28$
1. $3sqrt7$
2. $-3sqrt7$
3. $-2sqrt7$
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Simplify $sqrt(18)$.
1. $9sqrt(2)$
2. $3sqrt(2)$
3. 9
4. $2sqrt(3)$
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1. $x^(3/2)$
2. $x^(1/6)$
3. $1$
4. $1/x$
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1. $(-1/3)$
2. $1/3$
3. $-3$
4. 3
Which of the following is equal to $sqrt(75)$?
1. $2sqrt5$
2. $3sqrt5$
3. $5sqrt2$
4. $3sqrt3$
5. $5sqrt3$
Simplify. $sqrt360$
1. $3sqrt40$
2. $9sqrt20$
3. $12sqrt10$
4. $6sqrt10$
$9sqrt7+8sqrt7$
1. $sqrt14$
2. $17sqrt7$
3. $sqrt7$
4. $17$


text:
## Generalised Darboux-Koenigs metrics and 3-dimensional superintegrable systems.(English)Zbl 1420.37038

Summary: The Darboux-Koenigs metrics in 2D are an important class of conformally flat, non-constant curvature metrics with a single Killing vector and a pair of quadratic Killing tensors. In [arXiv:1804.06904] it was shown how to derive these by using the conformal symmetries of the 2D Euclidean metric. In this paper we consider the conformal symmetries of the 3D Euclidean metric and similarly derive a large family of conformally flat metrics possessing between 1 and 3 Killing vectors (and therefore not constant curvature), together with a number of quadratic Killing tensors. We refer to these as generalised Darboux-Koenigs metrics. We thus construct multi-parameter families of super-integrable systems in 3 degrees of freedom. Restricting the parameters increases the isometry algebra, which enables us to fully determine the Poisson algebra of first integrals. This larger algebra of isometries is then used to reduce from 3 to 2 degrees of freedom, obtaining Darboux-Koenigs kinetic energies with potential functions, which are specific cases of the known super-integrable potentials.

### MSC:

 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics 70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
Full Text:

### References:

 [1] Ballesteros, \'{A}ngel and Enciso, Alberto and Herranz, Francisco J. and Ragnisco, Orlando, Superintegrability on {$$N$$}-dimensional curved spaces: central potentials, centrifugal terms and monopoles, Annals of Physics, 324, 6, 1219-1233, (2009) · Zbl 1163.90353 [2] Ballesteros, \'{A}ngel and Enciso, Alberto and Herranz, Francisco J. and Ragnisco, Orlando and Riglioni, Danilo, Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability, Annals of Physics, 326, 8, 2053-2073, (2011) · Zbl 1163.90353 [3] Dubrovin, B. A. and Fomenko, A. T. and Novikov, S. P., Modern geometry – methods and applications, Vols. 1-3, (1984), Springer-Verlag, New York · Zbl 1163.90353 [4] Escobar-Ruiz, M. A. and Miller, Jr., Willard, Toward a classification of semidegenerate 3{D} superintegrable systems, Journal of Physics. A. Mathematical and Theoretical, 50, 9, 095203, 22 pages, (2017) · Zbl 1163.90353 [5] Fordy, Allan P., First integrals from conformal symmetries: Darboux-Koenigs metrics and beyond · Zbl 1163.90353 [6] Fordy, Allan P., A {K}aluza–{K}lein reduction of super-integrable systems, Journal of Geometry and Physics, 131, 210-219, (2018) · Zbl 1163.90353 [7] Fordy, Allan P. and Huang, Qing, Poisson algebras and 3{D} superintegrable {H}amiltonian systems, SIGMA. Symmetry, Integrability and Geometry. Methods and Applications, 14, 022, 37 pages, (2018) · Zbl 1163.90353 [8] Gilmore, Robert, Lie groups, {L}ie algebras, and some of their applications, (1974), Wiley, New York · Zbl 1163.90353 [9] Kalnins, E. G. and Kress, J. M. and Miller, Jr., W. and Winternitz, P., Superintegrable systems in {D}arboux spaces, Journal of Mathematical Physics, 44, 12, 5811-5848, (2003) · Zbl 1163.90353 [10] Kalnins, E. G. and Kress, J. M. and Winternitz, P., Superintegrability in a two-dimensional space of nonconstant curvature, Journal of Mathematical Physics, 43, 2, 970-983, (2002) · Zbl 1163.90353 [11] Koenigs, G. X. P., Sur les g{\'e}od{\'e}siques a integrales quadratiques, Le cons sur la th{\'e}orie g{\'e}n{\'e}rale des surfaces, Vol. 4, 368-404, (1972), Chelsea Publishing, New York · Zbl 1163.90353 [12] Kruglikov, Boris and The, Dennis, The gap phenomenon in parabolic geometries, Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle’s Journal], 723, 153-215, (2017) · Zbl 1163.90353 [13] Matveev, Vladimir S. and Shevchishin, Vsevolod V., Two-dimensional superintegrable metrics with one linear and one cubic integral, Journal of Geometry and Physics, 61, 8, 1353-1377, (2011) · Zbl 1163.90353 [14] Miller, Jr., Willard and Post, Sarah and Winternitz, Pavel, Classical and quantum superintegrability with applications, Journal of Physics. A. Mathematical and Theoretical, 46, 42, 423001, 97 pages, (2013) · Zbl 1163.90353 [15] Valent, Galliano, Superintegrable models on {R}iemannian surfaces of revolution with integrals of any integer degree ({I}), Regular and Chaotic Dynamics. International Scientific Journal, 22, 4, 319-352, (2017) · Zbl 1163.90353
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
8 Answered Questions for the topic performing

Performing Voice (music) Singing

02/11/21

#### Can people learn to sing or are you just born with a good voice?

This is a common question I am asked

06/27/19

#### Ritardando, Rallentando, and Allargando?

Three common musical markings for gradual slowing down are ritardando, rallentando, and allargando. How do these differ from each other in interpretation and execution? For example, I was taught... more

06/03/19

#### How to select a key-signature for a song?

There are so many songs in pretty odd key-signatures like 4,5,6 sharps or flats. At least this is my impression when I listen to songs on the radio/net while trying to follow them on my... more

05/16/19

#### Ritardando, Rallentando, and Allargando?

Three common musical markings for gradual slowing down are ritardando, rallentando, and allargando. How do these differ from each other in interpretation and execution? For example, I was taught... more

05/01/19

#### How can I make two chords on the ukulele sound interesting for a whole song?

I'm accompanying my friend on one of her own songs with my uke. However, the song only has two chords the whole way through!The chords are Dm and Am - eight even beats of each. It's mostly slow... more

04/29/19

#### How to select a key-signature for a song?

There are so many songs in pretty odd key-signatures like 4,5,6 sharps or flats. At least this is my impression when I listen to songs on the radio/net while trying to follow them on my... more

04/27/19

#### I have to perform a monologue that I hate, and I can't find a way to perform it without getting mad

I auditioned for a role to read a monologue, and I got in, but I couldn't choose what I'm performing. (All of the monologues were written by students in my school) I ended up getting a monologue... more

03/14/19

#### How can I make two chords on the ukulele sound interesting for a whole song?

I'm accompanying my friend on one of her own songs with my uke. However, the song only has two chords the whole way through! The chords are Dm and Am - eight even beats of each. It's mostly... more

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

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text:
PL EN

Preferencje
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## Studia Mathematica

2004 | 161 | 1 | 33-59
Tytuł artykułu

### Ideals in big Lipschitz algebras of analytic functions

Autorzy
Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
For 0 < γ ≤ 1, let $Λ⁺_{γ}$ be the big Lipschitz algebra of functions analytic on the open unit disc 𝔻 which satisfy a Lipschitz condition of order γ on 𝔻̅. For a closed set E on the unit circle 𝕋 and an inner function Q, let $J_{γ}(E,Q)$ be the closed ideal in $Λ⁺_{γ}$ consisting of those functions $f ∈ Λ⁺_{γ}$ for which
(i) f = 0 on E,
(ii) $|f(z)-f(w)| = o(|z-w|^{γ})$ as d(z,E),d(w,E) → 0,
(iii) $f/Q ∈ Λ⁺_{γ}$.
Also, for a closed ideal I in $Λ⁺_{γ}$, let $E_{I}$ = {z ∈ 𝕋: f(z) = 0 for every f ∈ I} and let $Q_{I}$ be the greatest common divisor of the inner parts of non-zero functions in I. Our main conjecture about the ideal structure in $Λ⁺_{γ}$ is that $J_{γ}(E_{I},Q_{I}) ⊆ I$ for every closed ideal I in $Λ⁺_{γ}$. We confirm the conjecture for closed ideals I in $Λ⁺_{γ}$ for which $E_{I}$ is countable and obtain partial results in the case where $Q_{I} = 1$. Moreover, we show that every wk* closed ideal in $Λ⁺_{γ}$ is of the form {f ∈ $Λ⁺_{γ}$: f = 0 on E and f/Q ∈ $Λ⁺_{γ}$} for some closed set E ⊆ 𝕋 and some inner function Q.
Słowa kluczowe
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Tom
Numer
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33-59
Opis fizyczny
Daty
wydano
2004
Twórcy
autor
• Department of Mathematics and Physics, The Royal Veterinary and Agricultural University, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
Bibliografia
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Bibliografia
Identyfikatory


text:
# Deciphering Mux/Demux/Switch Nomenclature: AxB:C?

I'm looking through Digikey's Interface - Switches, Multiplexers, Demultiplexers section (and, thanks to W5VO, the Logic - Signal Switches, Multiplexers, Decoders section as well), and I'm having trouble deciphering what circuit/topology I need.

I've got a processor with a 32-bit coprocessor interface, and I'd like to interface it with a parallel Flash or RAM chip. Ideally, I would have both, and could swap between the two in software. I imagined (wrongly, it appears) that this would be a fairly common need, and that I could buy a pair of ICs that would each break out 16 inputs into 2 banks of 16 outputs, with power, ground, a single channel select pin, maybe an enable/high impedance pin. This would ideally come in a 54-pin TSSOP or 64-pin QFP or something of that size. A 32-switch chip would also work, but I imagine that two switches would make routing the a bit easier. The interface would be digital (I don't really need an analog switch), and I'd like to keep up with the 150MHz maximum speed grade of my processor (but will settle for 72MHz or so of actual performance). I am confident that I don't need some of the $200+ crosspoint switches! I imagined that this would be a simple task, but it seems that my idea of what AxB:C should mean is different from Digikey's idea. I thought that the options would include 1x16:32 or 16x1:2, but (1) these options are not available at reasonable prices (I don't see why this device should cost$70 or $234!), and the other options (like 8x2:1, which seems popular) are designed for analog switching of Ethernet signals. 1. Where can I learn about the mux nomenclature? (An answer on this site would be ideal :) Also, where can I learn about the various functions listed, like AV/crosspoint/Ethernet/USB? 2. What topology or function should I use for to do this task (digital, ~100MHz, 32 or 16 lines)? 3. If all else fails, how can I build a switch out of discrete components or transistor arrays? ## 3 Answers There's a few questions in there, so I'll address them one by one. What does A x B : C Mean? Read this as A instances of a B number of inputs to C number of outputs. What you are looking for, if I understand correctly, is a 16x2:1 or a 32x2:1 chip. If C is more than 1, then your chip is significantly more complicated - you would no longer be selecting one input and connecting it to the output. Which leads well into the next sub-question - Why are there$200+ chips for this simple function?

The specific part you linked is a 1x32:16 wide-bandwidth, DC coupled, buffered, video MUX, which can select any of it's 32 video inputs and output them simultaneously on it's 16 buffered outputs, with a gain of 1-2x. You could sorta think of it as a 16x32:1 with a lot of features. It's got quite a bit more inside than just CMOS switches. It isn't really designed for your function, which is...

How do I connect two memories to a master CPU

The most common method for hooking up multiple memory chips to a driver/controller/cpu is to use a tri-state bus. The address lines drive both chips, and the data bus is shared between all chips. Both chips should have a pin like "output enable", which can be controlled by the CPU. I found this article discussing memory buses at a rudimentary level - it has descriptive images. See Figure 8 for the gist of what I think you want. It is the simplest way of hooking things up, and the way I would recommend if the chips support it.

How would I make one?

Well, I think you were on the right track. CPU buses can be bi-directional, so intercepting the right output enable signal may be risky. The part you were probably looking for was a digital switch, something like this 16x2:1 FET mux. This is the cheapest one at \$1.75 each. Wide bidirectional buses are best handled by ICs.

Note

I would check with the maker of your CPU to look for app notes and reference designs regarding memory buses. That will be the easiest way to see if you're on track.

• If it's bidirectional, why do we need a concept of inputs and outputs? Or, what's the difference between an AxB:C chip and an AxC:B chip? – Kevin Vermeer Feb 1 '11 at 18:33
• Ah, I was looking in 'Interface - Switches, Multiplexers, Demultiplexers' when I wanted 'Logic - Signal Switches, Multiplexers, Decoders' – Kevin Vermeer Feb 1 '11 at 18:36
• Not all MUX topologies are bidirectional. The MOSFET switch ones are, because the switch behaves that same in both directions. Only if a topology is bidirectional can B and C be interchangeable. Normally, a 1:2 circuit is considered a de-mux. – W5VO Feb 1 '11 at 18:42

I think you're confusing terms. It sounds like what you want is to connect a SRAM and Flash to a microcontroller. This has nothing to do with crosspoint switches.

I also see you deleted an answer stating the same about 2h ago; if you care to comment why this is wrong we can try to help you out. Otherwise I believe W5VO has answered your question about nomenclature quite well. (edit: nevermind, deleted by owner appears to me the owner of the answer, not the owner of the question.)

Run the address lines together, the data lines together, tie the RD (read strobe) lines together (if the flash has an OE, tie RD to OE as well). The WR lines should be tied together, and now you should be left with two CS (chip select) lines. Either run these to dedicated output enables on the microcontroller (many have built in address decoders) or build up some select logic that gives you a an OE for accesses to one memory range and another OE for another memory range. There are PLENTY of examples online, and the 74HC138 is a great chip for this. Googling for "memory address decoding" or "chip select decode" or even "microcontroller external memory interface" may get you started.

There are some different ways of going about this (Motorola-style bus vs Intel-style bus) but any book or articles on the older microprocessors or microcontrollers will give you plenty of information.

• Agreed - as I mentioned, this is really the preferred way to do multiple memory banks. – W5VO Feb 1 '11 at 19:25
• The 74HC138 is unlikely to work at the 72MHz desired by the original poster. Still, +1 this answer is perfect, because all the processors I've worked with either (a) run slow enough that many people use a 74HC138 and it works fine, or (b) have dedicated chip select pins. – davidcary Feb 28 '11 at 17:40

I think you are making this too hard. Just run the address and lines to the Flash and RAM in parallel. Then chip select chooses which to access. I assumed NOR flash.

An AV switch is designed for analog signal, so it will have a low impedance and high bandwidth (100's of MHz). Also don't forget that you need to pass the edge rates of the signals, not just the frequency.

A matrix switch can switch any input to any output. That is a more expensive and general than a 8x2:1 which is just 8 of 2:1 switches, i.e., 8 of SPDT switches.

• <_< Somehow, I assumed that I couldn't put Flash and RAM on the same bus at the same time. This is probably what I'll do, but I'll leave the question here because I still want to know what AxB:C means. – Kevin Vermeer Feb 1 '11 at 16:35
• Yes, good digital logic teachers tell the students "don't short output pins, or they will fight each other and cause permanent damage!" dozens of times. And yet there are a few devices seem to contradict that -- they are designed to have outputs shorted together in a "tri-state bus" or "open-collector bus" or "matrix" -- tri-state data buses, tri-state shared-memory multiprocessor address buses, I2C communication bus, multi-drop RS485 bus, LED charlieplexing, keyboard matrix, etc. – davidcary Feb 28 '11 at 17:57


text:
Source code for netket.optimizer

# Copyright 2021 The NetKet Authors - All rights reserved.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

from . import qgt, solver

from .sr import SR

from .linear_operator import LinearOperator
from .preconditioner import (
LinearPreconditioner,
PreconditionerT,
identity_preconditioner,
)

## Optimisers

from netket.utils import _hide_submodules

[docs]def Sgd(learning_rate: float):
The Stochastic Gradient Descent <https://en.wikipedia.org/wiki/Stochastic_gradient_descent>_
is one of the most popular optimizers in machine learning applications.
Given a stochastic estimate of the gradient of the cost function (:math:G(\mathbf{p})),
it performs the update:

.. math:: p^\prime_k = p_k -\eta G_k(\mathbf{p}),

where :math:\eta is the so-called learning rate.
NetKet also implements two extensions to the simple SGD,
the first one is :math:L_2 regularization,
and the second one is the possibility to set a decay
factor :math:\gamma \leq 1 for the learning rate, such that
at iteration :math:n the learning rate is :math:\eta \gamma^n.

Args:
learning_rate: The learning rate :math:\eta.

Examples:
Simple SGD optimizer.

>>> from netket.optimizer import Sgd
>>> op = Sgd(learning_rate=0.05)
"""
from optax import sgd

return sgd(learning_rate)

[docs]def Momentum(learning_rate: float, beta: float = 0.9, nesterov: bool = False):
r"""Momentum-based Optimizer.
The momentum update incorporates an exponentially weighted moving average
over previous gradients to speed up descent
Qian, N. (1999) <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.57.5612&rep=rep1&type=pdf>_.
The momentum vector :math:\mathbf{m} is initialized to zero.
Given a stochastic estimate of the gradient of the cost function
:math:G(\mathbf{p}), the updates for the parameter :math:p_k and
corresponding component of the momentum :math:m_k are

.. math::

m^\prime_k &= \beta m_k + (1-\beta)G_k(\mathbf{p})\\
p^\prime_k &= \eta m^\prime_

Args:
learning_rate: The learning rate :math:\eta
beta: Momentum exponential decay rate, should be in [0,1].
nesterov: Flag to use nesterov momentum correction

Examples:
Momentum optimizer.

>>> from netket.optimizer import Momentum
>>> op = Momentum(learning_rate=0.01)
"""
from optax import sgd

return sgd(learning_rate, momentum=beta, nesterov=nesterov)

learning_rate: float = 0.001,
epscut: float = 1.0e-7,
initial_accumulator_value: float = 0.1,
):
In many cases, in Sgd the learning rate :math:\eta should
decay as a function of training iteration to prevent overshooting
rate algorithm that automatically scales the learning rate with a sum
over past gradients. The vector :math:\mathbf{g} is initialized to zero.
Given a stochastic estimate of the gradient of the cost function :math:G(\mathbf{p}),
the updates for :math:g_k and the parameter :math:p_k are

.. math:: g^\prime_k &= g_k + G_k(\mathbf{p})^2\\
p^\prime_k &= p_k - \frac{\eta}{\sqrt{g_k + \epsilon}}G_k(\mathbf{p})

the gradients are sparse, but the learning rate may become too small
after many updates because the sum over the squares of past gradients is cumulative.

Args:
learning_rate: Learning rate :math:\eta.
epscut: Small :math:\epsilon cutoff.
initial_accumulator_value: initial value of the accumulator

Examples:

"""

learning_rate, eps=epscut, initial_accumulator_value=initial_accumulator_value
)

[docs]def Adam(learning_rate: float = 0.001, b1: float = 0.9, b2: float = 0.999, eps=1e-08):

Args:
learning_rate: Learning rate :math:\eta.
b1: Decay rate for the exponentially weighted average of grads.
b2: Decay rate for the exponentially weighted average of squared norm of grads.
eps: Term added to the denominator to improve numerical stability.
"""

[docs]def RmsProp(
learning_rate: float = 0.001,
beta: float = 0.9,
epscut: float = 1.0e-7,
centered: bool = False,
):
r"""RMSProp optimizer.

RMSProp is a well-known update algorithm proposed by Geoff Hinton
in his Neural Networks course notes Neural Networks course notes
<http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf>_.
After initializing the vector :math:\mathbf{s} to zero, :math:s_k and t
he parameters :math:p_k are updated as

.. math:: s^\prime_k = \beta s_k + (1-\beta) G_k(\mathbf{p})^2 \\
p^\prime_k = p_k - \frac{\eta}{\sqrt{s_k}+\epsilon} G_k(\mathbf{p})

Constructs a new RmsProp optimizer.

Args:
learning_rate: The learning rate :math:\eta
beta: Exponential decay rate.
epscut: Small cutoff value.
centered: whether to center the moving average.

Examples:
RmsProp optimizer.

>>> from netket.optimizer import RmsProp
>>> op = RmsProp(learning_rate=0.02)
"""
from optax import rmsprop

return rmsprop(learning_rate, decay=beta, eps=epscut, centered=centered)

_hide_submodules(__name__)


text:
# Solved papers for JEE Main & Advanced Physics Electrostatics & Capacitance NEET PYQ - Electrostatics and Capacitance

### done NEET PYQ - Electrostatics and Capacitance Total Questions - 82

• question_answer1) A point Q lies on die perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole) then electric field at Q is proportional to:               [AIPMT 1998]

A)
${{p}^{-1}}$ and ${{r}^{2}}$

B)
$p$ and ${{r}^{-2}}$

C)
${{p}^{2}}$ and ${{r}^{-3}}$

D)
$p$ and ${{r}^{-3}}$

• question_answer2) A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is :               [AIPMT 1998]

A)
$qE{{y}^{2}}$

B)
$q{{E}^{2}}y$

C)
$qEy$

D)
${{q}^{2}}Ey$

• question_answer3) A hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is 2 m? [AIPMT 1998]

A)
Zero

B)
$5\,\mu \,C{{m}^{-2}}$

C)
$20\,\mu \,C{{m}^{-2}}$

D)
$8\,\mu \,C{{m}^{-2}}$

• question_answer4) When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges, separated by a distance: [AIPMT 1999]

A)
decreases K times

B)
increase K times

C)
remains unchanged

D)
becomes $\frac{1}{{{K}^{2}}}$times

• question_answer5) In bringing an electron towards another electron, the electrostatic potential energy of the system: [AIPMT 1999]

A)
decreases

B)
increases

C)
remains same

D)
becomes zero

• question_answer6) A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomes:                             [AIPMT 1999]

A)
$\sqrt{2}\,C$

B)
2 C

C)
$\frac{C}{\sqrt{2}}$

D)
$\frac{C}{2}$

• question_answer7)  The effective capacitance between points x and y of figure shown is:            [AIPMT 1999]

A)
$6\,\mu F$

B)
$12\,\mu F$

C)
$18\,\mu F$

D)
$24\,\mu F$

• question_answer8) When a proton is accelerated through 1V its kinetic energy will be:                [AIPMT 1999]

A)
1540 eV

B)
13.6 eV

C)
1 eV

D)
zero

• question_answer9) A capacitor is charged by connecting a battery across its plates. It stores energy U. Now the battery is disconnected and another identical capacitor is connected across it, then the energy stored by both capacitors of the system will be:                                             [AIPMT 2000]

A)
U

B)
$\frac{U}{2}$

C)
2U

D)
$\frac{3}{2}U$

• question_answer10) A charged wire is bent in the form of a semi-circular arc of radius a. If charge per unit length is $\lambda$  coulomb/metre, the electric field at the centre O is:

A)
$\frac{\lambda }{2\pi {{a}^{2}}{{\varepsilon }_{0}}}$

B)
$\frac{\lambda }{4{{\pi }^{2}}{{\varepsilon }_{0}}a}$

C)
$\frac{\lambda }{2{{\pi }^{2}}{{\varepsilon }_{0}}a}$

D)
zero

• question_answer11) A man goes at the top of a smooth inclined plane. He releases a bag to fall freely and he himself slides on inclined plane to reach the bottom. If ${{v}_{1}}$ and ${{v}_{2}}$ are the velocities of the man and bag respectively, then: [AIPMT 2000]

A)
${{v}_{1}}>{{v}_{2}}$

B)
${{v}_{1}}<{{v}_{2}}$

C)
${{v}_{1}}={{v}_{2}}$

D)
${{v}_{1}}$ and ${{v}_{2}}$ cannot be compared

• question_answer12) The reactance of a capacitor of capacitance C is X. If both the frequency and capacitance be doubled, then new reactance will be: [AIPMT 2001]

A)
X

B)
2X

C)
4X

D)
$\frac{X}{4}$

• question_answer13) In a parallel plate capacitor, the distance between the plates is d and potential difference across plates is V. Energy stored per unit volume between the plates of capacitor is:        [AIPMT 2001]

A)
$\frac{{{Q}^{2}}}{2{{V}^{2}}}$

B)
$\frac{1}{2}{{\varepsilon }_{0}}\frac{{{V}^{2}}}{{{d}^{2}}}$

C)
$\frac{1}{2}\frac{{{V}^{2}}}{{{\varepsilon }_{0}}{{d}^{2}}}$

D)
$\frac{1}{2}{{\varepsilon }_{0}}\frac{{{V}^{2}}}{{{d}^{2}}}$

• question_answer14) A charge $q\mu C$ is placed at the centre of a cube of a side 0.1 m, then the electric flux diverging from each face of the cube is:                    [AIPMT 2001]

A)
$\frac{q\times {{10}^{-6}}}{24{{\varepsilon }_{0}}}$

B)
$\frac{q\times {{10}^{-4}}}{{{\varepsilon }_{0}}}$

C)
$\frac{q\times {{10}^{-6}}}{6{{\varepsilon }_{0}}}$

D)
$\frac{q\times {{10}^{-4}}}{12{{\varepsilon }_{0}}}$

• question_answer15) Torque acting on electric dipole of dipole moment $\vec{p}$ placed in uniform electric field $\vec{E}$ is:         [AIPMT 2001]

A)
$\vec{p}\times \vec{E}$

B)
$\vec{p}\,.\,\vec{E}$

C)
$\vec{p}\times \vec{E}\times \vec{p}$

D)
$\frac{\vec{E}\,.\,\vec{p}}{{{p}^{2}}}$

• question_answer16) Some charge is being given to a conductor then its potential is:                               [AIPMT 2002]

A)
maximum at surface

B)
maximum at centre

C)
same throughout the conductor

D)
maximum somewhere between surface and centre

• question_answer17) A capacitor of capacity ${{C}_{1}}$ is charged upto potential V volt and then connected in parallel to an uncharged capacitor of capacity ${{C}_{2}}$. The final potential difference across each capacitor will be: [AIPMT 2002]

A)
$\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}$

B)
$\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}$

C)
$\left( 1+\frac{{{C}_{2}}}{{{C}_{1}}} \right)V$

D)
$\left( 1-\frac{{{C}_{2}}}{{{C}_{1}}} \right)V$

• question_answer18) Identical charges $(-q)$ are placed at each corners of a cube of side b, then the electrostatic potential energy of charge $(+q)$ placed at the centre of the cube will be:

A)
$-\frac{4\sqrt{2}{{q}^{2}}}{\pi {{\varepsilon }_{0}}}$

B)
$\frac{8\sqrt{2}{{q}^{2}}}{\pi {{\varepsilon }_{0}}b}$

C)
$-\frac{4{{q}^{2}}}{\sqrt{3}\pi {{\varepsilon }_{0}}b}$

D)
$\frac{8\sqrt{2}{{q}^{2}}}{4\pi {{\varepsilon }_{0}}b}$

• question_answer19) An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb force $\vec{F}$ between the two is: [AIPMT 2003]

A)
$k\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}$

B)
$-k\,\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}$

C)
$k\frac{{{e}^{2}}}{{{r}^{2}}}\hat{r}$

D)
$-k\frac{{{e}^{2}}}{{{r}^{3}}}\hat{r}$

• question_answer20) A charge q is located at the centre of a cube. The electric flux through any face is:   [AIPMT 2003]

A)
$\frac{\pi q}{6(4\pi {{\varepsilon }_{0}})}$

B)
$\frac{q}{6(4\pi {{\varepsilon }_{0}})}$

C)
$\frac{2\pi q}{6(4\pi {{\varepsilon }_{0}})}$

D)
$\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}$

• question_answer21) Three capacitors each of capacity $4\,\mu F$ are to be connected in such a way that the effective capacitance is $6\,\mu F$. This can be done by: [AIPMT 2003]

A)
connecting two in series and one in parallel

B)
connecting two in parallel and one in series

C)
connecting all of diem in series

D)
connecting all of them in parallel

• question_answer22) An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively: [AIPMT (S) 2004]

A)
$2qE$ and minimum.

B)
$qE$ and $pE$

C)
zero and minimum

D)
$qE$ and maximum

• question_answer23) A bullet of mass 2g is having a charge of $2\,\mu C$. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?               [AIPMT (S) 2004]

A)
5 kV

B)
50 kV

C)
5 V

D)
50 V

• question_answer24)  A network of four capacitors of capacity equal to ${{C}_{1}}=C,\text{ }{{C}_{2}}=2C,\text{ }{{C}_{3}}=3C$ and ${{C}_{4}}=4C$ are connected to a battery as shown in the figure The ratio of the charges on ${{C}_{2}}$ an ${{C}_{4}}$ is: [AIPMT (S) 2005]

A)
$\frac{22}{3}$

B)
$\frac{3}{22}$

C)
$\frac{7}{4}$

D)
$\frac{4}{7}$

• question_answer25) As per this diagram a point charge +q is placed at the origin O. Work done in taking another point chargeQ  from the point A [co-ordinates $(0,\,\,a)$] to another points [co-ordinates $(a,\text{ }0)$] along the straight path AB is:                  [AIPMT (S) 2005]

A)
zero

B)
$\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}a$

C)
$\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\cdot \frac{a}{\sqrt{2}}$

D)
$\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}a$

• question_answer26)  As a result of change in the magnetic flux linked to the closed loop shown in the figure, an emf V volt is induced in the loop. The work done (joules) in taking a charge Q coulomb once along the loop is: [AIPMT (S) 2005]

A)
QV

B)
zero

C)
2 QV

D)
QV/2

• question_answer27)  Two charges ${{q}_{1}}$ and ${{q}_{2}}$ are placed 30 cm apart as shown in the figure. A third charge ${{q}_{3}}$ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{{q}_{3}}}{4\pi {{\varepsilon }_{0}}}\,k,$ where k is:                                               [AIPMT (S) 2005]

A)
$8\,{{q}_{2}}$

B)
$8\,{{q}_{1}}$

C)
$6\,{{q}_{2}}$

D)
$6\,{{q}_{1}}$

• question_answer28) An electric dipole of moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by ${{90}^{o}}$ is. [AIPMT (S) 2006]

A)
$\sqrt{2}\,pE$

B)
$\frac{pE}{2}$

C)
$2\text{ }pE$

D)
pE

• question_answer29) A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:  [AIPMT (S) 2006]

A)
decreases

B)
does not change

C)
becomes zero

D)
increases

• question_answer30)  A square surface of side L m is in the plane of the paper. A uniform electric field $\vec{E}$ (V/m), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is: [AIPMT (S) 2006]

A)
$E{{L}^{2}}/(2{{\varepsilon }_{0}})$

B)
$E{{L}^{2}}/2$

C)
zero

D)
$E{{L}^{2}}$

• question_answer31) Three point charges $+q,-2q$ and $+q$ are placed at points $(x=0,y=a,z=0),$ $(x=0,y=0,z=0)$ and $(x=a,y=0,z=0),$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are: [AIPMT (S) 2007]

A)
$\sqrt{2}\,qa$ along $+y$ direction

B)
$\sqrt{2}\,qa$ along the line joining points $(x=0,y=0,z=0)$         and       $(x=a,y=a,z=0)$

C)
$qa$ along the line joining points $(x=0,y=0,z=0)$           and       $(x=a,y=a,z=0)$

D)
$\sqrt{2}\,qa$ along $+x$ direction

• question_answer32)  Two condensers, one of capacity C and the other of capacity $\frac{C}{2},$ are connected to a V volt battery, as shown. The work done in charging fully both the condensers is:                    [AIPMT (S) 2007]

A)
$2\,C{{V}^{2}}$

B)
$\frac{1}{4}\,C{{V}^{2}}$

C)
$\frac{3}{4}\,C{{V}^{2}}$

D)
$\frac{1}{2}\,C{{V}^{2}}$

• question_answer33)  A hollow cylinder has a charge q coulomb within it. If $\phi$ is the electric flux in unit of voltmeter associated with the curved surface B, the  flux linked with the plane surface A in unit of voltmeter will be :     [AIPMT (S) 2007]

A)
$\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)$

B)
$\frac{q}{2\,{{\varepsilon }_{0}}}$

C)
$\frac{\phi }{3}$

D)
$\frac{q}{{{\varepsilon }_{0}}}-\phi$

• question_answer34)  Charges $+q$ and $-q$ are placed at points A and B respectively which are a distance 2 L apart, C is the midpoint between A and S. The work done in moving a charge +Q along the semicircle CRD is:[AIPMT (S) 2007]

A)
$\frac{qQ}{4\pi {{\varepsilon }_{0}}L}$

B)
$\frac{qQ}{2\pi {{\varepsilon }_{0}}L}$

C)
$\frac{qQ}{6\pi {{\varepsilon }_{0}}L}$

D)
$-\frac{qQ}{6\pi {{\varepsilon }_{0}}L}$

• question_answer35) The electric potential at a point in free space due to a charge Q coulomb is $Q\times {{10}^{11}}V$. The electric field at that point is  [AIPMPT (S) 2008]

A)
$4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}V/m$

B)
$12\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}V/m$

C)
$4\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}V/m$

D)
$12\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}V/m$

• question_answer36) The energy required to charge a parallel plate condenser of plate separation a and plate area of cross-section A such that the uniform electric field between the plates is E, is   [AIPMPT (S) 2008]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}/Ad$

B)
${{\varepsilon }_{0}}{{E}^{2}}/Ad$

C)
${{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

• question_answer37) Three concentric spherical shells have radii a, b and $c(a<b<c)$ and have surface charge densities   $\sigma ,\,-\sigma$ and $\sigma$ respectively.   If ${{V}_{A}},\,{{V}_{B}}$ and ${{V}_{C}}$ denote the potentials of the three shells, then for $C=a+b,$ we have [AIPMT (S) 2009]

A)
${{V}_{A}}={{V}_{C}}\ne {{V}_{B}}$

B)
${{V}_{C}}={{V}_{B}}\ne {{V}_{A}}$

C)
${{V}_{C}}\ne {{V}_{B}}\ne {{V}_{A}}$

D)
${{V}_{C}}={{V}_{B}}={{V}_{A}}$

• question_answer38) A student measures the terminal potential difference (V) of a cell (of emf s and internal resistance r) as a function of the current (I) flowing through it. The slope and intercept of the graph between V and I, then respectively, equal      [AIPMT (S) 2009]

A)
$\varepsilon$ and $-r$

B)
$-r$ and $\varepsilon$

C)
$r$ and $-\,\varepsilon$

D)
$-\,\varepsilon$ and $r$

• question_answer39) Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The [Capacitance and breakdown voltage of the combination will be    [AIPMT (S) 2009]

A)
$\frac{C}{3},\,\frac{V}{3}$

B)
$3C,\,\,\frac{V}{3}$

C)
$\frac{C}{3},\,3V$

D)
$3C,\,3V$

• question_answer40) The electric potential at a point $(x,\text{ }y,\text{ }z)$ is given by $V=-{{x}^{2}}\,y-x{{z}^{3}}+4$ The electric field $\vec{E}$ at that point is [AIPMT (S) 2009]

A)
$\vec{E}=\hat{i}\,(2xy+{{z}^{3}})+\hat{j}\,{{x}^{2}}+\hat{k}\,3x{{z}^{2}}$

B)
$\vec{E}=\hat{i}\,2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}\,(3xz-{{y}^{2}})$

C)
$\vec{E}=\hat{i}\,{{z}^{3}}+\hat{j}\,xyz+\hat{k}\,{{z}^{2}}$

D)
$\vec{E}\,=\,\hat{i}\,(2xy-{{z}^{3}})+\hat{j}\,x{{y}^{2}}+\hat{k}\,3{{z}^{2}}x$

• question_answer41) The mean free path of electrons in a metal is $4\times {{10}^{-8}}\,m$. The electric field which can give on an average 2 eV energy to an electron in the metal will be in unit of $V{{m}^{-1}}$               [AIPMT (S) 2009]

A)
$8\times {{10}^{7}}$

B)
$5\times {{10}^{-11}}$

C)
$8\times {{10}^{-11}}$

D)
$5\times {{10}^{7}}$

• question_answer42) Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)   [AIPMT (S) 2010]

A)
$\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}$

B)
$\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{e}^{2}}}{{{d}^{2}}}}$

C)
$\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}}$

D)
$\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{q}^{2}}}$

• question_answer43)  A square surface of side L metre in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same place at an angle $\theta$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of $V-m$, is                [AIPMT (S) 2010]

A)
$E{{L}^{2}}$

B)
$E{{L}^{2}}\cos \,\theta$

C)
$E{{L}^{2}}\sin \,\theta$

D)
0

• question_answer44) A series combination of n1 capacitors, each of value ${{C}_{1}},$ is charged by a source of potential difference 4V. When another parallel combination of ${{n}_{2}}$ capacitors, each of value ${{C}_{2}},$ is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of ${{C}_{2}},$ in terms of ${{C}_{1}},$ is then                      [AIPMT (S) 2010]

A)
$\frac{2{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}}$

B)
$16\frac{{{n}_{2}}}{{{n}_{1}}\,}{{C}_{1}}$

C)
$2\frac{{{n}_{2}}}{{{n}_{1}}\,}{{C}_{1}}$

D)
$\frac{16{{C}_{1}}}{{{n}_{1}}\,{{n}_{2}}\,}$

• question_answer45) Two parallel metal plates having charges $+Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will [AIPMT (M) 2010]

A)
become zero

B)
increase

C)
decrease

D)
remain same

• question_answer46) The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is           [AIPMT (M) 2010]

A)
zero

B)
E

C)
$\frac{E}{2}$

D)
$\frac{E}{3}$

• question_answer47) The electric potential V at any point $(x,y,z),$ all in metres in space is given by $V=4{{x}^{2}}$ volt. The electric field at the point $(1,0,2)$ in volt/metre is [AIPMT (M) 2011]

A)
8 along positive .X-axis

B)
16 along negative X-axis

C)
16 along positive X-axis

D)
8 along negative X-axis

• question_answer48)  Three charges, each $+q,$ are placed at the comers of an isosceles triangle ABC of sides Be and AC, 2a. D and E are the mid points of Be and CA. The work done in taking a charge Q from D to E is [AIPMT (M) 2011]

A)
$\frac{eqQ}{8\pi {{\varepsilon }_{0}}a}$

B)
$\frac{qQ}{4\pi {{\varepsilon }_{0}}a}$

C)
zero

D)
$\frac{3qQ}{4\pi {{\varepsilon }_{0}}a}$

• question_answer49) A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $A({{m}^{2}})$ the energy (joule) stored in the condenser is [AIPMT (S) 2011]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{\varepsilon }_{0}}EAd$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

• question_answer50) A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will    [AIPMT (S) 2011]

A)
be reduced to half

B)
remain the same

C)
be doubled

D)
increase four time

• question_answer51)  Pour electric charges $+q,+q,-q$ and $-q$ are placed at the comers of a square of side 2L (see figure). The electric potential at point A, mid-way between the two charges $+q$ and $+q,$ is [AIPMT (S) 2011]

A)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2q}{L}\left( 1+\frac{1}{\sqrt{5}} \right)$

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2q}{L}\left( 1-\frac{1}{\sqrt{5}} \right)$

C)
zero

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2q}{L}\left( 1+\sqrt{5} \right)$

• question_answer52) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron [AIPMT (S) 2011]

A)
speed will decrease

B)
speed will increase

C)
will turn towards left of direction of motion

D)
will turn towards right of direction a motion

• question_answer53) A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $A({{m}^{2}})$ the energy (joule) stored in the condenser is [AIPMT (S) 2011]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{\varepsilon }_{0}}EAd$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

• question_answer54) A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is [AIPMT (M) 2012]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{\varepsilon }_{0}}EAd$

• question_answer55) A cell having an emf e and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by [AIPMT (M) 2012]

A)

B)

C)

D)

• question_answer56) An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta ={{90}^{0}},$ the torque and the potential energy of the dipole will respectively be [AIPMT (S) 2012]

A)
$pE\sin \theta ,\,-pE\cos \theta$

B)
$pE\sin \theta ,-2\,pE\cos \theta$

C)
$pE\sin \theta ,-2pE\cos \theta$

D)
$pE\cos \theta ,-pE\sin \theta$

• question_answer57) Four point charges $-Q,\,-q,\text{ }2q$ and $2Q$ are placed, one at each comer of the square. The relation between Q and q for which the potential at the centre of the square is zero, is [AIPMT(S) 2012]

A)
$Q=-q$

B)
$Q=-\frac{1}{q}$

C)
$Q=q$

D)
$Q=\frac{1}{q}$

• question_answer58) What is the through a cube of side a if a point charge of q is a one of its corner? [AIPMT (S) 2012]

A)
$\frac{2q}{{{\varepsilon }_{0}}}$

B)
$\frac{q}{8{{\varepsilon }_{0}}}$

C)
$\frac{q}{{{\varepsilon }_{0}}}$

D)
$\frac{q}{2{{\varepsilon }_{0}}}6{{a}^{2}}$

• question_answer59)  Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become.    [NEET 2013]

A)
${{\left( \frac{1}{\sqrt{2}} \right)}^{2}}$

B)
$\left( \frac{r}{\sqrt[3]{2}} \right)$

C)
$\left( \frac{2r}{\sqrt{3}} \right)$

D)
$\left( \frac{2r}{3} \right)$

• question_answer60)  A, B and C are three points in a uniform electric field. The electric potential is        [NEET 2013]

A)
maximum at A

B)
maximum at B

C)
maximum at C

D)
same at all the three points A, B and C A

• question_answer61) In a region, the potential is represented by $V(x,\,y,\,z)=6x-8xy-8y+6yz,$ where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point $(1,\text{ }1,\text{ }1)$ is           [NEET 2014]

A)
$6\sqrt{5}N$

B)
$30\,N$

C)
$24\,N$

D)
$4\sqrt{35}N$

• question_answer62)  Two thin dielectric slabs of dielectric constants ${{K}_{1}}$ and ${{K}_{2}}({{K}_{1}}<{{K}_{2}})$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by                [NEET 2014]

A)

B)

C)

D)

• question_answer63) A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are   [NEET 2014]

A)
zero and $\frac{Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}$

B)
$\frac{Q}{4\pi {{\varepsilon }_{0}}R}$ and zero

C)
$\frac{Q}{4\pi {{\varepsilon }_{0}}R}$ and $\frac{Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}$

D)
Both are zero

• question_answer64) A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?                     [NEET 2015]

A)
The potential difference between the plates decreases K times

B)
The energy stored in the capacitor decreases K times

C)
The change in energy stored is $\frac{1}{2}C{{V}^{2}}\left( \frac{1}{K}-1 \right)$

D)
The charge on the capacitor is not conserved

• question_answer65) The electric field in a certain region is acting radially outward and is given by $E=Ar.\text{ }A$. charge contained in a sphere of radius $'a'$ centred at the origin of the field' will be given by [NEET 2015]

A)
$4\pi {{\varepsilon }_{0}}A{{a}^{2}}$

B)
$A{{\varepsilon }_{0}}{{a}^{2}}$

C)
$A\pi {{\varepsilon }_{0}}A{{a}^{3}}$

D)
${{\varepsilon }_{0}}A{{a}^{3}}$

• question_answer66) If potential (in volts) in a region is expressed as$V(x,y,z)=6xy-y+2yz,$ the electric field (in N/C) at point $(1,1,0)$is           [NEET (Re) 2015]

A)
$-(3\hat{i}+5\hat{j}+3\hat{k})$

B)
$-(6\hat{i}+5\hat{j}+2\hat{k})$

C)
$-(2\hat{i}+3\hat{j}+\hat{k})$

D)
$-(6\hat{i}+9\hat{j}+\hat{k})$

• question_answer67) A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is    [NEET (Re) 2015]

A)
$\frac{{{C}^{2}}{{V}^{2}}}{2d}$

B)
$\frac{C{{V}^{2}}}{2d}$

C)
$\frac{C{{V}^{2}}}{d}$

D)
$\frac{{{C}^{2}}{{V}^{2}}}{2{{d}^{2}}}$

• question_answer68)  A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:                                              [NEET - 2016]

A)
0%

B)
20%

C)
75%

D)
80%

• question_answer69) Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\,(d<<l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as: [NEET - 2016]

A)
$v\propto {{x}^{\frac{1}{2}}}$

B)
$v\propto x$

C)
$v\propto {{x}^{-\frac{1}{2}}}$

D)
$v\propto {{x}^{-1}}$

• question_answer70) A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system [NEET-2017]

A)
Increases by a factor of 2

B)
Increases by a factor of 4

C)
Decreases by a factor of 2

D)
Remains the same

• question_answer71) Suppose the charge of a proton and an electron differ slightly. One of them is $-\,e,$ the other is$(e+\Delta e)$. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of [Given mass of hydrogen${{m}_{h}}=1.67\times {{10}^{-27}}kg$] [NEET-2017]

A)
${{10}^{-47}}C$

B)
${{10}^{-20}}C$

C)
${{10}^{-23}}C$

D)
${{10}^{-37}}C$

• question_answer72)  The diagrams below show regions of equipotentials.                         [NEET-2017] A positive charge is moved from A to B in each diagram.

A)
Maximum work is required to move q in figure [b]

B)
Maximum work is required to move q in figure [c]

C)
In all the four cases the work done is the same

D)
Minimum work is required to move q in figure [a]

• question_answer73) An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is                [NEET - 2018]

A)
10 times greater

B)
5 times greater

C)
Smaller

D)
Equal

• question_answer74) The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is                      [NEET - 2018]

A)
Proportional to the square root of the distance between the plates

B)
Linearly proportional to the distance between the plates

C)
Independent of the distance between the plates

D)
Inversely proportional to the distance between the plates

• question_answer75) A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field$\overrightarrow{\text{E}}$. Due to the force q$\overrightarrow{\text{E}}$, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively      [NEET - 2018]

A)
1 m/s, 3.5 m/s

B)
1 m/s, 3 m/s

C)
2 m/s, 4 m/s

D)
1.5 m/s, 3 m/s

• question_answer76) A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:           [NEET 2019]

A)
Zero as r increases for r < R, increases as r increases for r > R

B)
Decreases as r increases for r < R and for r > R

C)
Increases as r increases for r < R and for r > R

D)
Zero as r increases for r < R, decreases as r increases for r > R

• question_answer77) Two parallel infinite line charges with linear charge densities +λ C/m and λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?                                 [NEET 2019]

A)
$\frac{\lambda }{\pi {{\in }_{0}}R}N/C$

B)
$\frac{\lambda }{2\pi {{\in }_{0}}R}N/C$

C)
Zero

D)
$\frac{2\lambda }{\pi {{\in }_{0}}R}N/C$

• question_answer78) Two point charges A and B, having charges +Q and Q respectively, are placed at certain distance apart and force acting between them is F. If 25 % charge of A is transferred to B, then force between the charges becomes-                   [NEET 2019]

A)
$\frac{16F}{9}$

B)
$\frac{4F}{3}$

C)
F

D)
$\frac{9F}{16}$

• question_answer79) In a certain region of space with volume$0.2\text{ }{{m}^{3}}$, the electric potential is found to be 5V throughout. The magnitude of electric field in this region is: [NEET 2020]

A)
0.5 N/C

B)
1 N/C

C)
5 N/C

D)
zero

• question_answer80) A short electric dipole has a dipole moment of $16\times {{10}^{9\text{ }}}C\text{ }m$. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of $60{}^\circ$ with the dipole axis is: $\left( \frac{1}{4\pi {{\in }_{0}}}=9\times {{10}^{9}}N\,{{m}^{2}}/{{C}^{2}} \right)$          [NEET 2020]

A)
200 V

B)
400 V

C)
zero

D)
50 V

• question_answer81) The capacitance of a parallel plate capacitor with air as medium is $6\mu F$. With the introduction of a dielectric medium, the capacitance becomes$30\mu F$. The permittivity of the medium is: $({{\in }_{0}}=8.85\times {{10}^{12}}{{C}^{2}}\text{ }{{N}^{1}}{{m}^{2}})$    [NEET 2020]

A)
$1.77\times {{10}^{12}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

B)
$0.44\times {{10}^{10}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

C)
$5.00\text{ }{{C}^{2}}{{N}^{1}}{{m}^{2}}$

D)
$0.44\times {{10}^{13}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

• question_answer82) A spherical conductor of radius 10 cm has a charge of $3.2\times {{10}^{7}}C$distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere?          [NEET 2020] $\left( \frac{1}{4\pi {{\in }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}/{{C}^{2}} \right)$

A)
$1.28\times {{10}^{5}}\,N/C$

B)
$1.28\times {{10}^{6}}\,N/C$

C)
$1.28\times {{10}^{7}}\,N/C$

D)
$1.28\times {{10}^{4}}\,N/C$


text:
# zbMATH — the first resource for mathematics

Quantized $$H_{\infty }$$ control for networked systems with communication constraints. (English) Zbl 1286.93163
Summary: The problem of quantized $$H_{\infty }$$ control for Networked Control Systems (NCSs) subject to time-varying delay and multiple packet dropouts is investigated in this paper. Both the control input and the measurement output signals are quantized before being transmitted and the quantized errors are described as sector bound uncertainties. The measurement channel and the control channel packet dropouts are considered simultaneously, and the stochastic variables satisfying Bernoulli random binary distribution are utilized to model the random multiple packet dropouts. Sufficient conditions for the existence of an observer-based controller are established to ensure the exponential mean-square stablility of the closed-loop system and achieve the optimal $$H_{\infty }$$ disturbance attenuation level. By using a globally convergent algorithm involving convex optimization, the nonconvex feasibility can be solved successfully. Finally, a numerical example is given to illustrate the effectiveness and applicability of the proposed method.

##### MSC:
 93E03 Stochastic systems in control theory (general) 93C55 Discrete-time control/observation systems 93E12 Identification in stochastic control theory 93B36 $$H^\infty$$-control
Full Text:
##### References:
 [1] Zhang, Stability of networked control systems, IEEE Control Syst. Mag. 21 (1) pp 84– (2001) [2] Yue, Guaranteed cost control of linear systems over networks with state and input quantisations, IET Contr. Theory Appl. 153 (6) pp 658– (2006) [3] Gao, H estimation for uncertain systems with limited communication capacity, IEEE Trans. Autom. Control 52 (11) pp 2070– (2007) · Zbl 1366.93155 [4] Chu, H quantized control for nonlinear networked control systems, Fuzzy Sets Syst. 174 (1) pp 99– (2011) · Zbl 1221.93139 [5] Lee , Y. S. Y. S. Moon W. H. Kwon Delay-dependent robust H control for uncertain systems with time-varying state-delay Proceedings of the 40th SICE Annual Conference 198 203 2001 [6] Fridman, Stability and guaranteed cost control of uncertain discrete delay systems, Int. J. Control 78 (4) pp 235– (2005) · Zbl 1083.93045 [7] Gao, New results on stability of discrete-time systems with time-varying state delay, IEEE Trans. Autom. Control 52 (2) pp 328– (2007) · Zbl 1366.39011 [8] Shao, New stability criteria for linear disctete-time systems with interval-like time-varying delays, IEEE Trans. Autom. Control 56 (3) pp 619– (2011) · Zbl 1368.93478 [9] Yan, Delay-range-dependent robust H filtering for uncertain linear systems with interval time-varying delays, Asian J. Control 13 (2) pp 356– (2011) · Zbl 1222.93227 [10] Sun, Optimal filtering for systems with multiple packet dropouts, IEEE Trans. Circuits Syst. II - Express Briefs 55 (7) pp 695– (2008) [11] Yang, Observer-based H for networked control systems with consecutive packet delays and losses, Int. J. Control, Autom. Syst. 8 (4) pp 769– (2010) [12] Wu, Desigen of networked control systems with packet dropouts, IEEE Trans. Autom. Control 52 (7) pp 1314– (2007) · Zbl 1366.93215 [13] Elia, Stabilitaion of linear systems with limited information, IEEE Trans. Autom. Control 46 (9) pp 1384– (2001) · Zbl 1059.93521 [14] Fu, The sector bound approach to quantized feedback control, IEEE Trans. Autom. Control 50 (2) pp 1698– (2005) · Zbl 1365.81064 [15] Fu , M. Y. L. H. Xie W. Z. Su Connections between quantized feedback control and quantized estimation 10th Int. Conf. on control, automation, robotics and vision 1413 1417 2008 [16] Coutinho, Input and output quantized feedback linear systems, IEEE Trans. Autom. Control 55 (3) pp 761– (2010) · Zbl 1368.93357 [17] Brockett, Quantized feedback stabilization of linear systems, IEEE Trans. Autom. Control 45 (7) pp 1279– (2000) · Zbl 0988.93069 [18] Liberzon, Hybrid feedback stabilization of systems with quantized signals, Automatica 39 (9) pp 1543– (2003) · Zbl 1030.93042 [19] Zhang, Quantized control design for impulsive fuzzy networked systems, IEEE Trans. Fuzzy Syst. 19 (6) pp 1153– (2011) [20] Yang, H control for networked systems with random communication delays, IEEE Trans. Autom. Control 51 (3) pp 511– (2006) · Zbl 1366.93167 [21] Xie, Output feedback H control of systems with parameter uncertainty, Int. J. Control 63 (4) pp 741– (1996) · Zbl 0841.93014 [22] Gao, A new delay system approach to network based control, Automatica 44 (1) pp 39– (2008) · Zbl 1138.93375 [23] Song, Networked H filtering for linear discrete-time systems, Inf. Sci. 181 (3) pp 686– (2011) · Zbl 1205.93096 [24] Hu, Stochastic optimal control and analysis of stability of networked control systems with long delay, Automatica 39 (2) pp 1877– (2003) · Zbl 1175.93240
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# xolotl: a fast and flexible neuronal simulator¶

xolotl is a fast single-compartment and multi-compartment simulator written in C++ with a MATLAB interface that you'll actually enjoy using.

Why use xolotl? This is why:

# xolotl is FAST¶

xolotl is written in C++, and it's fast. In our testing, it's more than 3 times faster than NEURON for single compartment neurons.

# xolotl is easy to use¶

Want to set up a Hodgkin-Huxley model, inject current, integrate it and plot the voltage trace? This is all you need:

x = xolotl;
x.I_ext = .2;
x.plot;

# xolotl has documentation¶

Unlike certain widely used NEURON simulators that shall remain nameless, xolotl has documentation that actually... exists.

This is what it looks like:

# xolotl lets you do this¶

xolotl lets you manipulate any parameter in any model and view the effects of changing that parameter in real time

# xolotl is fully programmable¶

xolotl is designed to be used from within MATLAB. It gives you the best of both worlds: the high performance of C++ compiled code with the rich power of all the toolboxes MATLAB has to offer. You can:

• write functions that pass models as arguments
• optimize parameters of neuron models using the Global Optimization Toolbox
• run simulations in parallel across multiple computers
• have a single script to run the simulation and analyze results

Hooked? Check out the quickstart to see how easy it is to use.


text:
# Quantitative Biology

#### NewsMore

ISSN 2095-4689 (Print)
ISSN 2095-4697 (Online)
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 For Selected: View Abstracts Download Citations Toggle Thumbnails
 Select Current progresses of 3D bioprinting based tissue engineering Zeyu Zhang, Xiu-Jie Wang Quant. Biol.    2017, 5 (2): 136-142.   DOI: 10.1007/s40484-017-0103-8 Abstract   HTML   PDF (610KB) Background: The shortage of available organs for transplantation is the major obstacle hindering the application of regenerative medicine, and has also become the desperate problem faced by more and more patients nowadays. The recent development and application of 3D printing technique in biological research (bioprinting) has revolutionized the tissue engineering methods, and become a promising solution for tissue regeneration.Results: In this review, we summarize the current application of bioprinting in producing tissues and organoids, and discuss the future directions and challenges of 3D bioprinting.Conclusions: Currently, 3D bioprinting is capable to generate patient-specialized bone, cartilage, blood vascular network, hepatic unit and other simple components/tissues, yet pure cell-based functional organs are still desired.
 Select Elastic restricted Boltzmann machines for cancer data analysis Sai Zhang, Muxuan Liang, Zhongjun Zhou, Chen Zhang, Ning Chen, Ting Chen, Jianyang Zeng Quant. Biol.    2017, 5 (2): 159-172.   DOI: 10.1007/s40484-017-0092-7 Abstract   HTML   PDF (247KB) Background: Restricted Boltzmann machines (RBMs) are endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties when dealing with approximation and inference issues. But little work has been developed to fully exploit the capacity of these models to analyze cancer data, e.g., cancer genomic, transcriptomic, proteomic and epigenomic data. On the other hand, in the cancer data analysis task, the number of features/predictors is usually much larger than the sample size, which is known as the$“p≫N ”$ problem and is also ubiquitous in other bioinformatics and computational biology fields. The $“p≫N ”$ problem puts the bias-variance trade-off in a more crucial place when designing statistical learning methods. However, to date, few RBM models have been particularly designed to address this issue. Methods: We propose a novel RBMs model, called elastic restricted Boltzmann machines (eRBMs), which incorporates the elastic regularization term into the likelihood function, to balance the model complexity and sensitivity. Facilitated by the classic contrastive divergence (CD) algorithm, we develop the elastic contrastive divergence (eCD) algorithm which can train eRBMs efficiently. Results: We obtain several theoretical results on the rationality and properties of our model. We further evaluate the power of our model based on a challenging task — predicting dichotomized survival time using the molecular profiling of tumors. The test results show that the prediction performance of eRBMs is much superior to that of the state-of-the-art methods. Conclusions: The proposed eRBMs are capable of dealing with the $“p≫ N”$ problems and have superior modeling performance over traditional methods. Our novel model is a promising method for future cancer data analysis.
 Select Bistability and oscillations in co-repressive synthetic microbial consortia Mehdi Sadeghpour, Alan Veliz-Cuba, Gábor Orosz, Krešimir Josić, Matthew R. Bennett Quant. Biol.    2017, 5 (1): 55-66.   DOI: 10.1007/s40484-017-0100-y Abstract   HTML   PDF (1445KB) Background: Synthetic microbial consortia are conglomerations of genetically engineered microbes programmed to cooperatively bring about population-level phenotypes. By coordinating their activity, the constituent strains can display emergent behaviors that are difficult to engineer into isogenic populations. To do so, strains are engineered to communicate with one another through intercellular signaling pathways that depend on cell density. Methods: Here, we used computational modeling to examine how the behavior of synthetic microbial consortia results from the interplay between population dynamics governed by cell growth and internal transcriptional dynamics governed by cell-cell signaling. Specifically, we examined a synthetic microbial consortium in which two strains each produce signals that down-regulate transcription in the other. Within a single strain this regulatory topology is called a “co-repressive toggle switch” and can lead to bistability. Results: We found that in co-repressive synthetic microbial consortia the existence and stability of different states depend on population-level dynamics. As the two strains passively compete for space within the colony, their relative fractions fluctuate and thus alter the strengths of intercellular signals. These fluctuations drive the consortium to alternative equilibria. Additionally, if the growth rates of the strains depend on their transcriptional states, an additional feedback loop is created that can generate oscillations. Conclusions: Our findings demonstrate that the dynamics of microbial consortia cannot be predicted from their regulatory topologies alone, but are also determined by interactions between the strains. Therefore, when designing synthetic microbial consortia that use intercellular signaling, one must account for growth variations caused by the production of protein. Cited: Crossref(1)
 Select Visualization of phage DNA degradation by a type I CRISPR-Cas system at the single-cell level Jingwen Guan, Xu Shi, Roberto Burgos, Lanying Zeng Quant. Biol.    2017, 5 (1): 67-75.   DOI: 10.1007/s40484-017-0099-0 Abstract   HTML   PDF (1177KB) Background: The CRISPR-Cas system is a widespread prokaryotic defense system which targets and cleaves invasive nucleic acids, such as plasmids or viruses. So far, a great number of studies have focused on the components and mechanisms of this system, however, a direct visualization of CRISPR-Cas degrading invading DNA in real-time has not yet been studied at the single-cell level. Methods: In this study, we fluorescently label phage lambda DNA in vivo, and track the labeled DNA over time to characterize DNA degradation at the single-cell level. Results: At the bulk level, the lysogenization frequency of cells harboring CRISPR plasmids decreases significantly compared to cells with a non-CRISPR control. At the single-cell level, host cells with CRISPR activity are unperturbed by phage infection, maintaining normal growth like uninfected cells, where the efficiency of our anti-lambda CRISPR system is around 26%. During the course of time-lapse movies, the average fluorescence of invasive phage DNA in cells with CRISPR activity, decays more rapidly compared to cells without, and phage DNA is fully degraded by around 44 minutes on average. Moreover, the degradation appears to be independent of cell size or the phage DNA ejection site suggesting that Cas proteins are dispersed in sufficient quantities throughout the cell. Conclusions: With the CRISPR-Cas visualization system we developed, we are able to examine and characterize how a CRISPR system degrades invading phage DNA at the single-cell level. This work provides direct evidence and improves the current understanding on how CRISPR breaks down invading DNA.
 Select Differential expression analyses for single-cell RNA-Seq: old questions on new data Zhun Miao, Xuegong Zhang Quant. Biol.    2016, 4 (4): 243-260.   DOI: 10.1007/s40484-016-0089-7 Abstract   HTML   PDF (3763KB) Background: Single-cell RNA sequencing (scRNA-seq) is an emerging technology that enables high resolution detection of heterogeneities between cells. One important application of scRNA-seq data is to detect differential expression (DE) of genes. Currently, some researchers still use DE analysis methods developed for bulk RNA-Seq data on single-cell data, and some new methods for scRNA-seq data have also been developed. Bulk and single-cell RNA-seq data have different characteristics. A systematic evaluation of the two types of methods on scRNA-seq data is needed. Results: In this study, we conducted a series of experiments on scRNA-seq data to quantitatively evaluate 14 popular DE analysis methods, including both of traditional methods developed for bulk RNA-seq data and new methods specifically designed for scRNA-seq data. We obtained observations and recommendations for the methods under different situations. Conclusions: DE analysis methods should be chosen for scRNA-seq data with great caution with regard to different situations of data. Different strategies should be taken for data with different sample sizes and/or different strengths of the expected signals. Several methods for scRNA-seq data show advantages in some aspects, and DEGSeq tends to outperform other methods with respect to consistency, reproducibility and accuracy of predictions on scRNA-seq data.
 Select A resistant method for landmark-based analysis of individual asymmetry in two dimensions Sebastián Torcida, Paula Gonzalez, Federico Lotto Quant. Biol.    2016, 4 (4): 270-282.   DOI: 10.1007/s40484-016-0086-x Abstract   HTML   PDF (1236KB) Background: Symmetry of biological structures can be thought as the repetition of their parts in different positions and orientations. Asymmetry analyses, therefore, focuses on identifying and measuring the location and extent of symmetry departures in such structures. In the context of geometric morphometrics, a key step when studying morphological variation is the estimation of the symmetric shape. The standard procedure uses the least-squares Procrustes superimposition, which by averaging shape differences often underestimates the symmetry departures thus leading to an inaccurate description of the asymmetry pattern. Moreover, the corresponding asymmetry values are neither geometrically intuitive nor visually perceivable. Methods: In this work, a resistant method for landmark-based asymmetry analysis of individual bilateral symmetric structures in 2D is introduced. A geometrical derivation of this new approach is offered, while its advantages in comparison with the standard method are examined and discussed through a few illustrative examples. Results: Experimental tests on both artificial and real data show that asymmetry is more effectively measured by using the resistant method because the underlying symmetric shape is better estimated. Therefore, the most asymmetric (respectively symmetric) landmarks are better determined through their large (respectively small) residuals. The percentage of asymmetry that is accounted for by each landmark is an additional revealing measure the new method offers which agrees with the displayed results while helping in their biological interpretation. Conclusions: The resistant method is a useful exploratory tool for analyzing shape asymmetry in 2D, and it might be the preferable method whenever a non homogeneous deformation of bilateral symmetric structures is possible. By offering a more detailed and rather exhaustive explanation of the asymmetry pattern, this new approach will hopefully contribute to improve the quality of biological or developmental inferences.
 Select XFEL data analysis for structural biology Haiguang Liu, John C. H. Spence Quant. Biol.    2016, 4 (3): 159-176.   DOI: 10.1007/s40484-016-0076-z Abstract   HTML   PDF (1880KB) X-ray Free Electron Lasers (XFELs) have advanced research in structure biology, by exploiting their ultra-short and bright X-ray pulses. The resulting “diffraction before destruction” experimental approach allows data collection to outrun radiation damage, a crucial factor that has often limited resolution in the structure determination of biological molecules. Since the first hard X-ray laser (the Linac Coherent Light Source (LCLS) at SLAC) commenced operation in 2009, serial femtosecond crystallography (SFX) has rapidly matured into a method for the structural analysis of nano- and micro-crystals. At the same time, single particle structure determination by coherent diffractive imaging, with one particle (such as a virus) per shot, has been under intense development. In this review we describe these applications of X-ray lasers in structural biology, with a focus particularly on aspects of data analysis for the computational research community. We summarize the key problems in data analysis and model reconstruction, and provide perspectives on future research using computational methods. Cited: Crossref(3)
 Select Advances in computational ChIA-PET data analysis Chao He, Guipeng Li, Diekidel M. Nadhir, Yang Chen, Xiaowo Wang, Michael Q. Zhang Quant. Biol.    2016, 4 (3): 217-225.   DOI: 10.1007/s40484-016-0080-3 Abstract   HTML   PDF (573KB) Genome-wide chromatin interaction analysis has become important for understanding 3D topological structure of a genome as well as for linking distal cis-regulatory elements to their target genes. Compared to the Hi-C method, chromatin interaction analysis by paired-end tag sequencing (ChIA-PET) is unique, in that one can interrogate thousands of chromatin interactions (in a genome) mediated by a specific protein of interest at high resolution and reasonable cost. However, because of the noisy nature of the data, efficient analytical tools have become necessary. Here, we review some new computational methods recently developed by us and compare them with other existing methods. Our intention is to help readers to better understand ChIA-PET results and to guide the users on selection of the most appropriate tools for their own projects. Cited: Crossref(2)
 Select De novo assembly of transcriptome from next-generation sequencing data Xuan Li, Yimeng Kong, Qiong-Yi Zhao, Yuan-Yuan Li, Pei Hao Quant. Biol.    2016, 4 (2): 94-105.   DOI: 10.1007/s40484-016-0069-y Abstract   HTML   PDF (212KB) Reconstruction of transcriptome by de novo assembly from next generation sequencing (NGS) short-sequence reads provides an essential mean to catalog expressed genes, identify splicing isoforms, and capture the expression detail of transcripts for organisms with no reference genome available. De novo transcriptome assembly faces many unique challenges, including alternative splicing, variable expression level covering a dynamic range of several orders of magnitude, artifacts introduced by reverse transcription, etc. In the current review, we illustrate the grand strategy in applying De Bruijn Graph (DBG) approach in de novo transcriptome assembly. We further analyze many parameters proven critical in transcriptome assembly using DBG. Among them, k-mer length, coverage depth of reads, genome complexity, performance of different programs are addressed in greater details. A multi-k-mer strategy balancing efficiency and sensitivity is discussed and highly recommended for de novo transcriptome assembly. Future direction points to the combination of NGS and third generation sequencing technology that would greatly enhance the power of de novo transcriptomics study. Cited: Crossref(1)
 Select Developing bioimaging and quantitative methods to study 3D genome Juntao Gao, Xusan Yang, Mohamed Nadhir Djekidel, Yang Wang, Peng Xi, Michael Q. Zhang Quant. Biol.    2016, 4 (2): 129-147.   DOI: 10.1007/s40484-016-0065-2 Abstract   HTML   PDF (2526KB) The recent advances in chromosome configuration capture (3C)-based series molecular methods and optical super-resolution (SR) techniques offer powerful tools to investigate three dimensional (3D) genomic structure in prokaryotic and eukaryotic cell nucleus. In this review, we focus on the progress during the last decade in this exciting field. Here we at first introduce briefly genome organization at chromosome, domain and sub-domain level, respectively; then we provide a short introduction to various super-resolution microscopy techniques which can be employed to detect genome 3D structure. We also reviewed the progress of quantitative and visualization tools to evaluate and visualize chromatin interactions in 3D genome derived from Hi-C data. We end up with the discussion that imaging methods and 3C-based molecular methods are not mutually exclusive - - - - actually they are complemental to each other and can be combined together to study 3D genome organization. Cited: Crossref(2)
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text:
# Floors and square roots

Algebra Level 4

Compute the largest integer $$x$$ such that $$\left \lfloor \sqrt{ \left \lfloor \sqrt{ \lfloor \sqrt{x} \rfloor} \right \rfloor} \right \rfloor = 2$$.

×


text:
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# In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD. - CBSE Class 10 - Mathematics

ConceptSimilarity Examples and Solutions

#### Question

In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD.

#### Solution

We have,
AB = 1 m = 100 cm, AC = 75 cm and BD = 125 cm

In ∆BAC and ∆BDA, we have

∠BAC = ∠BDA [Each equal to 90º] and, ∠B = ∠B

So, by AA-criterion of similarity, we have

∆BAC ~ ∆BDA

\Rightarrow \frac{BA}{BD}=\frac{AC}{AD}

\Rightarrow \frac{100}{125}=\frac{75}{AD}

\Rightarrow AD=\frac{125\times 75}{100}cm=93.75cm

Is there an error in this question or solution?

#### Video TutorialsVIEW ALL [1]

Solution In figure, ∠CAB = 90º and AD ⊥ BC. If AC = 75 cm, AB = 1 m and BD = 1.25 m, find AD. Concept: Similarity Examples and Solutions.
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