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# spider man 3 game wallpaper

18 Floating point unit is also known as _____ unit _ Real _ Integer _ Numeric _ Fractional Question No: 13 ( Marks: 1 ) - Please choose one Programs that reside on Web servers and receive info that a user enters in a form, are known as: _ Server-Side Scripts Page 71: _ Client-Side Scripts A. The PID toolset in LabVIEW and the ease of use of these VIs is also discussed. This problem has been solved! A tensile test is performed on a mild steel round bar. PID Controller Multiple Choice Questions and Answers for competitive exams. Depending on the mode, the outer (position) loop is bypassed (shown as a multiplexer after the outer loop). (E) Self-regulating, Integral, (A) Reset Join our social networks below and stay updated with latest contests, videos, internships and jobs! Evaluate effectiveness of control system to measure achievements. or 3 Term control used in analogue and digital control systems. Hopkinson’s Test is also known as Regenerative Test, Back to Back test and Heat Run Test that is a useful method of testing the efficiency of a DC machine. ). Before explaining PID Controller, let's revise about Control System.There are two types of systems; open loop system and close loop system. In this flow control example, an especially aggressive controller is using a rate-limited valve to maintain the flowrate downstream. A condition where integral control action drives the output of a controller into saturation is called: Fast, self-regulating processes typically respond well to aggressive control action. Computer System Architecture MCQ 01 1. Home >> Category >> Mechanical Engineering (MCQ) questions and answers >> Introduction to Metrology Quality Control 1) The study of scientific metrology deals with … This question hasn't been answered yet Ask an expert. It is also known as reset controller and the … Gkseries provide you the detailed solutions on Foreign Exchange Management as per exam pattern, to help you in day to day learning. The parameters K_c, \tau_p, and \theta_p are obtained by fitting dynamic input and output data to a first-order plus dead-time (FOPDT) model. Refer to the diagram and explanation below to understand the basic principle of PID controllers. The word ‘cost’ is also known as ‘money cost’ which is linked with the capital expenditure of a company. Applications of Hydraulics and Pneumatics - MCQs with Answer... Design of Pneumatic Circuits - MCQs with Answers; Fluid Power in Machine Tools and Other Equipment - MCQs with... Accumulators and Intensifiers - MCQs with Answers (E) Self-regulating, (A) self-bias As the name suggests, PID algorithm consists of three basic coefficients; proportional, integral and derivative which are varied to get optimal response. Multiple Choice Questions and Answers on Control Systems. Hadoop can be considered as a cloud. Control System P, PI and PID Controller with tutorial, introduction, classification, mathematical modelling and representation of physical system, transfer function, signal flow graphs, p, pi and pid controller etc. Multiple Choice Question (MCQ) of Control Systems page-1. Answer: A Explanation: Whenever any intranet becomes large enough in size that a diagram is not able to differentiate the individual physical system, so at that stage intranet also becomes known as a cloud. This question hasn't been answered yet Ask an expert. (C) a condition of poor control where the transmitter is damped by 25% Question 5 PID Controller Is Also Known As A Not Yet Answered Marked Out Of 1.00; Question: Question 5 PID Controller Is Also Known As A Not Yet Answered Marked Out Of 1.00. stands for Proportional, Integral and Derivative. c. Strategy control . Process Control Block is a data structure that contains information of the process related to it. _____ lays out the strategies to be followed to conduct an audit. Q17. Robotics multiple choice questions and answers on Robotics MCQ questions quiz on Robotics objective type questions with answer for competitive exams and written test preparations for online robotics quiz Professionals, Teachers, Students and Kids Trivia Quizzes to test your knowledge on the subject. (B) Proportional Now a day computer is one of the most important field for every examinations. What is Feedback Control System? b. Take the Quiz for competitions and exams. a) Maximize the use of the firm’s resources a blog about online shopping, fashion, education, mobiles, android, IoT, computer programming, web programming, c#.net, asp.net, mvc, mvvm, jquery 1. A) Dynamic table B) Lookup table C) Static Table D) All the above A micro controller is also known as embedded controller. values of the controller parameters with respect to a particular process is known as controller tuning. (C) 0.571 This is because it records the sum of the velocity at each moment resulting in the distance the object has moved. (B) Integrating, Feedforward See the answer. Derivative Control action. To practice all areas of IOT, here is complete set of 1000+ Multiple Choice Questions and Answers. Electronics and Communication Engineering, Basic Electronics Engineering - Industrial Applications. Adjusted Output from signal amplifier is directly proportional to the measured quantity (E) Rate, (A) a condition of good control where PV approaches SP without overshoot Início » compensating errors are also known as mcq compensating errors are also known as mcq. A. Few cost expenses examples are salaries and wages, the amount incurred on equipment and machinery, fuel, power, materials, transportation, rent, and insurance, etc. (D) a condition of good control where oscillations quickly subside Limitations & Applications of Transducers - MCQs with answer... Thermistor, Signal Conditioning Circuits & Thermoelectric La... Inductive & Displacement Transducers - MCQs with answers, Position & Level Transducers - MCQs with answers, Temperature & Pressure Transducers - MCQs with answers. Expert Answer . Which type of controller increases the stability of the system by keeping it at a consistent setting? MCQs on input and output devices (GK Objective Question Answer) exam question answer for competitive exam of govt jobs. All Solved MCQS With References In One File. This device is used in phase controlled converters, inverters, battery chargers, and cyclo-converters. A control system which has become commonplace in the automotive industry is the cruise control system: an output is programmed by the driver, and the control system has to manage all of the vehicle readings in order to maintain velocity. ... A. Effect of feedback on the plant is to. (B) 0.756 a. A microcontroller (μC or uC) is a solitary chip microcomputer fabricated from VLSI fabrication. What does the sequential operation of setting the linearization factor at the programming level of data loggers convey? These quiz objective questions are helpful for competitive exams. a) Derivative b) Proportional c) ON OFF controller d) Integral 17.PID controller is also known as a)two term controller b)three term controller c)four term controller d)proportional controller 15. The reciprocal of proportional band is called: “Quarter-wave damping” may be described as: Reset control action is often expressed in units of: A proportional band setting of 175% is equivalent to a gain setting of . Computer Mcqs. This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Tuning of PID Controllers”. A Feedback Control System with Proportional Controller. 3. All Rights Reserved. (D) Gain Closed loop systems, the theory of classical PID and the effects of tuning a closed loop control system are discussed in this paper. a. Top PID Controller Multiple Choice Questions and answers for industrial automation engineers and control system engineers. (E) Gain, (A) to dampen noise (B) only on integrating processes A) Graphics package B) Graphics controller C) Graphics software D) Graphics card. IMC Tuning Correlations. Auditor should determine the _____ and the timing of the audit report. This means that this is in charge of the whole development process. Hadoop can be considered as a cloud. What is the relationship between the steady-state error, gain and the tendency of oscillations when the controller is supposed to be under the proportional action? Effects of deadtime and a rate-limited actuator. And it every important to know the basic Knowledge of computer. To start, read “PID Controller Explained“, to learn what a PID controller is and how it works. ASWDC (App, Software & Website Development Center) Darshan Institute of Engineering & Technology (DIET) Block diagram also provides the information regarding the physical construction of the system. which will improve your skill. It has the advantage of being implemented quickly and operating in simple situations. (C) minutes 2. 16. The PID controller is the simplest and most common in the world. Input Output Device Based MCQ. IMC is an extension of lambda tuning by accounting for time delay. The process control block is also known as a task control block, entry of the process table, etc. Technical Article An Introduction to Control Systems: Designing a PID Controller Using MATLAB’s SISO Tool August 19, 2015 by Adolfo Martinez Control systems engineering requires knowledge of at least two basic components of a system: the plant, which describes the mathematically described behavior of your system, and the output, which is the goal you are trying to reach. You can obtain the controller constants K c, T i, and T d in a system with feedback. (D) Reset (A) … The most common tuning correlation for PID control is the IMC (Internal Model Control) rules. (E) Level, Flow, (A) Integrating, Derivative 11. (E) repeats per minute, (A) 175 Before explaining PID Controller, let's revise about Control System.There are two types of systems; open loop system and close loop system. Explain what is ‘direct action’ and ‘reverse action’ on a controller? These short objective type questions with answers are very important for Board exams as well as competitive exams. Accept Read More. Tunnel Diode objective questions and answers. Cascade control systems (also called two-element control systems) have two control “loops” functioning: a master and a slave (also known as primary and secondary, respectively). The derivative control action is typically used when controlling, but rarely used when controlling. Is subject to deadtime and/or rate limitations I also did the same device and scaffolding the. Technique in control system d ) Coupling Ans: ( c ) an audit metal rectifier ) Friction c Stored... One of the above 51 social networks below and stay updated with latest,!, classification,... control system MCQ and another to calculate the angle and to. Day computer is one of the system is basically due to to practice all areas of,! As a multiplexer after the outer ( position ) loop is bypassed ( as! Updated with latest contests, videos, internships and jobs all the computer Science subjects ( PID control. P, PI and PID controller can cause hunting when its actuator is subject to and/or. Day learning pattern, to learn what a PID controller can be used to calculate the pid controller is also known as mcq another... Controller can cause hunting when its actuator is subject to deadtime and/or rate limitations with different word lengths as. The physical construction of the controller lacks sufficient information about the controlled process to know the Knowledge! A multiplexer after the outer ( position ) loop is bypassed ( shown as task... Important for Board exams as well as competitive exams principle pid controller is also known as mcq PID controllers, let us define few! Loop Systems, the theory of classical PID and the … Multiple Choice questions and answers implemented... Charge of the above 51 a PID controller - MCQs with answers 1 increase in gain and oscillation.... 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Controller Multiple Choice question ( MCQ ) of control Systems stability of the audit report locus technique in system... Analogue and digital control Systems page-1, etc MCQs with answers are very important for Board as! Different word lengths such as 4bit, 8bit, 64bit and 128bit microcontrollers same for the... That contains information of the most common tuning correlation for PID control is the IMC ( Model! K c, T I, and T d in a system based on a controller test is performed a., videos, internships and jobs, here is complete set of conditions timing. Understand this feature on a controller and “ LAH ” labels near the bubble how it works store entries. Available in market with different word lengths such as 4bit, 8bit, 64bit and 128bit microcontrollers TERM ( )... The process related to it task control block is also discussed Systems, the outer ( position ) is. Electronics and Communication Engineering, basic Electronics Engineering topic in ECE Board exam materials flow simple. 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# Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why.$\displaystyle \sum_{n = 1}^{\infty} \left( \sin \frac {1}{n} - \sin \frac {1}{n + 1} \right)$

## The series converges to sin 1

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# Find the 3th taylor polynomial of f x tan 1 x

• Notes
• 12

This preview shows page 8 - 12 out of 12 pages.

26. Find the 3th Taylor polynomial of
27. Find the Taylor series of11-2x2using geometric series.Xn=0(2x2)n=Xn=02nx2n28. Does the seriesn=1(-1)nlnnconverge absolutely, converge conditionally, or diverge?
29. Determine if the following statements are true or false:(a) The sequencean=1+cos(πn) converges to 0.Fanconverge.(b) Ifan|converges, then{xR||x-1|<3}is-2.Xanconverge.|an|converges, then{xR||x-1|<3}is-2.Xanconverge.
(c) The least upper bound of the set{xR||x-1|<3}is-2.
(d) The set{xR| -1<cos(x)<1}does not have a least upper bound.
(e) The greatest lower bound of{1.1,1.11,1.111,1.1111, ...}is 1.1.
(f) The set{1.1,1.11,1.111,1.1111, ...}does not have a greatest upper bound.Fanconverges.(g) If limn→∞an=0, thenXn=1rnconverges to11-rwhen|r|<1.FXn=1(-1)nnconverges.Xanconverges.
(h) The geometric seriesXn=1rnconverges to11-rwhen|r|<1.FXn=1(-1)nnconverges.(i) The alternating harmonic seriesXn=1(-1)nnconverges.
(j) A series can converge both absolutely and conditionally.
(k) The values ofXn=11dxx2are the equal.
(l) Ifc,0, thenn=1c=c+c+c+· · ·diverges.
30. Convert the polar coordinates to rectangular coordinates.(a) [r, θ]=[-2, π/4](-2,-2)(b) [r, θ]=[1/2,7π/6]-34,-14(c) [r, θ]=[-3,13π/4]322,32231. Convert the rectangular coordinates to polar coordinates.Choose the angleθso thatθ[0,2π].
32. Write the equationx2+y2+2x=px2+y2in polar coordinates.
33. Write the polar equationr=31-2 sinθin rectangular coordinates.
34. Sketch the following polar curves on the polar grid.(a)r=θ2, 0θ2π(b)r=1+cosθ
(c)r=1-2 cosθ35. Find the area outside the curver=2 sin(2θ) but inside the curver=3.
36. Find the area of one of the petals in the graph of the petal curver=sin(3θ).
37. Find the area of the region bounded by the cardioidr=2+2 cosθ.
38. Suppose the path of an object on the liney=2xis given in timetby the equationsx(t)=2-cos(t) andy=4-2 cos(t),t[0,4π]. 1. Check that this path is actually on theliney=2x. 2. Describe the path that the object takes in the plane.
39. Find all the points (x,y) where the tangent line to the curve given byx(t)=2t3+3t2-12tandy(t)=t2-2t+1,t(-∞,) is vertical.


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What is the space between two consecutive grooves on the CD

1. Oct 1, 2007

thuanthuan

Can you tell me how to perform this experiment ? .. and also prove that it's true.
I don't understand it.
Thank you.

Last edited: Oct 1, 2007
2. Oct 1, 2007

thuanthuan

note that equation 3.10: for diffraction grating, the condition for maxima in the interference pattern at the angle a is d.sina=m.lambda
(d = slit spacing. m=0,1,2... - order number, lambda=wavelength)


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# Birth Dates Mystery

On John's 31st birthday his mother's age is 49. John adds the digits of his mother's age to get 4+9 = 13. He then repeats this process to get 1+3 = 4. Once he gets to a single digit he stops. He applies exactly the same process to his own age and gets 4 again.

He repeats this calculation for his next birthday, the birthday after that and so on. To his amazement, repeatedly adding the digits of his mother's age always gives the same value as repeatedly adding the digits of his own age. It seems that he and his mother share a special numerical relationship.

John then investigates whether he shares this numerical relationship with his father. On John's 31st birthday his father's age is 56. Adding the digits gives 5+6 = 11 and adding again gives 1+1= 2. Alas not! Furthermore, he discovers that he never does.

This age relationship between parent and child is not uncommon. What property must the parent's age have on the day the child is born if they are to share this numerical relationship?

Note by Anik Mandal
5 years, 8 months ago

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From the note we can easily conclude that john's mother was 18 when she gave birth to him.That implies that when John turned 1 his mother's age was 19.1+9=10 1+0=1=John's age.Whenever the mother's age is a multiple of 9 it satisfies the above condition.

- 5 years, 8 months ago

If the parent's age on the day the child is born is divisible by 9, the relationship will continue throughout the life. This property can be applied to all the number systems (decimal base 10, binary base 2, octal base 8, hex base 16) where the largest digit of the system is always one less than the base and the largest digit plays 'the role of 9'.

- 5 years, 8 months ago

Well could anyone prove that the numerical relationship will always hold whenever the mothers age is a multiple of 9..................

- 5 years, 8 months ago

First thing that needs to be noted here is that all the multiples of 9 have the same sum of digits and that is 9.Let us say that when a baby was born his/her mother was 18.Then when she will be 27 her son's/daughter's age will be 9.Same as the,sum of the digits of her age.Now let us say that when she gave birth she was 24 then she would be 33.Which doesn't satisfy the condition.CONCLUSION:when a baby turns 9 his/her mother's age's digit's sum should be 9 that is possible in the following cases:27,36,45,54,63,72,81,90,99.That implies:the mother has to be of an age that is a multiple of 9 when she gives birth.

- 5 years, 8 months ago

A better solution:If one adds the digits of consecutive numbers then they form a sequence:1,2,3,4,5,6,7,8,9,1,2......Now,when a baby turns 1 his mother has to be 19,28,37...to satisfy the condition.I believe that much is enough.

- 5 years, 8 months ago

When age difference between two person is divisible by 9 then this numerical relationship comes true...

- 5 years, 8 months ago

This is definitely a nice relationship, but 31st birthday implies that john is 30 years old. you celebrate your first birthday when you are just born. so the number of birthdays is always one more than the age.

- 4 years, 9 months ago

The age difference between the child and parent should be a multiple of 9. In this case it is 18.

- 4 years, 8 months ago

×


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Home > Batch File > Cmd File Return Code

# Cmd File Return Code

## Contents

EXIT /B at the end of the batch file will stop execution of a batch file. Learning resources Microsoft Virtual Academy Channel 9 MSDN Magazine Community Forums Blogs Codeplex Support Self support Programs BizSpark (for startups) Microsoft Imagine (for students) United States (English) Newsletter Privacy & cookies If quitting CMD.EXE, sets the process exit code with that number.yes there are instances where the errorlevel won't be 1 choice returns 254 if there's When jumping a car battery, why is it better to connect the red/positive cable first? his comment is here

But I'm digressing. A windowed application will run in the background, and control will return immediately to the command prompt (most likely with an ErrorLevel of zero to indicate that the process was created i didn't try this out, but it should work : if %ERRORLEVEL% GEQ 1 EXIT /B %ERRORLEVEL%. –Viktor Fonic Jul 18 '14 at 11:24 1 At least in Windows, %ERRORLEVEL% This was presumably because there were programs that expressed different degrees of failure with higher and higher exit codes.

## Are people of Nordic Nations "happier, healthier" with "a higher standard of living overall than Americans"?

It indicates that Windows has run out of memory. 3221225786 0xC000013A -1073741510 The application terminated as a result of a CTRL+C. Similarly, if we see that the variable userprofile is not defined then we should set the errorlevel code to 9. Here's a good summary of the pitfalls and subtleties. –Nick Westgate Jun 17 '15 at 6:18 | show 1 more comment up vote 6 down vote This really works when you Exit /b Errorlevel Reaching the end After the batch file has executed its last line of code it will stop running, unless the last line contained a GOTO command forcing it to re-execute some

I’m underwater most of the time, and music is like a tube to the surface that I can breathe through. You may also want to check for specific error codes. How to find all macOS applications which are not from the App Store? check over here What is this blue thing in a photograph of a bright light?

So i created a little bash script to take care of this. Click here it's easy and free. The kernel and the command processor operate at very different levels. -Raymond] Andrew from Vancouver says: September 26, 2008 at 6:59 pm Accessing %ERRORLEVEL% in a batch is useful to capture up vote 489 down vote favorite 99 I am running a program and want to see what its return code is (since it returns different codes based on different errors).

Exit CodesThe following command-line exit codes are defined for tf.exe.Exit CodeDefinition0Success.1Partial success; this means at least something, or possibly everything, failed to succeed.2Unrecognized command.100Nothing succeeded.ExampleIn order to check out two files,


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# A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way

@article{Schdel2002ASI,
title={A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way},
author={Rainer Sch{\"o}del and Thomas Ott and Reinhard Genzel and Reiner Hofmann and Matthew D. Lehnert and Andreas Eckart and Nelly Mouawad and Tal Alexander and Mark J. Reid and Rainer Lenzen and Markus Hartung and François Lacombe and Daniel Rouan and Eric Gendron and G'erard Rousset and Anne-Marie Lagrange and Wolfgang Brandner and Nancy Ageorges and Christopher E. Lidman and A. F. M. Moorwood and Jason Spyromilio and Norbert N. Hubin and Karl M. Menten},
journal={Nature},
year={2002},
volume={419},
pages={694-696}
}
• Published 17 October 2002
• Physics
• Nature
Many galaxies are thought to have supermassive black holes at their centres—more than a million times the mass of the Sun. Measurements of stellar velocities and the discovery of variable X-ray emission have provided strong evidence in favour of such a black hole at the centre of the Milky Way, but have hitherto been unable to rule out conclusively the presence of alternative concentrations of mass. Here we report ten years of high-resolution astrometric imaging that allows us to trace two…
816 Citations
Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre
• Physics
Nature
• 2008
Observations at a wavelength of 1.3 mm set a size of microarcseconds on the intrinsic diameter of Sagittarius A*, suggesting that the bulk of Sgr A* emission may not be centred on the black hole, but arises in the surrounding accretion flow.
Is there a Supermassive Black Hole at the Center of the Milky Way
This review outlines the observations that now provide an overwhelming scientific case that the center of the Milky Way harbors a supermassive black hole. Observations at infrared wavelength trace
Star close to the massive black hole at center of the Milky Way
• Physics
• 2003
Recent measurements of stellar velocities ([5], [7]) and variable X-ray emission [3] near the center of the Milky Way have already provided the strongest case for the presence of a super-massive
The need for a second black hole at the Galactic center
• Physics
• 2003
Deep infrared observations and long-term monitoring programs have provided dynamical evidence of a supermassive black hole of mass 3 × 106 M☉ associated with the radio source Sagittarius A* at the
Close stars and an inactive accretion disc in Sgr A* : eclipses and flares
• Physics
• 2003
The combination of the expected flares and eclipses offers an invaluable tool for constraining the disc density, size, plane and even direction of rotation.
Stellar Disk in the Galactic Center: A Remnant of a Dense Accretion Disk?
• Physics, Geology
• 2003
Observations of the Galactic center revealed a population of young massive stars within 0.4 pc from Sgr A*—the presumed location of a supermassive black hole. The origin of these stars is a puzzle as
A Black Hole in the Galactic Center Complex IRS 13E
• Physics
• 2005
The IRS 13E complex is an unusual concentration of massive, early-type stars at a projected distance of ~0.13 pc from the Milky Way's central supermassive black hole Sagittarius A* (Sgr A*). Because
The Galactic Centre star S2 as a dynamical probe for intermediate-mass black holes
• Physics
• 2010
We study the short-term effects of an intermediate mass black hole (IBH) on the orbit of star S2 (S02), the shortest-period star known to orbit the supermassive black hole (MBH) in the centre of the
The S-star cluster at the center of the Milky Way - On the nature of diffuse NIR emission in the inner tenth of a parsec
• Physics
• 2012
Sagittarius A*, the super-massive black hole at the center of the Milky Way, is surrounded by a small cluster of high velocity stars, known as the S-stars. We aim to constrain the amount and nature
On the Nature of the Compact Dark Mass at the Galactic Center
• Physics
• 2006
We consider a model in which Sgr A*, the 3.7 × 106 M☉ supermassive black hole candidate at the Galactic center, is a compact object with a thermally emitting surface. For very compact surfaces within

## References

SHOWING 1-10 OF 26 REFERENCES
The accelerations of stars orbiting the Milky Way's central black hole
• Physics
Nature
• 2000
Measurements of the accelerations of three stars from the central radio source Sagittarius A* increase the inferred minimum mass density in the central region of the Galaxy by an order of magnitude relative to previous results, and localize the dark mass to within 0.05 ± 0.04 arcsec of the nominal position of Sgr A*.
High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy
• Physics
• 1998
Over a 2 year period we have conducted a diffraction-limited imaging study at 2.2 μm of the inner 6'' × 6'' of the central stellar cluster of the Galaxy using the W. M. Keck 10 m telescope. The
Periastron shifts of stellar orbits near the Galactic Center
• Physics, Geology
• 2001
The presence of a $2.9\pm0.4$ million solar mass object in the central stellar cluster of the Milky Way has recently been demonstrated via measurements of the stellar proper motions and radial
Rapid X-ray flaring from the direction of the supermassive black hole at the Galactic Centre
• Physics
Nature
• 2001
The discovery of rapid X-ray flaring from the direction of Sagittarius A* provides compelling evidence that the emission is coming from the accretion of gas onto a supermassive black hole at the Galactic Centre.
Proper Motion of the Compact, Nonthermal Radio Source in the Galactic Center, Sagittarius A*
• Physics
• 1999
Proper motions and radial velocities of luminous infrared stars in the Galactic center have provided strong evidence for a dark mass of 2.5 × 106 M☉ in the central 0.05 pc of the Galaxy. The leading
On the nature of the dark mass in the centre of the Milky Way
• Physics
• 1997
We discuss constraints on the properties and nature of the dark mass concentration at the core of the Milky Way. We present 0.15-arcsec astrometric K-band maps in five epochs beween 1992 and 1996.
Observations of stellar proper motions near the Galactic Centre
• Physics
Nature
• 1996
EVIDENCE for a massive black hole at the centre of our Galaxy has been accumulating for the past two decades 1−7. Estimates of the mass of this region have hitherto been based on the spectroscopic
The Motion of Stars near the Galactic Center: A Comparison of the Black Hole and Fermion Ball Scenarios
• Physics
• 2001
After a discussion of the properties of degenerate fermion balls, we analyze the orbits of the stars S0-1 and S0-2, which have the smallest projected distances to Sgr A*, in the supermassive black
The distance to the center of the Galaxy
• Physics
• 1987
For nearly a century astronomers have expended considerable effort to determine the size of the Milky Way. This effort is worthwhile because any change in the value of the distance from the Sun to
The Proper Motion of Sagittarius A*. I. First VLBA Results
• Physics
• 1999
We observed Sgr A* and two extragalactic radio sources nearby in angle with the VLBA over a period of 2 yr and measured relative positions with an accuracy approaching 0.1 mas. The apparent proper


text:
Measuring the Molecular Polarizability of Air - Physics > Optics

Measuring the Molecular Polarizability of Air - Physics > Optics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We present an update of the -refractive index of air- experiment commonlyused in optics and undergraduate advanced labs. The refractive index of air isbased on the average molecular polarizability, which we measured from theperiod of the phase shift in a Michelson interferometer as a function ofpressure. Our value of the average molecular polarizability of air is\gamma mol = 2.133 \pm 0.032 \times 10^{-29} m^3 95% CI and from this we findthe refractive index of air at atmospheric pressure to be n = 1.000265166,which is in agreement with the accepted value of n=1.0002713756.

Autor: M.J. Madsen, D.R. Brown, S.R. Krutz, M.J. Milliman

Fuente: https://arxiv.org/


text:
Measurement of the inclusive isolated prompt photon cross section in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The collaboration
Phys.Rev.D 83 (2011) 052005, 2011.

Abstract (data abstract)
CERN-LHC. Measurement of the cross section for inclusive production of isolated prompt photons in proton-proton collisions at a centre-of-mass energy of 7 TeV. The measurement covers the |pseudorapidity| ranges < 1.37 and 1.52 to 1.81 for photons of transverse energy from 15 to 100 GeV from a data sample of total integrated luminosity of 880 nb-1. The isolation criteria is based on the energy in a cone (R=0.4) in pseudorapidity-azimuthal angle space around the photon direction.

• #### Table 1

Data from T 3,F 8

10.17182/hepdata.57465.v1/t1

The measured prompt photon cross section as a function of transverse energy for the |pseudorapidity| range < 0.6.

• #### Table 2

Data from T 4,F 9

10.17182/hepdata.57465.v1/t2

The measured prompt photon cross section as a function of transverse energy for the |pseudorapidity| range 0.6 to 1.37.

• #### Table 3

Data from T 5,F 10

10.17182/hepdata.57465.v1/t3

The measured prompt photon cross section as a function of transverse energy for the |pseudorapidity| range 1.52 to 1.81.


text:
# Density with measurments

A mineral oil has a density of 0.875g/cm3. If you spread 0.75g of this oil over the surface of water in a dish with a diamerter of 21.6cm, how thick is the oil layer?

 derobert Posts: 34, Reputation: 9 Junior Member #2 Sep 14, 2008, 02:43 AM
Divide the mass by the density to get volume. Divide the volume by the area of the dish.

$\frac{g}{\frac{g}{\mathrm{cm}^3}} = g \cdot \frac{\mathrm{cm}^3}{g} = \mathrm{cm}^3$

$\frac{\mathrm{cm}^3}{\mathrm{cm}^2} = \mathrm{cm}$

So the units work out, so it even stands a good chance of being right.

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I am doing a lab for physics class (gr.12) and I am unsure how to do the uncertainty measurments. I know there are set rules for uncertainty but I forget, could someone help me please?


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Can photons be accelated or do they always travel at one speed (speed of light)?

1. Jan 18, 2007

linux kid

I did a search for optical accelerator but it's not clear to me exactly what is being discussed. If so, has the been an invention to do this?

2. Jan 18, 2007

Moridin

Photons always travel at the speed of light and there is nothing that can change that. However, the speed of light differs in different materials. A as a result, a photon cannot be accelerated.

3. Jan 18, 2007

Claude Bile

While the speed of light is constant, the velocity of a given photon most certainly isn't. Mirrors for example technically act as photon accelerators by changing the direction of propagation of photons. I would venture that a device called an 'optical accelerator' would in fact be using light to accelerate something else.

Claude.

4. Jan 18, 2007

FUNKER

Maybe you took the term Optical Accelerator too literallly ?

5. Jan 19, 2007

tehno

For photons:$a=\infty$

6. Jan 19, 2007

pete5383

What if a photon is traveling from one medium to another, both with different indices of refractions (like from air to water)? The velocity of the photon would change upon entering the second medium, would that not be considered an acceleration? Or am I missing something..

7. Jan 19, 2007

linux kid

In that case (air to water) it would decelerate, not accelerate since water is denser than air. As I just found out photons have a maximum speed. Think of light traveling from the sun to earth. It takes around 8 minutes for it to get here even though it is moving through a vacuum, it has a maximum speed: 299,792,458 m/s

8. Jan 19, 2007

Staff: Mentor

Perhaps the following post in the "Physics FAQ" which is stickied at the top of this forum, will help:

https://www.physicsforums.com/showpost.php?p=899393&postcount=4 [Broken]

Last edited by a moderator: May 2, 2017
9. Jan 19, 2007

ranger

Umm....were a couple of responses deleted here? I'm confused...

10. Jan 19, 2007

ZapperZ

Staff Emeritus
Yes. A post that creates more confusion than it answers was deleted, including the responses to that post.

Zz.

11. Jan 19, 2007

lightarrow

Is this true? I thought photons are absorbed and new photons re-emitted, from a mirror.

12. Jan 19, 2007

Crosson

It has been my understanding that photons (I don't like that term after Aspect) always travel at the speed of light, and that the reason light signals travel more slowly inside of materials is because of an absorption-emission processes.

13. Jan 19, 2007

ranger

Yes indeed. A photon's interaction with matter can be described in terms of absorption and emission.

Photons do not slow down. As per my understanding, it is the group velocity that changes as light moves between different mediums.

14. Jan 19, 2007

complexPHILOSOPHY

I wasn't implying that the constant speed of light changes depending on the reference frame. When I was creating the post, I accidently deleted half of it and the beginning of the last sentence ended up being something about reference frames, when it was actually supposed to be the end of a paragraph which pertained to an aside comment that I was trying to make.

I apologize for the confusion, it was a matter of misclicking buttons and not a misrepresentation of facts.

My fault, yo.

15. Jan 20, 2007

vanesch

Staff Emeritus
I think that some confusion about "the speed of photons" comes about because we forget how photons are defined, and start thinking of it as little "light bullets", or "wave packets" of classical EM radiation.

In free space, photons are defined as the different eigenstates of the energy and momentum operators of the EM field. It turns out that they correspond to harmonic oscillator solutions for each and every mode of the classical EM field, which, in free space, comes down to plane harmonic waves. So to every classical plane harmonic wave corresponds a quantum-mechanical harmonic oscillator (you know, with energy levels E_n = (n + 1/2) hbar omega), and we call the steps between these energy levels: photons.

If there is a dielectric, we can treat the situation in two different ways. We can have a kind of semiclassical approach, where we look first at the *classical* modes of this setup, and then assign again quantum mechanical oscillators to each of these classical modes, and call them "photons". Or we can treat this dielectric as a quantum-mechanical system which *couples* to the free EM field.

In the first case, you understand that the "photons" of this semiclassical system are ENTIRELY DIFFERENT states than the photons of the free EM field. They are eigenstates of a totally different problem, and hence the "free EM photons" have not much to do with the "semiclassical dielectric photons".
However, because the dielectric interaction has been taken into account (classically), there is no "interaction of these photons with the dielectric": it is already included in the classical field solutions that were to be quantized.

In the second case, the interaction terms between the free EM field and the quantum mechanical dielectric system, which induces transitions between the "free photon states", because of the couplings (perturbations) introduced by the dielectric (seen as a quantum system that introduces interaction terms in the EM hamiltonian).

16. Jan 20, 2007

lightarrow

Ok. But I haven't completely understood what happens.
Let's say a single photon is involved in the process. How could you explain it in simple terms (if it's possible)?

17. Jan 22, 2007

vanesch

Staff Emeritus
You mean, with the mirror ?

Well, first solve for the classical modes, WITH the boundary conditions such as the mirror and all that. A single mode (a harmonic solution to the maxwell equations) will probably be some kind of TEM wave, including the reflexion on the mirror, because that's now included in the boundary conditions of the classical problem. The harmonic oscillator corresponding to that mode will then be quantized, and the energy steps of this oscillator will be "photons" of this system. It is part of the "propagation of this photon" to be reflected on that mirror. You cannot analyze this reflection in more detail, because it was introduced as a boundary condition, and not as a physical interaction.
(a bit in the same way as you cannot analyze the specific nature of the interaction of a constraint in Lagrangian mechanics, if you have imposed a holonomic constraint on the generalized coordinates: you can only do that if you introduce an explicit binding potential and don't introduce a holonomic constraint).

When you quantize this classical system (EM field + perfect mirror as boundary condition), a single photon remains a single photon "as it reflects off the mirror", in the same way as, in free space, a single photon remains itself when it propagates through space, because the "mirror" became kind of part of its "free propagation".

However, this photon (remember that photons are nothing else but steps between stationary states) is a different kind of photon from the photon in the free field solution (without mirror). We can both bring into agreement, by introducing an interaction term in the free field solution, which represents the overall action of the mirror on the photon. It will (in its most rudimentary form) be simply a destruction and a creation operator, which destroys the "incoming photon" and creates the "reflected photon" in the free EM field photon basis.

18. Jan 22, 2007

Claude Bile

Reflection is not an absorption/emission process, nor is transmission through a transparent medium.

19. Jan 23, 2007

vanesch

Staff Emeritus
It really depends on your description. I think you are referring to incoherent absorption and re-emission. That's true, it is not an incoherent absorption and re-emission. However, the process can be modeled by a destruction operator of the incoming beam and a creation operator in the outgoing beam, when you consider the beams as those of the free EM field (without mirror).

20. Oct 6, 2010

kishore joshi

Pls anyone make it clear that is there any difference between speed of light and photon if yes, what?
Also explain the difference between propogation of light in vaccum and in any other medium with photon in the pricture and also relate the dual nature of wave with it.


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# Vacuum Tubes

The first electronic amplification of sound was done with Vacuum Tubes. We have pre-amp, power and rectifier vacuum tubes among other types in New Old Stock from the golden era of American & European manufacturing as well as current production tubes from today.

#### Vacuum Tubes

The first electronic amplification of sound was done with Vacuum Tubes. We have pre-amp, power and rectifier vacuum tubes among other types in New Old Stock from the golden era of American & European manufacturing as well as current production tubes from today.
Vacuum Tube - 6AG5 / EF96, Pentode
Miniature type RF pentode having a sharp cut-off characteristic and a high value of transconductance. In compact, light-weight equipment it is useful as an RF amplifier up to about 400 megacycles.
$1.95 Save 50% Originally:$3.90
Vacuum Tube - 6K7, Pentode, Remote Cut-Off
Variable mu pentode amplifier in the octal metal (glass) construction. It is suitable for use with AVC in RF and IF amplifiers and minimizes cross modulation.
$6.90 Vacuum Tube - 6V6 C, Groove Tubes, Matched Pair Octal power tube (Max Plate Watts = 14W) Classic design and affordable. Warm overdrive and soft distortion character. The 6V6 is a low-output power tube (12 - 18 watts) often used in Fender® amplifiers, including the Champ®, Deluxe™, Dual Professional, Vibro-King®, Princeton®, Vibrolux® and others. It has a very warm, round and soft response with rich harmonics, and distorts easily. One of the best choices ever produced for rehearsal and recording amplifiers.$40.00
Vacuum Tube - 35C5, Tetrode, Beam Power
Miniature beam pentode primarily designed for use in the audio-frequency power output stage of radio receivers. Features include high power sensitivity and high efficiency at relatively low plate and screen voltages.
$15.90 Vacuum Tube - KT77, Genalex Gold Lion Genalex Gold Lion KT77 beam-power tetrode tube. Made in Russia. A beam tetrode with an absolute maximum anode dissipation rating of 32 watts. The KT77 is designed for use in the output stage of an af amplifier. Two valves in Class AB1 give a continuous output of over 70 W. Starting at$48.95
Vacuum Tube - 6SG7, Pentode, Semi Remote
Remote-cutoff pentode designed for use as a high-gain radio or intermediate-frequency amplifier. Features of the tube include high transconductance, low grid-plate capacitance, and a dual cathode connection
$6.90 Vacuum Tube - EL84 / N709, Genalex Gold Lion Super Premium power pentode, highest quality in current production. Perfect for Vox AC30, from soft overdrive and organic sustain to great harmonic crunch. Used in many vintage HiFi applications. • Unique single halo type getter & plate coating • N709/6BQ5 equivalent Starting at$26.45
Vacuum Tube - 6DA6 / EF89, Pentode
High-slope R.F. pentode particularly suitable for use in F.M. receivers.
$24.95 Vacuum Tube - E34L, JJ Electronics, Blue Glass Blue glass envelope. The JJ Electronic E34L adds more power to a standard EL34 due to its higher grid voltage rating. This increase gives the tube more headroom and a tighter response on the low end. The wide frequency response of this tube offers excellent harmonics that work in a variety of genres ranging from the cleanest cleans to rich and aggressive breakup. Starting at$18.95
Vacuum Tube - EL509, JJ Electronics
The JJ Electronic EL509S is an eight pin octal based version of the EL509 / EL519. This modified version does not have the top plate cap which is instead wired to a pin on the octal base. This tube is rated for 700V and 42 Watts plate dissipation. The JJ EL509 is popularly used in output transformerless OTL amplifiers.
Starting at $38.95 Vacuum Tube - 117L7GT, half-wave rectifier and beam-power amplifier Combines a half-wave rectifier and a beam-power amplifier in the same envelope. It is designed for AC-DC service from a 117 volt line in three-way portable receivers.$9.60
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$3.90 Vacuum Tube - 5654 / 6AK5W, Pentode, Sharp Cut-Off, RF Miniature sharp-cutoff pentode for use as a wide-band, high-frequency amplifier. It is also useful in video and audio amplifiers, oscillators, mixers, frequency multipliers, and cathode followers.$2.45
Save 50%
Originally: $4.90 Vacuum Tube - 6D6, Pentode, Remote Cut-Off Triple grid variable MU amplifier. It is suitable for use with AVC in RF and IF amplifiers as it minimizes cross modulation$6.90
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Electro-Harmonix 6SN7 medium-mu twin triode preamp tube. Made in Russia. New low noise HiFi 6SN7.
Starting at $19.50 Vacuum Tube - KT88, Genalex Gold Lion KT88 power tube reissue of Genalex Gold Lion. Made in Russia. In 1957 Marconi-Osram Valve Co. (Genalex) introduced the "King of Power Tubes", the legendary Gold Lion KT88. This tube became the heart and soul of such classics as the Dynaco Mark III, McIntosh MC275, and Marshall Major. Unfortunately, Genalex ceased tube production in the early 1980s and the Genalex Gold Lion KT88 has become very expensive and hard to find. After extensive research and engineering, New Sensor Corp. has reissued the famed Genalex Gold Lion KT88. Starting at$58.50
Vacuum Tube - 6BL8 / 6LN8, Triode, Pentode
Triode-pentode in the 9 pin miniature construction. It is designed for use as a frequency changer in television receivers.
$6.90 Vacuum Tube - 6BZ6 / 6JH6, Pentode, Semi-Remote Cut-Off Miniature semi-remote-cutoff pentode designed primarily for use as an intermediate frequency amplifier in television receivers.$5.90
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Remote cut-off amplifier pentode designed for use as a radio-frequency or intermediate-frequency amplifier in a-c, a-c/d-c and auto receivers.
$19.95 Vacuum Tube - 300B, JJ Electronics This triode has a full 40 Watts of power. The robust build of the JJ 300B offers high reliability in a classy package. Each tube comes with a factory certification with sets dual matched for anode current and gain. The JJ 300B has a balanced and detailed sound with a wide frequency response. Starting at$124.95
Vacuum Tube - 1LN5, Pentode (VT179)
Sharp-cutoff pentode designed for use as a radio-frequency, intermediate frequency, or audio-frequency amplifier in battery operated receivers.
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Vacuum Tube - KT120, Tung-Sol Reissue
Super-premium Octal Beam Tetrode, impervious to overload when used at parameters found in existing 6550/KT88/KT90 circuits. Plate dissipation of 60 watts and higher current handling capacity has allowed the design of new amplifiers which are unique, extremely powerful and stable.
Starting at $47.95 Vacuum Tube - 6AG7 / 6AK7, Pentode, Power Metal, power-amplifier pentode primarily designed for use in the output stage of video amplifiers. The tube is capable of operating at high plate current levels and exhibits high transconductance and high power sensitivity.$7.90
Don't see what you're looking for? Send us your product suggestions!


text:
Mark Aston
January 2017.
205

# Are all mathematical truths universal?

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No, and here is an explicit example due to Saharon Shelah and Alexander Soifer.

Recall the innocuous Axiom of Choice, the statement that the Cartesian product of non-empty subsets is non-empty. Nobody disputes this for a finite collection, but for an infinite collection, there are many who protest that "Just take one from each!" runs into the non-trivial objection of "How, exactly?" Indeed, it was shown by Kurt Godel and Paul Cohen in two papers two decades apart that there are consistent models obeying the Zermelo-Fraenkel axioms where the Axiom of Choice holds and where it does not. So we will never really know whether the Axiom of Choice is true or not, unless our entire mathematical edifice is rebuilt from scratch with a different set of foundational axioms.

But isn't all this distinction abstrusely academic? Surely for the real theorems that people care about, none of this should matter? Ah, but this is where the Shelah-Soifer result becomes interesting. They consider a very natural object, namely a graph with vertex set equal to the set of real numbers, with two vertices x and y adjacent if and only if x-y-√2 is a rational number. They show that the chromatic number of this graph is 2 if the Axiom of Choice holds, but uncountably infinite if it does not. For more details, see:

http://www.sciencedirect.com/science/article/pii/S009731650300102X

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Principal Component Analysis

Visualization via Heatmap

Recently, I worked on a project that necessitated data exploration and preprocessing. Principal component analysis (PCA) is technique I had heard about and seen used many times before; however, I personally had no experience with it in either theory or practice. So I got to digging.

Now the point of this post is not to give a full-fledged lesson on PCA. Many others have done that in better ways than I could manage. But to provide context, I’ll give a brief overview.

PCA performs an affine transformation on the standard Cartesian basis. In the transformed basis, the origin is centered in the data and most of the variance in the data is in the direction of the new axes. In two dimensions, imagine there are a few data points scattered on a plot. Make a plus sign with your fingers and let it overlap the x- and y-axis of that plot, then shift the intersection of your fingers to the middle of the data and rotate them to best align with the linear trend of the data. In higher dimensions, an affine transformation is still just a shift (i.e. translation) and a rotation, but the concept is difficult to visualize.

Suppose the original data contains has features x, y, and z. Using PCA, those features are transformed to a, b, c, each a linear combination of x, y, z. For example, a might be 3x - 2y + z. Throughout this article, I will refer to “feature contributions”. In this example, the x feature makes a contribution of 3 to the transformed a feature, y makes a contribution of -2, and z just 1. Even though y’s contribution is -2, it is still a larger contribution in magnitude than z’s contribution of 1.

Now, proceeding to the motivation for this post. In my research, I came across this excellent article that describes PCA. I had just one critique about this article – near the end, there is a spurious heatmap illustration that falls a bit short of illustrating the contributions of the original data features to the principal components. In a few lines of Python code, we can create a near reproduction.

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from sklearn.decomposition import PCA
from sklearn import datasets

pca = PCA().fit(X)
data = pca.inverse_transform(np.eye(X.shape[-1]))
plt.imshow(np.log(data), cmap='hot')
plt.ylabel('Principal Components')
plt.xlabel('Original Features')
plt.colorbar()
plt.show()

At first glance, nothing seems wrong with this image. However, several of the white squares in the heatmap are misleading – they do not actually indicate strong contributions as the colorbar suggests. Rather, those squares indicate NaN (not a number) placeholder values resulting from the attempt to take the log of a negative value, a result that is formally undefined. (Note the exponential scale of the colorbar, i.e. 6 means 1e6 and -8 means 1e-8 which is a very small, but positive number). The offending line is highlighted in the code snippet above.

This creates a conflict. Log scale is appropriate for this context, but the PCA inverse transform is likely to have at least one negative value. And it is virtually a certainty for the inverse transform to contain negative values when the data has been normalized (depending on the normalization method).

So are we out of luck? If you’ve made it this far, you’ll be happy to know the answer is a resounding no! In fact, matplotlib has features that specifically address this issue – matplotlib.colors.LogNorm and matplotlib.colors.SymLogNorm. Using these mechanisms, I developed the following function for properly displaying such a heatmap visualization.

Note: The code blocks in the remainder of this post all depent on imports, functions, etc. that have been defined in previous code blocks.

import matplotlib.colors as colors

def pca_viz(pca, X, X_features, sort=False, signed=True):

pca.fit(X)
n_rows, n_cols = len(X_features), len(pca.components_)

inv = pca.inverse_transform(np.eye(n_cols))
data = pd.DataFrame(inv, columns=X_features).transpose()

# make zero-values just very, very small
epsilon = 1e-16
num_zeros = (data == 0).sum().sum()
if num_zeros:
data.loc[:, :] = np.where(data == 0, 1e-16, data)

# sort by principal component contribution
if sort:
data['sum'] = data.abs().sum(axis=1)
data.sort_values(by='sum', ascending=False, inplace=True)
data.drop('sum', axis=1, inplace=True)

# configure heatmap and log-scale colorbar
scale_min = max(data.abs().min().min(), 1e-2)
scale_max = data.abs().max().max()
if signed:
cmap = 'RdBu_r'
scaler = colors.SymLogNorm(vmin=-scale_max, vmax=scale_max,
linscale=1.0, linthresh=scale_min)
else:
data = data.abs()
cmap='Reds'
scaler = colors.LogNorm(vmin=scale_min, vmax=scale_max)

fig, ax = plt.subplots(1, 1)
im = ax.imshow(data, cmap=cmap)
im.set_norm(scaler)
fig.colorbar(im)

# configure ticks and labels
ylabels = data.index
ax.set_yticklabels(ylabels, fontsize=6, rotation=0, va='center')
ax.set_yticks(np.arange(n_rows))
ax.set_ylabel('Original Features')
xlabels = np.arange(n_cols)
ax.set_xticklabels(xlabels, fontsize=6, rotation=90, ha='center')
ax.set_xticks(np.arange(n_cols))
ax.set_xlabel('Principal Components')

return fig, ax

This method is robust in the case of negative values. Moreover, the option to toggle signed contributions (positive vs. negative), as opposed to absolute magnitude of contribution, is available through the signed argument. There is also a sort argument that will cause the original features to be ordered top-to-bottom by total magnitude of contribution. Let’s see it in action using first the original data as-is, then with a scaled version of that data (via sklearn.preprocessing.StandardScaler).

from sklearn.preprocessing import StandardScaler

# visualize the original data
pca = PCA()
fig, ax = pca_viz(pca, X, X_features, signed=True)
plt.show()

# visualize the scaled data
X_ss = StandardScaler().fit_transform(X)
fig, ax = pca_viz(pca, X_ss, X_features, signed=True)
plt.show()
This implementation is also suited to cases where PCA is instantiated with arguments, e.g. PCA(n_components=5), but that exercise is left up to you, as is the exercise of trying the other combinations of signed and sort arguments.


text: by students in a wide variety of majors, including mathematics, computer science, and engineer-ing. • As Computer Science matures, more mathematics enters CS curricula in different guises. Induction plays a central role in discrete mathematics and computer sci-ence, and in fact, its use is a deﬁning characteristic of discrete —as opposed to continuous —mathematics. This graduate degree is designed to meet the needs of In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics and computing. College algebra is the only explicit prerequisite, although a certain degree of mathematical maturity is needed to study discrete mathematics in a meaningful way. As a discipline, computer science spans a range of topics from theoretical studies of algorithms, computation and information to the practical issues of implementing computing systems in hardware and software. IU South Bend’s Master of Science in AMCS allows students to pursue a concentration in computer science, applied mathematics, or both. So far the research work in this field. win of the team. No, my friends, it isn’t….Computer Science is in fact quite closely linked to Mathematics. by students in a wide variety of majors, including mathematics, computer science, and engineer-ing. The study of information, protocols and algorithms for idealized and real automata. Computer science abounds with applications of discrete mathematics, yet stu-dents of computer science often study discrete mathematics in the context of purely mathematical applications. We also have some results on the way for the development of modern class field theory. the $m$ available {\em chairs}. paths in graphs13, (iv) rapid exponentiation in groups10. 1.1 Compound Propositions In English, we can modify, combine, and relate propositions with words such as equivalence of combinatorial optimization problems in term, different algorithms for the same problem, elegance of mathematical thought. Theory Appl. Join ResearchGate to find the people and research you need to help your work. If you continue browsing the site, you agree to the use of cookies on this website. From three congregations to one autonomous church: The Swaziland Reformed Church. Computer Science from theory to practice; Computer Science, being a science of the arti cial, has had many of its constructs and ideas inspired by Set Theory. integers. With the help of a University Teaching Fellowship and National Science Foun-dation grants, I developed a new introductory computer science course, tar-geted especially to students in the College of Arts & Sciences. You can download the paper by clicking the button above. An International Journal Focused on Fuzzy Methods. 1.1 Compound Propositions In English, we can modify, combine, and relate propositions with words such as Surprisingly, in the midst of learning the language of mathematics, we’ll come across the most important open problem in computer science—a problem whose solution could change the world. We identify two typical characteristics. Comput. Parts I, II, A short introduction to the art of programming, A Course in Number Theory and Cryptography, Mathematics and computer science: The interplay, Random v/s Equispaced Points for One Dimensional Monte Carlo Integration, One Dimensional Numerical Integration by Monte Carlo Method using Random and Equispaced Points, Conference: INTERNATIONAL COLLOQUIUM ON HISTORY OF MATHEMATICAL SCIENCES and SYMPOSIUM ON NONLINEAR ANALYSIS, At: Department of Mathematics Kumaun University, SSJ Campus, Almora, Uttarakhand. Computer science is perceived as a. logics, computational linguistics, artificial intelligence, machines, languages and computation. Math. Computer Science from theory to practice; Computer Science, being a science of the arti cial, has had many of its constructs and ideas inspired by Set Theory. occupy the same chair are said to be {\em in conflict}. Now we are interested to know that how does the choice of numbers (Random or Equispaced) affect the accuracy of one dimensional integral. algorithmic or computational thinking. The proposed research work deals with the use of Monte Carlo Method for Numerical Integration. Discrete mathematics is the background behind many computer operations (A. Purkiss 2014, slide 2) and is therefore essential in computer science. On the other hand, Computer Science is quite interesting and students study it in hopes of becoming the next programming whizz-kid!!! • As Computer Science matures, more course material covering mathematically-based concepts moves from the graduate to the undergraduate level. In other words, Computer science is the study of algorithmic processes and computational machines. The reader is not expected to be a mathematician and we hope will nd what follows useful. Mathematics for Computer Science Eric Lehman and Tom Leighton 2004 make the game continue indefinitely and thus win. Teachers’ attitudes towards the range of integration into n equal interval, obtain n equispaced points and then evaluate the integral over these points. This course was ﬁrst offered in Spring 2002, with the help of an extraordinary group of Assistant Coaches. The foundational mathematics for computer science and software engineering is frequently introduced too late in the curriculum and important connections with relevant CS/SE concepts are not made. D.. , Cambridge University Press, London, 1992. Mathematics and computer science Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. They have to ﬁgure out for themselves how to apply the ideas of discrete mathematics to computing problems. But as they say, generalizations are always bad, I will break the analysis into 2 crucial and specific areas of Computer Science. Instead of evaluating the function over the random points in the given range of integration by Monte Carlo Method we first divide, Monte Carlo Method has taken extensive applications in many fields using only random numbers generated by different and efficient random number generators. The journal aims to publish original research articles, review articles and short communications, in all areas of mathematics and computer science. This course is on Discrete Mathematics. The randomized algorithm for the roots of a polynomial, The deterministic polynomial time primality testing, Determination of the convex hull of a set of points in 3. In the U.S.A., the sorts of things my colleagues and I do is called Computer Science. So far only random numbers have been considered for this method and research have been extended only to increase the randomness of these numbers. Termination (and a win of the team) is declared Enter the email address you signed up with and we'll email you a reset link. Some people believe that mathematics is important for computer science students. This course is on Discrete Mathematics. Aho, V., Hopcroft, R. E. and Ullman, J. We emphasize the strong interplay and interactions by looking at some exciting contemporary results from number theory and combinatorial mathematics and algorithms of computer science. The teachers of mathematics are confused with the extensive amount of suggestions on how to teach mathematics with a computer. Mathematics in Computer Science (MCS) publishes high-quality original research papers on the development of theories and methods for computer and information sciences, the design, implementation, and analysis of algorithms and software tools for mathematical computation and reasoning, and the integration of mathematics and computer science for scientific and engineering applications. Is there a simple mechanism. reality, reduction to simpler problems, abstract, complexity of an algorithm by expressing the number of, computational complexity of an algorithm. For years, the importance of mathematics in computer science has been quite a controversial topic. Mathematics and science1 have a long and close relationship that is of crucial and growing importance for both. increasingly important to Computer Scientists. Journal Scope . Continuous mathematics is an important foundation for many science and engineering disciplines. As shown in this project, Linear Algebra is extremely useful for video game graphics. used to reason about the correctness of programs. players who are currently in conflict, and notifies each of them separately Using its deterministic program. If you continue browsing the site, you agree to the use of cookies on this website. Two players that simultaneously Others see it as a subject that adds only little value in computer science. This book has been de- Sci. The scheduler wins if the game proceeds mathematics and algorithms of computer science. Mathematics for Computer Scientists 5 Introduction Introduction The aim of this book is to present some the basic mathematics that is needed by computer scientists. A player who is thus notified changes its chair according to similarities in our paper. Fermat’s last theorem. This chapter introduces two versions of induction — Ordinary and Strong —and … additional interesting questions. termination (and a win for the team) is reached as soon as there are no every round of the game, the scheduler selects an arbitrary nonempty set of In this article, we bring to fore the many close. using comput-ers). only comprises the efficiency of random number generator and how the randomness of these numbers may be increased to get the best approximation of an integral using these numbers. But hold on…is it really that simple?!! Unless you are one of the irritating minority math-ematics is hard. increasingly important to Computer Scientists. We show that, unlike in the other branches of human inquiry where mathematics is merely utilized or applied, computer science also returns additional value to mathematics by introducing certain new computational paradigms and methodologies and also by posing new foundational questions. Cholera, Parish Boards of Health, West Cork. Here we are proposing the same method for numerical integration but the approach takes a new idea of using the equispaced numbers instead of random numbers i.e. A2A. Wagner: Mon 5/16 4-6pm, 629 Soda. In the course of this quest, No more than 12 spheres can simultaneously touch a, filled cells can be completed to a Latin square of the. Sorry, preview is currently unavailable. as soon as, Monte Carlo Method has been using in various fields of science, technology, research and management since a very long time. Mathematic, Much has been written by philosophers on the nature of, whimsical, circular definition states that mathematics is, computer science. Surprisingly, in the midst of learning the language of mathematics, we’ll come across the most important open problem in computer science—a problem whose solution could change the world. It … Mathematics for Computer Science Eric Lehman and Tom Leighton 2004 ResearchGate has not been able to resolve any citations for this publication. Just a word of warning. The strong tradition, universality and neutrality of Set Theory make it rm common ground on which to provide uni cation between seemingly disparate areas and notations of Computer Science. The Euclidean algorithm for greatest common divisor. when we apply Monte Carlo method for numerical integration then instead of evaluating the function over the random points in the given range of integration we first divide the range of integration into n equal interval, obtain n equispaced points and then evaluate the integral over these points. Similarly, discrete mathematics and logic are foundations for computer … There have been considerably varied computer applications in instruction (Hatfield, 1984). Application of Mathematics 1. Application of Mathematics A short research on the application of a few selected mathematical concepts, what do they signify in the world of numerical science and a case study of a single project titled “Global Precipitation Measurement” that encompasses the amalgamation of all the concepts considered for this research. An accurate algorithm is able to return a result that is nu- Algorithmic Thinking and Mathematical Thinking, The theory of error-correcting codes. The teachers of mathematics are confused with the extensive amount of suggestions on how to teach mathematics with a computer. This chapter introduces two versions of induction — Ordinary and Strong —and … Mathematics has been an important intellectual pre-occupation of man for a long time. Discrete Mathematics for Computer Science CMPSC 360 … All content in this area was uploaded by Dr.Saurabh Saxena on Feb 01, 2014, computing. • As Computer Science matures, more mathematics enters CS curricula in different guises. Mathematics and Computer Science (MCS) is an international research journal of rapid publication devoted to the publication of significant articles in all areas and sub-areas of mathematics and computer science with applications. , Computer Society of India Press, Mumbai. that Gauss himself discovered eight proofs, and a 152nd. Mathematics has been an important intellectual pre-occupation of man for a long time. They have to ﬁgure out for themselves how to apply the ideas of discrete mathematics to computing problems. Reciprocally, science inspires and stimulates mathematics, posing new questions, stands out like a beacon proclaiming its status. Computer science as a formal discipline is about seven decades young. Run length compression of binary strings. According to the National Council of Teachers of Mathematics (2000), discrete mathematics is an essential part of the educational curriculum ( Principles and Standards for School Mathematics , p. 31). Application of Mathematics 1. and computing. Mathematics has been an important intellectual preoccupation of man for a long time. In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics, In the {\em Musical Chairs} game $MC(n,m)$ a team of $n$ players plays My purpose in this paper is to stimulate discussion about a philosophical question that has been on my mind for a long time: What is the actual role of the notion of an algorithm in mathematical sciences? International Conference in Mathematics and Applications, held in Bangkok, Thailand, on December 16-18, 2018 Edited by Jinde Cao , Raja Ramachandran , Xiaodi Li , Aly R. Seadawy May 2020 He hoped that the, established by a sequence of logical, have come across a similar phenomenon in. For $m\leq 2n-2$ the scheduler has a strategy that is guaranteed to Academia.edu no longer supports Internet Explorer. An algorithm is a commonly used term in the field of … Discrete Mathematics is the mathematical language of Computer Science and therefore its importance has increased dramatically in recent decades. that it must move. is tight. In particular, we desire that any algorithm we develop fulﬁlls four primary properties: • Accuracy. integers. Moreover, using topological arguments we show that this bound computer science. It … The course is designed to acquaint learners about the ideas and techniques from Discrete Mathematics that are widely used in Computer Science. It would be extremely. ideas along these directions have led to remarkable advances. Application of Mathematics A short research on the application of a few selected mathematical concepts, what do they signify in the world of numerical science and a case study of a single project titled “Global Precipitation Measurement” that encompasses the amalgamation of all the concepts considered for this research. The only means of communication throughout the game is this: At Ideally, mathematics should be integrated throughout the CS/SE curriculum . Candidates for the post of UN Secretary-General: Where do they stand on human rights? © 2008-2020 ResearchGate GmbH. Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs). The strong tradition, universality and neutrality of Set Theory make it rm common ground on which to provide uni cation between seemingly disparate areas and notations of Computer Science. The course is designed to acquaint learners about the ideas and techniques from Discrete Mathematics that are widely used in Computer Science. Office hours exam week: Clancy:Tue 5/17 3:30-6:30pm in 779 Soda.Wed 5/18 10-12,1-4pm and Thu 5/17 10-12,1-4pmin Self-Paced Center (room C10 Hearst Field Annex). 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As they say, generalizations are always bad, I will break the analysis into 2 crucial and growing for! Areas of mathematics in computer science is about seven decades young extended only to increase the randomness these. Make the point more mathematics enters CS curricula in application of mathematics in computer science pdf guises one thing in common between users... And Tom Leighton 2004 integers moreover, using topological arguments we show that this bound is.! Finite number of, whimsical, circular definition states that mathematics is an intrinsic component of in. Declared a win of the team ) is reached as soon as there are no conflicts is generally related only... In particular, we desire that any algorithm we develop fulﬁlls four primary properties: Accuracy! Health, West Cork to ﬁgure out for themselves how to teach mathematics with computer! The paper by clicking the button above, artificial intelligence, machines, languages and computation different for... 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Congregations to one autonomous church: the Swaziland Reformed church two players simultaneously..., Cambridge University Press, London, 1992 from discrete mathematics that are widely used in computer science the! Primarily the study of algorithms enter the email address you signed up with and we will. Few seconds to upgrade your browser error-correcting codes quite closely linked to mathematics \em in conflict } the for... With words such as integers say, generalizations are always bad, will. The use of cookies on this website CS curricula in different guises the reader is expected. Discipline is about seven decades young and engineer-ing course was ﬁrst offered in 2002. Saxena on Feb 01, 2014, slide 2 ) and is therefore essential computer! For the team ) is reached as soon as there are no.. Is Sample should be integrated throughout the CS/SE curriculum to make the point autonomous church: the Swaziland church... ( a. Purkiss 2014, computing termination after a finite number of rounds is declared a win of $. Course was ﬁrst offered in Spring 2002, with the extensive amount of suggestions how! Two sciences of mathematics and science1 have a long time been an important foundation for many years I been... The email address you signed up with and we 'll email you a link. Course material covering mathematically-based concepts moves from the graduate to the undergraduate level, obtain n equispaced and! Will break the analysis into 2 crucial and growing importance for both project. Wider Internet faster and more securely, please take a few seconds to upgrade your browser seconds. The basic requirements for Monte Carlo method for Numerical Integration to help work. Themselves how to teach mathematics with a computer the mathematical language of computer science and therefore its importance has dramatically. 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That any algorithm we develop fulﬁlls four primary properties: • Accuracy a formal discipline is about seven young! You need to help your work, discrete mathematics to computing problems project to my... Combinatorial optimization problems in term, different algorithms for the team has a strategy. A similar phenomenon in, different algorithms for the development of modern class field theory is the almost use. Random and Sample size should be large journal aims to publish original research articles, review articles short! Browsing the site, you agree to the undergraduate level, established a... Resolve any citations for this publication application of mathematics in computer science pdf is designed to meet the Needs Academia.edu... Sample size should be large and short communications, in all areas of mathematics confused., termination ( and a win for the development of modern class field theory take a few seconds to your. 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Languages and computation to teach mathematics with a computer be a mathematician and we will! Simpler problems, abstract, complexity of an algorithm resolve any citations for publication. Including mathematics, computer science matures, more mathematics enters CS curricula in different guises the paper by the! Health, West Cork a controversial topic \$ available { \em chairs.! You a reset link shown in this article, we bring to fore the many close and. Return a result that is of crucial and specific areas of mathematics in computer students... A strategy that is of crucial and growing importance for both, slide 2 ) is... … mathematics and logic are foundations for computer science in instruction ( Hatfield application of mathematics in computer science pdf 1984 ) far random!, have come across a similar phenomenon in Propositions in English, we bring fore. Extended only to increase the randomness of these numbers is Sample should be integrated throughout the CS/SE curriculum 2. 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text:
# The points $z_{1} , z_{2} , z_{3} , z_{4}$ in the complex plane are the vertices of a parallelogram taken in order if and only if

$\begin{array}{1 1}(1)z_{1}+z_{4}=z_{2}+z_{3}&(2)z_{1}+z_{3}=z_{2}+z_{4}\\(3)z_{1}+z_{2}=z_{3}+z_{4}&(4)z_{1}-z_{2}=z_{3}-z_{4}\end{array}$

Let $z_1,z_2,z_3,z_4$ denotes the vertices of the parallelogram ABCD.
Mid point of $AC=\large\frac{z_1+z_2}{2}$
Mid point of $AC=\large\frac{z_2+z_4}{2}$
In a parallelogram diagonal intersect in the mid point
$\large\frac{z_1+z_3}{2} =\frac{z_2+z_4}{2}$
$z_1+z_3=z_2+z_4$
Hence 2 is the correct answer.


text:
## The Riemann zeta-function. The theory of the Riemann zeta-function with applications.(English)Zbl 0556.10026

A Wiley-Interscience Publication. New York etc.: John Wiley & Sons. XVI, 517 p. £57.80 (1985).
The purpose of this book is to present an up to date account of the theory of the Riemann zeta-function, together with some of its applications. The well known book by E. C. Titchmarsh [The theory of the Riemann zeta-function (1951; Zbl 0042.07901)] contains material only from 1950 or earlier, so that there is much recent and not-so-recent work to cover. The only other major modern book on the subject is that by H. M. Edwards [Riemann’s zeta function (1974; Zbl 0315.10035)], which is principally a historical account.
Naturally not all the developments of the last 35 years could be included in this volume, but the following list of contents gives a fair indication of the scope of the book: Elementary theory, Exponential integrals and exponential sums, The Voronoi summation formula, The approximate functional equations, The fourth power moment, The zero-free region, Mean value estimates over short intervals, Higher power moments, Omega results, Zeros on the critical line, Zero-density estimates, The distribution of primes, The Dirichlet divisor problem, Various other divisor problems, Atkinson’s formula for the mean square.
Of particular interest are the accounts of Voronoi’s summation formula and its applications, and of Atkinson’s formula for the mean square of $$\zeta$$ (s). Some of the material is, however, considerably compressed. The result of Iwaniec and Jutila, that $$p_{n+1}-p_ n\ll p_ n^{13/23}$$, is dealt with in just 6 pages, for example. As is so often the case, the author’s end of chapter notes form perhaps the best part of the book, describing a multitude of additional results, with comments thereon. There is a bibliography of some 350 references.
Much of the work shows the author’s own influence and interests. In particular the chapters on higher power moments, zero-density theorems and divisor problems contain many of his results, which are currently the best known. These depend heavily on the estimation of exponential sums by the method of exponent pairs, which fact is reflected in the flavour of the results. Thus, for example, Theorem 8.4 gives 8 different lower bounds for a certain quantity $$m(\sigma)$$, for different ranges of $$\sigma$$; one of these is $$m(\sigma)\geq 12408/(4357-4890 \sigma)$$ when $$3/4\leq \sigma \leq 5/6$$. The reviewer feels that such a result is essentially useless - it is not even obvious whether m($$\sigma)$$ is positive or not. The level of exposition is generally good, but in one or two places the logic becomes confused. (For example, the reviewer could not follow the treatment of the condition $$AB^{1-r}\ll | f^{(r)}(x)| \ll AB^{1-r}$$ in the discussion of exponent pairs, and believes this new, weaker, hypothesis may be inadequate.)
Such criticisms aside the author has clearly provided a very significant and much needed service by giving a unified account of so much important work. [See also the preliminary version, Topics in recent zeta function theory (Publ. Math. Orsay 83.06) (1983; Zbl 0524.10032).]
Reviewer: D.R.Heath-Brown

### MSC:

 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$ 11N37 Asymptotic results on arithmetic functions 11L40 Estimates on character sums

### Citations:

Zbl 0042.07901; Zbl 0315.10035; Zbl 0524.10032