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Complex Analysis 4 - Exercises - Mathematics

Prove that jf0(z)j 1 ¡ jf(z)j2 · 1 1 ¡ jzj2 for all z 2 D: This is called the Schwarz-Pick lemma. Hint: Consider the limiting case of w ! z
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1
Mathematics
Mathematics

Complex Analysis 4 - Exercises Solution - Mathematics

(from Stein
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33
Mathematics
Mathematics

Complex Algebra 10 - Exercises - Mathematics

Prove that if Re(c) > Re(b) > 0 then F(a, b; c; z) = 1 B(b, c − b) Z 1 0 tb−1(1 − t)c−b−1(1 − zt)−a dt, and deduce the value of F(a, b; c; 1) = limz!1− F(a, b; c; z).
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0
Mathematics
Mathematics

Complex Algebra 8 - Exercises - Mathematics

In Ahlfors’ first exercise for V.1.3 (p.183) he gives a geometric description of the harmonic function PU(z) on the open unit disc  obtained from Poisson’s integral formula when U is the character...
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Mathematics
Mathematics

Complex Algebra 11 - Exercises - Mathematics

Let L  C be a lattice, F its field of doubly-periodic functions, zj (for j = 1, . . . , n) distinct points in C/L, and Pj 2 P[X] polynomials with each Pj(0) = 0. We saw that if there exists f 2 F...
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Mathematics
Mathematics

Complex Algebra 3 - Exercises - Mathematics

Let P(x, y) = Pd k=0 akxkyd−k (ak 2 C, x, y 2 R) be a homogeneous polynomial of degree d. Show directly that P is an analytic function of z = x iy if and only if P = adzd. Conclude that a polynom...
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0
Mathematics
Mathematics

Complex Algebra 5 - Exercises - Mathematics

Let f be a nonconstant analytic function on a neighborhood of z0, and let n be the multiplicity of the zero at z0 of the function f(z)−f(z0). We have seen that, for any a sufficiently close to f(z0...
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0
Mathematics
Mathematics

Complex Algebra 6 - Exercises - Mathematics

[Ahlfors IV.3.1, Ex.2 (p.153)] Express P 1n =−1 1/(z3 − n3) in closed form. ii) [Seen in B. Amend’s P Foxtrot cartoon, 6.ii.1996] Evaluate in closed form: 1k =1(−1)k 1k2/(k3 1).
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Mathematics
Mathematics

Algebraic Number Theory - Essay - Mathematics

An algebraic number field is a finite extension of Q; an algebraic number is an element of an algebraic number field. Algebraic number theory studies the arithmetic of algebraic number fields — the...
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Mathematics
Mathematics

Adavnced Calculus and Linear Algebra 8 - Exercises - Mathematics

It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe. | Thomas Carlyle (1795{1881), who apparently knew his John Donne (\if a clod be...
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Mathematics
Mathematics
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What QoS support can be given at Transaction-level

QoS support can be given at Transaction-level layer. Please tell details about this support.
tylar
30/07/2013

5

Answers

What are the main 2G standards?

There are many different 2G standards are implemented. Please state details.
tylar
30/07/2013

3

Answers

Explain the features of 3G TD-SCDMA

TD-SCDMA was firstly introduced in China. Please tell the major features of this technique.
tylar
29/07/2013

1

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Enlist some of the issues related to international pricing.

International market has to some serious issues regarding maintaining international prices of the product. Please mention some of the issues associated with International Pricing.
tylar
29/07/2013

1

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How Plates present in the soils can be separated?

Platy is normally a part of soil that is present in the form of plates. Please mention the techniques used to separate these plates from the soil structure.
tylar
29/07/2013

1

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What jobs are performed by Database Administrator?

DMS system uses the services of DBA to perform special tasks associated with Databases. Please mention some of the jobs performed by DBA.
tylar
29/07/2013

2

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Explain the features of HSCSD

HSCSD is new technology introduced in circuit switch mode. Please state its features.
tylar
29/07/2013

3

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What is the importance of Demand Conditions?

Factor Condition can ensure the production of goods. Please explain the significance of Demand Condition in a marketing Economic System.
tylar
29/07/2013

5

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Elaborate Piconet network in Bluetooth.

A very strange term I noticed while studying Bluetooth is piconet. Please someone explain it to me.
tylar
29/07/2013

2

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What is meant by Reactive Ion Etching?

One of the man advantages of Etching is the protection of semiconductor surface from contamination. Please explain the main features of Reactive Ion Etching.
tylar
26/07/2013
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