Analytic

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Good ranking is search engine like Google MSN and Yahoo Based on Google Analytic more than 74 visitor come from search engine

Planview Enterprise Insight : What Will You Do with Insight?

Tue, 28 Apr 2009 14:09:27 PDT

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Functions of a Complex Variable - help finding points where the function is not analytic?
Q. The function I have is: f(z) = (z^3 +z)/(z^2 + 4) I need to find the points where the function is not analytic. The back of my book says that the answer is 2i and -2i but I can't seen to get this answer. These problems are really confusing me and any help you could provide would be greatly appreciated! Thanks!
Asked by My Name - Sun Jul 10 17:08:26 2011 - Mathematics - 1 Answers - Comments

A. A function that is single-valued and differentiable in the set of all points in some region R is analytic in R. Thus, determine where f(z) isn't differentiable (just use the familiar quotient rule): f ' (z) = [(3z^2 + 1)(z^2 + 4) - (z^3 + z)(2z)] / [(z^2 + 4)^2] Without any simplification, we can just determine where the singularities are (where the denominator is zero): z^2 + 4 = 0 z = A sqrt(-4) = A 2i Done! P.S. Of course, you could compute the derivative directly from the definition of the derivative and show that its value is [(3z^2 + 1)(z^2 + 4) - (z^3 + z)(2z)] / [(z^2 + 4)^2] independently of the way Dz goes to 0, but that's going to be messy.
Answered by Mr G - Sun Jul 10 17:33:48 2011

Is the square root of a function that is not analytic necessarily not analytic in the complex plane?
Q. I'm trying to prove that the norm of z is nowhere differentiable using the definition of the limit in the complex plane. My thought is to square it, prove that the resulting function is not analytic, and taking the square root. Other methods/thoughts would be appreciated.
Asked by v - Mon Feb 9 20:13:12 2009 - Mathematics - 1 Answers - Comments

A. If I understand you correctly, your strategy is as follows: (1) Show that |z|^2 is nowhere differentiable. (2) Argue that because |z|^2 is nowhere differentiable, |z| can't be either. This will almost work, but there are two issues. The idea you're using in (2) is formulated more clearly without square roots. Textbooks often include a proof that if f and g are differentiable at a point z, then their product fg is also differentiable at z. In particular, if we take f and g to be the same: If f is differentiable at a point z, then so is f^2. This implies that: If f^2 is not differentiable at a point z, then f is not differentiable at z either. The reason for phrasing things in terms of squaring instead of square rooting is that the… [cont.]
Answered by mcbengt - Wed Feb 11 23:07:16 2009

Predixion Software Introduces Interface to Access and Run R Models in the Cloud - Business Wire (press release)
Tue, 09 Nov 2010 14:01:59 GMT+00:00
Business Wire (press release) R customers can now use, reuse and share statistical and predictive models via Predixion's collaborative predictive analytics platform while also gaining ...

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Please Participate in the 5th Annual Data Miner Survey

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2011-04-12 07:00:00

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unknown, asdnews.com
2011-05-05 09:00:00

Analytic Systems has just received their latest order (of a continuing 4 year contract) for the US Army's requirement. This is their first major order on.

Spectrum Analytic Inc
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Complex Analysis An Introduction to the Theory of Analytic Functions of One Complex Variable
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A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

The Practice of Functional Analytic Psychotherapy
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Since the earliest years of its development, Functional Analytic Psychotherapy (FAP) has been hailed for its clinical innovation and transformative power with clients across the range of disorders. Building on the foundations of their earlier volumes about this versatile therapy, the editors of The Practice of Functional Analytic Psychotherapy bring together noted clinicians and researchers to explain in depth how FAP can be used in conjunction with a broad spectrum of therapeutic approaches, and with diverse client populations. The hallmarks of the method, including therapist sensitivity and responding to client behavior in the moment, courage, mindfulness, acceptance, and egalitarianism, inform a wide array of interventions and strategies, among them:-Integrati ng FAP with other treatments, including cognitive behavioral therapy, acceptance and commitment therapy, dialectical behavior therapy, behavioral activation, psychodynamic therapies, and feminist therapies.-Appl ying FAP across cultures, nationalities, and ethnicities.-Em ploying FAP with couples.-Increa sing sensitivity to and effectiveness with sexual minority clients.-Modify ing FAP for developmentally appropriate use with adolescents.-En hancing a team approach with severely mentally ill patients in institutional settings.-Stren gthening the power of interpersonal process groups.As a new tool or an enhancement to current practice, these applications of FAP will give therapists an empowering complement to their work. The Practice of Functional Analytic Psychotherapy points to compelling directions in personal growth and change Aon both sides of the therapeutic bond."Functiona l Analytic Psychotherapy is a powerful intervention that is not psychodynamic, experiential, cognitive-behav ioral, or cognitive, but rather a clinical guideline for how to conduct good therapy. This volume demonstrates how the intervention can be used with different clinical populations, theoretical orientations, and modalities of treatment. Indeed, it is a transtheoretica l approach that can be readily integrated into all approaches to treatment."-Mar vin R. Goldfried, Distinguished Professor Of Psychology Stony Brook University