mega is a mixed-initiative system with the ultimate purpose of supporting theorem proving in main-stream mathematics and mathematics education. The current system consists of a proof planner and an integrated collection of tools for formulating problems, proving subproblems, and proof presentation.

This work is in a stream (see e.g. [4], [8], [10], [11], [7]) initiated by a paper of Killip and Simon [9], an earlier paper [5] also should be mentioned here. Using methods of Functional Analysis and the classical Szegö Theorem we prove sum rule identities in a very general form. Then, we apply the result to obtain new asymptotics for orthonormal polynomials.

background: posterior urethral valve presenting in adulthood is uncommon. this can be an unusual cause of primary male infertility as a result of abnormalities in sexual function. case presentation: this report describes a 40 year old man who presented to us on account of inability to impregnate his wife after 2 years of marriage. history revealed poor stream of urine since childhood and passag...

boundary layer growth and hence displacement thickness are the key factors in shock position over aerodynamical surfaces at transonic regimes. since boundary layer growth is a function of free stream reynolds number and also of the transition location, the free stream reynolds number and also the other parameters involved in the boundary layer growth and its transition location are determinant ...

We study functionally private approximations. An approximation function g is functionally private with respect to f if, for any input x, g(x) reveals no more information about x than f (x). Our main result states that a function f admits an efficiently-computable functionally private approximation g if there exists an efficiently-computable and negligibly-biased estimator for f . Contrary to pr...

We study the linear stability of Poiseuille flow a viscoelastic upper convected Maxwell fluid in which rheological parameters depend on concentration particles suspended (dense suspension with negligible diffusion). After determining basic and profile we consider temporal three dimensional perturbation form stream-wise span-wise wave. derive linearized perturbed equation prove validity Squire’s...