This book presents a method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results are recent, and a significant part of them has not been published yet. Numerous open problems are stated in the text.

Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world.This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.

Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world. This volume contains 14 high quality survey articles -- incorporating original results and describing the main research activities of contemporary applied mathematics -- written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.

Convergence of generalized singular integrals to the unit, multivariate case / George A. Anastassiou and Sorin G. Gal -- Two contemporary computational concepts in numerical analysis / Ioannis K. Argyros -- Linear integral operators with homogeneous kernel: Approximation properties in modular spaces. Applications to Mellin-type convolution operators and to some classes of fractional operators / Carlo Bardaro and Ilaria Mantellini -- On the simultaneous approximation of functions and their derivatives / Theodore Kilgore -- On the computation of minimal projections: Millennium report / B.L. Chalmers, F.T. Metcalf, and B. Shekhtman -- Copositive polynomial approximation revisited / Ying Kang Hu and Xiang Ming Yu -- Neuro-fuzzy adaptive control: Structure, algorithms, and performance / Augustine O. Esogbue -- Sampling theory and function spaces / Hans-Jurgen Schmeisser and Winfried Sickel -- Computational issues in stable financial modeling / Carlo Marinelli and Svetlozar T. Rachev -- Performance measurements: The stable paretian approach / G. Gotzenberger, S.T. Rachev, and E. Schwarz -- Evaluating statistical functionals by means of projections onto convex cones in Hilbert spaces: Part I & II / Thomas Rychlik -- Dynamical systems and discrete methods for solving nonlinear ill-posed problems / Ruben G. Airapetyan and Alexander G. Ramm -- Extrapolation: From calculation of [symbol] to finite element method of partial differential equations / Xiaoping Shen -- A survey on scaling function interpolation and approximation / En-Bing Lin