There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Theory of fuzzy integrals and its applications

Convex Analysis: (pms-28)

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

Lithium has been inserted into the spinel Li4Ti5O12 by both chemical and electrochemical methods. The cation distribution in the lithiated phases has been analyzed by 6,7Li NMR, Raman spectroscopy, and X-ray diffraction, and the distribution in the chemically inserted compound has been analyzed additionally by neutron diffraction. A refinement of structural parameters has been carried out by applying the Rietveld method to the neutron diffraction pattern. It is shown that the two insertion methods are based on different mechanisms. Chemically inserted lithium ions are trapped in the (48f) sites of the spinel structure from which they cannot be extracted by electrochemical means. In contrast to the electrochemical Li-insertion, which is accompanied by a spinel to rocksalt phase transition, no such structural change is found for chemical insertion. The consequences of the two different mechanisms for the reversibility of the insertion process are discussed.

Chemical and Electrochemical Li-Insertion into the Li4Ti5O12 Spinel

Introduction of q-calculus.- q-Discrete operators and their results.- q-Integral operators.- q-Bernstein type integral operators.- q-Summation-integral operators.- Statistical convergence of q-operators.- q-Complex operators.

Applications of q-Calculus in Operator Theory

1. Preliminaries.- 2. Approximation by Certain Operators.- 3. Complete Asymptotic Expansion.- 4. Linear and Iterative Combinations.- 5. Better Approximation.- 6. Complex Operators in Compact Disks.- 7. Rate of Convergence for Functions of BV.- 8. Convergence for BV/Bounded Functions on Bezier Variants.- 9. Some More Results on Rate of Convergence.- 10. Rate of Convergence in Simultaneous Approximation.- 11. Future Scope and Open Problems.

Convergence Estimates in Approximation Theory

Some approximation properties of q-Durrmeyer operators

A certain family of summation-integral type operators

In the present paper we propose a generalization of the Baskakov operators, based on q integers. We also estimate the rate of convergence in the weighted norm. In the last section, we study some shape preserving properties and the property of monotonicity of q-Baskakov operators.

https://www.degruyter.com/downloadpdf/j/ms.2011.61.issue-4/s12175-011-0032-3/s12175-011-0032-3.xml

Vijay Gupta

Papers

Applications of q-Calculus in Operator Theory

Convergence Estimates in Approximation Theory

Some approximation properties of q-Durrmeyer operators

A certain family of summation-integral type operators

Generalized q -Baskakov operators