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Extending quick hypervolume
We extend the functionality of the quick hypervolume ( QHV ) algorithm. Given a set of d -dimensional points this algorithm determines the hypervolume...
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Real Analysis
Real analysis starts with a treatment of sequences and series, including, among other things, applications to the Cauchy criterior of convergence,...
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The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The...
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Birth, growth and computation of pi to ten trillion digits (2013)
Paper 22: Ravi Agarwal, Hans Agarwal and Syamal K. Sen, “Birth, growth and computation of pi to ten trillion digits,” Advances in Di erence...
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Distances on Numbers, Polynomials, and Matrices
Here we consider the most important metrics on the classical number systems: the semiring...
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Asymptotic Properties of Fibonacci Cubes and Lucas Cubes
It is proved that the asymptotic average eccentricity and the asymptotic average degree of both Fibonacci cubes and Lucas cubes are
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Topological Stabilizer Codes
Protecting quantum information from decoherence is of prime importance to realize quantum information processing. Several approaches have been...
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P
P, die Komplexitätsklasse aller durch polynomiale Algorithmen (↗ polynomialer Algorithmus) lösbaren Probleme.
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Exponential generating function of hyperharmonic numbers indexed by arithmetic progressions
There is a circle of problems concerning the exponential generating function of harmonic numbers. The main results come from Cvijovic, Dattoli,...
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Buchstaber invariant theory of simplicial complexes and convex polytopes
The survey is devoted to the theory of a combinatorial invariant of simple convex polytopes and simplicial complexes that was introduced by V.M....
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Degree and Dimension Estimates for Invariant Ideals of \(P\) -Solvable Recurrences
Motivated by the generation of polynomial loop invariants of computer programs, we study...
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Cellular resolutions of ideals defined by nondegenerate simplicial homomorphisms
In this paper we introduce the class of ordered homomorphism ideals and prove that these ideals admit minimal cellular resolutions constructed as...
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Markoff–Rosenberger triples in geometric progression
We study solutions of the Markoff–Rosenberger equation ax 2 + by 2 + cz 2 = dxyz whose coordinates belong to the ring of integers of a number field and...
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Zeilberger’s Algorithm
In this chapter, we introduce Zeilberger’s extension of Gosper’s algorithm, using which one can not only prove hypergeometric identities but also sum...
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Accelerating Indefinite Summation: Simple Classes of Summands
We present the history of indefinite summation starting with classics (Newton, Montmort, Taylor, Stirling, Euler, Boole, Jordan) followed by modern...
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Creators
The title of any book, monograph, or article tells the reader broadly what he can expect to attain from the book by reading it. The title is...
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Birth, growth and computation of pi to ten trillion digits
The universal real constant pi, the ratio of the circumference of any circle and its diameter, has no exact numerical representation in a finite...
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Inner Issues
THE SPECIAL SINGNS that consititute part of the written mathematical record from a numerous and colorful addition to the signs of the natural...
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The Last Period
The sixth chapter covers the last quarter of the century. We present first the large sieve and its applications (Bombieri’s density theorem and the...