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Payne–Polya–Weinberger, Hile–Protter and Yang’s Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices
In this paper, we prove some analogues of Payne–Polya–Weinberger, Hile–Protter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues...
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Counting the Number of τ-Exceptional Sequences over Nakayama Algebras
The notion of a τ -exceptional sequence was introduced by Buan and Marsh in (
2018 ) as a generalisation of an exceptional sequence for finite... -
Mathematical Experiments on Paper and Computer
We propose a characterization of mathematical experiments in terms of a setup, a process with an outcome, and an interpretation. Using a broad notion...
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Mathematical Experiments on Paper and Computer
We propose a characterization of mathematical experiments in terms of a setup, a process with an outcome, and an interpretation. Using a broad notion...
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Quantum and classical study of prime numbers, prime gaps and their dynamics
A wave function constructed from prime counting function is employed to study the properties of primes using quantum dynamics. The prime gaps are...
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A Plancherel–Polya Inequality in Besov Spaces on Spaces of Homogeneous Type
In this work, we establish a Plancherel–Polya inequality for functions in Besov spaces on spaces of homogeneous type as defined in Han and Yang (Diss...
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Enumeration with Symmetries
In the previous chapters we saw some powerful tools which allow us to count many objects, tools which were especially useful if we wanted to count...
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Enumeration and Pölya’s Theorem
George Pölya was born on December 13, 1887 at Budapestm Austria Hungary. He became a professor of mathematics in 1914 at ETH Zurich in Suritzerland...
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Asymptotic Behavior of Some Types of Solutions of Differential Equations with Different Types of Nonlinearities
We consider a differential equation of the n th order containing a sum of terms with regularly and rapidly varying nonlinearities on the right-hand...
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Some Results Regarding Partial Differential Polynomials and the Uniqueness of Meromorphic Functions in Several Variables
In this paper, we mainly investigate the value distribution of meromorphic functions in ℂ m with its partial differential and uniqueness problem on...
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On character sums with determinants
We estimate weighted character sums with determinants ad − bc of 2 × 2 matrices modulo a prime p with entries a , b , c and d varying over the interval...
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Normed Linear Spaces
In order to do analysis on vector spaces, we need to endow these spaces with a topological structure which is compatible with the linear structure....
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Two results about the Sackin and Colless indices for phylogenetic trees and their shapes
The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics....
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Global Introduction to the Artificial Mathematical Intelligence General Program
A modern version of one of the most fundamental original visions of artificial intelligence concerning mathematical conceptual creation/invention is...
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On Eigenvalue Distribution of Varying Hankel and Toeplitz Matrices with Entries of Power Growth or Decay
We study the distribution of eigenvalues of varying Toeplitz and Hankel matrices such as...
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Circle measurement
The problem with the circle is, that before measuring it, one has to prove that it has length, called perimeter). This appears difficult to...
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Math Puzzles as Learning Devices
As Polya (1957) cogently argued, the use of puzzles and games has always been part of doing and learning mathematics since its emergence as an...
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Totally Positive Functions in Sampling Theory and Time-Frequency Analysis
Totally positive functions play an important role in approximation theory and statistics. In this chapter I will present recent new applications of...
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“That Which a Minority Construct”: Abelian Mathematics in Abel, Galois, Noether, and Grothendieck
This chapter considers the nature of radical transformations of mathematics, enabled by minority mathematics. It will be particularly concerned with...