Related papers: The solution to the Kadison--Singer Problem: yet a…
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
By creating a new method, the author proved the well-known world's baffling problems Goldbach conjecture, twin primes conjecture, the Proposition (C) and the Proposition $n^2+1$.
The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed in a mathematical viewpoint. All these multiple solutions were found via a fit process previously,…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
Some facts about 4-spinors listed and discussed. None, well perhaps some, of the work is original. However, locating formulas in other places has proved a time-consuming process in which one must always worry that the formulas found in any…
We study Cantor's powerset theorem from a graph-theoretic perspective, consider some alternative proofs to Cantor's original, and provide a new proof.
The first paper is an invited comment on arXiv:1110.5527 presented at Hypercomplex Seminar 2012 and on sixteen earlier published papers by Zhidong Zhang and Norman H. March. All these works derive from an erroneous solution of the…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We provide both human and computer (even better collaboration between the two) proofs to four recent American Mathematical Monthly problems, namely problem 11897, problem 11899, problem 11916, and problem 11928. We also show that problem…
We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using $KK$-theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the…
This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compares its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of…
We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group $S$, that contain…
In [10] the third author of this paper presented two conjectures on the additive decomposability of the sequence of ''smooth'' (or ''friable'') numbers. Elsholtz and Harper [4] proved (by using sieve methods) the second (less demanding)…
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
Existing singing voice synthesis (SVS) models largely rely on fine-grained, phoneme-level durations, which limits their practical application. These methods overlook the complementary role of visual information in duration prediction.To…
A modified equation, the S-K equation, fits data that the current neural conduction equation, the K-R equation, does not. The S-K equation is a modified Heaviside equation, based on a new interpretation of cross terms. Elements of neural…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
We provide an historical account of equivalent conditions for the Riemann Hypothesis arising from the work of Ramanujan and, later, Guy Robin on generalized highly composite numbers. The first part of the paper is on the mathematical…