Related papers: On Schurs exponent conjecture and its relation to …

I begin by reviewing the arguments leading to a nonlinear generalisation of Schrodinger's equation within the context of the maximum uncertainty principle. Some exact and perturbative properties of that equation are then summarised: those…

Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On one hand, such an equation generalizes the traditional Schrodinger-Newton and…

I review a number of the open questions about neutrino properties, critique recent hints of neutrino mass, and discuss one recently proposed neutrino mass matrix to illustrate the direction in which we may be headed. I also present one…

By using a language as accessible to a broad audience as possible, in this note we present evidence suggesting scientific caution prior to final claims that neutrinos and quarks are actual physical particles existing in our spacetime. We…

Motivated by Sato and Mori's work on the Korteweg-de Vries (KdV) equation and the modified KdV equation, Mizukawa, Nakajima, and Yamada made a conjecture on 2-reduced Schur functions and Schur's Q-functions. The conjecture claims that…

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and…

In this paper, we prove a conjecture of Schnell in the surface case.

Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in…

This paper is a continuation of Arai's paper on derivability conditions for Rosser provability predicates. We investigate the limitations of the second incompleteness theorem by constructing three different Rosser provability predicates…

We give certain generalization of Niederreiter's result concerning famous Zaremba's conjecture on existence of rational numbers with bounded partial quotients.

The search for a point set configurations of the R^3 space which contains the smallest value of the Euclidean Steiner Ratio is almost finished. In the present work we introduce some analytical methods which aim to support a famous…

The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…

We prove Szpiro's conjecture for elliptic curves over the rationals having $j$-invariant with denominator of logarithmic size with respect to its numerator.

We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…

Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least…

We highlight recent theoretical and observational progress in several areas of neutron star astrophysics, and discuss the prospect for advances in the next decade.

In this note we study some sequences whose ratio converges to the square root of rationals. Further we analyze some related sequences obtained when the above mentioned ratio simplifies.

In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{\"o}dinger equation with random initial conditions. Namely, we describe the nonlinear…

In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.

The Nonstationary Schr\"{o}dinger equation with potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function is considered here in the framework of the extended resolvent approach.…