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This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

In this paper, we propose a generalization of a congruence due to Carlitz.

We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.

A generalization of the law of total covariance is presented and proved.

An algebraic deformation theory of coalgebra morphisms is constructed.

We present here another proof of Oscar Rojo's theorems about the spectrum of graph Laplacian on certain balanced trees, by taking advantage of the symmetry properties of the trees in question, and looking into the eigenfunctions of…

We give a simple non-analytic proof of Biggins' theorem on martingale convergence for branching random walks.

We prove a theorem which implies a quantum (multiplicative) analogue of the Horn conjecture, and also of the saturation conjecture. We obtain transversality statements for quantum schubert calculus in any characteristic and also determine…

Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

We present a self-contained proof of the reflection principle for Brownian Motion.

In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of…

We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.

We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometric measure theory, harmonic analysis, and homogeneous…

We show that the existence of disintegration for cylindrical measures follows from a general disintegration theorem for countably additive measures.

We consider the Brown measure of $a+\mathfrak{c}$, where $a$ lies in a commutative tracial von Neumann algebra $\mathcal{B}$ and $\mathfrak{c}$ is a $\mathcal{B}$-valued circular element. Under certain regularity conditions on $a$ and the…

In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs and several results seem to be new.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…