Related papers: Schottky's theorem in $\mathbb{C}^n$

Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We present a characterization of sets for which Cartwright's theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

For sums $S_n=\sum_{k=1}^n X_k$, $n\ge 1$ of independent random variables $ X_k $ taking values in $\Z$ we prove, as a consequence of a more general result, that if (i) For some function $1\le \phi(t)\uparrow \infty $ as $t\to \infty$, and…

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…

In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…

Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being…

Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the…

Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension $2^n$, is extended to the case, when both sets of elements depend smoothly on points of…

We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case. Precisely, we give a theorem characterizing first order…

This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.

In this short paper we prove a quantitative version of the Khintchine-Groshev Theorem with congruence conditions. Our argument relies on a classical argument of Schmidt on counting generic lattice points, which in turn relies on a certain…

We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…

We prove a general solvable subgroup theorem in terms of length functions. As applications, we obtain a solvable subgroup theorem in dynamical systems: any solvable group of finite Hirsch length acting on a smooth manifold with uniformly…

The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.

We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of…

We prove a characterization theorem for the test functions in a CKS-space. Some crucial ideas concerning the growth condition are given.

We show that Fueter's theorem holds for a more general class of quaternionic functions than those constructed by the Fueter's method.