Related papers: Higher Trigonometry: A Class Of Nonlinear Systems

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…

Let $1 < c < 24/19$. We show that the number of integers $n \le N$ that cannot be written as $[p_1^c] + [p_2^c]$ ($p_1$, $p_2$ primes) is $O(N^{1-\sigma+\varepsilon})$. Here $\sigma$ is a positive function of $c$ (given explicitly) and…

We prove that the maximal dimension of a $p$-central subspace of the generic symbol $p$-algebra of prime degree $p$ is $p+1$. We do it by proving the following number theoretic fact: let $\{s_1,\dots,s_{p+1}\}$ be $p+1$ distinct nonzero…

The main objective of this talk is to develop a matrix pencil approach for the study of an initial value problem of a class of singular linear matrix differential equations whose coefficients are constant matrices. By using matrix pencil…

Given a pattern $p = s_1x_1s_2x_2\cdots s_{r-1}x_{r-1}s_r$ such that $x_1,x_2,\ldots,x_{r-1}\in\{x,\overset{{}_{\leftarrow}}{x}\}$, where $x$ is a variable and $\overset{{}_{\leftarrow}}{x}$ its reversal, and $s_1,s_2,\ldots,s_r$ are…

We consider first the zero-nonzero determination problem, which consists in determining the list of zero-nonzero conditions realized by a finite list of polynomials on a finite set Z included in C^k with C an algebraic closed field. We…

We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for…

The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions…

The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…

We show that a special class of (nonconvex) NMPC problems admits an exact solution by reformulating them as a finite number of convex subproblems, extending previous results to the multi-input case. Our approach is applicable to a special…

It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

Let $\bX=(X_1, \hdots, X_d)$ be a $\mathbb R^d$-valued random vector with i.i.d. components, and let $\Vert\bX\Vert_p= (\sum_{j=1}^d|X_j|^p)^{1/p}$ be its $p$-norm, for $p>0$. The impact of letting $d$ go to infinity on $\Vert\bX\Vert_p$…

We show that if {1, b, c, d} is a D(-1) diophantine quadruple with b<c<d and c=1+s^2, then the cases s=p^k, s=2p^k, c=p and c=2p^k do not occur, where p is an odd prime and k is a positive integer. For the integer d=1+x^2, we show that it…

In this paper we introduce an integer-valued degree for second order fully nonlinear elliptic operators with nonlinear oblique boundary conditions. We also give some applications to the existence of solutions of certain nonlinear elliptic…

This is a continuation of our recent paper. We continue studying properties of the triangular projection ${\mathscr P}_n$ on the space of $n\times n$ matrices. We establish sharp estimates for the $p$-norms of ${\mathscr P}_n$ as an…

Let $s\ge 2$ be an integer. Denote by $\mu_s$ the least integer so that every integer $\ell >\mu_s$ is the sum of exactly $s$ integers $>1 $ which are pairwise relatively prime. In 1964, Sierpi\'nski asked a determination of $\mu_s$. Let…