Related papers: On Evaluation of Nonlinear Exponential Sums
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
We present several sequences of Euler sums involving odd harmonic numbers. The calculational technique is based on proper two-valued integer functions, which allow to compute these sequences explicitly in terms of zeta values only.
We discuss the last version as well as applications of a method for obtaining exact solutions of nonlinear partial differential equations. As this version is based on more than one simple equation we call it Simple Equations Method (SEsM).…
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}} $, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational…
This paper evaluates some generalised Euler sums involving the digamma function.
The effective sample size (ESS) measures the informational value of a probability distribution in terms of an equivalent number of study participants. The ESS plays a crucial role in estimating the Expected Value of Sample Information…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
Nonparametric regression models have recently surged in their power and popularity, accompanying the trend of increasing dataset size and complexity. While these models have proven their predictive ability in empirical settings, they are…
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from $C^0$ estimates. Also, the method is flexible and can be…
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…
Explicit exponential stability tests are obtained for the scalar neutral differential equation $$ \dot{x}(t)-a(t)\dot{x}(g(t))=-\sum_{k=1}^m b_k(t)x(h_k(t)), $$ together with exponential estimates for its solutions. Estimates for solutions…