Related papers: A birational Nevanlinna constant and its consequen…

Theorem 1 Let F:N-->R stand for any function which a) $F$ monotonically weakly increases; b) $F$ tends to infinity; and c) such that $q/F(q)$ tends to infinity. Let Z_F(q) equal the number of divisors of q less than sqrt{F(q)} minus the…

Let $(W,H,\mu)$ be the classical Wiener space on $\R^d$. Assume that $X=(X_t(x))$ is a diffusion process satisfying the stochastic differential equation with diffusion and drift coefficients $\sigma: \R^n\to \R^n\otimes \R^d$, $b: \R^n\to…

Recently, diffusion distillation methods have compressed thousand-step teacher diffusion models into one-step student generators while preserving sample quality. Most existing approaches train the student model using a diffusive divergence…

Let g be a (say, sufficiently differentiable) function on the reals. One knows how to apply g to Hermitian elements A of a C* algebra. Yet the question of differentiability of the mapping A to g(A) is not trivial, since in general "A and dA…

A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville…

It has recently been proven that the generalised Cauchy fractional derivative (also known as the Riemann-Liouville fractional derivative) is equal to the Grunwald-Letnikov derivative. However, we observe that there are "Grunwald…

The advantage of using a Discrete Variable Representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However the DVR Hamiltonian is approximate and, as a consequence, the results…

This paper deals with the quantitative Schmidt's subspace theorem and the general from of the second main theorem, which are two correspondence objects in Diophantine approximation theory and Nevanlinna theory. In this paper, we give a new…

In this article, we generalize several fundamental results for arithmetic divisors, such as the continuity of the volume function, the generalized Hodge index theorem, Fujita's approximation theorem for arithmetic divisors and Zariski…

In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve the constant functions involving non-negative parameter ?. We derive the approximation behaviour of these operators including global…

Bayesian neural networks (BNN) promise to combine the predictive performance of neural networks with principled uncertainty modeling important for safety-critical systems and decision making. However, posterior uncertainty estimates depend…

Let $\tau(n)$ denote the classical divisor function. In this paper, we consider the hyperbolic fractional sum of the divisor function defined by $$ T(x) = \sum_{n_1 n_2 \leqslant x} \tau\left( \left[ \frac{x}{n_1 n_2} \right] \right) =…

Helmholtz decompositions of elastic fields is a common approach for the solution of Navier scattering problems. Used in the context of Boundary Integral Equations (BIE), this approach affords solutions of Navier problems via the simpler…

We give stability and consistency results for higher order Gr\"unwald-type formulae used in the approximation of solutions to fractional-in-space partial differential equations. We use a new Carlson-type inequality for periodic Fourier…

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

In this paper a type D breakdown of the Navier Stokes (NS) in d=3 is demonstrated. The element of the breakdown also occurs in the Euler equation. We consider the fact that in d=2 Ladyzhenskaya found a generalized type B solution. The…

We consider the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d; the quadratic term in these equations arises from the bilinear map sending two velocity fields v, w : T^d -> R^d into v . D w, and also…

Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford's…

In 1988 P. Erd\"os asked if the prime divisors of $x^n -1$ for all $n=1,2, >...$ determine the given integer $x$; the problem was affirmatively answered by Corrales-Rodorig\'a\~nez and R. Schoof in 1997 together with its elliptic version.…

As the title suggests, we give a formula for the $n^{th}$ derivative of a quotient of two functions, analogous to Leibniz's formula for the product. This particular note has remained unpublished since 2007 (available only my website),…