相关论文: Integral Representations for Computing Real Parabo…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…
In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
A new integral representation is derived using a definite integral given by Cauchy and used to evaluate a number of integrals containing the finite series of special functions.
This monograph presents a detailed analysis of hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions. It continues with a detailed analysis of hypercomplex numbers in n…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
To evaluate the Hadamard finite-part integrals accurately, a novel interpolatory-type quadrature is proposed in this article. In our approach, numerical divided difference is utilized to represent the high order derivatives of the…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way…
We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.