A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a n...

This article discusses the mathematical concepts of multivariate parametric solids and their description by B-spline basis functions. Parametric solids can model both the shape and unisotropic interior. Three types of parametric solids, Coons body of types 0, 1, and 2, are used to demonstrate the interior modelling often used as initial or boundary conditions in numerical simulation. Multiple p...

In the present article, we construct Szász-Jakimovski-Leviatan operators in parametric form by including sequences of continuous functions and then investigate approximation properties. We have successfully estimated convergence use modulus continuity spaces Lipschitz functions, Peetres $ K $-functional weighted functions.

This paper describes novel methods for evoking a multichannel audio experience over stereo headphones. In contrast to the conventional convolution-based approach where, for example, five input channels are filtered using ten head-related transfer functions, the current approach is based on a parametric representation of the multichannel signal, along with either a parametric representation of t...

Tropical Newton-Puiseux polynomials, defined as piece-wise linear functions with rational coefficients of the variables, play a role tropical algebraic functions. We provide explicit formulas for polynomials being zeroes univariate polynomial parametric coefficients.

OBJECTIVE In recent years, a new type of speaker called the parametric speaker has been used to generate highly directional sound, and these speakers are now commercially available. In our previous study, we verified that the burden of the parametric speaker was lower than that of the general speaker for endocrine functions. However, nothing has yet been demonstrated about the effects of the sh...

Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint a...

Two algorithms for the general case of parametric mixed-integer linear programs (MILPs) are proposed. Parametric MILPs are considered in which a single parameter can simultaneously influence the objective function, the right-hand side and the matrix. The first algorithm is based on branch-and-bound on the integer variables, solving a parametric linear program (LP) at each node. The second algor...

We study parametric integration of functions from the class C([0, 1]12) to C([0, 1]1) in the quantum model of computation. We analyze the convergence rate of parametric integration in this model and show that it is always faster than the optimal deterministic rate and in some cases faster than the rate of optimal randomized classical algorithms.

The non-parametric maximum likelihood estimator and semi-parametric regression models are fundamental estimators for interval censored data, along with standard fullyparametric regression models. The R-package icenReg is introduced which contains fast, reliable algorithms for fitting these models. In addition, the package contains functions for imputation of the censored response variables and ...