Single-reed instruments can produce multiphonic sounds when they generate quasi-periodic oscillations. The aim of this article is to identify a minimal model of a single reedinstrument producing quasi-periodic oscillations. To better understand the influence of model parameters on the production of quasi-periodic regimes, the mapping between parameters and quasi-periodic regimes is explicitly i...

The result of Siegel that the Tamagawa number of SLr over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the betti numbers of the moduli of parabolic vector bundles using the Weil conjucture.

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...

The improved computation presented in this paper is aimed to optimize the neural networks learning process using Levenberg-Marquardt (LM) algorithm. Quasi-Hessian matrix and gradient vector are computed directly, without Jacobian matrix multiplication and storage. The memory limitation problem for LM training is solved. Considering the symmetry of quasi-Hessian matrix, only elements in its uppe...

The purpose of this article was to establish manifold versions existence theorems for generalized vector quasi-equilibrium problems in locally compact and σ-compact spaces without any continuity assumption. fixed-point theorem a product Hadamard is the key focus our discussion. We further applied saddle point minimax problems.

Abstract The objective of this work is the study probability occurrence phase portraits in a family planar quasi-homogeneous vector fields quasi degree q , that natural extension linear fields, which correspond to $$q=1.$$ q = 1 . We ob...

This paper proves the equilibrium existence for abstract economies with non-compact infinitedimensional strategy spaces, infinitely many agents, and discontinuous payolT (utility) functions by using the quasi-variational inequality approach. The motivations come from economic applications showing that payoff functions are discontinuous in many cases and the set of feasible allocations generally...