‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...

In this note, we study the total positivity of a class of infinite recursive matrices that depend on three infinite sets of independent variables and on an integer parameter. We give a simple algebraic proof and provide a few examples.

In the present work the radiation of sound from a bifurcated circular waveguide formed by a semi-infinite rigid duct inserted axially into a larger infinite tube with discontinuous wall impedance is reconsidered through an alternative approach which consists of using the mode matching technique in conjunction with the Wiener-Hopf method. By expressing the total field in the appropriate waveguid...

A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GLn defined on certain infinite-dimensional Grassmannians is studied. It is proved that every finite-dimensional orbit of the action of traceless elements of these commutative Lie algebras is isomorphic...

The disturbance rejection, defined as the problem of designing control laws that ensure, where possible, exogenous disturbances that do not affect the output of the perturbed system, has been resolved by means of algebraic and geometric techniques. This is a steady linear case by means of the static feedback state. Modifications of the Smith form through the SPR0 substitutions are presented whi...

We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given.

We construct a computable, computably categorical field of infinite transcendence degree over Q, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically computable (infinite) transcendence basis.

An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is presented. The method that was used was to replace the Weyl-Heisenberg algebra by other dynamical algebra of low dimension that admits infinite-dimensional irreducible representations with naturally defined generalized coherent states. We have selected the Lie algebra su(1, 1), due to that this algebra posses the necessary c...

Abstract. Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological space X can be canonically embedded into the infinite-dimensional vector space C(X)∗, the dual space of the algebra of continuous functions C(X), as an “algebraic variety", specified by an infinite system of quadratic equations. Buchstaber and Rees have recently extended this to all symmetric powers Symn(X) usi...

The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic quanta, strings and fields of particles ...