Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

The purpose of this section is to describe a construction, due to Totaro [5], of an algebro-geometric substitute for the classifying space of topological group. For topological group G, the spaces EG and BG are infinite dimensional, it is hard to control in general. What Totaro produces for a reductive algebraic group is a directed system of G-bundles En → Bn with the following property: for an...

Several structural properties of an algebraic structure can be seen from the higher commutators its congruences. Even on a finite algebra, sequence commutator operations is infinite object. In this paper, we exhibit representations for algebras congruence modular varieties.

in this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. the error dynamics of each player depends on its neighbors’ information. detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. the introduced reinforcement learning-based algorithms learn online the approximate solution...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a mean to characterize the scrambling properties quantum system. We show that presence local conserved quantities typically results in, at fastest, an algebraic OTOC provided (i) dynamics is and (ii) system follows eigenstate thermalization hypothesis. Our result relies on scaling infinite-time value OTOCs with size, ...

The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with 2 compact elements. We show that every algebraic lattice with at most 2 compact elements is a complete sublattice of Cl(X). 1. How complicated is the clone lattice? Fix a base set X and denote for all n ≥ 1 the set of all n-ary operations on X by O(n). Then O = ⋃ n≥1 O (n) is the set of all functions on X which ...