A collection of converse theorems for integral quadratic constraints (IQCs) is established linear time-invariant systems. It demonstrated that when a system interconnected in feedback with an arbitrary satisfying IQC stable, then the given must necessarily satisfy complementary IQC. These are specialized to derive multiple versions passivity results. They cover standard notions strict as well i...

In this paper, fractional differential equations in the sense of Caputo-Fabrizio derivative are transformed into integral equations. Then a high order numerical method for equation is investigated by approximating integrand with piece-wise quadratic interpolant. The scheme capable handling both linear and nonlinear A detailed error analysis stability region rigorously established.

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, the bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (iemtl) through expansion methods (collocation method, partition method, galerkin method). the method is discussed in detail and illustrated by solving some numerical examples. comparison between the exact and approximated results obtained from these methods is...

in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

We prove that the representations numbers of a ternary definite integral quadratic form defined over Fq[t], where Fq is a finite field of odd characteristic, determine its integral equivalence class when q is large enough with respect to its successive minima. Equivalently, such a quadratic form is determined up to integral isometry by its theta series.

We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and a numb...