Related papers: Generalized QCD$_2$ via the Bilocal Method
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods…
A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to polynomials with the complex coefficients. For a given pair of polynomials and a…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
We consider two approaches for obtain of the generalized Ito-Wentzell formula: the first way uses the generalized Ito's formula; the second one is based on a concept of kernel functions for integral invariants.
In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…
A sum where each of the $N$ summands can be independently chosen from two choices yields $2^N$ possible summation outcomes. There is an $\mathcal{O}(K^2)$-algorithm that finds the $K$ smallest/largest of these sums by evading the…
We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The…
A large-N_f expansion is used to compute the partially quenched chiral condensate of QCD in the microscopic finite-volume scaling region.
Greatest Common Divisor (GCD) computation is one of the most important operation of algorithmic number theory. In this paper we present the algorithms for GCD computation of $n$ integers. We extend the Euclid's algorithm and binary GCD…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
The N=2 supersymmetric KdV equations are studied within the framework of Hirota's bilinear method. For two such equations, namely $N=2, a=4$ and $N=2, a=1$ supersymmetric KdV equations, we obtain the corresponding bilinear formulations.…
We construct a systematic expansion for full QCD. The leading term gives the valence (quenched) approximation.
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
A method is proposed of obtaining (2+1)-dimensional non- linear equations with non-analytic dispersion relations. Bilocal formalism is shown to make it possible to represent these equations in a form close to that for their counterparts in…
We study an optimization problem originated from the Grothendieck constant. A generalized normal equation is proposed and analyzed. We establish a correspondence between solutions of the general normal equation and its dual equation.…