Related papers: Generalized QCD$_2$ via the Bilocal Method
A q-discrete version of the two-dimensional Toda molecule equation is proposed through the direct method. Its solution, B\"acklund transformation and Lax pair are discussed. The reduction to the q-discrete cylindrical Toda molecule equation…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
In the paper, a variant of the \ssstar Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild…
In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the…
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…
We present a method for ordering two-nucleon interactions based upon their scaling with the number of QCD colors, $N_c$, in the limit that $N_c$ becomes large. Available data in the two-nucleon sector shows general agreement with this…
A method of local approximation of holomorphic solutions of algebraic equations is discussed
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We show analytically that the QCD potential can be expressed, up to an O(Lambda_QCD^3 r^2) uncertainty, as the sum of a ``Coulomb'' potential (with log corrections at short distances) and a linear potential, within an approximation based on…
There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations…
We propose a new algorithm solving the extended gcd problem, which provides a solution minimizing one of the two coordinates. The algorithm relies on elementary arithmetic properties.
Non-overlapping codes are a set of codewords in $\bigcup_{n \ge 2} \mathbb{Z}_q^n$, where $\mathbb{Z}_q = \{0,1,\dots,q-1\}$, such that, the prefix of each codeword is not a suffix of any codeword in the set, including itself; and for…
The aim of this paper is the study of the bisection method in $\mathbb{R}^n$. In this work we propose a multivariate bisection method supported by the Poincar\'e-Miranda theorem in order to solve non-linear system of equations. Given an…
In this paper, we introduce and develop the method of diagonalization of functions $f:\mathbb{N}\longrightarrow \mathbb{R}$. We apply this method to show that the equations of the form $\Gamma_r(n)+k=m^2$ has a finite number of solutions…
I review the known approaches to two-body nonleptonic $B$ meson decays, including factorization assumption, modified factorization assumption, QCD factorization, and perturbative QCD factorization. Important phenomenological aspects of…
We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the collection of convergent generalised power series, a class of…
We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.
This paper is devoted to bifurcations of periodic solutions of nonlinear measure differential equations with a parameter. Main tools are nonlinear generalized differential equations (in the sense of Kurzweil) and the Kurzweil gauge type…
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…