相关论文: Exact Solution of 1-matrix Model
The formulation of integrable models with open boundary conditions and the functional relations of fused transfer matrices are discussed. It is shown that finite-size corrections to the transfer matrices and unitarity relations of free…
The fully discrete problem for convection-diffusion equation is considered. It comprises compact approximations for spatial discretization, and Crank-Nicolson scheme for temporal discretization. The expressions for the entries of inverse of…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form…
Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gr\"obner basis and a…
We consider the exact solution of a many-body problem of spin-$s$ particles interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The solution is based on a unified formulation of the quantum inverse scattering method for…
We discuss the 1/N expansion of the free energy of N logarithmically interacting charges in the plane in an external field. For some particular values of the inverse temperature beta this system is equivalent to the eigenvalue version of…
Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the…
In this paper we consider estimating the number of solutions to multiplicative equations in finite fields when the variables run through certain sets with high additive structure. In particular, we consider estimating the multiplicative…
The superelastic constitutive model implemented in the commercial finite element code ABAQUS is verified using the method of exact solutions (MES). An analytical solution for uniaxial strain is first developed under a set of simplifying…
A finite expansion of the exponential map for a $N\times N$ matrix is presented. The method uses the Cayley-Hamilton theorem for writing the higher matrix powers in terms of the first N-1 ones. The resulting sums over the corresponding…
A new non-universal abelian extension $\mathrm{G_{SM}}\otimes \mathrm{U(1)}_{X}$ to the Standard Model free from chiral anomalies is presented. The new $X$ charges distinguish among generations so as the fermion mass matrices get…
We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power beta by the Vandermonde) to all orders of 1/N expansion in the case where the limiting eigenvalue…
A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples…
An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified…
We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…