An integral representation of the variance of the number of correctly guessed pairs in the matching problem of a two-dimensional sample

1986 ◽  
Vol 33 (1) ◽  
pp. 768-772
Author(s):  
K. P. Latyshev ◽  
L. A. Zolotukhina
Keyword(s):  
Integral Representation ◽  
Two Dimensional ◽  
Matching Problem

Computing internal viscous flow problems for the circle by integral methods

1977 ◽  
Vol 79 (3) ◽  
pp. 609-624 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Integral Representation ◽  
Analytical Solutions ◽  
Reynolds Numbers ◽  
Cylinder Wall ◽  
Two Dimensional ◽  
Discontinuous Surface ◽  
Flow Problems ◽  
Integral Methods

Steady two-dimensional viscous motion within a circular cylinder generated by (a) the rotation of part of the cylinder wall and (b) fluid entering and leaving through slots in the wall is considered. Studied in particular are moving-surface problems with continuous and discontinuous surface speeds, simple inflow–outflow problems and the impinging-jet problem within a circle. The analytical solutions at zero Reynolds number are given for the last two types of problem. Numerical results are obtained at various Reynolds numbers from the integral representation of the solution. At zero Reynolds number this approach involves a quadrature around the circumference of the cylinder. At other Reynolds numbers it involves an iterative–integral technique based on the use of the ‘clamped-plate’ biharmonic Green's function.

MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE

2006 ◽  
Vol 04 (01) ◽  
pp. 31-60 ◽  
Author(s):  
KARIM TRABELSI
Keyword(s):  
Integral Representation ◽  
Internal Energy ◽  
Elastic Membrane ◽  
Gamma Convergence ◽  
Two Dimensional ◽  
Incompressible Materials ◽  
Plate Models ◽  
Γ Convergence ◽  
Nonlinearly Elastic

In this paper, we derive nonlinearly elastic membrane plate models for hyperelastic incompressible materials using Γ-convergence arguments. We obtain an integral representation of the limit two-dimensional internal energy owing to a result of singular functionals relaxation due to Ben Belgacem [6].

TWO-DIMENSIONAL (HALF-) INTEGER SPIN CONFORMAL THEORIES WITH CENTRAL CHARGE c<1

1988 ◽  
Vol 03 (12) ◽  
pp. 2945-2958 ◽  
Author(s):  
V.B. PETKOVA
Keyword(s):  
Ising Model ◽  
Integral Representation ◽  
Central Charge ◽  
Scalar Fields ◽  
Operator Product ◽  
Two Dimensional ◽  
Model Order ◽  
Integer Spin ◽  
Half Integer ◽  
Spin Fields

A generalized integral representation involving two types of charges is explored to construct correlation functions on the plane for c=1–6/(m(m+1))<1 discrete unitary Virasoro series. The various local operator product algebras emerging contain integer, or half-integer, spin fields along with scalar fields. The examples also include a generalization for arbitrary m of the ℤ2-statistics of the Ising model order-disorder fields.

Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method

2017 ◽  
Vol 14 (01) ◽  
pp. 1750028 ◽  
Author(s):  
Gantulga Tsedendorj ◽  
Hiroshi Isshiki
Keyword(s):  
Diffusion Equation ◽  
Integral Representation ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Infinite Domain ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Representation Method ◽  
Advective Diffusion

Generalized integral representation method (GIRM) is designed to numerically solve initial and boundary value problems for differential equations. In this work, we develop numerical schemes based on 1- and 2-step GIRMs for evaluation of the two-dimensional problem of advective diffusion in an infinite domain. Accurate approximate solutions are obtained in both cases of GIRM and compared to the exact ones. The derivation of GIRM is straightforward and implementation is simple.

Two Dimensional Matching

1997 ◽  
Author(s):  
A. Amir ◽  
M. Farach
Keyword(s):  
Pattern Matching ◽  
String Matching ◽  
Higher Dimensions ◽  
Natural Generalization ◽  
Theoretical Problem ◽  
Two Dimensional ◽  
Exact Matching ◽  
Matching Problem ◽  
Deterministic Algorithms ◽  
Special Case

String matching is a basic theoretical problem in computer science, but has been useful in implementating various text editing tasks. The explosion of multimedia requires an appropriate generalization of string matching to higher dimensions. The first natural generalization is that of seeking the occurrences of a pattern in a text where both pattern arid text are rectangles. The last few years saw a tremendous activity in two dimensional pattern matching algorithms. We naturally had to limit the amount of information that entered this chapter. We chose to concentrate on serial deterministic algorithms for some of the basic issues of two dimensional matching. Throughout this chapter we define our problems in terms of squares rather than rectangles, however, all results presented easily generalize to rectangles. The Exact Two Dimensional Matching Problem is defined as follows: . . . INPUT: Text array T[n x n] and pattern array P[m x m]. OUTPUT: All locations [i,j] in T where there is an occurrence of P, i.e. T[i+k+,j+l] = P[k+1,l+1] 0 ≤ k, l ≤ n-1. . . . A natural way of solving any generalized problem is by reducing it to a special case whose solution is known. It is therefore not surprising that most solutions to the two dimensional exact matching problem use exact string matching algorithms in one way or another. In this section, we present an algorithm for two dimensional matching which relies on reducing a matrix of characters into a one dimensional array. Let P' [1 . . .m] be a pattern which is derived from P by setting P' [i] = P[i,l]P[i,2]…P[i,m], that is, the ith character of P' is the ith row of P. Let Ti[l . . .n — m + 1], for 1 ≤ i ≤ n, be a set of arrays such that Ti[j] = T[i, j] T [ i , j + 1 ] • • • T[i, j + m-1]. Clearly, P occurs at T[i, j] iff P' occurs at Ti[j].

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