For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

This paper studies the effect of truncation on the large deviations behavior of the partial sum of a triangular array coming from a truncated power law model. Each row of the triangular array consists of i.i.d. random vectors, whose distribution matches a power law on a ball of radius going to infinity, and outside that it has a light-tailed modification. The random vectors are assumed to be R-...

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular, and honeycomb lattices with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement w...

Let L n be a lower triangular matrix of dimension n each of whose nonzero entries is an independent N(0; 1) variable, i.e., a random normal variable of mean 0 and variance 1. It is shown that n , the 2-norm condition number of L n , satisses n p n ! 2 almost surely as n ! 1. This exponential growth of n with n is in striking contrast to the linear growth of the condition numbers of random dense...

We review recent studies about anisotropic flows ($v_1, v_2, v_3$) of charmonium in the quark-gluon plasma produced relativistic heavy-ion collisions. Collective bulk medium are developed due to pressure gradient medium. Strongly coupled with medium, charm quarks carry collective from expanding which will be inherited by regenerated via coalescence process. In event-by-event collisions where nu...

In the Manning equation the hydraulic radius can be defined as the cross-section dimension of the shape. In pipe flow the bed shear stress is assumed to be uniformly distributed along the wetted perimeter which cannot be true in open channel flow. Hence, three approximation of the true boundary shear-stress distribution are examined and more practical conveyance depth or resistance radius formu...

The concept of fuzzy random variable has been applied in several papers to model the present value of life insurance liabilities. It allows the fuzzy uncertainty of the interest rate and the probabilistic behaviour of mortality to be used throughout the valuation process without any loss of information. Using this framework, and considering a triangular interest rate, this paper develops closed...

We examine whether a causal interpretation can be given to the function identified by the conditional moment restriction (CMR). It is shown that in a general nonseparable triangular system the CMR does not identify the average structural function (ASF) nor any other structural object. This implies that the CMR identifies a causal relation only if the model is structurally separable in observabl...

We consider linear equality systems where all the parameters may be fuzzy variables specified by their possibility distribution, the operations addition and multiplication by a real number of fuzzy parameters are defined via a suptriangular norm composition, and the equations are understood in possibilistic sense. We show that when the triangular norm defining the operations and equations is co...