After careful introduction and discussion of the concepts involved, procedures are developed to compute Racah and Clebsch-Gordan coefficients for general r-fold tensor products of the U(N) groups. In the process, the multiplicity of a given irreducible representation (irrep) in the direct sum basis is computed, and generalized Casimir operators are introduced to uniquely label the multiple irre...

We study the tensor category of modules over a semisimple bialgebra H under the assumption that irreducible H -modules of the same dimension >1 are isomorphic. We consider properties of Clebsch–Gordan coefficients showing multiplicities of occurrences of each irreducible H -module in a tensor product of irreducible ones. It is shown that, in general, these coefficients cannot have small values....

This paper introduces a way of understanding correlation coefficients based on the notion of scaled-score similarity (i.e., closeness to identity). It is suggested that the proposed framework has intuitive al)peal. It points to the equivalence among various correlation coefficients by showing that correlation problems involve the notion of agreement between interval or ordinal measures expresse...

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.

This study addresses the problem of finding the range of efficiency for each Decision Making Unit (DMU) considering uncertain data. Uncertainty in the DMU coefficients in each factor (input or output) is captured through interval coefficients (i.e., these are uncertain but bounded). A twophase additive Data Envelopment Analysis (DEA) model for performance evaluation is used, which is adapted to...

This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0 +a1x+a2x2 +···+an−1xn−1. The coefficients aj (j = 0,1,2, . . . ,n−1) are assumed to be independent normal random variables with nonidentical means. Previous results aremainly for identically distributed coefficients. Our result remains valid when the means of the coefficients are...

The authors address the complex oscillation problems of all solutions homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating growth solution infinite order have been proposed based on Nevanlinna value distribution theory. Compared existing results, hyper-order can be estimated in terms a bounded interval which includes information functions ...

this paper studies the sequential sampling scheme, as a solution to the problem of aliasing, where the sampling interval is restricted to a minimum allowable value d t. in the sequential sampling, the signal is sampled at intervals of d t, d t+ dt , d t+2 dt , d t+3 dt , ...; where dt < d t and may be selected as desirable. the sequential sampling is, however, analyzed and it is proven that, wh...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

This paper proposes a new technique to solve n-th order linear uncertain but bounded (interval) differential equations with interval initial conditions using the interval midpoint. First, the interval differential equation is solved in terms of the interval midpoint. This solution is then used to find the solution of the original interval differential equation. The method is discussed by consid...