Integer datasets frequently appear in many applications in science and engineering. To analyze these datasets, we consider an integer matrix approximation technique that can preserve the original dataset characteristics. Because integers are discrete in nature, to the best of our knowledge, no previously proposed technique developed for real numbers can be successfully applied. In this study, w...

In this paper a model for the specification of the multivariate density of the transaction process is presented. The transaction process is characterized by four marks: price changes, transaction volumes, bid-ask spreads and trade durations. The resulting four dimensional density is decomposed into its conditional and unconditional densities. The density of price changes is modelled with an int...

BK-factorization of bivariate LPDOs is outlined. As an example, class of factorized hyperbolic operators is constructed as well as general solution in quadratures for operators of this class. Coupling of BK-factorization with Darboux-Laplace transformations is described which provided additional factorization conditions (demand of generalized commutativity) in the case when BK-factorization doe...

Let Z+, where d is a positive integer, denote the positive integer d-dimensional lattice points. The notation m ≺ n, where m = (m1,m2, ...,md) and n = (n1, n2, ..., nd) ∈ Z d +, means that mi 6 ni, 1 6 i 6 d. Let {αi, 1 6 i 6 d} be positive constants, and let n = (n1, n2, ..., nd) ∈ Z d +, we denote |n| = ∏d i=1 ni, |n(α)| = ∏d i=1 n αi i , I(n) = {(a1, . . . , ad) ∈ Z d + : 2 ni−1 6 ai < 2 ni ...

This work presents novel methods for verification of reachability and termination properties of programs that manipulate unbounded integer data. Most of these methods are based on acceleration techniques which compute transitive closures of program loops. Firtly, we present an algorithm that accelerates several classes of integer relations and show that the new method performs up to four orders...

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/ or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, ...

One of the issues in Data Envelopment Analysis (DEA) is sensitivity and stability region of the speci c decision making unit (DMU), included ecient and inecient DMUs. In sensitivity analysis of ecient DMUs,the largest region should be found namely stability region thatdata variations are only for ecient DMU under evaluation and the data for the remainingDMUs are assumed xed. Also ecient DMU u...