On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables

In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithm computing reducts of decision tables by relational database approach. Let DS = (U, C ∪ {d}) be a consistent decision table, we say that A ⊆ C is a relative reduct of DS if A contains a reduct of DS. Let s = be a relation schema on the attribute set C ∪ {d}, we say that A ⊆ C is a relative minimal set of the attribute d if A contains a minimal set of d. Let Qd be the family of all relative reducts of DS, and Pd be the family of all relative minimal sets of the attribute d on s. We prove that the problem whether Qd ⊆ Pd is co-NP-complete. However, the problem whether Pd ⊆ Qd is in P .

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)

A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

Renewal Processes of Mittag-Leffler and Wright Type

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

Recent Results on Stability Analysis of an Optimal Assembly Line Balance

Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V . Another subset V ⊆ V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V , then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, ..., tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈ V .

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12