Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

On Blocking Sets in Affine Hjelmslev Planes

ACM Computing Classification System (1998): G.2.1.

On Affine Connections in a Riemannian Manifold with a Circulant Metric and two Circulant Affinor Structures

Ива Р. Докузова, Димитър Р. Разпопов - В настоящата статия е разгледан клас V оттримерни риманови многообразия M с метрика g и два афинорни тензора q и S. Дефинирана е и друга метрика ¯g в M. Локалните координати на всички тези тензори са циркулантни матрици. Намерени са: 1) зависимост между тензора на кривина R породен от g и тензора на кривина ¯R породен от ¯g; 2) тъждество за тензора на кривина R в случая, когато тензорът на кривина ¯R се анулира; 3) зависимост между секционната кривина на прозволна двумерна q-площадка {x, qx} и скаларната кривина на M.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

A New Method for Computing the Eccentric Connectivity Index of Fullerenes

ACM Computing Classification System (1998): G.2.2, G.2.3.

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.

Orthogonal Resolutions and Latin Squares

Resolutions which are orthogonal to at least one other resolution (RORs) and sets of m mutually orthogonal resolutions (m-MORs) of 2-(v, k, λ) designs are considered. A dependence of the number of nonisomorphic RORs and m-MORs of multiple designs on the number of inequivalent sets of v/k − 1 mutually orthogonal latin squares (MOLS) of size m is obtained. ACM Computing Classification System (1998): G.2.1.

Remarks on the Balaban Index

In this paper we compute some bounds of the Balaban index and then by means of group action we compute the Balaban index of vertex transitive graphs. ACM Computing Classification System (1998): G.2.2 , F.2.2.

Programming and Testing a Two-Tree Algorithm

ACM Computing Classification System (1998): G.2.2, F.2.2.

Test, Teachers, Quorum (Pure Populations)

The “trial and error” method is fundamental for Master Minddecision algorithms. On the basis of Master Mind games and strategies weconsider some data mining methods for tests using students as teachers.Voting, twins, opposite, simulate and observer methods are investigated.For a pure data base these combinatorial algorithms are faster then manyAI and Master Mind methods. The complexities of these algorithms arecompared with basic combinatorial methods in AI. ACM Computing Classification System (1998): F.3.2, G.2.1, H.2.1, H.2.8, I.2.6.

Mapping and Merging of Anatomical Ontologies

This article presents the principal results of the Ph.D. thesis Intelligent systems in bioinformatics: mapping and merging anatomical ontologies by Peter Petrov, successfully defended at the St. Kliment Ohridski University of Sofia, Faculty of Mathematics and Informatics, Department of Information Technologies, on 26 April 2013.

Constructing 7-Clusters

ACM Computing Classification System (1998): G.2, G.4.