Hasil untuk "math.AT"

Jovan Radosavljevic, Zoran Stanic, Miodrag Zivkovic

We study diameter 2-critical graphs (for short, D2C graphs), i.e. graphs of diameter 2 whose diameter increases after removing any edge. Our results include structural considerations, new examples and a particular relationship with minimal 2-self-centered graphs stating that these graph classes are almost identical. We pay an attention to primitive D2C graphs (PD2C graphs) which, by definition, have no two vertices with the same set of neighbours. It is known that a graph of diameter 2 and order n, which has no dominating vertex, has at least 2n ? 5 edges, and the graphs that attain this bound are also known. It occurs that exactly three of them are PD2C. The next natural step is to consider PD2C graphs with 2n ? 4 edges. In this context, we determine an infinite family of PD2C graphs which, for every n > 6, contains exactly one graph with 2n ? 4 edges. We also prove that there are exactly seven Hamiltonian PD2C graphs with the required number of edges. We show that for n 6 13, there exists a unique PD2C graph with 2n ? 4 edges that does not belong to the obtained family nor is Hamiltonian. It is conjectured that this is a unique example of such a graph.

Mohammad Masjed-Jamei

We present a generic refinement to the Cauchy-Schwarz inequality in both inner product space and probability space and study some of its special cases.

Mamoru Nunokawa, Janusz Sokół

We determine the sufficient conditions for function f(z) = z + a2z2 + ... to be starlike of order 1/2, which shows also the starlikeness of f.

Bhaskar Srivastava

On expanding Ramanujan's continued fraction in power series, we observe that the sign of the coefficients is periodic with period 4. We also give a combinatorial interpretation for the coefficients.

Chang-Jian Zhao

We establish some new inequalities for s-th functions and means of order k by using Popoviciu?s, Bellman?s, Menon?s and Mitrinovic, Bullen and Vasic?s inequalities. The new inequalities in special cases yield some related inequalities published recently, which provide also new estimates on inequalities of these type.

Abdul Haseeb, Rajendra Prasad

We characterize ?-Kenmotsu manifolds admitting *-conformal ?- Ricci solitons. At last, an example of 7-dimension ?-Kenmotsu manifold is given.

Edward Omey, Kosto Mitov, Rein Vesilo

Jovana Duretic

We give a construction of the Piunikhin-Salamon-Schwarz isomorphism between the Morse homology and the Floer homology generated by Hamiltonian orbits starting at the zero section and ending at the conormal bundle. We also prove that this isomorphism is natural in the sense that it commutes with the isomorphisms between the Morse homology for different choices of the Morse function and the Floer homology for different choices of the Hamiltonian. We define a product on the Floer homology and prove triangle inequality for conormal spectral invariants with respect to this product.

Peter Danchev

We define and investigate the class of almost ?1-n-simply presented p-torsion abelian groups, which class properly contains the subclasses of almost n-simply presented groups and ?1-n-simply presented groups, respectively. The obtained results generalize those obtained by us in Korean J. Math. (2014) and J. Algebra Appl. (2015).

Nela Milosevic

We study topology of the independence complexes of comaximal (hyper)graphs of commutative rings with identity. We show that the independence complex of comaximal hypergraph is contractible or homotopy equivalent to a sphere, and that the independence complex of comaximal graph is almost always contractible.

Emrah Kılıç, Helmut Prodinger

Four generalizations of the Filbert matrix are considered, with additional asymmetric parameter settings. Explicit formula are derived for the LU-decompositions, their inverses, and the inverse matrix. The approach is mainly to use the q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger?s algorithm for some of them, and for the rest of the necessary identities, to guess the relevant quantities and proving them later by induction.

Philippe Blanc

Assuming the Riemann hypothesis, we show that the odd order derivatives of Hardy?s function have, under some condition, an unexpected behavior for large values of t.

Milenko Mosurovic, Michael Zakharyaschev

We consider a new description logic ALCIr that extends ALCI with role inclusion axioms of the form R ? QR1 . . .Rm satisfying a certain regularity condition. We prove that concept satisfiability with respect to RBoxes in this logic is ExpTime-hard. We then define a restriction ALCIr? of ALCIr and show that concept satisfiability with respect to RBoxes in ALCIr? is PSpace-complete.

Dragan Lambic, Miodrag Zivkovic

Random bijective S-box generation methods are considered. An alternative S-box generation method by forming compositions of permutations from some fixed set is proposed. Experiments show that the rate of acceptable S-boxes for all the methods considered is essentially the same. The advantage of the composition method is an obvious parametrization, with the potentially large key space.

Edward Omey

The gamma class ??(g) consists of positive and measurable functions that satisfy f(x + yg(x))/f(x) ? exp(?y). In most cases the auxiliary function g is Beurling varying and self-neglecting, i.e., g(x)/x ? 0 and g??0(g). Taking h = log f, we find that h?E??(g, 1), where E??(g, a) is the class of positive and measurable functions that satisfy (f(x + yg(x))? f(x))/a(x) ? ?y. In this paper we discuss local uniform convergence for functions in the classes ??(g) and E??(g, a). From this, we obtain several representation theorems. We also prove some higher order relations for functions in the class ??(g) and related classes. Two applications are given.

Dung Van

We characterize sequence-covering (resp., 1-sequence-covering, 2-sequence-covering) mssc-images of locally separable metric spaces by means of ?-locally finite cs-networks (resp., sn-networks, so-networks) consisting of ?0-spaces (resp., sn-second countable spaces, so-second countable spaces). As the applications, we get characterizations of certain sequence-covering, quotient mssc-images of locally separable metric spaces.

Dragan Stankov

We investigate the class of ?1 polynomials evaluated at q defined as: A(q) = { ?0 + ?1q + ? ? ? + ?mqm : ?i ? {-1, 1}} and usually called spectrum, and show that, if q is the root of the polynomial xn - xn-1 - ? ? ? - xk+1 + xk + xk-1 + ? ? ? + x + 1 between 1 and 2, and n > 2k + 3, then A(q) is discrete, which means that it does not have any accumulation points.

Georg Nowak

In the classical sense, the set B consists of all integers which can be written as a sum of two perfect squares. In other words, these are the values attained by norms of integral ideals over the Gaussian field Q(i). G. J. Rieger (1965) and T. Cochrane, R. E. Dressler (1987) established bounds for the number of pairs (n; n + h), resp., triples (n; n + 1; n + 2) of B-numbers up to a large real parameter x. The present article generalizes these investigations into two directions: The result obtained deals with arbitrary M-tuples of arithmetic progressions of positive integers excluding the trivial case that one of them is a constant multiple of one of the others. Furthermore, the estimate applies to the case of an arbitrary normal extension K of the rational field instead of Q(i).

Slavko Simic

We prove a theorem concerning asymptotic behavior of general complex-valued kernel convolutions with slowly varying functions in the sense of Karamata. In applications we showed that the content of some classical theorems can be naturally extended on some parts of complex z-plane.