The concept of a homoclinic tube was introduced by Silnikov 14) in a study on the structure of the neighborhood of a homoclinic tube asymptotic to an invariant torus σ under a diffeomorphism F in a finite dimensional phase space. The asymptotic torus is of the saddle type. The homoclinic tube consists of a doubly infinite sequence of tori {σj , j = 0,±1,±2, · · ·} in the transversal intersectio...

In SU(2) gluodynamics we calculate the gluon polarization tensor in an Abelian homogeneous magnetic field in one-loop order in the Lorentz background field gauge. It turned out to be non transversal and consisting of ten tensor structures and corresponding form factors four in color neutral and six in color charged sector. Seven tensor structures are transversal, three are not. The non transver...

A clique-transversal set S of a graph G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set in G. In this paper we present an upper bound and a lower bound on τc(G) for cubic graphs, and characterize the extremal cubic graphs achieving the lower bound. In addition, we present a sharp u...

Let G = (V, E) be a graph with chromatic number χ(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by γct(G). In this paper we characterize the class of trees, unicyclic graphs and c...

Let A be an m n matrix in which the entries of each row are all distinct. Drisko 4] showed that, if m 2n ? 1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as we...

Contractile properties of skeletal muscle are studied for various purposes and mainly by means of force or torque twitch responses. This study compared contractile properties estimated from isometric longitudinal and transversal vastus lateralis twitch mechanical actions using torque and tensiomyography (TMG) as assessment methods, respectively. We calculated delay, contraction, sustain, half r...

As an explicit example of an A∞-structure associated to geometry, we construct an A∞-structure for a Fukaya category of finitely many lines (Lagrangians) in R , i.e., we define also non-transversal A∞-products. This construction is motivated by homological mirror symmetry of (two-)tori, where R is the covering space of a two-torus. The strategy is based on an algebraic reformulation of Morse ho...

The study of gene functions requires the development of a DNA library of high quality through much of testing and screening. Pooling design is a mathematical tool to reduce the number of tests for DNA library screening. The transversal design is a special type of pooling design, which is good in implementation. In this paper, we present a new construction for transversal designs. We will also e...

The standard Pirogov–Sinai theory is generalized to the class of models with two modes of interaction: longitudinal and transversal. Under rather general assumptions about the longitudinal interaction and for one specific form of the transversal interaction it is proved that such system has a variety of phase transitions at any temperature: the parameter which plays the role of inverse temperat...

In this work we consider the problem of finding a minimum Ck-transversal (a subset of vertices hitting all the induced chordless cycles with k vertices) in a graph with bounded maximum degree. In particular, we seek for dichotomy results as follows: for a fixed value of k, finding a minimum Ck-transversal is polynomial-time solvable if k ≤ p, and NP -hard otherwise.