Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in the spinor representation, the dual gauge group G breaks to a group H such that π2(G/H) = Z2. The quantum numbers of the associated Z2 monopole and those of ...

If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossing number of the graph G0 + xy is equal to d. Riskin asked if his result holds for arbitrary 3-con...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

The paper deals with calculation methods for failure and repair frequencies of multi-state monotone systems, both for the instantaneous and steady state cases. Being based on the binary representation of multi-state structure, new general formula for the failure/repair frequency is derived. This formula is used to obtain simple rules for the calculation of failure/repair frequency. In particula...

Let (W, S) be a finite Coxeter system and A := Z[0] be the group algebra of a finitely generated free abelian group 0. Let H be an Iwahori-Hecke algebra of (W, S) over A with parameters vs . Further let K be an extension field of the field of fractions of A and KH be the extension of scalars. In this situation Kazhdan and Lusztig have defined their famous basis and the so called left cell modul...

For every composition λ of a positive integer r , we construct a finite chain complex whose terms are direct sums of permutation modules M for the symmetric group Sr with Young subgroup stabilizers Sμ. The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ the chain complex has homology concentrated in one degree (at...

If the integer translates of a function φ with compact support generate a frame for a subspace W of L 2 (R), then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. We demonstrate that considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. For example, we present a condition for the existenc...

Adult non-native perception is subject to influence from a variety of factors, including native language experience. The present research examines the effect of linguistic experience on non-native tone perception and tone word learning. Native Thai and English-speaking participants completed seven sessions of lexical identification training on words distinguished by Cantonese tones. A tone iden...

An almost general consensus exists on the idea that deconfinement is an order disorder transition. The present experimental upper limits on the observation of free quarks are 15 orders of magnitude smaller than what is expected in the absence of confinement. The only natural interpretation is that confinement is an absolute property relying on symmetry. The confined phase of QCD is disordered (...

A linear program is typically specified by a matrix A together with two vectors b and c, where A is an n-by-d matrix, b is an n-vector and c is a d-vector. There are several canonical forms for defining a linear program using (A, b, c). One commonly used canonical form is: max cx s.t. Ax ≤ b and its dual min by s.t A y = c, y ≥ 0. In [Ren95b, Ren95a, Ren94], Renegar defined the condition number...