Let Un; r be a uniform oriented matroid having as bases, B, all r-subsets (resp. as circuits, C, all (r + 1)-subsets) of {1; : : : ; n}. We say that C1 ⊆ C is a covering, of Un; r , if for any base B∈B there is a circuit C ∈C1 such that B ⊂ C. Let G(C1) be the graph having as set of vertices the elements of C1 and where two vertices are joined if they have one base in common. We say that C1 ⊆ C...

One of the most notorious problems with ferroelectric liquid crystal is obtaining zigzag free bistable devices. By investigating the balance between surface azimuthal anchoring energy and bulk elastic energy within the confined chevron layer geometry of C1 and C2, we propose that it is possible to get a zigzag free C1 state by low azimuthal anchoring alignment at a low pretilt angle. The critic...

We calculate one-loop renormalization factors of bilinear quark operators for gluon action including six-link loops and O(a)-improved quark action in the limit of massless quark. We find that finite parts of one-loop coefficients of renormalization factors diminish monotonically as either of the coefficients c1 or c2 + c3 of the six-link terms are decreased below zero. Detailed numerical result...

These notes give a brief summary of the major techniques of the class, and an example for each. The descriptions are kept short so that this can be a useful, quick reference. 1. Executive Summary We record below the types of equations we can solve. In the next sections we give more details, including conditions on the functions and, if possible, explicit solutions. This section is meant to be a...

an analytical equation of state was applied to calculate the thermodynamic properties for argon.the equation of state is that of song and mason. it is based on a statistical-mechanical perturbationtheory of the hard convex bodies and can be written as fifth-order polynomial in the density. thereexist three temperature-dependent parameters: the second virial coefficient, an effective molecularvo...

In this paper C1, C2 are non empty sets. Let C be a non empty set. One can verify that every membership function of C is quasi total. Let C1, C2 be non empty sets. A membership function of C1, C2 is a membership function of [:C1, C2 :]. Let C1, C2 be non empty sets and let h be a membership function of C1, C2. A fuzzy relation of C1, C2, h is a FuzzySet of [:C1, C2 :], h. In the sequel f , g de...

We introduce the notion of twisted balanced metrics. These metrics are induced from specific projective embeddings and can be understood as zeros of a certain moment map. We prove that on a polarized manifold, twisted constant scalar curvature metrics are limits of twisted balanced metrics, extending a result of S.K. Donaldson and T. Mabuchi. Let M be a smooth projective manifold of complex dim...