The SU(2)L ⊗ SU(2)R symmetric Yukawa model with mirror-fermions in the limit where the mirror-fermion is decoupled is studied both analytically and numerically. The bare scalar self-coupling λ is fixed at zero and infinity. The phase structure is explored and the relevant phase transition is found to be consistent with a second order one. The fermionic mass spectrum close to that transition is ...

Introduction. The hypersurfaces in weighted projective spaces often appear as important examples in the context of mirror symmetry. In this paper, we describe the relation between polar duality and duality of weight systems. The duality of weights partly suggests why [CLS] produced a mirror symmetric phenomena using only a resolution of weighted hypersurface in weighted P. In fact, recently it ...

For a given n by n matrix the ratio between the componentwise distance to the nearest singular matrix and the inverse of the optimal Bauer-Skeel condition number cannot be larger than (3 + 2 √ 2) · n. In this note a symmetric matrix is presented where the described ratio is equal to n for the choice of most interest in numerical computation, for relative perturbations of the individual matrix c...

Electrophysiological and behavioral studies in many species have demonstrated mirror-image confusion for objects, perhaps because many objects are vertically symmetric (e.g., a cup is the same cup when seen in left or right profile). In contrast, the navigability of a scene changes when it is mirror reversed, and behavioral studies reveal high sensitivity to this change. Thus, we predicted that...

We study the asymmetric respectively symmetric conflict matrix of a multi-clause-set F , where the entry at position (i, j) is the number of literals, which appear positively in clause Ci of F and negatively in clause Cj (at the same time), respectively the number of clashes (at all) between Ci and Cj . A central problem is the determination of the symmetric/asymmetric conflict number of a (sym...

In this paper, characterizations of secondary κkernel symmetric fuzzy matrices are obtained. Relation between sκkernel symmetric, skernel symmetric, κkernel symmetric and kernel symmetric matrices are discussed. Necessary and sufficient conditions are determined for a matrix to be sκkernel symmetric.

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems where fuzzy coefficient matrix is a positive matrix. This paper mainly discusses a new decomposition of a nonsingular fuzzy matrix, a symmetric matrix times to a triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy s...

This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...

The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L-R) symmetric if the crystals are formed from the surrounding vapor. L-R symmetry of a halo display implies here that the cross sectio...

Given an undamped gyroscopic system GðλÞ 1⁄4 Mλ þ CλþK with M , K symmetric and C skew-symmetric, this paper presents a real-valued spectral decomposition of GðλÞ by a real standard pair ðX;TÞ and a skew-symmetric parameter matrix S . When T is assumed to be a block diagonal matrix, the parameter matrix S has a special structure. This spectral decomposition is applied to solve the quadratic inv...