in this paper, we deal with the subdierential concept onhadamard spaces. flat hadamard spaces are characterized, and nec-essary and sucient conditions are presented to prove that the subdif-ferential set in hadamard spaces is nonempty. proximal subdierentialin hadamard spaces is addressed and some basic properties are high-lighted. finally, a density theorem for subdierential set is establi...

The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and quarks, of left and right chirality, and their antiparticles) can be accommodated. The branching of these su(1|5) representations with respect to its subalgebra su(3)× su(2)×u(1) reproduces precisely the classification of these fundamental fermions ac...

1 Summary Su¢ cient-component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of su¢ cient causes, synergism and su¢ cient cause interactions. Doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of su¢ cient cause interactions. The conditions are novel in that, unlike other conditions in t...

We study a novel five-dimensional, N=5 supergravity in the context of Lie superalgebra SU(5/2). The possible successive superalgebraic truncations from N=5 theory to the lower supersymmetric N=4,3,2, and 1 supergravity theories are systematically analyzed as a sub-superalgebraic chain of SU(5/2)⊃ SU(4/2) ⊃ SU(3/2) ⊃ SU(2/2) ⊃ SU(1/2) by using the Kac-Dynkin weight techniques. PACS Nos: 04.65.+e...

We present two 3-family SU(5) grand unified models in the heterotic string theory. One model has 3 chiral families and 9 pairs of 5+ 5 Higgs fields, and an asymptotically-free SU(2) ⊗ SU(2) hidden sector, where the two SU(2)s have different matter contents. The other model has 6 left-handed and 3 righthanded 10s, 12 left-handed and 9 right-handed 5s, and an asymptotically-free SU(3) hidden sect...

In this talk we discuss the phenomenology of models with replicated elec-troweak gauge symmetries, based on a framework with the gauge structure [SU (2) or U (1)] × U (1) × SU (2) × SU (2). In this talk we discuss the phenomenology of models with replicated elec-troweak gauge symmetries. The general framework we use is based on the gauge structure [SU (2) or U (1)] × U (1) × SU (2) × SU (2), an...

We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo methods. The exactly known SU(2) results are reproduced to very high precision. Our calculations for SU(3) agree closely with an extension of a conjecture due to Green and Gutperle concerning the exact value of the SU(N) partition functions. ∗k...

We consider the construction of SU(2)L ⊗ SU(2)R ⊗ SU(4) partial unification models as an example of phenomenologically acceptable unification models in the absence of supersymmetry in non-commutative geometry. We exploit the Chamseddine, Felder and Fröhlich generalization of the Connes and Lott model building prescription. By introducing a bi-module structure and appropriate permutation symmetr...

Ecotropic murine leukemia virus (MuLV) infection is initiated by the interaction between the surface glycoprotein (SU) of the virus and its cell-surface receptor mCAT-1. We investigated the SU-receptor interaction by using a naturally occurring soluble SU which was encoded by the envelope (env) gene of a defective endogenous MuLV, Fv-4(r). Binding of the SU to mCAT-1-positive mouse cells was co...

This paper discuss Fuzzy SU -ideal Topological Structure on SU algebras, by connecting the two notions SU -algebras and Fuzzy Topology.