Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.

Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

we consider a 2-dimensional representation of the hecke algebra h(g7; u), whereg7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):after specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the ...

A spin model (for link invariants) is a square matrix W with non-zero complex entries which satisfies certain axioms. Recently (Jaeger and Nomura, J. Alg. Combin. 10 (1999), 241–278) it was shown that t WW−1 is a permutation matrix (the order of this permutation matrix is called the “index” of W ), and a general form was given for spin models of index 2. In the present paper, we generalize this...

Nopadon Pirarat* Yumi Une** Yasuo Nomura** IMMUNOHISTOCHEMICAL DETECTION OF FELINE VIRAL RHINOTRACHEITIS IN A CAT A female, 10-month old, mixed breed cat showed clinical signs of severe dehydration, purulent nasal discharge, dyspnea, severe crepitating lung sounds and no response to antibiotic treatment. Upon necropsy, histopathology revealed severe, diffuse, fibrinopurulent pleuropneumonia and...

X iv :0 70 8. 10 44 v1 [ co nd -m at .m es -h al l] 8 A ug 2 00 7 Typeset using jjap.cls Aharonov-Bohm Oscillations in Photoluminescence from Charged Exciton in Quantum Tubes Kohei Tsumura, Shintaro Nomura, Pamela Mohan, Junichi Motohisa, and Takashi Fukui Institute of Physics, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8571, Japan CREST-JST, 4-1-8 Hon-cho, Kawaguchi 332-...