A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, while the tracel...

The SO(5)⊃ SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1, 1)× SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃ SO(3) spherical harmonics and use them to compute the Clebsc...

I USE the term covariants to include invariants, and I write particularly concerning lists of covariants (groundforms) of the binary quintic and sextic, those of quantics of lower degree being few and well known. When the weight of a covariant is spoken of in this article, it must be understood to mean the weight of its first term or "source." The symbol 5ft will denote that covariant of the qu...

GLh(n) × GLh′(m)-covariant (hh)-bosonic (or (hh)-fermionic) algebras Ahh′±(n,m) are built in terms of the corresponding Rh and Rh′-matrices by contracting the GLq(n) × GLq±1(m)-covariant q-bosonic (or q-fermionic) algebras A q± (n,m), α = 1, 2. When using a basis of A q± (n,m) wherein the annihilation operators are contragredient to the creation ones, this contraction procedure can be carried o...

Many non-Abelian finite subgroups of SU(3) have been used to explain the flavor structure of the Standard Model. In order to systematize and classify successful models, a detailed knowledge of their mathematical structure is necessary. In this paper we shall therefore look closely at the series of finite non-Abelian groups known as ∆(6n), its smallest members being S3 (n = 1) and S4 (n = 2). Fo...

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(ĝln), as defined by Leclerc and Thibon [LT], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur alge...

in traditional portfolio selection model coefficients often are certain and deterministic, but in real world these coefficients are probabilistic. so decision maker cannot estimate them exactly. financial optimization is one of the most attractive areas in decision under uncertainty. in the portfolio selection problem the decision maker considers simultaneously conflicting objectives such as ra...