A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.Comment: 4 pages in REVTeX format, 2 figure

Analyticity of The Ground State Energy For Massless Nelson Models

We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive an explicit expression for the ground state energy which is used to determine the effective mass.Comment: 33 pages, 1 figure, added a section on the calculation of the effective mas

Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur

A nested sequence of projectors (2): Multiparameter multistate statistical models, Hamiltonians, S-matrices

Our starting point is a class of braid matrices, presented in a previous paper, constructed on a basis of a nested sequence of projectors. Statistical models associated to such $N^2\times N^2$ matrices for odd $N$ are studied here. Presence of $\frac 12(N+3)(N-1)$ free parameters is the crucial feature of our models, setting them apart from other well-known ones. There are $N$ possible states at each site. The trace of the transfer matrix is shown to depend on $\frac 12(N-1)$ parameters. For order $r$, $N$ eigenvalues consitute the trace and the remaining $(N^r-N)$ eigenvalues involving the full range of parameters come in zero-sum multiplets formed by the $r$-th roots of unity, or lower dimensional multiplets corresponding to factors of the order $r$ when $r$ is not a prime number. The modulus of any eigenvalue is of the form $e^{\mu\theta}$, where $\mu$ is a linear combination of the free parameters, $\theta$ being the spectral parameter. For $r$ a prime number an amusing relation of the number of multiplets with a theorem of Fermat is pointed out. Chain Hamiltonians and potentials corresponding to factorizable $S$-matrices are constructed starting from our braid matrices. Perspectives are discussed.Comment: 32 pages, no figure, few mistakes are correcte

A new eight vertex model and higher dimensional, multiparameter generalizations

We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of $(2n)^2\times(2n)^2$ dimensions with $2n^2$ free parameters $(n=1,2,3,...)$. The simplest, $4\times 4$ case is treated in detail. Powerful recursion relations are constructed giving the dependence on the spectral parameter $\theta$ of the eigenvalues of the transfer matrix explicitly at each level of coproduct sequence. A brief study of higher dimensional cases ($n\geq 2$) is presented pointing out features of particular interest. Spin chain Hamiltonians are also briefly presented for the hierarchy. In a long final section basic results are recapitulated with systematic analysis of their contents. Our eight vertex $4\times 4$ case is compared to standard six vertex and eight vertex models.Comment: 24 pages, 2 figures, some misprints are correcte

Tensor Operators for Uh(sl(2))

Tensor operators for the Jordanian quantum algebra Uh(sl(2)) are considered. Some explicit examples of them, which are obtained in the boson or fermion realization, are given and their properties are studied. It is also shown that the Wigner-Eckart's theorem can be extended to Uh(sl(2)).Comment: 11pages, LaTeX, to be published in J. Phys.

Forecasting demand: development of a fuzzy growth adjusted holt-winters approach

Irrespective of the type of items manufactured by an industry, environment is now becoming progressively more and more competitive than the past few decades. To sustain in this severe competition, companies have no choice but to manage their operations optimally and in this respect the importance of more accurate demand prediction cannot be exaggerated. This research presents a forecasting approach tailoring the multiplicative Holt-Winters method with growth adjustment through incorporation of fuzzy logic. The growth parameter of the time series values is adjusted with the conventional Holt-Winters method and tested for predicting the real-life demand of transformer tank experienced by a local company. The result obtained by applying the new approach shows a significant improvement in the accuracy of the forecasted demand and sheds light on further enhancement of the proposed method by optimizing other time series parameters through fuzzy logic application for possible application in prediction of demand having trend, seasonal and cyclical changes

First Observation of the Hadronic Transition Υ(4S)→ηhb(1P)and New Measurement of the hb(1P) and ηb(1S) Parameters

Using a sample of 771.6×106 ΥΥ(4S) decays collected by the Belle experiment at the KEKB e+e− collider, we observe, for the first time, the transition Υ(4S)→ηhb(1P) with the branching fraction B[Υ(4S)→ηhb(1P)]=(2.18±0.11±0.18)×10−3 and we measure the hb(1P) mass Mhb(1P)=(9899.3±0.4±1.0)  MeV/c2, corresponding to the hyperfine (HF) splitting ΔMHF(1P)=(0.6±0.4±1.0)  MeV/c2. Using the transition hb(1P)→γηb(1S), we measure the ηb(1S) mass Mηb(1S)=(9400.7±1.7±1.6)  MeV/c2, corresponding to ΔMHF(1S)=(59.6±1.7±1.6)  MeV/c2, the ηb(1S) width Γηb(1S)=(8+6−5±5)  MeV/c2and the branching fraction B[hb(1P)→γηb(1S)]=(56±8±4)%