Let U, V, W be independent random variables having a standard gamma distribution with respective shape parameters a, b, c, and define X = U/(U + W), Y = V/(V + W). Clearly, X and Y are correlated each having a beta distribution, X ∼ B(a, c) and Y ∼ B(b, c). In this article we derive probability density functions of XY, X/Y and X/(X + Y).

We discuss the construction of the spectral curve and the action integrals for the " elliptic " XY Z spin chain of the length Nc. Our analysis can reflect the integrable structure behind the " elliptic " N = 2 supersymmetric QCD with N f = 2Nc .

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Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2|2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented.

Shaw, Keefer, Refsdsl and others (1) have shown that goopotential height is represented on the tcphigrani by an area, and that an isentropic at'mosphere XY (figure l), equal in geopotential height to a given atmosphe,re AB, may be const8ruct8ed by so placing the line XY on the tepliigram t,hat the area XAZ is equal to the area YBZ. The effect of moistmure is normally negligible, but may be allo...

In this note we demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized XY models, and also

Let Mn be the collection of n×n complex matrices equipped with operator norm. Suppose U, V ∈ Mn are two unitary matrices, each possessing a gap larger than ∆ in their spectrum, which satisfy ‖UV −V U‖ ≤ ǫ. Then it is shown that there are two unitary operators X and Y satisfying XY −Y X = 0 and ‖U−X‖+‖V −Y ‖ ≤ E(∆/ǫ) “ ǫ ∆2 ” 1 6 , where E(x) is a function growing slower than x 1 k for any posit...

Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at least a hole is incorporated. We also address the issue of 'in-plane' vortices, in the XY regime. Interestingly, the energy of a single vortex no longer blows u...

the present paper aimed at studying the current models of credit portfolio management. there are currently three types of models which consider the risk of credit portfolio: the structural models (moody's kmv model, and credit- metrics model), the intensity models (the actuarial models) and the econometric models (the macro-factors model). the development of these three types of models is based...