In this note we demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized XY models, and also 1 point out the connection between them and annealed site-diluted (lattice-gas) continuous-spin models.

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional gl 2 -modules. As a byproduct we show that there exist exactly ( n l )

To use soil hydrology processe (SHP) models, which have increasingly extended during the last years, comprehensive knowledge about these models and their modeling approaches seems to be necessary. The modeling approaches can be categorized as either classical or non-classical. Classical approaches mainly model the SHP through solving the general unsaturated flow (Richards) equation, numerically...

To use soil hydrology processes (SHP) models, which have increasingly extended during the last years, comprehensive knowledge about these models and their modeling approaches seems to be necessary. The modeling approaches can be categorized as either classical or non-classical. Classical approaches mainly model the SHP through solving the general unsaturated flow (Richards) equation, numericall...

In this note we demonstrate the occurrence of first-order transitions in temperature for some recently introduced generalized XY models, and also 1 point out the connection between them and annealed site-diluted (lattice-gas) continuous-spin models.

The integral octonions arise from the octonion XY-product. A parallel is shown to exist with the quaternion Z-product. Connections to the laminated lattices in dimensions 4, 8, 16 and 24 (Leech) are developed.

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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