Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Maximum packings of K-v-K-u with triples

We construct, for all positive integers u, and v with u less than or equal to v, a decomposition of K-v - K-u (the complete graph on v vertices with a. hole of size u) into the maximum possible number of edge disjoint triangles.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Timing and duration of the last interglacial inferred from high resolution U-series chronology of stalagmite growth in Southern Hemisphere

High-precision Th-230-U-238 ages for a stalagmite from Newdegate Cave in southern Tasmania, Australia define a rare record of precipitation between 100 and 155 ka before the present. The fastest stalagmite growth occurred between 129.2 +/- 1.6 and 122.1 +/- 2.0 ka (similar to 61.5 mm/ka), coinciding with a time of prolific coral growth from Western Australia (128-122 ka). This is the first high-resolution continental record in the Southern Hemisphere that can be compared and correlated with the marine record. Such correlation shows that in southern Australia the onset of full interglacial sea level and the initiation of highest precipitation on land were synchronous. The stalagmite growth rate between 129.2 and 142.2 ka (similar to 5.9 mm/ka) was lower than that between 142.2 and 154.5 ka (similar to 18.7 mm/ka), implying drier conditions during the Penultimate Deglaciation, despite rising temperature and sea level. This asymmetrical precipitation pattern is caused by latitudinal movement of subtropical highs and an associated Westerly circulation, in response to a changing Equator-to-Pole temperature gradient. Both marine and continental records in Australia strongly suggest that the insolation maximum between 126 and 128 ka at 65 degreesN was directly responsible for the maintenance of full Last Interglacial conditions, although the triggers that initiated Penultimate Deglaciation (at similar to 142 ka) remain unsolved. (C) 2001 Elsevier Science B.V. All rights reserved.

Thermal ionization mass spectrometry U-series dating of a hominid site near Nanjing, China

Mass spectrometric U-series dating of speleothems from Tangshan Cave, combined with ecological and paleoclimatic evidence, indicates that Nanjing Man, a typical Homo erectus morphologically correlated with Peking Man at Zhoukoudian, should be at least 580 k.y. old, or more likely lived during the glacial oxygen isotope stage 16 (similar to 620 ka). Such an age estimate, which is similar to 270 ka older than previous electron spin resonance and alpha counting U-series dates, has significant implications for the evolution of Asian H. erectus. Dentine and enamel samples from the coexisting fossil layer yield significantly younger apparent ages, that of the enamel sample being only less than one-fourth of the minimum age of Nanjing Man. This suggests that U uptake history is far more complex than existing models can handle. As a result, great care must be taken in the interpretation of electron spin resonance and U-series dates of fossil teeth.

Heritability and gene-environment interactions for melanocytic nevus density examined in a U.K. adolescent twin study

Risk factors for melanoma include environmental (particularly ultraviolet exposure) and genetic factors. In rare families, susceptibility to melanoma is determined by high penetrance mutations in the genes CDKN2A or CDK4, with more common, less penetrant genes also postulated. A further, potent risk factor for melanoma is the presence of large numbers of melanocytic nevi so that genes controlling nevus phenotype could be such melanoma susceptibility genes. A large Australian study involving twins aged 12 y of predominantly U.K. ancestry showed strong evidence for genetic influence on nevus number and density. We carried out essentially the same study in the U.K. to gain insight into gene-environment interactions for nevi. One hundred and three monozygous (MZ) and 118 dizygous (DZ) twin pairs aged 10-18 y were examined in Yorkshire and Surrey, U.K. Nevus counts were, on average, higher in boys (mean = 98.6) than girls (83.8) (p = 0.009) and higher in Australia (110.4) than in the U.K. (79.2, adjusted to age 12 y, p < 0.0001), and nevus densities were higher on sun-exposed sites (92 per m(2)) than sun-protected sites (58 per m(2)) (p < 0.0001). Correlations in sex and age adjusted nevus density were higher in MZ pairs (0.94, 95% CI 0.92-0.96) than in DZ pairs (0.61, 95%CI 0.49-0.72), were notably similar to those of the Australian study (MZ = 0.94, DZ = 0.60), and were consistent with high heritability (65% in the U.K., 68% in Australia). We conclude that emergence of nevi in adolescents is under strong genetic control, whereas environmental exposures affect the mean number of nevi.