The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of the deformed W_N algebra are derived explicitly.Comment: 15 pages, to appear in Journal of physics A special issue - RAQIS0

The geometry of dual isomonodromic deformations

The JMMS equations are studied using the geometry of the spectral curve of a pair of dual systems. It is shown that the equations can be represented as time-independent Hamiltonian flows on a Jacobian bundle

A qq-anaolg of the sixth Painlev\'e equation

A $q$-difference analog of the sixth Painlev\'e equation is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of $q$-hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected

Symmetries and tau function of higher dimensional dispersionless integrable hierarchies

A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables $(k,x)$ of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions compactified to a two (or any even) dimensional torus. Integrability of this hierarchy and the existence of an infinite dimensional of ``additional symmetries'' are ensured by an underlying twistor theoretical structure (or a nonlinear Riemann-Hilbert problem). An analogue of the tau function, whose logarithm gives the $F$ function (``free energy'' or ``prepotential'' in the contest of matrix models and topological conformal field theories), is constructed. The infinite dimensional symmetries can be extended to this tau (or $F$) function. The extended symmetries, just like those of the dispersionless KP hierarchy, obey an anomalous commutation relations.Comment: 50 pages, (Changes: a few references are added; numbering of formulas are slightly modified

Elliptic Deformed Superalgebra uq,p(sl^(M∣N))u_{q,p}(\hat{{sl}}(M|N))

We introduce the elliptic superalgebra $U_{q,p}(\hat{sl}(M|N))$ as one parameter deformation of the quantum superalgebra $U_q(\hat{sl}(M|N))$. For an arbitrary level $k \neq 1$ we give the bosonization of the elliptic superalgebra $U_{q,p}(\hat{sl}(1|2))$ and the screening currents that commute with $U_{q,p}(\hat{sl}(1|2))$ modulo total difference.Comment: LaTEX, 25 page

On the Vertex Operators of the Elliptic Quantum Algebra Uq,p(sl2^)kU_{q,p}(\widehat{sl_2})_{k}}

A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ for any given level $k$ is constructed in terms of three free boson fields and their accompanying twisted partners. It can be viewed as the elliptic deformation of Wakimoto realization. Two screening currents are constructed; they commute or anti-commute with $U_{q,p}(\widehat{sl_2})$ modulo total q-differences. The free fields realization for two types vertex operators nominated as the type $I$ and the type $II$ vertex operators are presented. The twisted version of the two types vertex operators are also obtained. They all play crucial roles in calculating correlation functions.Comment: 23 page

Utilizing micro-computed tomography to evaluate bone structure surrounding dental implants: a comparison with histomorphometry

Although histology has proven to be a reliable method to evaluate the ossoeintegration of a dental implant, it is costly, time consuming, destructive, and limited to one or few sections. Microcomputed tomography (µCT) is fast and delivers three-dimensional information, but this technique has not been widely used and validated for histomorphometric parameters yet. This study compared µCT and histomorphometry by means of evaluating their accuracy in determining the bone response to two different implant materials. In total, 32 titanium (Ti) and 16 hydroxyapatite (HA) implants were installed in 16 lop-eared rabbits. After 2 and 4 weeks, the animals were scarified, and the samples retrieved. After embedding, the samples were scanned with µCT and analyzed three-dimensionally for bone area (BA) and bone-implant contact (BIC). Thereafter, all samples were sectioned and stained for histomorphometry. For the Ti implants, the mean BIC was 25.25 and 28.86% after 2 and 4 weeks, respectively, when measured by histomorphometry, while it was 24.11 and 24.53% when measured with µCT. BA was 35.4 and 31.97% after 2 and 4 weeks for histomorphometry and 29.06 and 27.65% for µCT. For the HA implants, the mean BIC was 28.49 and 42.51% after 2 and 4 weeks, respectively, when measured by histomorphometry, while it was 33.74 and 42.19% when measured with µCT. BA was 30.59 and 47.17% after 2 and 4 weeks for histomorphometry and 37.16 and 44.95% for µCT. Direct comparison showed that only the 2 weeks BA for the titanium implants was significantly different between µCT and histology (p = 0.008). Although the technique has its limitations, µCT corresponded well with histomorphometry and should be considered as a tool to evaluate bone structure around implants

Form factor expansion of the row and diagonal correlation functions of the two dimensional Ising model

We derive and prove exponential and form factor expansions of the row correlation function and the diagonal correlation function of the two dimensional Ising model

Quantum Lie algebras associated to Uq(gln)U_q(gl_n) and Uq(sln)U_q(sl_n)

Quantum Lie algebras \qlie{g} are non-associative algebras which are embedded into the quantized enveloping algebras $U_q(g)$ of Drinfeld and Jimbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The quantum Lie product on \qlie{g} is induced by the quantum adjoint action of $U_q(g)$. We construct the quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$. We determine the structure constants and the quantum root systems, which are now functions of the quantum parameter $q$. They exhibit an interesting duality symmetry under $q\leftrightarrow 1/q$.Comment: Latex 9 page