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For the noncommutative torus T , in the case of the noncommutative parameter θ = &fracZn;, we construct the basis of Hilbert space &Hamilt;[SUBn] in terms of θ functions of the positions z[SUBi] of n solitons. The wrapping around the torus generates the algebra A[SUBn], which is the Z[SUBn] × Z[SUBn] Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of A[SUBn]. By acting on &Hamilt;[SUBn] we establish the isomorphism of A[SUBn] and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero-Moser models to give the dynamics. The moment map of this twisted cotangent su[SUBn](T) bundle is matched to the D-equation with the Fayet-Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k; u) of the spectral curve det|L(u)- k| = 0 describes the brane configuration, with the dynamical variables z[SUBi] of the noncommutative solitons as the moduli T[SUP⊗n]/S[SUBn]. Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative su[SUBn] (T) cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz. [ABSTRACT FROM AUTHOR]

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid''s theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy S4, which is the base of the bundle S7 obtained by the second Hopf fibration, i.e., S7/S3=S4, appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in the non-commutative algebra of functions on S4, are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. We also discuss some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory. [Copyright &y& Elsevier]

We study the algebra A[sub n], the basis of the Hilbert space H[sub n] in terms of θ functions of the positions of n solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrices of various integrable models. Finally we generalize our result to the generic θ case. [ABSTRACT FROM AUTHOR]

The prevalence of papillary thyroid cancer (PTC) has been rising in recent years. Despite its relatively low mortality, PTC frequently metastasizes to lymph nodes and often recurs, posing significant health and economic burdens. The role of iodine in the pathogenesis and advancement of thyroid cancer remains poorly understood. Circular RNAs (circRNAs) are recognized to function as competing endogenous RNAs (ceRNAs) that modulate gene expression and play a role in various cancer stages. Consequently, this research aimed to elucidate the mechanism by which circRNA influences the impact of iodine on PTC. Our research indicates that high iodine levels can exacerbate the malignancy of PTC via the circ_0004851/miR-296-3p/FGF11 axis. These insights into iodine's biological role in PTC and the association of circRNA with the disease could pave the way for novel biomarkers and potentially effective therapeutic strategies to mitigate PTC progression. [ABSTRACT FROM AUTHOR]

In this paper, the solutions of the Yang–Baxter equation both in the vertex model (R matrix) and in the face model (braiding matrix) are computed explicitly for the octet representation of the quantum Kac–Moody A(1)2 enveloping algebra where there is multiplicity greater than one in the decomposition of the coproduct 8x8. [ABSTRACT FROM AUTHOR]

The development of a Riemann–Hilbert (RH) problem approach to the representation of the Virasoro group introduced in our earlier paper [W. Li and B. Y. Hou, J. Math. Phys. 30, 1198 (1989)] is continued. The Rouche theorem is employed to prove that there exists a set of scalar functions in the complex τ plane, in terms of which the structure of the Virasoro group can be decided. The general form of the RH problem will also be presented and the uniqueness of its solution will be proven. For future use, a standard form of a matrix Fredholm equation equivalent to our RH problem will be deduced. This may help to establish in a future paper the existence of a solution of the RH problem. [ABSTRACT FROM AUTHOR]

The quantum and classical algebras connected with the Zn-symmetric elliptic solution of the Yang–Baxter equation are derived; their structure constants and the relations between the quantum algebra and the classical one are investigated in detail. Moreover, the trigonometric limit of these algebras is worked out. [ABSTRACT FROM AUTHOR]

In this paper, it is the intent to apply the Riemann–Hilbert transformation developed by Hauser and Ernst [J. Math. Phys. 21, 1126, 1418 (1980)] in providing a new representation of the Virasoro group. It is found that the Geroch group that acts on the solution space of the Einstein field equations is extended to the semidirect product of the Virasoro and Kac–Moody groups; also, the relationship between the infinitesimal transformation given previously [B. Y. Hou and W. Li, Lett. Math. Phys. 13, 1 (1987); J. Phys. A 20, L897 (1987); W. Li, Phys. Lett. A 129, 301 (1988)] and the infinitesimal Riemann–Hilbert transformation is pointed out. Finally, it is shown that the well-known Neugebauer–Backlund transformation can be derived from the Riemann–Hilbert transformation. [ABSTRACT FROM AUTHOR]

Using the natural connection form on a principal bundle P(M,G) and the bundle [ATOTHER]@FA[/ATOTHER]([ATOTHER]@FA[/ATOTHER]/G,G) a systematic derivation of the double-cohomological series constituted by the exterior differential d on space-time M and arbitrary, horizontal, and vertical variations in connection space is given. The relationship between these cohomologies and the family index theorem is clarified. The formalism is then used to analyze Abelian gauge structure inside non-Abelian gauge theory. The pertinent functional U(1) connection form, curvature form, and three-form ‘‘curvature’’ are identified and computed, and are related to the θ vacuum, anomalous commutation relation, and Jacobi identity, respectively. Some of the results differ from those obtained by Wu and Zee [Nucl. Phys. B 258, 157 (1985)] and Niemi and Semenoff [Phys. Rev. Lett. 55, 227 (1985)] and the results of this paperrecover theirs under certain conditions. Finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed background connection form is discussed. [ABSTRACT FROM AUTHOR]

We study the elliptic C[sub n] and BC[sub n] Ruijsenaars–Schneider models which are elliptic generalization of systems given in previous paper by the present authors [Chen et al., J. Math. Phys. 41, 8132 (2000)]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parametrized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero–Moser and Toda types. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars). The corresponding r-matrix is shown to be the classical Z[sub n]-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version--the A[sub n-1] Calogero-Moser model. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a non-diagonal reflecting end under domain wall boundary condition. [ABSTRACT FROM AUTHOR]

We study the C[sub n] and BC[sub n] Ruijsenaars-Schneider models with interaction potential of trigonometric and rational types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking a nonrelativistic limit, we also obtain the Lax pairs for the corresponding Calogero-Moser systems. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

One neurotoxic mechanism of amyloid-beta peptide (Aβ), the major component of senile plaques in the brains of Alzheimer's disease (AD) patients, is to trigger cell cycle reentry in fully differentiated neurons. However, the detailed underlying mechanisms remain unclear. Using Aβ25-35–treated primary rat cortical neurons as the experimental system, in the present study we tested whether Aβ-induced inhibitor of differentiation-1 (Id1)/hypoxia-inducible factor-1alpha (HIF-1α) and cyclin-dependent kinase-5 (CDK5) contribute to cell cycle reentry in fully differentiated post-mitotic neurons. We found that Id1-induced HIF-1α mediated Aβ25-35–dependent expression of the cell cycle markers cyclin D1 and proliferating cell nuclear antigen (PCNA), both colocalized with microtubule-associated protein-2 (MAP-2) + cells, indicative of cell cycle reentry in the mature neurons. Aβ25-35 also enhanced p35 cleavage to p25 without affecting CDK5 expression. The CDK5 inhibitor roscovitine and the siRNA targeting CDK5 both suppressed Aβ25-35–dependent HIF-1α expression and cell cycle reentry. Intriguingly, Aβ25-35–induced Id1 repressed p25 production while CDK5/p25 reciprocally inhibited Id1 expression, despite the observation that both Id1 and CDK5/p25 acted upstream of HIF-1α. These results demonstrated that both Id1/HIF-1 and CDK5/HIF-1 contribute to Aβ-induced cell cycle reentry in post-mitotic neurons; furthermore, Id1 and CDK5/p25 reciprocally suppress expression of each other. • Id1-dependent HIF-1 induction contributes to Aβ25-35-mediated cell cycle reentry in post-mitotic cortical neurons. • Id1 and cobalt chloride capable of stabilizing HIF-1α are both sufficient to directly trigger neuronal cell cycle reentry. • Aβ25-35-induced p25 production is required for HIF-1α induction and neuronal cell cycle reentry. • Id1 and CDK5/p25 show antagonism in suppressing expression of each other in cortical cultures. [ABSTRACT FROM AUTHOR]