Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Quantum and super-quantum group related to the Alexander-Conway polynomial

We describe the quasitriangular structure (universal R-matrix) on the nonstandard quantum group U_q(H₁, H₂, X^±) associated to the Alexander-Conway matrix solution of the Yang-Baxter equation. We show that this Hopf algebra is connected with the super-Hopf algebra U_qgl(1 | 1) by a general process of superization.     

Quantum poincaré algebra with standard real structure

A new real quantum Poincaré algebra which is a standard *-Hopf algebra is obtained by the construction of U_q (O(3,2)) (q real). The deformation parameter K is mass-like, and the classical Poincaré algebra is obtained in the limit K → ∞. For our K-Poincaré algebra both Casimirs are given.     

磁共振碳谱研究:应用分子子图指数估计与预测卤代烃化学位移

系统研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文提出了一组含多元素组成的分子子图指数矢量(VMSG),并发现它与卤代烃化学位移(CSRX)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Fredholm modules for quantum Euclidean spheres

The quantum Euclidean spheres, S_q^N−1, are (noncommutative) homogeneous spaces of quantum orthogonal groups, SO_q(N). The *-algebra A(S^N−1_q) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres S_q^N−1. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i.e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra A(S^N−1_q).     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

Gauge-Higgs unification in the left–right model

We construct a supersymmetric left–right model in four dimension with gauge-Higgs unification starting from a SU(3)_c×SU(4)_w×U(1)_B−L gauge symmetry in five dimension. The model has several interesting features, such as, the CKM mixings in the quark sector are naturally small while for the neutrino sector it is not, light neutrino masses can be generated via the seesaw mechanism in the usual way, and the model has a U(1)_R symmetry which naturally forbid dimension five proton decay operators. We also discuss the grand unification of our model in SO(12) in five dimensions.     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

Eigen microstates and their evolutions in complex systems

Emergence refers to the existence or formation of collective behaviors in complex systems. Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A, whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as ■, where r= min(N,M), eigenvalue σIbehaves as the probability amplitude of the eigen microstate U_I so that ■ and U_I evolves following V_I. In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σIbecomes finite in the thermodynamic limit, there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U_I and a phase transition in complex system. Our framework has been applied successfully to equilibrium threedimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.     

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

We present the procedure of exactly solving the Izergin–Korepin model with open boundary conditions by using the algebraic Bethe ansatz, which include constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations. We give a proof about our conclusions on the multi-particle state based on an assumption. When the model is U_q(su(2)) quantum invariant, our results agree with that obtained by analytic Bethe ansatz method.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Remarks on bicovariant differential calculi and exterior Hopf algebras

We show that every bicovariant differential calculus over the quantum groupA defines a bialgebra structure on its exterior algebra. Conversely, every exterior bialgebra ofA defines bicovariant bimodule overA. We also study a quasitriangular structure on exterior Hopf algebras in some detail.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions

Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {J_ij} distributed according to the family of continuous probability distributions P_q(J_ij) ∝ 1/[1 + (q − 1)J_ij²/2J²]^{1/(q − 1)} (if 1 + (q − 1) J_ij²/2J² > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment J_ij² proportional to (5 − 3q)⁻¹ for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, P_q(J_ij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature T_c. We show numerically that T_c does not scale with J_ij^21/2 (contrary to the usual belief), but rather with the width at midheight of P_q(J_ij). Our results suggest that T_c vanishes as −1/q when q → −∞; furthermore, we verified that T_c diverges exponentially when q approaches 3 from below.     

Probing the isospin dependent in-medium nucleon–nucleon cross section by nucleon emissions

The effects of the symmetry potential and the isospin dependent in-medium nucleon–nucleon (NN) cross section on the number of proton(neutron) emissions N_p(N_n) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N_p(N_n) but N_p(N_n) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies. We propose to make use of the N_p(N_n) as a probe to extract information on the isospin dependent in-medium NN cross section.     

A Pati–Salam model from branes

We explore the possibility of embedding the Pati–Salam model in the context of Type I brane models. We study a generic model with U(4)_C×U(2)_L×U(2)_R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/brane scale of the order of 5–7 TeV, when the U(4)_C and U(2)_R brane stack couplings are equal. Proton stability is assured as baryon number is associated to a global symmetry remnant of the broken abelian factors. It is also shown that this scenario can accommodate an extra low energy abelian symmetry that can be associated to lepton number. The issue of fermion and especially neutrino masses is also discussed.     

Bosonic string theory in Lorentzian principal circle bundles over anti-de-Sitter space AdS3

In this note we show a bosonic conformal string theory on U(1)-bundles over AdS₃. To this end, we first look for r-elastic helices in the space AdS₃, because they generate solutions of the motion equation on backgrounds P which are principal circle-bundles over AdS₃ endowed with the standard metric or generalized Kaluza–Klein metrics. In fact, we reduce the search ofU(1)-symmetric string configurations on P to the search of r-elastic curves in the orbit space AdS₃.