One-Dimensional Structures Behind Twisted and Untwisted SuperYang–Mills Theory

We give a one-dimensional interpretation of the four-dimensional twisted N = 1 superYang–Mills theory on a Kähler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 superYang–Mills theory.     

Twisted Burnside–Frobenius Theory for Endomorphisms of Polycyclic Groups

Let R(?) be the number of ?-conjugacy (or Reidemeister) classes of an endomorphism ? of a group G. We prove, for several classes of groups (including polycyclic ones), that the number R(?) is equal to the number of fixed points of the induced mapping on an appropriate subspace of the unitary dual space ?, when R(?) < ∞. Applying the result to iterations of ?, we obtain Gauss congruences for Reidemeister numbers. In contrast to the case of automorphisms, studied previously, there are plenty examples having the above finiteness condition, even among groups with R_∞ property.     

The Implication of Kamiokande-Ⅱ Sun Neutrino Data

The cross section of B solar neutrino scattering involving the contribution of neutrino magnetic moment (NMM) is investigated. The constraints on the probability of flip of neutrino helicity and the possible value of NMM are extracted from the Kamiokande-II solar neutrino data and calculated cross section of v_e, scattering. It is found that the probability of neutrino helicity flip allowed by the Kamiokande-Ⅱ data may be small, which would be difficult to understand the ³⁷Cl data.     

An Evaluation of Oracle for Persistent Data Storage and Analysis of LHC Physics Data

The LHC experiments at CERN will generate huge volumes of data-several PB per year at data rates between 100MB/s and 1.5GB/s.The storage and analysis of these data present a major challenge.In collaboration with other members of the former RD45 project,the central database support group at CERN has been working on this issue for several years,leading to production use of a potential solution,based on the combination of an Object Database and Mass Storage system,bothe at CERN and outside.     

The duality principle and inversion of Laplace–Stielties transforms

The fundamental relation between the Laplace transform, the Stielties transform, and the generalized integral equation of refraction is revealed, and a duality principle is formulated for the solution of inverse problems of radio physics. New formulas of the Laplace-transform inversion satisfying the duality principle are obtained. There is no necessity of contour integration in a complex plane for the relations found, which considerably simplifies the reconstruction of originals and makes it possible to control systematic errors in the experimental data.     

The Bertlmann–Martin Inequality and Spin Degrees of Freedom

The Bertlmann–Martin inequality based on the dipole sum rule is revisited taking into account the spin degrees of freedom. We consider 1 and 2 particles of spin 1/2 in a mean field, adding a spin dependent interaction. The derivation of the inequality relies on the closure relation. We discuss the effect of the Pauli principle, and the restrictions it imposes on the use of the closure relation. The problem is exemplified by a simple model based on harmonic forces. Moreover, in the 2 particle case, the model we use is separable in the relative and centre of mass coordinates. In this case, we show that for operators connecting only singlet states, their sum rule can be calculated in the usual way, i.e. via the double commutator of this operator with the Hamiltonian. An upper bound can also be obtained by using the Bertlmann–Martin technique. This is not possible for operators involving a transition between singlet and triplet states.     

The Baker–Akhiezer Function and Factorization of the Chebotarev–Khrapkov Matrix

A new technique is proposed for the solution of the Riemann–Hilbert problem with the Chebotarev–Khrapkov matrix coefficient \({G(t) = \alpha_{1}(t)I + \alpha_{2}(t)Q(t)}\) , \({\alpha_{1}(t), \alpha_{2}(t) \in H(L)}\) , I = diag{1, 1}, Q(t) is a \({2\times2}\) zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann–Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker–Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann–Hilbert problem requires the finding of the \({\rho}\) zeros of the Baker–Akhiezer function ( \({\rho}\) is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree- \({\rho}\) polynomial and solution of a certain linear algebraic system of \({\rho}\) equations.     

Twisted Traces of Quantum Intertwiners¶and Quantum Dynamical R-Matrices¶Corresponding to Generalized Belavin–Drinfeld Triples

We consider weighted traces of products of intertwining operators for quantum groups U _q (?), suitably twisted by a “generalized Belavin–Drinfeld triple”. We derive two commuting sets of difference equations – the (twisted) Macdonald–Ruijsenaars system and the (twisted) quantum Knizhnik–Zamolodchikov–Bernard (qKZB) system. These systems involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler ([ESS]). When the generalized Belavin–Drinfeld triple comes from an automorphism of the Lie algebra ?, we also derive two additional sets of difference equations, the dual Macdonald–Ruijsenaars system and the \textit{dual} qKZB equations. Received: 20 March 2000 / Accepted: 11 December 2000     

The Use of the Levenberg–Marquardt and Variable Projection Curve-Fitting Algorithm in Intravoxel Incoherent Motion Method for DW-MRI Data Analysis

The objective of this study was to evaluate the performances of different algorithms for diffusion parameters estimation in intravoxel incoherent motion method for diffusion-weighted magnetic resonance imaging (DW-MRI) data analysis. Traditionally, the method of non-linear least squares analysis by means of Levenberg–Marquardt algorithms has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the Variable Projection curve-fitting algorithm and the performance of two non-linear regression methods when single and multiple starting points were used. Analysis was done on simulation data to which different amounts of Gaussian noise had been added. The performance of two non-linear regression methods was compared using the residual sum of squares and the number of failures in data fitting. We conclude that the VarPro algorithm is superior to the LM algorithm for curve fitting in intravoxel incoherent motion method for DW-MRI data analysis.     

Hydrodynamical Reformulation and Quantum Limit of The Barut–Zanghi Theory

One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a probabilistic fluid, we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to quantize the BZ theory: by employing this time the tensorial language, more popular in first-quantization. Quantizing the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual quantum limit of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical Weyssenhoff fluid, while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.     

The Co-luminescence Effect of Eu–Gd–Ofloxacin–SDBS System and its Analytical Application

A fluorescence enhancement phenomenon in the europium (Eu)–Ofloxacin (OF)–Sodium Dodecyl Benzene Sulfonate (SDBS) fluorescence system was observed when Gd³⁺ was added. The fluorescence intensity of the systems was measured (λ _ex/λ _em = 280/612 nm) at pH 7.8. Under optimum conditions, a linear relationship between the enhanced fluorescence intensity and the Eu³⁺ concentration in the range of 5.0 × 10⁻¹⁰ ∼ 2.0 × 10⁻⁷ mol·L⁻¹ was observed. The detection limit of Eu³⁺ was 1.46 × 10⁻¹⁰ mol·L⁻¹ (S/N = 3). This method was used for the determination of trace amounts of europium in synthetic rare earth samples with satisfactory results. In addition, the interaction mechanism is also studied.     

The phase and critical point of quantum Einstein–Cartan gravity

By introducing diffeomorphism and local Lorentz gauge invariant holonomy fields, we study in the recent article [S.-S. Xue, Phys. Rev. D 82 (2010) 064039] the quantum Einstein–Cartan gravity in the framework of Regge calculus. On the basis of strong coupling expansion, mean-field approximation and dynamical equations satisfied by holonomy fields, we present in this Letter calculations and discussions to show the phase structure of the quantum Einstein–Cartan gravity, (i) the order phase: long-range condensations of holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range fluctuations of holonomy fields in weak gauge couplings. According to the competition of the activation energy of holonomy fields and their entropy, we give a simple estimate of the possible ultra-violet critical point and correlation length for the second-order phase transition from the order phase to disorder one. At this critical point, we discuss whether the continuum field theory of quantum Einstein–Cartan gravity can be possibly approached when the macroscopic correlation length of holonomy field condensations is much larger than the Planck length.     

The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

The existence of the Carter constant in the Vaidya–Einstein–Kerr (VEK) spacetime and its relation to the Petrov type is investigated. This spacetime is an example of a black hole in an asymptotically non-flat background. We construct the Carter constant and obtain the Killing tensor in the VEK spacetime. The Newman–Penrose formalism is employed to obtain the spin coefficients. We present a complete (Petrov) classification of the VEK spacetime and the special case of the non-rotating Vaidya–Einstein–Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.     

Recent Advances in Moiré Superlattice Structures of Twisted Bilayer and Multilayer Graphene

Twisted bilayer graphene(TBG), which has drawn much attention in recent years, arises from van der Waals materials gathering each component together via van der Waals force. It is composed of two sheets of graphene rotated relatively to each other. Moiré potential, resulting from misorientation between layers, plays an essential role in determining the band structure of TBG, which directly relies on the twist angle. Once the twist angle approaches a certain critical value, flat bands will show u...