A general method for obtaining the double Bäcklund transformations

The double Bäcklund transformations are obtained for the isospectral deformation equations related to the general N × N linear spectral problem and to the 2 × 2 quadratic spectral problem.     

Constraining the anisotropy of the Universe with the Pantheon supernovae sample

We test the possible dipole anisotropy of the Finslerian cosmological model and the other three dipole-modulated cosmological models, i.e. the dipole-modulated ΛCDM, wCDM and Chevallier–Polarski–Linder (CPL) models, by using the recently released Pantheon sample of SNe Ia. The Markov chain Monte Carlo (MCMC) method is used to explore the whole parameter space. We find that the dipole anisotropy is very weak in all cosmological models used. Although the dipole amplitudes of four cosmological models are consistent with zero within the \begin{document}$1\sigma$\end{document} uncertainty, the dipole directions are close to the axial direction of the plane of the SDSS subsample in Pantheon. This may imply that the weak dipole anisotropy in the Pantheon sample originates from the inhomogeneous distribution of the SDSS subsample. A more homogeneous distribution of SNe Ia is necessary to constrain the cosmic anisotropy.     

Spontaneous compactification and CPN: SU(3) × SU(2) × U(1), sin2θW, g3/g2 and SU(3)-triplet chiral fermions in four dimensions

We examine the compactification of D=4+2N, Einstein-Maxwell-Dirac theory. It is shown that the manifold CP_N × M₄ is a solution of the equations of motion. The structure of the fermions, gauge bosons and their couplings in the four-dimensional effective theory is investigated. The scale of CP_N is quantized by a generalized Dirac condition. When the results are applied to the solution with internal space CP₁×CP₂, the weak mixing angle and the ratio of the couplings of SU(3) (g₃) and SU(2) (g₂) are defined by two integers and a hypercharge. An SU(3)-triplet chiral fermion can appear in four-dimensional effective theory.     

Projective spacetime

It is suggested that the world is locally projectively flat rather than Euclidean. From this postulate it is shown that an (N+1)-particle system has the global geometry of the symmetric spaceSO(4,N+1)/SO(4)×SO(N+1). A complex representation also exists, with structureSU(2,N+1)/S[U(2)×U(N+1)]. Several aspects of these geometrics are developed. Physical states are taken to be eigenfunctions of the Laplace-Beltrami operators. The theory may provide a rational basis for comprehending the groupsSO(4, 2),SU(2)×U(1),SU(3), etc., of current interest.     

Magnetic properties of a random system of rodlike Ising dipoles

A generalized mean field theory is constructed for a system of rodlike Ising magnetic dipoles of a finite length a with configuration disorder. The theory is based on an analysis of the local magnetic field distribution function. It is shown that the magnetic state of such a system is determined by the dipole concentration n: the system is paramagnetic for na³ ? 5×10², while ferromagnetic ordering exists for na³ ? 5×10². The susceptibility of the system in the paramagnetic state is determined.     

Electric dipole moment and chromoelectric dipole moment of the top quark inSU(3)C×SU(3)L×U(1)X model

We show that inSU(3) _C ×SU(3) _L ×U(1) _X model, the leading contribution to the electric and chromolelectric dipole moment of the top quark is due to the one-loop diagrams which come from exchanging the charged and neutral Higgs bosons. The dipole moments are typically of the order of 10^?19 e-cm and 10^?19 g-cm respectively, for the values of relative phases of the vev's such that CP violation is maximal. From an experimental point of view, theq ² dependence of dipole moment form factors is given.     

Cooperative phenomena of random electric dipoles in an amorphous matrix

A ferroelectric phase transition has been observed for the first time in a series of glasses containing WO₆-octahedra. The techniques of thermally stimulated depolarization currents were used to observe the transition from independent dipole behavior to cooperative behavior in this amorphous system as a function of concentration. These measurements yielded the activation energy ΔE=1.2eV, the pre-exponential τ₀=2 × 10^-22sec, and the dipole moment p?=1.3 × 10^?15 esu cm for WO₃ in Li₂B₄O₇. A dipole moment bearing species due to Li₂B₄O₇ was observed with ΔE=0.44eV and pre-exponential τ₀=5 × 10^?8 sec. The depolarization peaks of WO₃ occur in the temperature range 265–275 K depending upon WO₃ concentration and are pressure dependent with an initial slope of 2 × 10^?5K dyne^?1 cm². A model was developed for a possible phase transition associated with a random “pseudo-spin” system in an amorphous matrix.     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

Twisted reduced chiral models at large N

We construct and study the twisted reduced SU(N)×SU(N) chiral model in two dimensions. The equivalence of the reduced model to the field theory is established by examining the Dyson-Schwinger equations and weak coupling perturbation expansion. We evaluate the internal energy and two-point correlation function by extensive Monte Carlo simulations for N=12, 24 and 36. We find a non-analyticity near the weak coupling edge of the crossover region in which the system flips back and forth between the “normal” state and one characterised by a strongly disordered correlation function.     

The AB Equations and the ∂ ̄ -dressing Method in Semi-Characteristic Coordinates

The dressing method based on the 2 × 2 matrix \(\bar \partial \) -problem is generalized to study the canonical form of AB equations. The soliton solutions for the AB equations are given by virtue of the properties of Cauchy matrix. Asymptotic behaviors of the N-soliton solution are discussed.     

Infrared plasma reflectivity minimum in heavily doped n-Si

This paper presents a numerical analysis of infrared (IR) plasma reflectivity minimum in ultra heavily doped (UHD) n-Si (impurity concentration N up to 6 × 10²¹cm⁻³) by using a self-consistent method (SCM) and a complex physical model. The necessity of taking into account the dependence of effective mass on impurity concentration is shown. The scattering on defects (N_def = 5 × 10¹⁷ cm⁻³) and dislocation (N_dis = 5 × 10¹¹ cm⁻²) is included. The approximate relation for the wavelength λ_m(N) of the reflectivity minimum is given. The results obtained are compared with the experimental results for n-Si and satisfactory agreement is found.     

The candelas-weinberg model for spaces M4 × S2N

A method for calculating the one-loop effective potential for matter fields in Kaluza-Klein theories with the structure M⁴ × S^N for both even and odd N is presented. The cases M⁴ × S^N (N = 1, 2, 3, 4, 5, 6, and 8) have been examined. The method leads to finite results when N = odd and divergent results when N = even as expected.     

A nontrivial vacuum state in D = 10, N = 1 supergravity

We find a ground state of D = 10, N = 1 supergravity of the form (AdS(3) × R¹) × S³ × T³ which preserves all supersymmetries and should provide a gauged D = 4, N = 4 supergravity coupled to supermatter after dimensional reduction.     

Spectral duality in integrable systems from AGT conjecture

We describe relationships between integrable systems with N degrees of freedom arising from the Alday-Gaiotto-Tachikawa conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl _N Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the Alday-Gaiotto-Tachikawa relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrödinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2 × 2 and N × N representations of the Toda chain and the famous Adams-Harnad-Hurtubise duality.     

Photophysical characteristics of three novel benzanthrone derivatives: Experimental and theoretical estimation of dipole moments

The effect of solvents on absorption and fluorescence spectra and dipole moments of novel benzanthrone derivatives such as 3-N-(N′,N′-Dimethylformamidino) benzanthrone (1), 3-N-(N′,N′-Diethylacetamidino) benzanthrone (2) and 3-morpholinobenzanthrone (3) have been studied in various solvents. The fluorescence lifetime of the dyes (1-3) in chloroform were also recorded. Bathochromic shift observed in the absorption and fluorescence spectra of these molecules with increasing solvent polarity indicates that the transitions involved are π→π^?. Using the theory of solvatochromism, the difference in the excited-state (μ_e) and the ground-state (μ_e) dipole moments was estimated from Lippert-Mataga, Bakhshiev, Kawski-Chamma-Viallet, and McRae equations by using the variation of Stokes shift with the solvent’s relative permittivity and refractive index. AM1 and PM6 semiempirical molecular calculations using MOPAC and ab-initio calculations at B3LYP/6-31 G^? level of theory using Gaussian 03 software were carried out to estimate the ground-state dipole moments and some other physicochemical properties. Further, the change in dipole moment value (Δμ) was also calculated by using the variation of Stokes shift with the molecular-microscopic empirical solvent polarity parameter (E_T^N). The excited-state dipole moments observed are larger than their ground-state counterparts, indicating a substantial redistribution of the π-electron densities in a more polar excited state for all the systems investigated.     

Magnetic black holes with string-loop corrections

String-loop corrections to magnetic black holes are studied. 4D effective action is obtained by compactification of the heterotic string theory on the manifold K3×T² or on a suitable orbifold yielding N=1 supersymmetry in 6D. In the resulting 4D theory with N=2 local supersymmetry, the prepotential receives only one-string-loop perturbative correction. The loop-corrected black hole is obtained in two approaches: (i) by solving the system of the Einstein-Maxwell equations of motion derived from the loop-corrected effective action and (ii) by solving the system of spinor Killing equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. We consider a particular tree-level solution with the magnetic charges adjusted so that the moduli connected with the metric of the internal two-torus are constant. In this case, the loop correction to the prepotential is independent of coordinates, and it is possible to solve the system of the Einstein-Maxwell and spinor Killing equations in the first order in string coupling analytically. The set of supersymmetric solutions of the loop-corrected spinor Killing equations is contained in a larger set of solutions of the equations of motion derived from the string-loop-corrected effective action. Loop corrections to the metric and dilaton are large at small distances from the center of the black hole.     

CUDA accelerated method for motion correction in MR PROPELLER imaging

In PROPELLER, raw data are collected in N strips, each locating at the center of k-space and consisting of M_x sampling points in frequency encoding direction and L lines in phase encoding direction. Phase correction, rotation correction, and translation correction are used to remove artifacts caused by physiological motion and physical movement, but their time complexities reach O(M_x × M_x × L × N), O(N × R_A × M_x × L × (M_x × L + R_N × R_N)), and O(N × (R_N × R_N + M_x × L)) where R_N × R_N is the coordinate space each strip gridded onto and R_A denotes the rotation range. A CUDA accelerated method is proposed in this paper to improve their performances. Although our method is implemented on a general PC with Geforce 8800GT and Intel Core(TM)2 E6550 2.33 GHz, it can directly run on more modern GPUs and achieve a greater speedup ratio without being changed. Experiments demonstrate that (1) our CUDA accelerated phase correction achieves exactly the same result with the non-accelerated implementation, (2) the results of our CUDA accelerated rotation correction and translation correction have only slight differences with those of their non-accelerated implementation, (3) images reconstructed from the motion correction results of CUDA accelerated methods proposed in this paper satisfy the clinical requirements, and (4) the speed up ratio is close to 6.5.     

Four-Body Faddeev–Yakubovsky Equations Using Two-Cluster RGM Kernels: Applications to 4N and 4α Systems

Four-cluster Faddeev–Yakubovsky calculations using two-cluster RGM kernels are carried out for identical clusters. A precise ground-state energy of the α-particle, predicted by the quark-model nucleon–nucleon (NN) interaction fss2, is E _α  = ?26.61 MeV, including approximate effects of the Coulomb force and the charge dependence of the 2N force. The missing ?1.7 MeV in the experimental value ?28.3 MeV is about half of 3–4 MeV, predicted by modern meson-exchange 2N potentials, implying that almost half of 3–4 MeV is attributed to the off-shell effect of our nonlocal NN interaction fss2. As to the applications to four-α system, a method to eliminate the Faddeev redundant components from the basic Faddeev–Yakubovsky equations is proposed.     

The interaction of F and Cl atoms with N2 molecule at medium distances

The asymptotic method was used to obtain analytic equations for the elements of the 3 × 3 interaction matrix between an N₂ molecule in the ground electronic state X ¹∑ _g ⁺ and F and Cl atoms in the ² P _j states at interparticle distances that determine halogen atom electronic relaxation processes. Spin-orbit, quadrupolequadrupole, dispersion, and exchange interactions were taken into account.     

Dynamic simulation using a multipolar model of particles under dielectrophoretic force

This article presents the simulation of an electrorheological (ER) fluid system by using a multipole model that includes multipolar interactions between particles. The model uses the multipole re-expansion and the method of images for calculating electric field and force. The highest order of multipoles (N_mp) and the number of iterations (N_iter) used in the method of images can be chosen for the accuracy of the force approximation and the simulation time required. Study of a two-particle configuration shows that the force does not increase linearly with increasing N_mp and N_iter. The specific case N_mp=4 and N_iter=2 is chosen for dynamic simulation. We have performed the simulation of a system of 20 particles, and compared the formulation of particle chains with that obtained using the dipole model. The results imply that the response time for the change in viscosity of real-ER fluids is significantly shorter than that predicted by the dipole model.