Bäcklund Transformation,Lax Pair and Solitons of the (2+1)-dimensional Davey-Stewartson-like Equations with Variable Coefficients for the Electrostatic Wave Packets

The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in the ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via the Bell polynomials and symbolic computation, the bilinear form, Bäcklund transformation and Lax pair for such equations are obtained. Based on the Hirota method, we construct the soliton solutions, analyze the elastic collisions with the constant and variable coefficients, and observe that solitons no longer keep rectilinear propagation and display different shapes because of the variable coefficients. Besides, localized excitations are derived through the variable separation.     

Rogue Waves for a (2+1)-Dimensional Coupled Nonlinear Schr?dinger System with Variable Coefficients in a Graded-Index Waveguide

Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.     

Clebsch-Gordan Coefficients for Two-Parameter Deformed Quantum Algebra SU(1,1)q,s(Ⅱ)

Abstract The Bargmann represen tations in the tensor product space of the irreducible representations for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the negative discrete series (b) are introduced, and the corresponding Bargmann expressions for the bases of irreps, the coherent state and the operators are also derived. The Clebsch-Gordan coeficients (CGC) for the two-parameter deformed quantum algebra SU(1,1)_q,s corresponding to the negative discrete series (b) are obtained.     

Final-state interactions in (e,e′p) reactions with polarized nuclei

The cross section for coincidence, quasielastic proton knock-out by electrons from a polarized ³⁹K nucleus is computed in DWIA using an optical potential in describing the wave function of the ejected nucleon. The dependence of the FSI on the initial polarization angles of the nucleus is analyzed and explained in a new, semi-classical picture of the reaction in which the nuclear transparency decreases as a function of the amount of nuclear matter that the proton has to cross, thus providing a method for obtaining detailed information on its mean free path in finite nuclei. We propose a procedure to find the best initial kinematical conditions for minimizing the FSI which will be useful as a guide for future experiments with polarized nuclei.     

Search for low-energy resonances in 27Al(p, α)24Mg

The known low-energy resonances in ²⁷Al(p, γ)²⁸Si at e_R = 203, 223, 293 and 327 keV have been searched for in the ²⁷Al(p, α)²⁴Mg reaction. The observed upper limits for the resonance strength together with the results from previous work show that the MgAl cycle is not closed at all stellar temperatures of interest and that in the important temperature range near T₉ = 0.1 the (p, γ) reaction proceeds at least 100 times faster than the (p, α) reaction. The results might be of importance for the explanation of extinct ²⁶Al in meteoritic samples as well as of the 4 solar masses of ²⁶Al found in the interstellar medium via γ-astronomy.     

~(186)W(d,p)~(187)W,~(186)W(d,2n)~(186)Re,~(nat)Fe(p,x)~(56)Co和~(nat)Ti(a,x)~(51)Cr反应激发函数评价

考虑特征γ射线分支比、衰变常数和标准截面等修正,对带电粒子引起的核反应~(186)W(d,p)~(187)W,~(186)W(d,2n)~(186)Re,~(nat)Fe(p,x)~(56)Co和~(nat)Ti(a,x)~(51)Cr的激发函数进行了研究。全面收集了这些反应激发函数的实验测量数据,对这些实验数据进行了分析处理,应用数学方法对分析处理后的实验数据进行了拟合。经过评价,给出了50 Me V以下~(186)W(d,p)~(187)W,~(186)W(d,2n)~(186)Re,~(nat)Fe(p,x)~(56)Co和~(nat)Ti(a,x)~(51)Cr反应激发函数的推荐值。     

Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications

In this paper, the authors introduce the (p,q)-trapezoidal integral inequalities, which are the (p,q)-analogues of the recently introduced q-trapezoidal integral inequalities. We derive a new (p,q)-integral identity for twice (p,q)-differentiable function. Utilizing this as an auxiliary result, we establish several new (p,q)-trapezoidal type integral inequalities for the function whose absolute value of twice (p,q)-derivative is (η₁,η₂)-convex functions. Some special means of real numbers are also given. At the end, we give brief conclusion. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.

     

Explicit Solutions of （2A-1）-Dimensional Canonical Generalized KP,KdV, and （2A-1）-Dimensional Burgers Equations with Variable Coefficients

In this paper, using the generalized （G1/G）-expansion method and the auxiliary differential equation method, we discuss the （2＋1）-dimensional canonical generalized KP （CGKP）, KdV, and （2＋1）-dimensional Burgers equations with variable coetticients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.     

Drinfeld Currents of Dynamical Elliptic Algebra Aq,p,π(gln)

From the generalized Yang-Baxter relations RLL=LLR^*,where R and R^* are the dynamical R matrix of A⁽¹⁾_n-1 type face model with the elliptic module shifted by the center of the algebra, using the Ding-Frenkel correspondence, we obtain the Drinfeld currents of algebra A_q,p,π(gl_n).     

Search for the 70 keV resonance in17O(p, α)14N

A direct search for theE _R =70 keV resonance in¹⁷O(p, )¹⁴N was carried out using¹⁷O enriched Ta₂O₅ targets in combination with a 1 mA proton beam and suitable detectors of large solid angle. The observed upper limit for the resonance strength is8×10^–10 eV.Work supported in part by Deutsche Forschungsgemeinschaft (Ro429/21-2) and the Science Program SC1-0065 of the European Economic Community     

The S(E) factor of7Li(p, γ)8Be and consequences for S(E) extrapolation in7Be(p, γ0)8B

Excitation functions and forward-backward anisotropies have been measured for the⁷Li(p, )⁸Be capture reaction over the proton energy rangeE _p =100 to 1500 keV, using a 4 summing crystal and Ge(Li) detectors, respectively. The data show at all energies the presence of El and M1 capture amplitudes arising from the direct capture (DC) process and theE _R =441 and 1030 keV resonances, respectively. Due to the observed DC process, the present data increase significantly the reaction rates (up to a factor of 110) compared to values given in the compilation. The data and their analyses remove the recent criticism on DC model calculations, which had implied a significant reduction in the extrapolated S(E) factor for⁷Be(p,)B and thus in the predicted flux of high-energy solar neutrinos; thus, the solar neutrino problem is still with us.Supported in part by the Deutsche Forschungsgemeinschaft (Ro429/21-3 and Ro429/21-4) and the German-Hungarian Collaboration (X238.6 and OTKA3808)     

Separation of Spin 0, 1/2, 1 Field Equations in Lemaître-Tolman-Bondi Cosmological Model with Cosmological Constant

The problem of variable separation of the scalar field equation is approached within the Lemaître-Tolman-Bondi (LTB) cosmological model with cosmological constant Λ. Parametric solutions of the cosmological Newton-like equation of the model are preliminary determined that result factorized in the parameter and in the radial dependence. The result holds on a sufficient condition that relates the two arbitrary integration functions of the model. The condition is of the same type of the one that ensures, in absence of cosmological term, the separability of the spin field equations for spin 0, 1/2, 1. It is then shown that the scalar field equation results automatically separable in the class of LTB models determined. The separated radial equation results independent of Λ, while the separated time equation strictly depends on Λ. The separability of the field equations is then checked to hold, in the same context, for spinor field equation of spin 1/2 and spin 1.     

Spectroscopy of50V with (p,nγ) reaction

Information on the low-lying levels up to ～1.9 MeV excitation of the doubly odd nucleus⁵⁰V has been obtained through the Ge (Li)-Ge (Li) coincidence study with the⁵⁰Ti(p, nγ)⁵⁰V reaction. Branching ratios have been measured and tentative spin-parity assignments have been made. A detailed comparison with other measurements reported recently has also been made. Using the lowest seniority wave functions with (f_7/2) _p ³ (f _7/2) _n ^?1 configuration, energy levels and electromagnetic properties have been calculated. These have been compared with the present and earlier experimental data.     

Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear SchrÕdinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium*

Twin-core optical fibers are applied in such fields as the optical sensing and optical communication,and propagation of the pulses,Gauss beams and laser beams in the non-Kerr media is reported.Studied in this paper are the coupled cubic-quintic nonlinear Schrodinger equations with variable coefficients,which describe the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical fiber or non-Kerr medium.Based on the integrable conditions,bilinear forms are derived,and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction.Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis.With different values of the delayed nonlinear response effect b(z),where z represents direction of the propagation,the linear-and parabolic-shaped one dark-dark soltions can be derived.Interactions between the parabolic-and periodic-shaped two dark-dark solitons are presented with b(z) as the linear and periodic functions,respectively.Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed.Interactions between the two dark-dark solitons of different types are displayed,and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z.We find that those interactions are elastic.     

Multi-scattering effects in (e,e′p) knockout

Multistep direct scattering of the ejectile proton is considered in (e,e′p) reactions in the quasi-free region as an improvement over the usual treatment of final-state interactions by means of an optical potential. The theory is applied to ⁴⁰Ca(e,e′p) as a case example. Important contributions of two- and three-step processes are found at high missing energy and momentum in agreement with the experimental trend.     

Painlev Analysis,Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin-Bona-Mahony-Burger (BBMB) Equation

In this paper,a variable-coefficient Benjamin-Bona-Mahony-Burger (BBMB) equation arising as a mathematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated.The integrability of such an equation is studied with Painlev analysis.The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method.Furthermore different types of solitary,periodic and kink waves can be seen with the change of variable coefficients.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).