The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)symmetric, relativistic, quantum field theory of a N -component scalar field in d spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N = 1 d = 1 case: this model describes the critical point of the ...

this paper has focused on vibration and buckling of thin rectangular plates when at least two opposite sides are simply supported condition and subjected to axial and biaxial initially stresses. analysis is based on exact solution method, without further usage of any approximate method. first analytic techniques are used to discuss the free vibrations of plate. then, natural frequencies and cri...

we assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the dirac matrices. then by making use of a suitable ansatz, the dirac equation has a very simple solution which is exact. we then have calculated the static properties of the nucleon in the ground...

In this paper, we present the exact solution of the Riemann problem for the nonlinear one-dimensional so-called shallow-water or Saint-Venant equations with friction proposed by SAVAGE and HUTTER to describe debris avalanches. This model is based on the depth-averaged thin layer approximation of granular flows over sloping beds and takes into account a Coulomb type friction law with a constant ...

For any arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D ≥ 2) hyperradial Schrödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels (Enl) of all the bound-states are easily calculated from this EQR method. The corresponding n...

The paper studies Sard’s problem on construction of optimal quadrature formulas in the space W 2 (,0) by Sobolev’s method. This consists two parts: first calculating norm error functional and then finding minimum this coefficients formulas. Here is calculated with help extremal function. Then using method Lagrange multipliers system linear equations for obtained, moreover existence uniqueness s...

Abstract Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of system domain Z ≤ 10. For odd d = 3, 5, variational given by rational algebraic parameters whilst for even 2, 4 it shown first time th...

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut −A(t)ux x −B(t)u= 0; 0¡x¡p; t ¿ 0, u(0; t)= u(p; t)= 0; u(x; 0)= f(x); 06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given ¿ 0 and t0; t1; with 0¡t0¡t1 and D(t0; t1)= {...