Space–time symmetry violation,configuration mixing model and E-infinity theory

We have studied the time reversal symmetry violation on the bases of the configuration mixing model and E-infinity theory. With the use of the Cabibbo angle approximation, we have presented the transformation matrix in terms of the golden ratio (?), and shown that the time reversal symmetry violation is described by the configuration mixing of the unstable and stable manifolds (W^u, W^s). The magnitude of the mixing for the weak interaction field is given by the expression sin² θ_T(theor) ≈ sin⁴ θ_C(theor) ≈ (?)¹² = 3.105 × 10^?3, which is compared to the Kaon decay experiment ～2.3 × 10^?3. We have also discussed the space–time symmetry violation by using the CPT theorem.     

Numerical simulation of magnetohydrodynamic buoyancy-induced flow in a non-isothermally heated square enclosure

Numerical simulation of magnetohydrodynamic (MHD) buoyancy-induced heat transfer and fluid flow has been analyzed in a non-isothermally heated square enclosure using finite volume method. The bottom wall of enclosure were heated and cooled with a sinusoidal function and top wall was cooled isothermally. Vertical walls of the enclosure were adiabatic. Effects of Rayleigh number (Ra = 10⁴, 10⁵ and 10⁶), Hartman number (Ha = 0, 50 and 100) and amplitude of sinusoidal function (n = 0.25, 0.5 and 1) on temperature and flow fields were analyzed. It was observed that heat transfer was decreased with increasing Hartmann number and decreasing value of amplitude of sinusoidal function.     

Solution of the Burgers equation using an implicit linearizing transformation

The initial-boundary-value problem on the semi-infinite interval and on a finite interval for the Burgers equation u_t = u_xx + 2u_xu is solved using a stream function ? and a linearizing transformation w = e^?. The transformation reduces the equation to a heat equation with appropriate initial and homogeneous time-dependent linear boundary conditions. One advantage of this method is that we never need to find an explicit expression for ? in our computations.     

Unsteady magnetohydrodynamic Hartmann–Couette flow and heat transfer in a Darcian channel with Hall current,ionslip, viscous and Joule heating effects: Network numerical solutions

A theoretical study of unsteady magnetohydrodynamic viscous Hartmann–Couette laminar flow and heat transfer in a Darcian porous medium intercalated between parallel plates, under a constant pressure gradient is presented. Viscous dissipation, Joule heating, Hall current and ionslip current effects are included as is lateral mass flux at both plates. The dimensionless conservation equations for the primary (x¹-direction), secondary (z¹-direction) momentum and also energy conservation equation are derived and solved using a computational technique known as Network Simulation Methodology (NSM). Velocity distributions (u¹, w¹) and temperature distribution (T¹) at the channel centre (y¹ = 0) over time (t¹) are studied graphically for the effects of Darcy number (Da), Hartmann number (Ha), transpiration (N_t), Hall current parameter (Be), ionslip parameter (Bi), pressure gradient parameter (dP/dx¹) with Prandtl number prescribed at 7.0 (electrically conducting water), Eckert number held constant at 0.25 (heat convection from the plates to the fluid) and Reynolds number (Re) fixed at 5.0 (for Re < 10, Darcian model is generally valid). Increasing Darcy number causes an increase in temperature, T¹; values are however significantly reduced for the higher Hartmann number case (Ha = 10). For the case of low transpiration (i.e. N_t = 1 which corresponds to weak suction at the upper plate and weak injection at the lower plate), both primary velocity (u¹) and secondary velocity (w¹) are increased with a rise in Darcy number (owing to a simultaneous decrease in Darcian porous drag); temperature T¹ is also increased considerably with increasing Da. However, for stronger transpiration (N_t = 10), magnitudes of u¹, w¹ and T¹ are significantly reduced and also significant overshoots are detected prior to the establishment of steady state flow. With increasing Hall current parameter, Be, (for the purely fluid regime i.e. Da → ∞), primary velocity is considerably increased, whereas secondary velocity is reduced; temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing Be. With strong Darcian drag present (Da = 0.01 i.e. very low permeability), magnitudes of u¹, w¹ and T¹ are considerably reduced and temperatures are found to be reduced for all t¹, with increasing Hall current effect (Be). Increasing ionslip current parameter (Bi) increases primary velocity (u¹), decreases secondary velocity (w¹) and also temperature (T¹) for all time (t¹), in the infinite permeability case (Da → ∞). For weakly Darcian flow, ionslip parameter (Bi) has a much reduced effect on the velocity distributions. Temperature, T¹ is strongly increased with a rise in pressure gradient parameter, dP¹/dx¹, as is primary velocity (u¹); however, secondary velocity (w¹) is reduced. The present study has applications in hybrid magnetohydrodynamic (MHD) energy generators, materials processing, geophysical hydromagnetics, etc.     

Radical Rings with Soluble Adjoint Groups

An associative ring R, not necessarily with an identity, is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R^∘ under the circle operation r ∘ s = r + s + rs on R. It is proved that every radical ring R whose adjoint group R^∘ is soluble must be Lie-soluble. Moreover, if the commutator factor group of R^∘ has finite torsion-free rank, then R is locally nilpotent.     

Simulación numérica del flujo turbulento de aire con gotas dispersas de agua a través de separadores de torres de refrigeración

This work presents a numerical study on the turbulent flow of air with dispersed water droplets in separators of mechanical cooling towers. The averaged Navier-Stokes equations are discretised through a finite volume method, using the Fluent and Phoenics codes, and alternatively employing the turbulence models k ? ?, k ? ω and the Reynolds stress model, with low-Re version and wall enhanced treatment refinements. The results obtained are compared with numerical and experimental results taken from the literature. The degree of accuracy obtained with each of the considered models of turbulence is stated. The influence of considering whether or not the simulation of the turbulent dispersion of droplets is analyzed, as well as the effects of other relevant parameters on the collection efficiency and the coefficient of pressure drop. Focusing on four specific eliminators (‘Belgian wave’, ‘H1-V’, ‘L-shaped’ and ‘Zig-zag’), the following ranges of parameters are outlined: 1 ≤ U_e ≤ 5 m/s for the entrance velocity, 2 ≤ D_p ≤ 50 μm for the droplet diameter, 650 ≤ Re ≤ 8.500 for Reynolds number, and 0.05 ≤ P_i ≤ 5 for the inertial parameter. Results reached alternately with Fluent and Phoenics codes are compared. The best results correspond to the simulations performed with Fluent, using the SST k ? ω turbulence model, with values of the dimensionless scaled distance to wall y⁺ in the range 0.2 to 0.5. Finally, correlations are presented to predict the conditions for maximum collection efficiency (100 %), depending on the geometric parameter of removal efficiency of each of the separators, which is introduced in this work.     

New exact solitary-wave special solutions for the nonlinear dispersive K(m, n) equations

In this paper, we study the nonlinear dispersive K(m, n) equations: u_t + (u^m)_x − (uⁿ)_xxx = 0 which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the decomposition method in K(m, n) equations. The nonlinear equations K(m, n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m, n) equations are established.     

Free in-plane vibration analysis of a curved beam (arch) with arbitrary various concentrated elements

In the existing literature, the information regarding the exact solutions for free in-plane vibrations of the curved beams (or arches) carrying various concentrated elements is rare, particularly for the case with multiple attachments including eccentricities and mass moments of inertias. For this reason, this paper aims at presenting an effective approach to tackle the title problem. First of all, the un-coupled equation of motion for the circumferential displacement of an arch segment is derived. Next, based on the value of the discriminate parameter for a cubic equation, the exact solutions for the three types of roots of the un-coupled equation are determined and, corresponding to each type of roots, all displacement functions for the arch segment in terms of the real numbers (instead of the complex ones) are obtained. Finally, use of the compatible equations for the displacements and slopes together with the equilibrium equations for the forces and moments at each intermediate node and two ends of the entire curved beam, a frequency equation of the form ∣H(ω)∣ = 0 is obtained. It is found that the conventional approach by using the condition “∣H(ω^t)∣ ? ε” to search for the approximate value of ω^t is difficult even if the convergence tolerance ε is greater than 10⁺³ (i.e., ε > 10⁺³) instead of less than 10^?3 (i.e., ε < 10^?3), however, the half-interval method is one of the effective tools for solving the problem if all coefficients of the determinant ∣H(ω)∣ are the real numbers. In addition to comparing with the existing literature, most of the numerical results obtained from the presented method are compared with those obtained from the conventional finite element method (FEM) and good agreement is achieved.     

Vacuum polarization in light two-electron atoms and ions

A general theory of the vacuum polarization in light atomic and muon-atomic systems is considered. We derive the closed analytical expression for the Uehling potential and evaluate corrections on vacuum polarization for the 1¹S-state of the two-electron ³He and ⁴He atoms and for some two-electron ions, including the Li⁺, Be²⁺, B³⁺ and C⁴⁺ ions. The correction for vacuum polarization in two-electron He atoms has been evaluated as ΔE_ueh ≈ 7.253 ± 0.0025 × 10⁻⁷ a.u. The analogous corrections in the two-electron He-like ions rapidly increase with the nuclear charge Q (ΔE_ueh ≈ 2.7061 × 10⁻⁶ a.u. for the Li⁺ ion and ΔE_ueh ≈ 2.3495 × 10⁻⁵ a.u. for the C⁴⁺ ion). The corresponding corrections have also been evaluated for the electron–nucleus and electron–electron interactions.     

Equivalent Blocks of Finite General Linear Groups in Non-describing Characteristic

J. Chuang, R. Kessar, and J. Rickard have proved Broué's Abelian defect group conjecture for many symmetric groups. We adapt the ideas of Kessar and Chuang towards finite general linear groups (represented over non-describing characteristic). We then describe Morita equivalences between certain p-blocks of GL_n(q) with defect group C_p^α × C_p^α, as q varies (see Theorem 2). Here p and q are coprime. This generalizes work of S. Koshitani and M. Hyoue, who proved the same result for principal blocks of GL_n(q) when p = 3, α = 1, in a different way.     

On the stability of fractional neutron point kinetics (FNPK)

The aim of this work is investigate the stability of fractional neutron point kinetics (FNPK). The method applied in this work considers the stability of FNPK as a linear fractional differential equation by transforming the s − plane to the W − plane. The FNPK equations is an approximation of the dynamics of the reactor that includes three new terms related to fractional derivatives, which are explored in this work with an aim to understand their effect in the system stability. Theoretical study of reactor dynamical systems plays a significant role in understanding the behavior of neutron density, which is important in the analysis of reactor safety. The fractional relaxation time (τ^α) for values of fractional-order derivative (α) were analyzed, and the minimum absolute phase was obtained in order to establish the stability of the system. The results show that nuclear reactor stability with FNPK is a function of the fractional relaxation time.     

Fast Rectangular Matrix Multiplication and Applications

First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of ann×nmatrix by ann×n²matrix in arithmetic timeO(n^ω),ω=3.333953…, which is less by 0.041 than the previous record 3.375477…. Then we present fast multiplication algorithms for matrix pairs of arbitrary dimensions, estimate the asymptotic running time as a function of the dimensions, and optimize the exponents of the complexity estimates. For a large class of input matrix pairs, we improve the known exponents. Finally we show three applications of our results:   (a) we decrease from 2.851 to 2.837 the known exponent of the work bounds for fast deterministic (NC) parallel evaluation of the determinant, the characteristic polynomial, and the inverse of ann×nmatrix, as well as for the solution to a nonsingular linear system ofnequations,   (b) we asymptotically accelerate the known sequential algorithms for the univariate polynomial composition mod xⁿ, yielding the complexity boundO(n^1.667) versus the old record ofO(n^1.688), and for the univariate polynomial factorization over a finite field, and   (c) we improve slightly the known complexity estimates for computing basic solutions to the linear programming problem withmconstraints andnvariables.     

High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations

In this paper, we propose a new three-level implicit nine point compact cubic spline finite difference formulation of order two in time and four in space directions, based on cubic spline approximation in x-direction and finite difference approximation in t-direction for the numerical solution of one-space dimensional second order non-linear hyperbolic partial differential equations. We describe the mathematical formulation procedure in details and also discuss how our formulation is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method.     

Filter matrix based on interpolation wavelets for solving Fredholm integral equations

The interpolation wavelet is used to solve the Fredholm integral equation of the second kind in this study. Hence, by the extension of interpolation wavelets that [−1, 1] is divided to 2^N+1 (N ⩾  − 1) subinterval, we have polynomials with a degree less than M + 1 in each new interval. Therefore, by considering the two-scale relation the filter coefficients and filter matrix are used as the proof of theorems. The important point is interpolation wavelets lead to more sparse matrix when we try to solve integral equation by an approximate kernel decomposed to a lower and upper resolution. Using n-time, where (n ⩾ 2), two-scale relation in this method errors of approximate solution as O((2^−(N+1))ⁿ⁺¹). Also, the filter coefficient simplifies the proof of some theorems and the order of convergence is estimated by numerical errors.     

On generalized Jordan 1-derivation in rings

Let n ⩾ 1 be a fixed integer and let R be an (n + 1)!-torsion free 1-ring with identity element e. If F, d:R → R are two additive mappings satisfying F(xⁿ⁺¹) = F(x)(x¹)ⁿ + xd(x)(x¹)ⁿ⁻¹ + x²d(x)(x¹)ⁿ⁻²+ ⋯ +xⁿd(x) for all x ∈ R, then d is a Jordan 1-derivation and F is a generalized Jordan 1-derivation on R.     

Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method

Based on a new kind of analytic method, namely the Homotopy analysis method, an analytic approach to solve non-linear, chaotic system of ordinary differential equations is presented. The method is applied to Lorenz system; this system depends on the three parameters: σ, b and the so-called bifurcation parameter R are real constants. Two cases are considered. The first case is when R = 20.5 which corresponds to the transition region and the second case corresponds to R = 23.5 which corresponds to the chaotic region.The validity of the method is verified by comparing the approximation series solution with the results obtained using the standard numerical techniques such as Runge-Kutta method.     

Integrals,Quantum Galois Extensions,and the Affineness Criterion for Quantum Yetter–Drinfel'd Modules

In this paper we shall generalize the notion of an integral on a Hopf algebra introduced by Sweedler, by defining the more general concept of an integral of a threetuple (H, A, C), where H is a Hopf algebra coacting on an algebra A and acting on a coalgebra C. We prove that there exists a total integral γ: C → Hom(C, A) of (H, A, C) if and only if any representation of (H, A, C) is injective in a functorial way, as a corepresentation of C. In particular, the quantum integrals associated to Yetter–Drinfel'd modules are defined. Let now A be an H-bicomodule algebra, ^H$\text{Y}$$\text{D}$_A the category of quantum Yetter–Drinfel'd modules, and B = {a ∈ A|∑S^− 1(a_〈1〉)a_{〈 − 1〉} ⊗ a_〈0〉 = 1_H ⊗ a}, the subalgebra of coinvariants of the Verma structure A ∈ ^H$\text{Y}$$\text{D}$_A. We shall prove the following affineness criterion: if there exists γ: H → Hom(H, A) a total quantum integral and the canonical map β: A ⊗ _B A → H ⊗ A, β(a ⊗ _B b) = ∑S^− 1(b_〈1〉)b_{〈 − 1〉} ⊗ ab_〈0〉 is surjective (i.e., A/B is a quantum homogeneous space), then the induction functor – ⊗ _B A: $\text{M}$_B → ^H$\text{Y}$$\text{D}$_A is an equivalence of categories. The affineness criteria proven by Cline, Parshall, and Scott, and independently by Oberst (for affine algebraic groups schemes) and Schneider (in the noncommutative case), are recovered as special cases.     

RBFs approximation method for time fractional partial differential equations

In this paper, radial basis functions (RBFs) approximation method is implemented for time fractional advection–diffusion equation on a bounded domain. In this method the first order time derivative is replaced by the Caputo fractional derivative of order α ∈ (0, 1], and spatial derivatives are approximated by the derivative of interpolation in the Kansa method. Stability and convergence of the method is discussed. Several numerical examples are include to demonstrate effectiveness and accuracy of the method.     

Second-order approximation of angle-ply composite laminated thin plate under combined excitations

The influence of the quadratic and cubic terms on non-linear dynamic characteristics of the angle-ply composite laminated rectangular plate with parametric and external excitations is investigated. The method of multiple time scale perturbation is applied to solve the non-linear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted and investigated at this approximation order. Two cases of the sub-harmonic resonances cases (Ω₂ ? 2ω₁ and Ω₂ ? 2ω₂) in the presence of 1:2 internal resonance ω₂ ? 2ω₁ are considered. The stability of the system is investigated using both frequency response equations and phase-plane method. It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system as they represent some of the worst behavior of the system. Such cases should be avoided as working conditions for the system. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.