Some further <Emphasis Type="Italic">q</Emphasis>-series identities related to divisor functions

We give new generalizations of some q-series identities of Dilcher and Prodinger related to divisor functions. Some interesting special cases are also deduced, including an identity related to overpartitions studied by Corteel and Lovejoy.     

Dual Lie Bialgebra Structures of W -algebra W (2, 2) Type

In the present paper, we investigate the dual Lie coalgebras of the centerless W(2, 2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2, 2) Lie bialgebra. As by-products, four new infinite dimensional Lie algebras are obtained.     

Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

Mathematische Zeitschrift - We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $$C^{k}$$ quasi-periodic $$SL(2,{\mathbb {R}})$$ cocycle is...     

Waring-Goldbach Problem: One Square and Nine Biquadrates

In this paper it is proved that every sufficiently large even integer N satisfying one of the congruence conditions N ≡ 10, 58, 130, or 178(mod 240) may be represented as the sum of one square and nine fourth powers of prime numbers.     

O(1/t) complexity analysis of the generalized alternating direction method of multipliers

Science China Mathematics - Owing to its efficiency in solving some types of large-scale separable optimization problems with linear constraints, the convergence rate of the alternating direction...     

The Effect of Surface Roughness on Immiscible Displacement Using Pore Scale Simulation

Transport in Porous Media - Pore scale immiscible displacement is crucial in oil industry. The surface roughness of throat is an important factor affecting water–oil interface movement. In...     

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3 − $ν$ can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.     

Elastic,mechanical, electronic properties and hardness of Nb2AsC from first principles

The study aims at the elastic, mechanical, electronic properties and hardness of Nb₂AsC using first principles based on the density functional theory method within the generalised gradient approximation. The calculated lattice parameters of Nb₂AsC are in good agreement with the experimental data. The five independent elastic constants are firstly calculated as a function of pressure, and our results indicate that it is mechanically stable in the applied pressure. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. The pressure dependences of the bulk modulus, shear modulus, average velocity of acoustic waves and Debye temperature of Nb₂AsC are systematically investigated. The band structure and density of states are discussed, and the results show that the strong hybridisations C p–Nb d and As p–Nb d would be beneficial to the structure stability of Nb₂AsC. Based on the Mulliken population analysis, the hardness of Nb₂AsC is predicted.     

Intermolecular multiple-quantum coherence NMR signals modulated by double distant dipolar fields

A modified CRAZED pulse sequence was applied to obtain the intermolecular multiple-quantum coherence NMR signals from double distant dipolar fields in highly polarized spin systems. Complete theoretical analyses were explicitly derived from the dipolar field treatment combined with product operator formalism. Two typical samples containing several different components were chosen for the experimental verifications. The computer simulations and experimental observations are consistent with the theoretical predictions. The results presented herein provide a convenient way to understand the combined effects of multiple distant dipolar fields from the different components in complicated chemical or biological solutions. When experimental conditions such as selective radio-frequency pulses are not optimal, it may be helpful to identify possible unexpected signals or artefacts of high-resolution NMR spectroscopy in inhomogeneous fields.     

Temperature effects of Hamiltonian dark solitons on the stability of holographic solitons in a separate holographic–Hamiltonian soliton pair

We investigate theoretically the temperature effects on the evolution and stability of a separate holographic–Hamiltonian dark–dark or bright–dark soliton pair formed in an unbiased serial photorefractive crystal circuit. Our numerical results show that, for a stable dark–dark or bright–dark soliton pair originally formed in a crystal circuit at given temperatures, when the crystal in which formed a Hamiltonian dark soliton changes, the holographic dark or bright soliton supported by the other crystal tends to evolve into another stable soliton or experiences larger cycles of compression or breaks up into beam filaments or exhibit a common decaying process. The holographic dark soliton is more sensitive to the temperature change than the holographic bright one.