Complexity analysis research of financial and economic system under the condition of three parameters’ change circumstances

This paper studies the characteristics of a series of complex systems, which are in combination of interest rate, investment, and price index parameters meeting the condition c?b?abc??0, including stable node, saddle points, bifurcation, Hopf bifurcation, and chaos, and the corresponding mathematical expressions of Lyapunov index are given. Based on this, we perform complexity analysis of the system and study the change circumstances of Lyapunov index when one or two parameters synchronously change. Numerical simulation results verify the theoretical analysis and conclusion. The results of this economic and financial system provide reference to practical problems, and have a positive effect on the actual application of the system of this type.     

Connection and inversion coefficients for basic hypergeometric polynomials

In this paper, we give a closed-form expression of the inversion and the connection coefficients for general basic hypergeometric polynomial sets using some known inverse relations. We derive expansion formulas corresponding to all the families within the q-Askey scheme and we connect some d-orthogonal basic hypergeometric polynomials.     

Investigation of critical phenomena and magnetism in amorphous Ising nanowire in the presence of transverse fields

A cylindrical magnetic nanowire system composed of ferromagnetic core and shell layers has been investigated by using effective field theory (EFT) with correlations in the presence of transverse fields and surface shell amorphization. Both weak and strong exchange couplings at the core–shell interface have been considered. The main attention has been focused on the former situation where the system exhibits similar characteristic features with that observed in thin film and semi-infinite systems in which the surface effects are prominent. A complete picture of the phase diagrams and magnetization profiles has been represented and the effect of the surface shell amorphization on these properties has been discussed. Furthermore, we have investigated the ground state behavior of total magnetization _mT$m_T$ curves and we have observed that _mT$m_T$ curves exhibit highly non-monotonous and exotic ground states in the presence of frustration in the surface shell. We have also analyzed the necessary conditions for the occurrence of reentrant behavior in the system.     

Semidefinite Approximations of the Matrix Logarithm

Foundations of Computational Mathematics - The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator...     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Operational rules and a generalized Hermite polynomials

In this paper, we use operational rules associated with three operators corresponding to a generalized Hermite polynomials introduced by Szegö to derive, as far as we know, new proofs of some known properties as well as new expansions formulae related to these polynomials.     

Nd(III) and Gd(III) Sorption on Mesoporous Amine-Functionalized Polymer/SiO2 Composite

The strong demand for rare-earth elements (REEs) is driven by their wide use in high-tech devices. New processes have to be developed for valorizing low-grade ores or alternative metal sources (such as wastes and spent materials). The present work contributed to the development of new sorbents for the recovery of rare earth ions from aqueous solutions. Functionalized mesoporous silica composite was synthesized by grafting diethylenetriamine onto composite support. The physical and chemical properties of the new sorbent are characterized using BET, TGA, elemental analysis, titration, FTIR, and XPS spectroscopies to identify the reactive groups (amine groups: 3.25 mmol N g⁻¹ and 3.41 by EA and titration, respectively) and their mode of interaction with Nd(III) and Gd(III). The sorption capacity at the optimum pH (i.e., 4) reaches 0.9 mmol Nd g⁻¹ and 1 mmol Gd g⁻¹. Uptake kinetics are modeled by the pseudo-first-order rate equation (equilibrium time: 30–40 min). At pH close to 4–5, the sorbent shows high selectivity for rare-earth elements against alkali-earth elements. This selectivity is confirmed by the efficient recovery of REEs from acidic leachates of gibbsite ore. After elution (using 0.5 M HCl solutions), selective precipitation (using oxalate solutions), and calcination, pure rare earth oxides were obtained. The sorbent shows promising perspective due to its high and fast sorption properties for REEs, good recycling, and high selectivity.     

Atomic decomposition of identity: General formalism for population analysis and energy decomposition

The concept of “atomic resolution of identity” has been introduced, leading to a very simple general formalism for generating different decomposition schemes of molecular quantities. Thus, different population analysis and energy partitioning schemes can be treated as special cases of a common framework. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005