An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations

Joint Symbol-Level Precoding and Reflecting Designs for IRS-Enhanced MU-MISO Systems

Intelligent reflecting surfaces (IRSs) have emerged as a revolutionary solution to enhance wireless communications by changing propagation environment in a cost-effective and hardware-efficient fashion. In addition, symbol-level precoding (SLP) has attracted considerable attention recently due to its advantages in converting multiuser interference (MUI) into useful signal energy. Therefore, it is of interest to investigate the employment of IRS in symbol-level precoding systems to exploit MUI in a more effective way by manipulating the multiuser channels. In this article, we focus on joint symbol-level precoding and reflecting designs in IRS-enhanced multiuser multiple-input single-output (MU-MISO) systems. Both power minimization and quality-of-service (QoS) balancing problems are considered. In order to solve the joint optimization problems, we develop an efficient iterative algorithm to decompose them into separate symbol-level precoding and block-level reflecting design problems. An efficient gradient-projection-based algorithm is utilized to design the symbol-level precoding and a Riemannian conjugate gradient (RCG)-based algorithm is employed to solve the reflecting design problem. Simulation results demonstrate the significant performance improvement introduced by the IRS and illustrate the effectiveness of our proposed algorithms

Market timing with aggregate accruals

We propose a market-timing strategy that aims to exploit aggregate accruals' return forecasting power. Using several performance measures of the aggregate accruals-based market-timing strategy, such as excess portfolio return, Sharpe ratio, and Jensen's alpha, we find robust evidence that, relative to the passive investment strategy of buying and holding the stock market, the market-timing strategy delivers superior performance that is both statistically and economically significant. Specifically, on average, the market-timing strategy beats the SP500 index by 6 to 22 percentage points (annualized) after controlling for transaction costs over the 1980-2004 period.© 2009 Palgrave Macmillan.postprin

The Sarbanes-Oxley act and corporate investment: A structural assessment

We assess the impact of the Sarbanes-Oxley Act of 2002 on corporate investment in an investment Euler equation framework. We allow a dummy for the passage of the Act to affect the rate at which managers discount future investment payoffs. Using generalized method of moments estimators, we find that the rate U.S. firm managers apply to discount investment projects rises significantly after 2002, while the discount rate for U.K. firms remains unchanged. The effects of the legislation on corporate investment are asymmetric, and are much more significant among relatively small firms. We also find that well-governed firms, firms with a credit rating, and accelerated filers of Section 404 of the Act have become more cautious about investment. © 2010 Elsevier B.V.postprin

Corrections to Tribimaximal Mixing from Nondegenerate Phases

We propose a seesaw scenario that possible corrections to the tribimaximal pattern of lepton mixing are due to the small phase splitting of the right-handed neutrino mass matrix. we show that the small deviations can be expressed analytically in terms of two splitting parameters($\delta_1$ and $\delta_2$) in the leading order. The solar mixing angle $\theta_{12}$ favors a relatively smaller value compared to zero order value ($35.3^\circ$), and the Dirac type CP phase $\delta$ chooses a nearly maximal one. The two Majorana type CP phases $\rho$ and $\sigma$ turn out to be a nearly linear dependence. Also a normal hierarchy neutrino mass spectrum is favored due to the stability of perturbation calculations.Comment: 19 pages 6 figures, Accepted by Mod. Phy. Lett.

Geometric entanglement from matrix product state representations

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state representations. It is systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim [Q.-Q. Shi, R. Or\'{u}s, J. O. Fj{\ae}restad, and H.-Q. Zhou, New J. Phys \textbf{12}, 025008 (2010); J.-M. St\'{e}phan, G. Misguich, and F. Alet, Phys. Rev. B \textbf{82}, 180406R (2010)] that the leading finite-size correction to the geometric entanglement per lattice site is universal, with its remarkable connection to the celebrated Affleck-Ludwig boundary entropy corresponding to a conformally invariant boundary condition.Comment: 4+ pages, 3 figure

Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

A proper bilinear form is proposed for the N=1 supersymmetric modified Korteweg-de Vries equation. The bilinear B\"{a}cklund transformation of this system is constructed. As applications, some solutions are presented for it.Comment: 8 pages, LaTeX using packages amsmath and amssymb, some corrections mad