Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

EXPLICIT ERROR ESTIMATE FOR THE NONCONFORMING WILSON'S ELEMENT

In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models:a comparison based on normal and Student's t-error distribution

Background:Modeling exchange rate volatility has remained crucially important because of its diverse implications.This study aimed to address the issue of error distribution assumption in modeling and forecasting exchange rate volatility between the Bangladeshi taka(BDT)and the US dollar($).Methods:Using daily exchange rates for 7 years(January 1,2008,to April 30,2015),this study attempted to model dynamics following generalized autoregressive conditional heteroscedastic(GARCH),asymmetric power ARCH(APARCH),exponential generalized autoregressive conditional heteroscedstic(EGARCH),threshold generalized autoregressive conditional heteroscedstic(TGARCH),and integrated generalized autoregressive conditional heteroscedstic(IGARCH)processes under both normal and Student’s t-distribution assumptions for errors.Results and Conclusions:It was found that,in contrast with the normal distribution,the application of Student’s t-distribution for errors helped the models satisfy the diagnostic tests and show improved forecasting accuracy.With such error distribution for out-of-sample volatility forecasting,AR(2)–GARCH(1,1)is considered the best.

On the Error Estimate of Adini's Element for the Second Order Problems

The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.

Convergence ball and error analysis of Ostrowski-Traub’s method

Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.

Assimilating temperature and salinity profiles using Ensemble Kalman Filter with an adaptive observation error and T-S constraint

Temperature （T） and salinity （S） profiles from conductivity-temperature-depth data collected during the Northern South China Sea Open Cruise from August 16 to September 13, 2008 are assimilated using Ensemble Kalman Filter （EnKF）. An adaptive observational error strategy is used to prevent filter from diverging. In the meantime, aiming at the limited improvement in some sites caused by the T and S biases in the model, a T-S constraint scheme is adopted to improve the assimilation performance, where T and S are separately updated at these locations. Validation is performed by comparing assimilated outputs with independent in situ data （satellite remote sensing sea level anomaly （SLA）, the OSCAR velocity product and shipboard ADCP）. The results show that the new EnKF assimilation scheme can significantly reduce the root mean square error （RMSE） of oceanic T and S compared with the control run and traditional EnKF. The system can also improve the simulation of circulations and SLA.

EDITOR＇S CHOICE： FOCUS ON RECENT LITERATURE

In a clinical situation, repair of distal peripheral nerve defects can present a major challenge to neurosurgenns. Construction of tissue-engineered nerves is a novel solution for repairing peripheral nerve defects. The sciatic nerve is the largest peripheral nerve in the body and is known to have a relatively constant anatomical position, sufficient diameter to be easily exposed and operated upon with good repeatability, satisfactory local blood circulation, and is difficult to infect. Owing to these advantages, rat models of sciatic nerve defects are commonly used to study nerve regeneration and repair.

Editor＇s comments

This review article entitled ＂Physiological approaches to understanding molecular actions on dorsolateral prefrontal cortical neurons underlying higher cognitive processing＂ examines the relationship between neurotransmitters and prefrontal cognitive function. The authors of this article are leading the field in such research.

EDITOR’S CHOICE: FOCUS ON RECENT LITERATURE

Following spinal cord injury, nerve repair is difficult due to limited regenerative potential of the central nervous system and inability of oli- godendrocytes to guide axonal growth. Several factors pose a challenge for neural regeneration following spinal cord injury. First, glial scars and cavities, which form after spinal cord injury, hinder axonal growth and result in degenerative necrosis of the nerve fibers. Second.

Editor's Note

It is with great pleasure that I am serving asa Guest Editor for a special issue of the ChinaCommunications on Communications and InformationSecurity for a second time.The goal of this issue is a continuation of theSpecial Issue by the same Editor which waspublished by CIC in February 2007.We

EDITOR'S CHOICE: FOCUS ON RECENT LITERATURE

Central nervous system injury often leads to incorrect links formed between dendrites and axons in neurons in the regeneration process resulting in histological injury and related dysfunction. The surrounding environment of neurons also inhibits neuronal regeneration by not providing enough support.

EDITOR'S NOTE

The CHINESE JOURNAL OF METAL SCIENCE AND TECHNOLOGY was startedin 1985 and was the only metallurgical periodical in English at that time in China.It is pub-lished under the auspices of The Chinese Society for Metals and managed by the Institute ofMetal Research,The Chinese Academy of Sciences(CAS).The editor-in-chief is ProfessorChangxu SHI,member of CAS and director of the Division of Technological Science,CAS.

THE ERROR ESTIMATES OF HALLEY'S METHOD

In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.

Editor's Choice—Adenovirus-mediated gene transfection of stem cells

Neural stem cells transplantation plays an important role in repair and cell replacement therapy for nervous system degenerative diseases. However, the self-repair effects are minimal because of a limited absolute number, as well as the local microenvironment, post-transplantation. A combined treatment utilizing stem cell transplantation and gone therapy can exert a dual effect involving stem cells and neurotrophic factors. The adenovirus carrier is

Editor's Choice——Retinal ganglion cell damage and regeneration

Retinal ganglion cell apoptosis is considered to be the main cause of loss of vision in glaucoma patients. Microglia cells are phagocytic cells present in the retina. In the retina of glaucoma rat models, microglia cells become activated, which suggests a role for microglia in the pathogenesis of optic nerve injury in glaucoma patients. The retinal ganglion cell is the only cell that can produce action potential in the retina,

Impulsive stabilization of a class of nonlinear system with bounded gain error

Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.

Editor's Choice—Specificity of acupuncture acupoints:observation by functional magnetic resonance imaging

Acupuncture at certain acupoints （specific sites for needle insertion） can induce the activation of specific regions of the brain. This activated brain region influences the target organ or tissue in order to treat the disease. Acupoint specificity is the basis of acupuncture therapy.

Editor's Choice—Electrophysiological characteristics of epilepsy

Elect roencephalographic signals can act as an indicator of abnormal discharge during epileptic seizures, providing important evidence for diagnosing epilepsy. Abnormal electroencephalographic activity was detected during seizures, and high-amplitude epileptic discharge waveforms were observed during intermission in approximately 50% of patients.