A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

Considerations in Applying the General Equilibrium Approach to Environmental Health Assessment

There are currently two commonly used approaches to assessing economic impacts of health damage resulting from environmental pollution： human capital approach （HCA） and willingness-to-pay （WTP）. WTP can be further divided into averted expenditure approach （AEA）, hedonlc wage approach （HWA）, contingent valuation approach （CVA） and hedonlc price approach （HPA）. A general review of the principles behind these approaches by the authors indicates that these methods are incapable of unveiling the mechanism of health impact from the point of view of national economy. On a basis of economic system, the shocks brought about by health effects of environmental pollution change the labor supply and medical expenditure, which in turn affects the level of production activity in each sector and the total final consumption pattern of the society. The general equilibrium approach within the framework of macroeconomic theory is able to estimate the health impact on national economy comprehensively and objectively. Its mechanism and applicability are discussed in detail by the authors.

Multi-linear Variable Separation Approach to Solve a (2+1)-DimensionalGeneralization of Nonlinear Schroedinger System

By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.

Comparison of Patient Satisfaction between Brachial Plexus Block (Axillary Approach) and General Anesthesia for Surgical Treatment of Distal Radius Fractures: A Historical Cohort Study

Background: Distal radius fracture surgery is performed under general (GA) or regional anesthesia with brachial plexus block (NB). Whether anesthesia type affects patient outcomes is unclear. This study retrospectively compared patient satisfaction between GA and NB after surgery. Methods: This was a historical cohort study of 80 (34 GA and 46 NB) patients who underwent volar plate fixation of distal radius fractures. Propensity score analysis was used to generate a set of matched cases (NB) and controls (GA), yielding 14 matched patient-pairs. The simplified patient satisfaction scale was compared for primary outcomes. Secondary outcomes were anesthesia and surgery duration, hospital stay length, adverse events, postoperative analgesic requirement, and wrist range of motion (ROM) 2 weeks and 3 months postoperatively. Results: After propensity score matching, patients in almost all cases in both groups were “Satisfied” (effect size: 0.1, p = 0.572), indicating little significant difference. Significant differences in adverse events and postoperative analgesic use observed before matching disappeared after matching. Anesthesia duration and hospital stay length were significantly shorter in the NB group (effect size: -1.27 and -0.77, p = 0.00074 and p = 0.0388, respectively), as was surgery duration (effect size: -0.84, p = 0.0122) after matching. Similar to before matching, wrist ROM significantly improved in the NB group (effect size: 1.11, p = 0.0279) in the early postoperative period, but the difference disappeared at 3 months postoperatively. Conclusions: Patient satisfaction between distal radius fracture surgery under GA and NB was similar. Nerve block could help shorten hospital stay length and surgery duration and improve postoperative functional recovery.

The extended symmetry approach for studying the general Korteweg-de Vries-type equation

The extended symmetry approach is used to study the general Korteweg-de Vries-type （KdV-type） equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be constructed by the solutions of original models if their solutions are well known, such as the standard constant coefficient KdV equation and the standard compound KdV--Burgers equation, and so on. Then any one of these variable-coefficient equations can be considered as an original model to obtain new variable-coefficient equations whose solutions can also be known by means of transformation relations between solutions of the resulting new variable-coefficient equations and the original equation.

Remarks on Definitions of Perturbation in General Relativity

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.

General formula for phonon-assisted n-photon absorption in solids

A general formula for phonon-assisted n-photon absorption in solids is obtained by （n ＋ 1）-th order perturbation technique. The complicated calculation process for transition element of n-photon absorption is simply demonstrated by a diagram approach that is proposed in this work. We find that the transition element for the n-photon absorption has a simple form, i.e., it is just the first term of the n-th order fist kind Bessel function.

Development of a Scale to Evaluate Depressive States among Elderly Patients in General Wards —Verification of the Contents to Improve the Accuracy of the Scale

Purpose: This study aims to verify the validity of the contents of the Nurse Administered Depression Scale for Elderly Inpatients16 (NDE16) using the Delphi approach in order to further improve the accuracy of the NDE16, a scale for rating potential depressive states in elderly inpatients through the observations reported by nurses. Methods: Participants were nurses working in general wards for longer than 3 years and who expressed consent to the study participation. Data were collected using the Delphi method (3 times). Responses are scored from 1 to 5 (3 - 5 points as positive) using the Likert method. The standard criteria for inclusion in the further evaluation are “mean ≥ 3.0”, “standard deviation < 1.0”, “median ≥ 3.0”, and “IQR ≤ 1.0”. Items that meet all the criteria at the third survey are employed as question items in the final questionnaire. Results: The respondents were 139 females, 10 males, and 1 unknown, aged 25 to 65. The collection rates of the three surveys were 75% to 82%. Based on the results of the first survey, wordings of 9 questions were modified. Since Question 13 “Queries are not really responded to.” did not meet the criteria (IQR = 2) at the third survey, we excluded this question and named the revised scale NDE15. Discussion: The reason why Question 13 did not meet the criteria could be due to the difficulty in distinguishing “Expressing thought suppression” from the state of cognitive decline in dementia. Further studies are needed to determine cutoff points.

A Theory of the Risk for Empirical CVaR with Application to Portfolio Selection

When decisions are based on empirical observations,a trade-off arises between flexibility of the decision and ability to generalize to new situations.In this paper,we focus on decisions that are obtained by the empirical minimization of the Conditional Value-at-Risk(CVa R)and argue that in CVa R the trade-off between flexibility and generalization can be understood on the ground of theoretical results under very general assumptions on the system that generates the observations.The results have implications on topics related to order and structure selection in various applications where the CVa R risk-measure is used.A study on a portfolio optimization problem with real data demonstrates our results.

Development of Optimal City Size Theory: A Critical View

Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.

ABUNDANT LOCALIZED COHERENT STRUCTURES FOR THE (2+1)-DIMENSIONAL LONG DISPERSIVE WAVE SYSTEM

In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler forms, which are coupled and linear partial differentialequations, then obtain its general solution. Some special types of the localized excitations, suchas oscillating dromion, multi-solitoff, multi-dromion, multi-lump and multi-ring soliton solutionsare derived by selecting the arbitrary functions appropriately.