Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.

Multiple dimensions of urban design development from a practice perspective:A case study of an institute in Nanjing

The rapid urbanization process in China has promoted the active state of urban design practice.In the process of solving complex problems,the practical scope of urban design has gradually expanded.This paper took a design institution in Nanjing as a case study and sorted the trends in design project types and themes over the past 20 years,which presented a partial and diverse state of evolution in urban design practice.Concept,technology and management were extracted as the three main dimensions of cognitive urban design practice development.The relative positions and relationships of different types of urban design work were interpreted through mapping analysis of these three dimensions.This study provided a foundation for the practical orientation of urban design in China and a platform for communication a mong managers,urban design practitioners,scholars of related disciplines,and the public.

Outcome assessment of stroke convalescence using multiple scales based on different dimensions

BACKGROUND: Convalescence is an important stage of stroke treatment. A lot of patients have somatic and mental disorders at various degrees. The primary standard can only reflect partial conditions of somatic disorder; in addition, multiple dimensions of patients at the phase of stroke convalescence are further observed by using a lot of standards, such as signs and symptoms of traditional Chinese medicine, daily activity and psychological status. OBJECTIVE: To analyze the outcome assessments of the cases of stroke convalescence measured with different criteria consisting of various dimensions by a cross-sectional investigation of the condition of stroke convalescent patients. DESIGN: Scale evaluation. SETTING: Departments of Clinical Epidemiology Exploratory Development and Neurology, the Second Affiliated Hospital of Guangzhou University of Traditional Chinese Medicine; National Center for Training of Design, Measurement and Evaluation in Clinical Research,Guangzhou University of Traditional Chinese Medicine. PARTICIPANTS: A total of 194 stroke convalescent patients treated in the Second Affiliated Hospital of Guangzhou University of Traditional Chinese Medicine from July 26, 2000 to February 28, 2001 were taken as subjects of the study. There were 126 males and 68 females aged from 40 to 89 years, and the illness course ranged from 14 to 181 days. All patients met diagnosis-treatment criteria of stroke (the second version)[DTCS(V2.0)] and various kinds of diagnostic points of cerebrovascular diseases; moreover, all patients provided confirmed consents. METHODS: They were assessed by assessment methods including the following assessment instruments: DTCS(V2.0), self-designed scale of traditional Chinese medicine (TCM) symptoms (28 symptoms and physical signs were scored as 0, 1, 2 marks from none to severity), modified Edinburgh-Scandinavia stroke scale (a total of 45 marks, 0 to 15 marks as mild defect, 16 to 30 as moderate defect, 31 to 45 as severe defect), modified Barthel activities of daily life (ADL) index (a total of 100 marks, less than 60 marks as unable self-care), vitality and mental health (subscales derived from Health Survey Questionnaire, SF-36). The collected data from scales and inter-scale correlation were processed by the statistic methods mainly including descriptive analysis, Spearmen correlation analysis, factor analysis, etc. MAIN OUTCOME MEASURES: ① Average scores of scales and criteria; ② correlation between modified Edinburgh-Scandinavia stroke scale and other scales. RESULTS: All of the patients completed the assessment, and analyzed in the final analysis. ① The average scores of the scales and criteria: The average scores of DTCS(V2.0), self-designed scale of TCM symptoms, modified Edinburgh-Scandinavia stroke scale, modified Barthel ADL index, vitality and mental health scales were 6.51±6.29, 13.73±6.97, 7.56±7.35, 63.58±23.68, 52.79±23.32 and 62.83±22.75 respectively. ② Correlation between modified Edinburgh-Scandinavia stroke scale and other scales: The Spearman correlation coefficients (R ’) of modified Edinburgh-Scandinavia stroke scale with diagnosis-treatment criteria of stroke, scales of TCM symptoms, modified Barthel ADL index, vitality scale and mental health scale were 20.885, 0.302, -0.824, -0.294 and -0.258 respectively. CONCLUSION: The modified Edinburgh-Scandinavia stroke scale and DTCS(V2.0) shared the same assessment dimension, so they can be mutually alternated in some clinical practices. Discrepancy in measurements of health status was gained due to the diverse dimensions applied in outcome assessments. It is necessary to build up a multi-dimensional assessment criteria system, such as signs and symptoms, daily activities and psychological status, for assessing the stroke convalescent cases in a more comprehensive scope and reflecting the efficacy of TCM treatment scientifically.

Geographical patterns and determinants of insect biodiversity in China

Insects play important roles in the maintenance of ecosystem functioning and the provision of livelihoods for millions of people.However,compared with terrestrial vertebrates and angiosperms,such as the giant panda,crested ibis,and the metasequoia,insect conservation has not attracted enough attention,and a basic understanding of the geographical biodiversity patterns for major components of insects in China is lacking.Herein,we investigated the geographical distribution of insect biodiversity across multiple dimensions(taxonomic,genetic,and phylogenetic diversity)based on the spatial distribution and molecular DNA sequencing data of insects.Our analysis included 18 orders,360 families,5,275 genera,and 14,115 species of insects.The results revealed that Southwestern and Southeastern China harbored higher insect biodiversity and numerous older lineages,representing a museum,whereas regions located in Northwestern China harbored lower insect biodiversity and younger lineages,serving as an evolutionary cradle.We also observed that mean annual temperature and precipitation had significantly positive effects,whereas altitude had significantly negative effects on insect biodiversity in most cases.Moreover,cultivated vegetation harbored the highest insect taxonomic and phylogenetic diversity,and needleleaf and broadleaf mixed forests harbored the highest insect genetic diversity.These results indicated that human activities may positively contribute to insect spatial diversity on a regional scale.Our study fills a knowledge gap in insect spatial diversity in China.These findings could help guide national-level conservation plans and the post-2020 biodiversity conservation framework.

JACOBI SPECTRAL METHODS FOR MULTIPLE- DIMENSIONAL SINGULAR DIFFERENTIAL EQUATIONS

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

Design of heterojunction with components in different dimensions for electrocatalysis applications

Searching for high-performance and cost-effective catalysts is of particular importance for the practical electrocatalysis applications.The heterojunctions with components in different dimensions show unique physical and chemical properties,which can offer large space for rational design of electrocatalysts.In this paper,we firstly reviewed recently related works,and then proposed a few perspectives on exploring heterojunction for electrocatalysis applications.

ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.