Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model i...The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.展开更多
In the software engineering literature, it is commonly believed that economies of scale do not occur in case of software Development and Enhancement Projects （D＆EP）. Their per-unit cost does not decrease but increa...In the software engineering literature, it is commonly believed that economies of scale do not occur in case of software Development and Enhancement Projects （D＆EP）. Their per-unit cost does not decrease but increase with the growth of such projects product size. Thus this is diseconomies of scale that occur in them. The significance of this phenomenon results from the fact that it is commonly considered to be one of the fundamental objective causes of their low effectiveness. This is of particular significance with regard to Business Software Systems （BSS） D＆EP characterized by exceptionally low effectiveness comparing to other software D＆EP. Thus the paper aims at answering the following two questions： （1） Do economies of scale really not occur in BSS D＆EP？ （2） If economies of scale may occur in BSS D＆EP, what factors are then promoting them？ These issues classify into economics problems of software engineering research and practice.展开更多
The influence of spatial differences, which are caused by different anthropogenic disturbances, and temporal changes, which are caused by natural conditions, on macroinvertebrates with periphyton communities in Baiyan...The influence of spatial differences, which are caused by different anthropogenic disturbances, and temporal changes, which are caused by natural conditions, on macroinvertebrates with periphyton communities in Baiyangdian Lake was compared. Periphyton and macrobenthos assemblage samples were simultaneously col- lected on four occasions during 2009 and 2010. Based on the physical and chemical attributes in the water and sediment, the 8 sampling sites can be divided into 5 habitat types by using cluster analysis. According to coefficients variation analysis （CV）, three primary conclusions can be drawn ： （1） the metrics of Hilsenhoff Biotic Index （HBI）, Percent Tolerant Taxa （PTT）, Percent dominant taxon （PDT）, and community loss index （CLI）, based on macroinvertebrates, and the metrics of algal density （AD）, the proportion of chlorophyta （CHL）, and the proportion of cyanophyta （CYA）, based on periphytons, were mostly constant throughout our study; （2） in terms of spatial variation, the CV values in the macroinvertebratebased metrics were lower than the CV values in the periphyton-based metrics, and these findings may be caused by the effects of changes in environmental factors; whereas, the CV values in the macroinvertebrate-based metrics were higher than those in the periphyton-based metrics, and these results may be linked to the influences of phenology and life history patterns of the macroinvertebrate individuals; and （3） the CV values for the functionalbased metrics were higher than those for the structuralbased metrics. Therefore, spatial and temporal variation for metrics should be considered when assessing applying the biometrics.展开更多
The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l...The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
文摘The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.
文摘In the software engineering literature, it is commonly believed that economies of scale do not occur in case of software Development and Enhancement Projects （D＆EP）. Their per-unit cost does not decrease but increase with the growth of such projects product size. Thus this is diseconomies of scale that occur in them. The significance of this phenomenon results from the fact that it is commonly considered to be one of the fundamental objective causes of their low effectiveness. This is of particular significance with regard to Business Software Systems （BSS） D＆EP characterized by exceptionally low effectiveness comparing to other software D＆EP. Thus the paper aims at answering the following two questions： （1） Do economies of scale really not occur in BSS D＆EP？ （2） If economies of scale may occur in BSS D＆EP, what factors are then promoting them？ These issues classify into economics problems of software engineering research and practice.
文摘The influence of spatial differences, which are caused by different anthropogenic disturbances, and temporal changes, which are caused by natural conditions, on macroinvertebrates with periphyton communities in Baiyangdian Lake was compared. Periphyton and macrobenthos assemblage samples were simultaneously col- lected on four occasions during 2009 and 2010. Based on the physical and chemical attributes in the water and sediment, the 8 sampling sites can be divided into 5 habitat types by using cluster analysis. According to coefficients variation analysis （CV）, three primary conclusions can be drawn ： （1） the metrics of Hilsenhoff Biotic Index （HBI）, Percent Tolerant Taxa （PTT）, Percent dominant taxon （PDT）, and community loss index （CLI）, based on macroinvertebrates, and the metrics of algal density （AD）, the proportion of chlorophyta （CHL）, and the proportion of cyanophyta （CYA）, based on periphytons, were mostly constant throughout our study; （2） in terms of spatial variation, the CV values in the macroinvertebratebased metrics were lower than the CV values in the periphyton-based metrics, and these findings may be caused by the effects of changes in environmental factors; whereas, the CV values in the macroinvertebrate-based metrics were higher than those in the periphyton-based metrics, and these results may be linked to the influences of phenology and life history patterns of the macroinvertebrate individuals; and （3） the CV values for the functionalbased metrics were higher than those for the structuralbased metrics. Therefore, spatial and temporal variation for metrics should be considered when assessing applying the biometrics.
基金supported by the National Science Foundation of China under Grant Nos.61573342,61473126the Key Research Program of Frontier Sciences,Chinese Academy of Sciences,under Grant No.QYZDJ-SSWSYS011 the Fundamental Research Funds for the Central Universities
文摘The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).
