A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with i...A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.展开更多
In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped i...In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.展开更多
The substantial increase in the efficiency of organic solar cells achieved in recent years would not have been possible without work on the synthesis of new materials and understanding the relationship between the mor...The substantial increase in the efficiency of organic solar cells achieved in recent years would not have been possible without work on the synthesis of new materials and understanding the relationship between the morphology and performance of organic photovoltaic devices.The structure of solvent-cast active layers is a result of phase separation in mixtures of donor and acceptor components.To a large extent,this process depends on the interactions between the components of the mixture.Here,we present a systematic analysis of the morphology of poly[N-9'-heptadecanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl-2',1',3'-benzothiadiazole)](PCDTBT)and[6,6]-phenyl-C71-butyric acid methyl ester(PC70BM)films in terms of the ternary phase diagram.The interaction parameters between PCDTBT and four different solvents,namely chloroform,chlorobenzene,o-dichlorobenzene,and toluene,were estimated based on swelling experiments.Based on these values,ternary phase diagrams of PCDTBT:PC70BM in different solvents were calculated.The morphology of spin-coated films with different blend ratios cast from different solvents is discussed in terms of the obtained phase diagrams.展开更多
In this article, the authors consider the existence of a nontrivial solution for the following equation： -△u＋u=q（x）（｜u｜^2＊1/｜x｜）u, x∈R^3, where q（x） satisfies some conditions. Using a Min-Max method, th...In this article, the authors consider the existence of a nontrivial solution for the following equation： -△u＋u=q（x）（｜u｜^2＊1/｜x｜）u, x∈R^3, where q（x） satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation.展开更多
We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these condition...We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are violated, there can be blow up of the gradient in the interior or on the boundary of the domain. In particular we de- rive sharp results on local and global Lipschitz continuity of continuous viscosity solutions under more general growth conditions than before. Lipschitz regularity near the boundary allows us to predict when the Dirichlet condition is satisfied in a classical and not just in a viscosity sense, where detachment can occur. Another consequence is this： if interior gra- dient blow up occurs, Perron-type solutions can in general become discontinuous, so that the Dirichlet problem can become unsolvable in the class of continuous viscosity solutions.展开更多
The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox（1952）,has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems...The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox（1952）,has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given（much earlier）by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.展开更多
We construct an example of an isolated singularity f: (C3,0)→(C,0) for which oneof the polar relative monodromies is not of finite order,by using a nonisolated singularity with transversal type the A'Campo example.
The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for app...The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.展开更多
Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibr...Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.展开更多
General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A cla...General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A classical theory of gravitation in flat space-time also avoids the singularity under natural conditions on the density parameters. The universe contracts to a positive minimum and then it expands during all times. It is not symmetric with regard to its minimum implying a finite age measured with proper time of the universe. The space of the universe is flat and the total energy is conserved. Under the assumption that the sum of the density parameters is a little bit bigger than one the universe is very hot in early times. Later on, the cosmological model agrees with the one of general relativity. A new interpretation of a non-expanding universe may be given by virtue of flat space-time theory of gravitation.展开更多
The locally noncentrosymmetric heavy fermion superconductor CeRh_(2)As_(2) has attracted considerable interests due to its rich superconducting phases,accompanied by possible quadrupole density wave and pronounced ant...The locally noncentrosymmetric heavy fermion superconductor CeRh_(2)As_(2) has attracted considerable interests due to its rich superconducting phases,accompanied by possible quadrupole density wave and pronounced antiferromagnetic excitations.To understand the underlying physics,here we report measurements from highresolution angle-resolved photoemission.Our results reveal fine splittings of the conduction bands related to the locally noncentrosymmetric structure,as well as a quasi-two-dimensional Fermi surface(FS)with strong 4f contributions.The FS shows signs of nesting with an in-plane vector q_(1)=(π/α,π/α),which is facilitated by the heavy bands nearˉ𝑋arising from the characteristic conduction-X hybridization.The FS nesting provides a natural explanation for the observed antiferromagnetic spin fluctuations at(π/α,π/α),which might be the driving force for its unconventional superconductivity.Our experimental results can be reasonably explained by density functional theory plus dynamical mean field theory calculations,which can capture the strong correlation effects.Our study not only provides spectroscopic signature of the key factors underlying the field-induced superconducting transition,but also uncovers the critical role of FS nesting and lattice Kondo effect in the underlying magnetic fluctuations.展开更多
We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method,...We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.展开更多
Introduction:The availability of essential nutrients,such as nitrogen(N)and phosphorus(P),can feedback on soil carbon(C)and the soil microbial biomass.Natural cycles can be supplemented by agricultural fertiliser addi...Introduction:The availability of essential nutrients,such as nitrogen(N)and phosphorus(P),can feedback on soil carbon(C)and the soil microbial biomass.Natural cycles can be supplemented by agricultural fertiliser addition,and we determined whether the stoichiometry and nutrient limitation of the microbial biomass could be affected by an unbalanced nutrient supply.Methods:Samples were taken from a long-term trial(in effect since 1968)with annual applications of 0,15 and 30 kg P ha^(−1) with constant N and potassium.Soil and microbial biomass CNP contents were measured and nutrient limitation assessed by substrate-induced respiration.Linear regression and discriminant analyses were used to identify the variables explaining nutrient limitation.Results:Soil and biomass CNP increased with increasing P fertiliser,and there was a significant,positive,correlation between microbial biomass P and biomass C,apart from at the highest level of P fertilisation when the microbial biomass was over-saturated with P.The molar ratios of C:N:P in the microbial biomass remained constant(homeostatic)despite large changes in the soil nutrient ratios.Microbial growth was generally limited by C and N,except in soil with no added P when C and P were the main limiting nutrients.C,N and P,however,did not explain all the growth limitation on the soils with no added P.Conclusions:Increased soil C and N were probably due to increased net primary production.Our results confirm that C:N:P ratios within the microbial biomass were constrained(i.e.homeostatic)under near optimum soil conditions.Soils with no added P were characterised by strong microbial P limitation and soils under high P by over-saturation of microorganisms with P.Relative changes in biomass C:P can be indicative of nutrient limitation within a site.展开更多
We give sufficient and necessary conditions for the existence and nonexistence of positive ground state solutions of a class of coupled nonlinear Schroedinger equations.
The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥...The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥2, q≠9), then G is isomorphic toPSL(2, q), where π_e(G) denotes the set of all orders of elements in G.展开更多
The paper presents a comprehensive model of a banking system that integrates network effects,bankruptcy costs,fire sales,and cross-holdings.For the integrated financial market we prove the existence of a price-payment...The paper presents a comprehensive model of a banking system that integrates network effects,bankruptcy costs,fire sales,and cross-holdings.For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium.The number of defaults corresponding to the greatest price-payment equilibrium is analyzed in several comparative case studies.These illustrate the individual and joint impact of interbank liabilities,bankruptcy costs,fire sales and cross-holdings on systemic risk.We study policy implications and regulatory instruments,including central bank guarantees and quantitative easing,the significance of last wills of financial institutions,and capital requirements.展开更多
In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization （LPS）. These methods preserve the favourable stability and a...In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization （LPS）. These methods preserve the favourable stability and approximation properties of classical residual-based stabilization （RBS） techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the NavierStokes equations. Furthermore, we apply it to optimal control problems with linear（ized） flow problems, since the symmetry of the stabilization leads to the nice feature that the operations ＂discretize＂ and ＂optimize＂ commute.展开更多
Let F be a family of holomorphic functions and suppose that there exists ε 】 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is...Let F be a family of holomorphic functions and suppose that there exists ε 】 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.展开更多
文摘A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.
文摘In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.
基金the National Science Center(No.UMO-2013/11/B/ST5/04473)the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program(Contract No.POIG.02.01.00-12-023/08).
文摘The substantial increase in the efficiency of organic solar cells achieved in recent years would not have been possible without work on the synthesis of new materials and understanding the relationship between the morphology and performance of organic photovoltaic devices.The structure of solvent-cast active layers is a result of phase separation in mixtures of donor and acceptor components.To a large extent,this process depends on the interactions between the components of the mixture.Here,we present a systematic analysis of the morphology of poly[N-9'-heptadecanyl-2,7-carbazole-alt-5,5-(4',7'-di-2-thienyl-2',1',3'-benzothiadiazole)](PCDTBT)and[6,6]-phenyl-C71-butyric acid methyl ester(PC70BM)films in terms of the ternary phase diagram.The interaction parameters between PCDTBT and four different solvents,namely chloroform,chlorobenzene,o-dichlorobenzene,and toluene,were estimated based on swelling experiments.Based on these values,ternary phase diagrams of PCDTBT:PC70BM in different solvents were calculated.The morphology of spin-coated films with different blend ratios cast from different solvents is discussed in terms of the obtained phase diagrams.
基金Financial support in part by the Volkswagen Foundation of Germany and in part by NNSF of China
文摘In this article, the authors consider the existence of a nontrivial solution for the following equation： -△u＋u=q（x）（｜u｜^2＊1/｜x｜）u, x∈R^3, where q（x） satisfies some conditions. Using a Min-Max method, the authors prove that there is at least one nontrivial solution for the above equation.
基金financed by the Alexander von Humboldt Foundationcontinued in March 2009 at the Mathematisches Forschungsinstitut Oberwolfach in the "Research in Pairs"program
文摘We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are violated, there can be blow up of the gradient in the interior or on the boundary of the domain. In particular we de- rive sharp results on local and global Lipschitz continuity of continuous viscosity solutions under more general growth conditions than before. Lipschitz regularity near the boundary allows us to predict when the Dirichlet condition is satisfied in a classical and not just in a viscosity sense, where detachment can occur. Another consequence is this： if interior gra- dient blow up occurs, Perron-type solutions can in general become discontinuous, so that the Dirichlet problem can become unsolvable in the class of continuous viscosity solutions.
文摘The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox（1952）,has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given（much earlier）by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.
文摘We construct an example of an isolated singularity f: (C3,0)→(C,0) for which oneof the polar relative monodromies is not of finite order,by using a nonisolated singularity with transversal type the A'Campo example.
文摘The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.
文摘Based on the framework introduced in [4] or [5], the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of inhomogeneous equations of elasticity is studied. We are able to reach equilibrium even though the nonlinear stress term is not strictly increasing.
文摘General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A classical theory of gravitation in flat space-time also avoids the singularity under natural conditions on the density parameters. The universe contracts to a positive minimum and then it expands during all times. It is not symmetric with regard to its minimum implying a finite age measured with proper time of the universe. The space of the universe is flat and the total energy is conserved. Under the assumption that the sum of the density parameters is a little bit bigger than one the universe is very hot in early times. Later on, the cosmological model agrees with the one of general relativity. A new interpretation of a non-expanding universe may be given by virtue of flat space-time theory of gravitation.
基金supported by the National Key R&D Program of China(Grant Nos.2022YFA140220 and 2023YFA1406303)the State Key Project of Zhejiang Province(Grant No.LZ22A040007)+2 种基金the National Natural Science Foundation of China(Grant Nos.U23A20580,12174331,12204159,and 12274364)the Key R&D Program of Zhejiang Province,China(Grant No.2021C01002)the Bridging Grant(Grant No.BG11-072020)with China,Japan,South Korea and ASEAN region funded by the Swiss State Secretariat for Education,Research and Innovation。
文摘The locally noncentrosymmetric heavy fermion superconductor CeRh_(2)As_(2) has attracted considerable interests due to its rich superconducting phases,accompanied by possible quadrupole density wave and pronounced antiferromagnetic excitations.To understand the underlying physics,here we report measurements from highresolution angle-resolved photoemission.Our results reveal fine splittings of the conduction bands related to the locally noncentrosymmetric structure,as well as a quasi-two-dimensional Fermi surface(FS)with strong 4f contributions.The FS shows signs of nesting with an in-plane vector q_(1)=(π/α,π/α),which is facilitated by the heavy bands nearˉ𝑋arising from the characteristic conduction-X hybridization.The FS nesting provides a natural explanation for the observed antiferromagnetic spin fluctuations at(π/α,π/α),which might be the driving force for its unconventional superconductivity.Our experimental results can be reasonably explained by density functional theory plus dynamical mean field theory calculations,which can capture the strong correlation effects.Our study not only provides spectroscopic signature of the key factors underlying the field-induced superconducting transition,but also uncovers the critical role of FS nesting and lattice Kondo effect in the underlying magnetic fluctuations.
基金supported by National Natural Science Foundation of China(Grant Nos.11471042,11171027 and 11361020)the Alexander von Humboldt Foundation+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60 and 2014KJJCA10)
文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.
基金BSG is supported by Science Foundation Ireland grant no.07/SK/B1236b.
文摘Introduction:The availability of essential nutrients,such as nitrogen(N)and phosphorus(P),can feedback on soil carbon(C)and the soil microbial biomass.Natural cycles can be supplemented by agricultural fertiliser addition,and we determined whether the stoichiometry and nutrient limitation of the microbial biomass could be affected by an unbalanced nutrient supply.Methods:Samples were taken from a long-term trial(in effect since 1968)with annual applications of 0,15 and 30 kg P ha^(−1) with constant N and potassium.Soil and microbial biomass CNP contents were measured and nutrient limitation assessed by substrate-induced respiration.Linear regression and discriminant analyses were used to identify the variables explaining nutrient limitation.Results:Soil and biomass CNP increased with increasing P fertiliser,and there was a significant,positive,correlation between microbial biomass P and biomass C,apart from at the highest level of P fertilisation when the microbial biomass was over-saturated with P.The molar ratios of C:N:P in the microbial biomass remained constant(homeostatic)despite large changes in the soil nutrient ratios.Microbial growth was generally limited by C and N,except in soil with no added P when C and P were the main limiting nutrients.C,N and P,however,did not explain all the growth limitation on the soils with no added P.Conclusions:Increased soil C and N were probably due to increased net primary production.Our results confirm that C:N:P ratios within the microbial biomass were constrained(i.e.homeostatic)under near optimum soil conditions.Soils with no added P were characterised by strong microbial P limitation and soils under high P by over-saturation of microorganisms with P.Relative changes in biomass C:P can be indicative of nutrient limitation within a site.
文摘We give sufficient and necessary conditions for the existence and nonexistence of positive ground state solutions of a class of coupled nonlinear Schroedinger equations.
文摘The well-known theorem of Dickson provides information on the element ordersof the groups PSL(2, q). In search of a converse to this, Refs. [1] and [2] proved thatif π_e.(G)=π_e(PSL(2, q)) and if q=2~m or q=3~m (m≥2, q≠9), then G is isomorphic toPSL(2, q), where π_e(G) denotes the set of all orders of elements in G.
文摘The paper presents a comprehensive model of a banking system that integrates network effects,bankruptcy costs,fire sales,and cross-holdings.For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium.The number of defaults corresponding to the greatest price-payment equilibrium is analyzed in several comparative case studies.These illustrate the individual and joint impact of interbank liabilities,bankruptcy costs,fire sales and cross-holdings on systemic risk.We study policy implications and regulatory instruments,including central bank guarantees and quantitative easing,the significance of last wills of financial institutions,and capital requirements.
文摘In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization （LPS）. These methods preserve the favourable stability and approximation properties of classical residual-based stabilization （RBS） techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the NavierStokes equations. Furthermore, we apply it to optimal control problems with linear（ized） flow problems, since the symmetry of the stabilization leads to the nice feature that the operations ＂discretize＂ and ＂optimize＂ commute.
基金Supported by the EU Research Training Network CODY, the ESF Networking Programme HCAA and the Deutsche Forschungsgemeinschaft, Be 1508/7-1
文摘Let F be a family of holomorphic functions and suppose that there exists ε 】 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.
基金supported by the Morningside Center of Mathematics and the Deutsche Forschungsgemeinschaft (Grant No. DE 1646/2-1)National Natural Science Foundation of China (Grant No. 10901150)the National Key Basic Research Programm (973 Program) (Grant No. 2013CB834202)
文摘We determine the sum of two integral squares over imaginary quadratic fields Q(√-2p),where p≡1 mod 8 is a prime satisfying 2p=r2+s2with r,s≡±3 mod 8.
