The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the firs...The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the first Brillion Zone. The C-G coefficients are calculated for K.HA.展开更多
This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 ...This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn＇s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modem astronomy as here it is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn＇s characterisation of the paradigm for astronomy which emerges from antiquity （geocentrism） is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn＇s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn＇s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification.展开更多
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic...In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.展开更多
The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective al...The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.展开更多
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^...In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.展开更多
The authors compute the(rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes p.
We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
Let D be an integral domain, ＊a star-operation on D, and S a multiplicative subset of D. We define D to be an S-＊w-principal ideal domain if for each nonzero ideal I of D, there exist an element s ∈ S and a princip...Let D be an integral domain, ＊a star-operation on D, and S a multiplicative subset of D. We define D to be an S-＊w-principal ideal domain if for each nonzero ideal I of D, there exist an element s ∈ S and a principal ideal （c） of D such that sI （c） In this paper, we study some properties of S-＊w-principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-＊w-principal ideal domains.展开更多
文摘The eigenfunction method put forward by Chen Jin-quan is illustrated. We apply this theory to the space group D1_ 6h. The selection rules of this space are worked out in the points of higher symmetry A,K,H in the first Brillion Zone. The C-G coefficients are calculated for K.HA.
文摘This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn＇s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modem astronomy as here it is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn＇s characterisation of the paradigm for astronomy which emerges from antiquity （geocentrism） is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn＇s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn＇s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification.
文摘In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.
基金supported by the National Natural Science Foundation of China (No. 10801099)the Zhejiang Provincial Natural Science Foundation of China (No. J20080154)the grant from Science Technology Department of Zhejiang Province (No. 2011R10051)
文摘The authors give a discription of the finite representation type over an algebraically stable categories of selfinjective algebras of closed field, which admits indecomposable Calabi-Yau obdjects. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ1022)the Fundamental Research Funds for the Central Universities (Grant No. GK201802015)
文摘In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(Nos.NRF-2016R1D1A1A09917654,NRF-2015R1C1A1A01053495)
文摘The authors compute the(rational) Betti number of real toric varieties associated to Weyl chambers of type B, and furthermore show that their integral cohomology is p-torsion free for all odd primes p.
基金supported by National Natural Science Foundation of China (Grant Nos.10726014, 10801010)
文摘We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.
文摘Let D be an integral domain, ＊a star-operation on D, and S a multiplicative subset of D. We define D to be an S-＊w-principal ideal domain if for each nonzero ideal I of D, there exist an element s ∈ S and a principal ideal （c） of D such that sI （c） In this paper, we study some properties of S-＊w-principal ideal domains. Among other things, we study the local property, the Nagata type theorem, and the Cohen type theorem for S-＊w-principal ideal domains.
