It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
ASTEC and ICARE / CATHARE are computer codes allowing analysing severe accidents in LWRs. The applicability of these codes to Russian reactors of VVER type is a clear common IRSN-GRS objective. The current work in col...ASTEC and ICARE / CATHARE are computer codes allowing analysing severe accidents in LWRs. The applicability of these codes to Russian reactors of VVER type is a clear common IRSN-GRS objective. The current work in collaboration between IRSN and RRC K1 （Russia） aims at reaching this objective. This paper is devoted to ASTEC and ICARE / CATHARE simulations of a severe accident scenario on a VVER-1000. A Large Break LOCA （850 mm） sequence accompanied with the station blackout was selected for analysis. ICARE / CATHARE V2.2 successfully predicted main events of the accident： heat-up of the core, core degradation and melt relocation to the lower part of the core. A simulation of a complete accidental sequence was performed with ASTEC V 1.3-rev3 code： core heat-up and melting, melt relocation, reactor vessel rupture, molten corium / concrete interaction, release and distribution of steam, H2, CO, CO2, fission products and aerosols in the RCS and the containment. It must be pointed out that, as concerns the thermalhydraulics front-end phase and the in-vessel degradation phase, the ASTEC simulation exhibited consistent results with respect to the best-estimate ICARE / CATHARE ones.展开更多
In the present paper was investigated the influence of the surface geometry on the amount of solar radiation arriving on that surface. The total, beam and diffuse radiation incident onto a surface was simulated using ...In the present paper was investigated the influence of the surface geometry on the amount of solar radiation arriving on that surface. The total, beam and diffuse radiation incident onto a surface was simulated using WINSUN software, which is a simulation tool developed at Lund Technical University, Sweden. The irradiation analysis are made for Maputo, latitude 25°58＇ South, longitude 32°36＇ East, Mozambique. The climate date was derived from Meteonorm files. Such study has practical value since the output of solar systems is depending upon the amount of solar radiation reaching to the surface of the collector.展开更多
Let V be a 2-dimensional vector space over the real field R with an affine or indefinite symmetric bilinear form. The infinite dihedral group W can be viewed as a subgroup of GL(V). In the present paper we will class...Let V be a 2-dimensional vector space over the real field R with an affine or indefinite symmetric bilinear form. The infinite dihedral group W can be viewed as a subgroup of GL(V). In the present paper we will classify all crystallographic groups associated with W up to conjugation in the affine group A(V).展开更多
The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spe...The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.展开更多
In this paper,we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities,Vr,b={(x,y,z,t)∈C4|xy-z2r+t2=0}/μr(a,-a,b,0),r 2,where b=1 appears in Mori...In this paper,we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities,Vr,b={(x,y,z,t)∈C4|xy-z2r+t2=0}/μr(a,-a,b,0),r 2,where b=1 appears in Mori’s minimal model program and b=1 is a new class of singularities in symplectic birational geometry.We prove that two symplectic 3-orbifolds which are singular flops to each other have isomorphic Ruan cohomology rings.The proof is based on the symplectic cutting argument and virtual localization technique.展开更多
The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The...The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.展开更多
We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indic...We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.展开更多
Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T_1~1(M) its(1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T_1~1(M) called the interm...Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T_1~1(M) its(1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T_1~1(M) called the intermediate lift connection, which lies somewhere between the complete lift connection and horizontal lift connection. Properties of this intermediate lift connection are studied. Finally, they consider an affine connection induced from this intermediate lift connection on a cross-section σ_ξ(M) of T_1~1(M) defined by a(1, 1)-tensor field ξ and present some of its properties.展开更多
文摘It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
文摘ASTEC and ICARE / CATHARE are computer codes allowing analysing severe accidents in LWRs. The applicability of these codes to Russian reactors of VVER type is a clear common IRSN-GRS objective. The current work in collaboration between IRSN and RRC K1 （Russia） aims at reaching this objective. This paper is devoted to ASTEC and ICARE / CATHARE simulations of a severe accident scenario on a VVER-1000. A Large Break LOCA （850 mm） sequence accompanied with the station blackout was selected for analysis. ICARE / CATHARE V2.2 successfully predicted main events of the accident： heat-up of the core, core degradation and melt relocation to the lower part of the core. A simulation of a complete accidental sequence was performed with ASTEC V 1.3-rev3 code： core heat-up and melting, melt relocation, reactor vessel rupture, molten corium / concrete interaction, release and distribution of steam, H2, CO, CO2, fission products and aerosols in the RCS and the containment. It must be pointed out that, as concerns the thermalhydraulics front-end phase and the in-vessel degradation phase, the ASTEC simulation exhibited consistent results with respect to the best-estimate ICARE / CATHARE ones.
文摘In the present paper was investigated the influence of the surface geometry on the amount of solar radiation arriving on that surface. The total, beam and diffuse radiation incident onto a surface was simulated using WINSUN software, which is a simulation tool developed at Lund Technical University, Sweden. The irradiation analysis are made for Maputo, latitude 25°58＇ South, longitude 32°36＇ East, Mozambique. The climate date was derived from Meteonorm files. Such study has practical value since the output of solar systems is depending upon the amount of solar radiation reaching to the surface of the collector.
文摘Let V be a 2-dimensional vector space over the real field R with an affine or indefinite symmetric bilinear form. The infinite dihedral group W can be viewed as a subgroup of GL(V). In the present paper we will classify all crystallographic groups associated with W up to conjugation in the affine group A(V).
基金supported by the Key Project of Chinese Ministry of Education(Grant No. 108117)National Natural Science Foundation of China (Grant No. 10871123,61071066,11171201)
文摘The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171235,11071176,11071173 and 11221101)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100181110071)the Fundamental Research Funds for the Central Universities of China (Grant No. SWJTU12BR028)
文摘In this paper,we study the global singular symplectic flops related to the following affine hypersurface with cyclic quotient singularities,Vr,b={(x,y,z,t)∈C4|xy-z2r+t2=0}/μr(a,-a,b,0),r 2,where b=1 appears in Mori’s minimal model program and b=1 is a new class of singularities in symplectic birational geometry.We prove that two symplectic 3-orbifolds which are singular flops to each other have isomorphic Ruan cohomology rings.The proof is based on the symplectic cutting argument and virtual localization technique.
基金supported by National Natural Science Foundation of China (Grant No.11171201)
文摘The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.
基金supported by National Natural Science Foundation of China (Grant Nos.10425101,10631050)National Basic Research Program of China (973 Project) (Grant No. 2006cB805905)
文摘We study the local Gromov-Witten invariants of O（k）⊕O（-k-2） → P1 by localization techniques and the Marino-Vafa formula, using suitable circle actions. They are identified with the equivariant Riemann-Roch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.
文摘Let M be an n-dimensional differentiable manifold with an affine connection without torsion and T_1~1(M) its(1, 1)-tensor bundle. In this paper, the authors define a new affine connection on T_1~1(M) called the intermediate lift connection, which lies somewhere between the complete lift connection and horizontal lift connection. Properties of this intermediate lift connection are studied. Finally, they consider an affine connection induced from this intermediate lift connection on a cross-section σ_ξ(M) of T_1~1(M) defined by a(1, 1)-tensor field ξ and present some of its properties.
