Multiplicities and relative position of eigenvalues of a quadratic pencil of Sturm-Liouville operators

For boundary value problems generated by a second-order differential equation with regular nonseparated boundary conditions, criteria for the eigenvalues to be multiple are given and the relative position of the eigenvalues is studied. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 369–381, March, 2000.     

A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray

In reply to a problem posed by Jean Leray in 1950, a nontrivial example of application of the Nielsen fixed-point theory to differential systems is given. So the existence of two entirely bounded solutions or three periodic (harmonic) solutions of a planar system of ODEs is proved by means of the Nielsen number. Subsequently, in view of T. Matsuoka's results in Invent. Math. (70 (1983), 319-340) and Japan J. Appl. Math. (1 (1984), no. 2, 417-434), infinitely many subharmonics can be generically deduced for a smooth system. Unlike in other papers on this topic, no parameters are involved and no simple alternative approach can be used for the same goal.

     

多元代数方程组解的重数的计算

本文利用多项式理想对偶基的理论给出了当代数方程组只有孤立解(即零维理想的零点)时解的重数的一个算法,同时得到了零维理想有重零点的几个判定准则.     

一类四阶边值问题的多解结果

本文研究一类弹性梁方程边值问题y(1)-α₁y+β₁y"+g(x,y,y")=e,02(0.1),而g:[0,1]×R×R→R为连续有界函数,特征对(α₁,β₁)满足α₁+(0+0.5)2π2β₁=(0+0.5)4π4及α₁+(k+0.5)2π2β₁≠(k+0.5)4π4,?k∈N     

Detailed 1H and 13C NMR structural assignment of ent-polyalthic acid,a biologically active labdane diterpene

In this paper, a complete ¹H and ¹³C NMR data assignment of ent-polyalthic acid, a biologically active labdane-type diterpene, is presented. The assignments were carried on the basis of spectroscopic data from ¹H NMR, ¹³C{¹H} NMR, gCOSY, gHMQC, and gHMBC experiments. Furthermore, a software-assisted methodology, using FOMSC3_rm_NB and NMR_MultSim programs, supported the detailed and unequivocal assignment of ¹H and ¹³C signals, allowing all hydrogen coupling constants to be determined and thus clarifying all hydrogen signal multiplicities.     

Research on the prompt neutron multiplicity of fission fragments for 235U（n,f）

According to some experimental and evaluated data,the total excitation energy partitioning way between both of the fission fragments was given with a semi-empirical method. With the calculated energy partitioning way,the prompt neutron multiplicity as a function of fragment mass,（A） ,for neutron-induced fission of 235U at En=0.0253 eV,3 MeV,and 5 MeV was calculated. The results are checked with the total average prompt neutron multiplicities  and compared with the experimental and evaluated data.     

On Some Families of Smooth Affine Spherical Varieties of Full Rank

Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify:(a) all such varieties for G = SL(2) × C~×and(b) all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and Knop's classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of Woodward's result that every reflective Delzant polytope is the moment polytope of such a manifold.