On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

The Variety of Commutative BCI-Algebras is 2-Based

In this note, we first solve the following open problem in [5]: Can the variety of commutative BCI-algebras be defined by two identities? An algebra of type (2, 0) is a commutative BCI-algebra if and only if it satisfies $u\ast\left(((x \ast y) \ast (x \ast y))(z \ast y)\right) = uIn this note, we first solve the following open problem in [5]: Can the variety of commutative BCI-algebras be defined by two identities? An algebra of type (2, 0) is a commutative BCI-algebra if and only if it satisfies and (see Theorem 2 below).Next, we prove that I-variety [2] is also 2-based. Finally, we show that I-variety is a proper subvariety of the variety of commutative BCI-algebras.AMS Subject Classification (2000): 03G25, 06A10, 06D99     

Undecidability of the word problem in relatively free rings

An example of a series of varieties of rings with the finite basis property is constructed for which the word problem in the relatively free ring of rankn in the variety is decidable if and only ifn <p. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000.     

Komlós Theorem for Unbounded Random Sets

We present the Komlós theorem for multivalued functions whose values are closed (possibly unbounded) convex subsets of a separable Banach space. Komlós theorem can be seen as a generalization of the SLLN for it deals with a sequence of integrable multivalued functions that do not have to be identically distributed nor independent. The Artstein–Hart SLLN for random sets with values in Euclidean spaces is derived from the main result. Finally, since the main theorem concerns multifunctions whose values are allowed to be unbounded, we can restate it in terms of normal integrands (random lower semicontinuous functions).     

Densely Continuous Forms in Vietoris Hyperspaces

For countably paracompact normal spaces X and locally compact separable metric spaces Y, a characterization is given for the closure of the set of densely continuous forms from X to Y in the hyperspace of nonempty closed subsets of X × Y under the Vietoris topology. This shows that for such X having no isolated points, every closed subset of X × R that is dense over X can be Vietoris approximated by a semicontinuous function on X.     

Orthogonality of the range and the kernel of some elementary operators

We prove the orthogonality of the range and the kernel of an important class of elementary operators with respect to the unitarily invariant norms associated with norm ideals of operators. This class consists of those mappings , , where is the algebra of all bounded Hilbert space operators, and , , , are normal operators, such that , and . Also we establish that this class is, in a certain sense, the widest class for which such an orthogonality result is valid. Some other related results are also given.

     

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.     

色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

A Mechanical Model for Analyzing the Runaway Solutions in the Radiation Reaction Problem

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis.     

Vibrational dynamics of the organometallic compound triarylorganoantimony (V) SbPh<Subscript>3</Subscript>[O<Subscript>2</Subscript>CC(OH)Ph<Subscript>2</Subscript>]<Subscript>2</Subscript>

A complete normal coordinate analysis was performed for five-coordinate non-rigid triarylantimony diester SbPh₃(O₂CR)₂, known to be a bioactive molecule, using Wilson G-F matrix method and Urey Bradley force field. The study of vibrational dynamics was performed using the concept of group frequencies and band intensities.