A Modified Method for Deriving Self-Conjugate Dirac Hamiltonians in Arbitrary Gravitational Fields and Its Application to Centrally and Axially Symmetric Gravitational Fields

We have proposed previously a method for constructing self-conjugate Hamiltonians Hh in the h-representation with a flat scalar product to describe the dynamics of Dirac particles in arbitrary gravitational fields. In this paper, we prove that, for block-diagonal metrics, the Hamiltonians Hh can be obtained, in particular, using “reduced” parts of Dirac Hamiltonians, i.e. expressions for Dirac Hamiltonians derived using tetrad vectors in the Schwinger gauge without or with a few summands with bispinor connectivities. Based on these results, we propose a modified method for constructing Hamiltonians in the h-representation with a significantly smaller amount of required calculations. Using this method, here we for the first time find self-conjugate Hamiltonians for a number of metrics, including the Kerr metric in the Boyer-Lindquist coordinates, the Eddington-Finkelstein, Finkelstein-Lemaitre, Kruskal, Clifford torus metrics and for non-stationary metrics of open and spatially flat Friedmann models.

Some Remarks on the Symmetry of Self-Conjugate Minimal Surfaces in R^3

Symmetry properties of self-conjugate minimal surfaces,i.e.minimal surfaces which are congruent with their conjugate ones in R^3 are studied.

APPROXIMATION PROBLEMS ON THE SMOOTHNESS CLASSES

This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conjugate differential operator P_(r)(D)induced by■Also,the modulus of continuity of the r-th derivative,or r-th self-conjugate differential,does not exceed a given modulus of continuityω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.

The Monotonicity Problems for Generalized Inverses of Matrices in H (n, ≥)

On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

On the Construction of the Conjugate Hull of Brandt Semigroups

In this paper the characterizations of conjugate hulls Ψ(S), φ(S), T(S) and θ(S) on a Brandt semigroup S are given. By using these results we can prove that T(S) is self-conjugate in Ψ(S) for a Brandt semigroup S.

Pluriharmonic Functions on Bounded Symmetric Domains of C^n

1 Introduction Let Ω be a bounded symmetric domain in the complex vector space Cn, 0∈Ω, with Bergman-Silov boundary b, Γ the group of holomorphic automorphisms of Ω and Γ0 its isotropy group. It is known that Ω is circular and star-shaped with respect to 0 and that b is circular. The group Γ0 is transitive on b and b has a unique normalized Γ0-invariant measure σ with σ（b）= 1. Hua constructed by group representation theory a system {φkv}

Gamma Spectroscopy along N～Z towards ^(100)Sn

A wide range of research topics in different fields of physics can be addressed by study of the self-conjugate N = Z nuclei, such as the np pairing, isospin symmetry, the rp-process and the properties of the electroweak interaction. This contribution focuses on the spectroscopy of N^Z nuclei towards ^(100)Sn. The latest results on the isomeric decay spectroscopy of N^Z nuclei below ^(100)Sn, such as the N = Z +2 nuclides ^(94)Pd and ^(96)Ag, the N = Z nuclide ^(96)Cd and so on are highlighted. New opportunities in in-beam γ spectrscopy of N^Z nuclei towards ^(100)Sn, like ^(90)Rh and ^(92)Pd, with radioactive ion beams are discussed.

OSCILLATION OF A CLASS OF HILLE EQUATION

This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are established. Our results generalize the known Hille＇s ones.