Quasi-measures with image transformations as generalized variables

We introduce an image transformation as a generalization of measurable maps. Structure properties of the image transformation is given. Unique extension of image transformations from solid sets is proven. The multidimensional median and sample median are presented as image transformations, providing a construction suitable for probability theorists.     

Calculating Entropy of Plane Symmetry Black Hole via Generalized Uncertainty Relation

The generalized uncertainty relation is introduced to calculate entropy of the black hole. By using quantum statistical method, we directly obtain the partition function of Bose and Fermi field on the background of the plane symmetry black hole. Then we calculate the entropy of Bose and Fermi field on the background of black hole near the horizon of the black hole. In our calculation, we need not introduce cutoff. There are not the left out term and the divergent logarithmic term in the original brick-wall method. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of black hole and the area of horizon is opened out. Further it is shown the entropy of black hole is entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect.     

Relaxation of the (1 1 1) surface of δ-Pu and effects on atomic adsorption: An ab initio study

The computational formalism of the full-potential all-electron linearized augmented plane wave plus local orbitals (FP-LAPW+lo) method has been employed to study the relaxation of the δ-Pu(1 1 1) surface and the consequent effects for atomic adsorption of C, N, and O atoms on this surface. The underlying theoretical principle is the generalized gradient approximation to density functional theory (GGA-DFT) and the surface was modeled by a five-layer slab with a (2×2) surface unit cell. Upon relaxation of the slab, the interlayer separation between the surface and the subsurface layers expanded by 7.1% with respect to the bulk interlayer separation, while the separation between the subsurface and central layers expanded by 0.4%. To study adsorption on the surface, the adatoms were allowed to approach the surface at four high symmetry adsorption sites, namely, the top, bridge, hollow FCC, and hollow HCP sites, the adlayer structure corresponding to a coverage of 0.25 of a monolayer in all cases. The hollow FCC adsorption site was found to be the most stable site for C and N with chemisorption energies of 6.420 and 6.549 eV, respectively, while the hollow HCP adsorption site was found to be the most stable site for O with a chemisorption energy of 7.858 eV. The respective distances of the C, N, and O adatoms from the surface were found to be 1.22, 1.09, and 1.22 Å. The work function and net magnetic moments, respectively, increased and decreased in all cases upon chemisorption compared with the bare δ-Pu(1 1 1) surface. The electronic structure of the interactions between the adsorbates and the substrate is discussed in detail.     

Thermodynamics with generalized ensembles: The class of dual orthodes

We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the heat exchanged divided by the temperature is an exact differential. This approach can be seen as a mechanical approach alternative to the well established information-theoretic one based on the maximization of generalized information entropy. Our starting point are the Tsallis escort ensembles which have been previously proved to be orthodes, and have been proved to interpolate between canonical and microcanonical ensembles. Here we shall see that the Tsallis escort ensembles belong to a wider class of orthodes that include the most diverse types of ensembles. All such ensembles admit both a microcanonical-like parametrization (via the energy), and a canonical-like one (via the parameter β). For this reason we name them “dual”. One central result used to build the theory is a generalized equipartition theorem. The theory is illustrated with a few examples and the equivalence of all the dual orthodes is discussed.     

The Crossing Number of C(mk;{1, k})

Calculating the crossing number of a given graph is, in general, an elusive problem. Garey and Johnson have proved that the problem of determining the crossing number of an arbitrary graph is NP-complete. The crossing number of a network(graph) is closely related to the minimum layout area required for the implementation of a VLSI circuit for that network. With this important application in mind, it makes most sense to analyze the the crossing number of graphs with good interconnection properties, such as the circulant graphs. In this paper we study the crossing number of the circulant graph C(mk;{1,k}) for m3, k3, give an upper bound of cr(C(mk;{1,k})), and prove that cr(C(3k;{1,k}))=k.Research supported by Chinese Natural Science Foundation     

A Unified Monotonic Approach to Generalized Linear Fractional Programming

We present an efficient unified method for solving a wide class of generalized linear fractional programming problems. This class includes such problems as: optimizing (minimizing or maximizing) a pointwise maximum or pointwise minimum of a finite number of ratios of linear functions, optimizing a sum or product of such ratios, etc. – over a polytope. Our approach is based on the recently developed theory of monotonic optimization.     

On Equitorsion Holomorphically Projective Mappings of Generalized Kählerian Spaces

In this paper we investigate holomorphically projective mappings of generalized Kählerian spaces. In the case of equitorsion holomorphically projective mappings of generalized Kählerian spaces we obtain five invariant geometric objects for these mappings.