Kähler Surfaces of Positive Scalar Curvature

We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.     

Kähler Metrics on the Projective Bundle of a Holomorphic Finsler Vector Bundle

Let (M, g) be a compact Kähler manifold and (E, F) be a holomorphic Finsler vector bundle of rank r ≥ 2 over M. In this paper, we prove that there exists a Kähler metric φ defined on the projective bundle P (E) of E, which comes naturally from g and F. Moreover, a necessary and sufficient condition for φ having positive scalar curvature is obtained, and a sufficient condition for φ having positive Ricci curvature is established.     

芬斯勒射影几何中的Ricci曲率

本文研究了保持Ricci曲率不变的Finsler射影变换。给定一个紧致无边的n维可微流形M，证明了：对于一个从M上的Berwald度量到Riemann度量的C-射影变换，如果Berwald度量的Ricci曲率关于Riemann度量的迹不超过Riemann度量的标量曲率，则该射影变换是平凡的。     

Dual nature of Ricci scalar and creation of spinless particles

Manifestation of Ricci scalar like a matter field as well as a geometrical field, at high energy, has been noted earlier [9]. Here, its interaction with another scalar field is considered in four-dimensional curved space-time. This interaction leads to the production of a large number of pairs of spinless particle-antiparticle due to expansion of the early universe in the vacuum state (provided by temperature dependent Coleman-Weinberg like potential for Ricci field), where spontaneous symmetry breaking takes place.     

Set inertia-preserving matrices

The inertia-preservers of several sets of matrices are identified. The sets include: all real matrices, all complex matrices, triangular matrices, real symmetric matrices and Hermitian matrices.     

Algebraically Decaying Modes in Many Dimensions: Application of Fubini’s Identity to Guided-Wave Optics

We show analytically that application of an identity in conformal invariant field theories to multidimensional guided-wave optics predicts a generic family of modes with algebraic (power-law) tails in the evanescent field.     

On theoretical and numerical aspects of symplectic Gram–Schmidt-like algorithms

Gram–Schmidt-like orthogonalization process with respect to a given skew-symmetric scalar product is a key step in model reduction methods, structure-preserving, for large sparse Hamiltonian eigenvalue problem. Theoretical as well as numerical aspects of this step do not benefit of enough attention, compared to the one allowed to the classical Gram–Schmidt algorithm and its modified version. The aim of this paper is to revisit the symplectic Gram–Schmidt algorithms, to built some modified versions and to deal with their theoretical and numerical features. AMS subject classification 65F15, 65F50     

A perturbed elementary operator and range-kernel orthogonality

Let denote the algebra of operators on a Hilbert . If and are commuting normal operators, and and are commuting quasi-nilpotents such that , then define and by , , and . It is proved that and , where is some scalar and is the quasi-nilpotent part of the operator .

     

Dark Energy Model with Canonical Scalar Field and Non-Linear Born–Infeld Type Scalar Field

In this paper, we propose the non-linear Born–Infeld scalar field and canonical scalar field dark energy models with the potential , which admits late time de Sitter attractor solution. The attractor solution corresponds to an equation of state ω_φ → − 1 and a cosmic density parameter Ω_φ → 1, which are important features for a dark energy model that can meet the current observations. dark energy; canonical scalar field, non-linear Born–Infeld type scalar field, attractor solution. PACS number(s):98.80.-k; 98.80.Cq; 98.80.Es.