A gap theorem for Ricci-flat 4-manifolds

Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K-min(p)) denote the maximum (respectively the minimum) of sectional curvatures at p. We prove that if K-max(p) <= -cK(min)(P) for all p is an element of M, for some constant c with 0 <= c < 2+root 6/4 then (M, g) is fiat. We prove a similar result for compact Ricci-flat Kahler surfaces. Let (M, g) be such a surface and for p is an element of M let H-max(p) (respectively H-min(P)) denote the maximum (respectively the minimum) of holomorphic sectional curvatures at p. If H-max(P) <= -cH(min)(P) for all p is an element of M, for some constant c with 0 <= c < 1+root 3/2, then (M, g) is flat. (C) 2015 Elsevier B.V. All rights reserved.

Experimental Study of the Earthquake Recurrence Period and the Trend of Post-Seismic Development

In order to study the earthquake recurrence and the characteristics of earthquake series, rupture tests of rock samples and plexiglass samples were made. On rock samples, a number of acoustic emission (AE) and strain measuring points were deployed; the load was one side direct shear. The variation characteristics of AE and strain at different detecting points around the extra large fracture were observed and studied. On plexiglass samples, a series of inclined cracks were prefabricated by a small-scale compressive testing machine. The samples were then loaded on a shockproof platen, when the samples were loaded, the stress intensity factor (SIF) was determined by the laser interferometric technique and shadow optical method of caustics. The fracture conditions such as material toughness around the extra large fracture were also studied. From those experimental results and the theory of fracture mechanics, the earthquake recurrence period and the trend of post-seismic development were studied.

Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

The Complete Proof of the Virial Theorem in the Refined TFD Theory for all Electrons of an Atom in a Solid

The complete proof of the virial theorem in refined Thomas-Fermi-Dirac theory for all electrons of an atom in a solid is given.

Recurrence plot analysis of DNA sequences

Recurrence plot technique of DNA sequences is established on metric representation and employed to analyze correlation structure of nucleotide strings. It is found that, in the transference of nucleotide strings, a human DNA fragment has a major correlation distance, but a yeast chromosome's correlation distance has a constant increasing. (C) 2004 Elsevier B.V All rights reserved.

A Simplified Evaluation Procedure of the Scale of Fluctuation Combined Recurrence Averaging and Weighted Linear Regression

The divergence of properties from one location to another within a soil mass is termed spatial variability, which traditionally includes three parameters the mean, the standard deviation, and the scale of fluctuation, in order to stochastically describe a soil property. Among them, determining the scale of fluctuation in the evaluation of spatial variability of soil profiles is not easy due to soil condition complexity. A simplified procedure is presented in the paper to determine the scale of fluctuation combined recurrence averaging and weighted linear regression. The alternative approach utilizes widely usable spreadsheet to solve the problem more directly and efficiently.

An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

23 p. -- An extended abstract of this work appears in the proceedings of the 2012 ACM/IEEE Symposium on Logic in Computer Science

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..