WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY

Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed

Modification of rock mass rating system:Interbedding of strong and weak rock layers

Rock mass classification systems are the very important part for underground projects and rock mass rating(RMR) is one of the most commonly applied classification systems in numerous civil and mining projects. The type of rock mass consisting of an interbedding of strong and weak layers poses difficulties and uncertainties for determining the RMR. For this, the present paper uses the concept of rock bolt supporting factor(RSF) for modification of RMR system to be used in such rock mass types. The proposed method also demonstrates the importance of rock bolting practice in such rock masses. The geological parameters of the Shemshak Formation of the Alborz Tunnel in Iran are used as case examples for development of the theoretical approach.

ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS

It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).

P-kernel Normal Systems in Weakly P-inversive Semigroups

In this paper, we first give the concept of weakly P-inversive semigroup S（P）. Then we describe the strong P-congruences on S（P） in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S（P） are isomorphic.

THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.

Global existence of weak solutions to a prey-predator model with strong cross-diffusion

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. I: Deduction and geometric illustration

Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.

Checking weak and strong optimality of the solution to interval convex quadratic program

In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

Strong and Weak Property of Travelling Wave Front Solutions for a Class of Degenerate Parabolic Equations

In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction diffusion terms are showed.

Key Technical Points of Wheat Moisture-resistant Strain Sowing and Management of Promoting Seedlings from Weak to Strong in Daiyue District

According to the meteorological conditions of sowing period and the characteristics of seedling in each key growth period,the measures of rushing drainage,rushing harvest stubble,rushing sow,implementing late sowing,strengthening field management before winter and in spring are taken in Daiyue District during the autumn planting period of wheat,which reduce the influence of natural disasters and increase the yield of wheat.

DIRECT TITRATION OF VERY WEAK ACIDS(BASES)IN AQUEOUS SOLUTION WITH STRONG BASES(ACIDS)USING VISUAL END-POINT INDICATION WITHOUT INDICATOR

This paper reports a new method of titration for very weak acids and bases using the appearance of incisions on oscillopolarogram to indicate the end-point.This method has the advantages of rapidity,simplicity,no indicator needed as well as good precision.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

Weak harmonic signal detection method in chaotic interference based on extended Kalman filter

The traditional methods of weak harmonic signal detection under strong chaotic interference often suffer from high computational complexity and poor performance. In this paper, an Extended Kalman Filter (EKF) based detection method is proposed for the detection of weak harmonic signal. The EKF method avoids matrix inversion by iterating measurement equation and state equation, which simultaneously improves the robustness and reduces the complexity. Compared with the existing detection methods, the proposed method has the following advantages: 1) it has better performance than the neural network method;2) it has similar performance with the optimal filtering method, but with lower computational complexity;3) it is more robust compared with the optimal filtering method.

Application of local polynomial estimation in suppressing strong chaotic noise

In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.

Generic Transformation from Weakly to Strongly Unforgeable Signatures

Current techniques for transforming unforgeable signature schemes （the forged message has never been signed） to strongly unforgeable ones （the forged message could have been signed） require supplementary components to be added onto the original key pairs of the schemes. In addition, some of them can only be applied to a certain type of signature schemes. In this paper, we propose a new generic transformation technique which converts any unforgeable signature scheme into a strongly unforgeable one without modifying any component in the original key pair. This makes our technique especially compatible for practical use. Our technique is based on strong one-time signature schemes. We show that they can be constructed efficiently from any one-time signature scheme that is based on one-way functions. The performance of our technique also compares favorably with that of current ones. Besides, it is shown in this paper that our transformation can further be applied to schemes satisfying only a weak variant of unforgeability without any further modification. Furthermore, our technique can also be used for constructing strongly unforgeable signature schemes in other cryptographic settings which include certificateless signature, identity-based signature, and several others. To the best of our knowledge, similar extent of versatility is not known to be supported by any of those comparable techniques. Finally and of independent interest, we show that our generic transformation technique can be modified to an on-line/off-line signature scheme, which possesses a very efficient signing process.

Strong Law of Large Numbers under an Upper Probability

Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.

CRITERIA OF STRONG TRANSIENCE FOR OPERATOR-SELF-SIMILAR MARKOV PROCESSES

Yamamuro in [1] defines strong and weak transience of Markov processes; gives a criterion for strong transience of Feller processes; and further, discusses strong and weak transience of Ornstein-Uhlenbeck type processes. In this article, the authors weaken the Feller property of the result in [1] to weak Feller property and discuss the strong transience of operator-self-similar Markov processes.

Weak gravitational lensing of quantum perturbed lukewarm black holes and cosmological constant effect

The aim of the paper is to study weak gravitational lensing of quantum （perturbed） and classical lukewarm black holes （QLBHs and CLBHs respectively） in the presence of cosmological parameter A. We apply a numerical method to evaluate the deflection angle of bending light rays, image locations θ of sample sourceβ = π- 4, and corresponding magnifications μ. There are no obtained real values for Einstein ring locations θE（β = 0） for CLBHs but we calculate them for QLBHs. As an experimental test of our calculations, we choose mass M of 60 types of the most massive observed galactic black holes acting as a gravitational lens and study quantum matter field effects on the angle of bending light rays in the presence of cosmological constant effects. We calculate locations of non-relativistic images and corresponding magnifications. Numerical diagrams show that the quantum matter effects cause absolute values of the quantum deflection angle to be reduced with respect to the classical ones. The sign of the quantum deflection angle is changed with respect to the classical values in the presence of the cosmological constant. This means dominance of the anti-gravity counterpart of the cosmological horizon on the angle of bending light rays with respect to absorbing effects of 60 local types of the most massive observed black holes. Variations of the image positions and magnifications are negligible when increasing dimensionless cosmological constant ∈ = 16AM2 /2The deflection angle takes positive （negative） values for CLBHs （QLBHs） and they decrease very fast （slowly） by increasing the closest distance x0 of bending light ray and/or dimensionless cosmological parameter for sample giant black holes with 0.001 〈 ∈ 〈 0.01.