Uncertainty Analysis of the Residual Strength of Non-Uniformly Loaded Casingsin Deep Wells

An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.

How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations

We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.

Uniformly Most Powerful Invariant Test and Its Application

The authors consider the uniformly most powerful invariant test of the testing problems (Ⅰ) H 0: μ′Σ -1 μ≥CH 1: μ′Σ -1 μ<C and (Ⅱ) H 00 : β′X′Xβσ 2≥CH 11 : β′X′Xβσ 2<C under m dimensional normal population N m(μ, Σ) and normal linear model (Y, Xβ, σ 2) respectively. Furthermore, an application of the uniformly most powerful invariant test is given.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY L-LIPSCHITZIAN MAPPINGS

The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].

Hermite Non-Uniformly Correlated Array Beams and Its Propagation Properties

We study the evolution of spectral intensity and degree of coherence of a new class of partially coherent beams,Hermite non-uniformly correlated array beams,in free space and in turbulence,based on the extended Huygens–Fresnel integral.Such beams possess controllable rectangular grid distributions due to multi-self-focusing propagation property.Furthermore,it is demonstrated that adjusting the initial beam parameters,mode order,shift parameters,array parameters and correlation width plays a role in resisting intensity and degree of coherence degradation effects of the turbulence.

Uniformly ultimate boundedness for discontinuous systems with time-delay

The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).

UNIFORMLY HIGHER ORDER ACCURATE EXTRAPOLATIONS TO SOLUTIONS OF UNIFORMLY CONVERGENT DISCRETIZATION METHODS FOR SINGULARLY PERTURBED PROBLEMS

We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

ITERATIVE APPROXIMATION OF FIXED POINTS FOR MULTIVALUED OPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES

In this paper, let K be a nonempty subset of a uniformly smooth Banach space X, and T:K→2~k be a multivalued operator of the monotone type. The iterative sequence which converges strongly to the unique fixed point of T is given. Our results are the extension and improvements of the results obtained previously by several authors including Dunn, Chidume, Deng and Ding.

MARTINGALE REPRESENTATION IN NEARLY UNIFORMLY CONVEX SPACES

In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.

THE MODULUS OF CONVEXITY AND THE EQUIVALENT CONDITIONS OF UNIFORMLY NON-SQUARE SPACES

This paper shows that X is uniformly non-square iff P(η_o)】0 for someη_o∈(0,2).Thus X is super-reflexive if and only if for X there exists an equivalent normwhich meets the above condition.By virtue of the before mentioned result,the author derives the necessary,and suffi-cient conditions for X and l^p(X_j)being uniformly non-square,respectively,and gives acharacterization of finite-dimensional spaces which are uniformly non-square.

PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL

We present an overview of the properties of the pseudohyperbolic metric in several real dimensions and study uniformly discrete sequences for the real unit ball in R^n.

Thermodynamic Properties of Spherically-Symmetric, Uniformly-Accelerated Reference Frames

We aim to study the thermodynamic properties of the spherically symmetric reference frames with uniform acceleration, including the spherically symmetric generalization of Rindler reference frame and the new kind of uniformly accelerated reference frame. We find that, unlike the general studies about the horizon thermodynamics, one cannot obtain the laws of thermodynamics for their horizons in the usual approaches, despite that one can formally define an area entropy （Bekenstein-Hawking entropy）. In fact, the common horizon for a set of uniformly accelerated observers does not always exist, even though the Hawking-Unruh temperature is still well-defined. This result indicates that the Hawking-Unruh temperature is only a kinematic effect, and to gain the laws of thermodynamics for the horizon, one needs the help of dynamics. Our result is in accordance with those from the various studies about the acoustic black holes.

ISHIKAWA ITERATIVE PROCESS IN UNIFORMLY SMOOTH BANACH SPACES

Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.

UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS

By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.

The Uniformly Valid Solution for a Top System of Two Free Dimensions with Parameter

A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.

On the Uniformly Balancedness of Graphs

In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence of this difference and obtained some new results.

A New System of Generalized Variational Inclusions Involving H-η-monotone Operators in Uniformly Smooth Banach Spaces

In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.