深水采油树Spring-Seal密封圈接触模型构建与实验测试

为提高深水采油树在高压、高温、低温等工况下长时间工作的稳定性,对采油树密封圈进行重新设计,提出Spring-Seal密封圈(以下简称S密封圈);基于赫兹接触理论、填料密封接触理论,重新构建S密封圈接触力学模型;建立有限元仿真分析模型,分析不同条件下S密封圈的密封性能,同时验证新建接触模型的合理性;利用实验测试S密封圈的实际密封效果。研究结果表明:S密封圈在高压、高温、低温等工况下能够长时间稳定工作且密封性能良好。研究结果可为S密封圈的接触研究及工程运用提供理论参考。

<i>S</i>-Injective Modules and Rings

We introduce and investigate the concept of s-injective modules and strongly s-injective modules. New characterizations of SI-rings, GV-rings and pseudo-Frobenius rings are given in terms of s-injectivity of their modules.

Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question

Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.

Energy Gap in Saturn’s Rings

In this article, we consider, based on the super-diamagnetic model, the new problems of Saturn’s rings discovered by Cassini, such as: 1) anomalous purity of water ice;2) Saturn’s magnetic field alignment with the planet’s rotation axis;3) “ring rain” of the submicron particles;4) the deviation in the qualitative composition of the “rain” from the composition of the rings;5) “dirt” concentrated in the ring gaps;6) “plateaus” in Saturn’s C ring;7) age of the rings;8) roll-off in the spectrum of Saturn’s rings, and 9) “propellers” in Saturn’s A ring. Interpretation of Cassini’s observations of spectral roll-off in Saturn’s rings in the wavelength range from 100 micrometers to 0.5 mm is given. It was concluded that the substance of the rings could be in the superconducting state. An explanation of the Cassini spectral data is given using the hypothesis of the existence of a superconducting energy gap in the substance of rings.

A COMMUTATIVITY CONDITION FOR S-UNITAL RINGS

Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

Gauss-Newton法的半局部收敛性

设f:Rn→Rm 是Frechet可微的 ,m≥n .则非线性最小二乘问题可描述为下面的极小化问题 :minF(x) :=12 f(x) Tf(x) .Gauss Newton法是求解非线性最小二乘问题的最基本的方法之一 ,其n + 1步迭代定义为 :xn + 1=xn - f′(xn) Tf′(x) -1f′(xn) Tf(xn) .本文主要研究解非线性最小二乘问题的Gauss Newton法的半局部收敛性 .假设f(x)在B(x0 ,r)内连续可导且f′(x0 )满秩 ,若f的导数满足Lipschitz连续F′(x) -f′(x′)≤γx -x′ , x ,x′∈B(x0 ,r) .在一个关于初始点x0 的判断准则c =f(x0 ) ,β =f′T(x0 )f′(x0 ) -1f′(x0 ) T ,β2 cγ <1 1 0下 ,Gauss Newton法产生的序列 {xn}收敛到一个驻点x ,从而给出了Gauss Newton法的半局部收敛性 .

关于Newton-Cote's数值积分公式的修正

对Newton-Cote's数值积分公式进行了研究,证明了当n=9时的Newton-Cote's数值积分公式是可行,积分误差是可以控制.最后通过数值例子验证了Newton-Cote's积分当8≤n≤200时,除n=9以外理论上是不可行.

Novel Newton’s learning algorithm of neural networks

Newton＇s learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton＇s method must be faster than BP＇s and other learning algorithms, because the gradient method is linearly convergent while Newton＇s method has second order convergence rate. The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton＇s learning algorithm. Simulation results show that the convergence rate of Newton＇s learning algorithm is high and apparently faster than the traditional BP method＇s, and the robustness of Newton＇s learning algorithm is also better than BP method＇ s.

APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

The Research of the Flow of Bodies with Use of the Vector Form of the Newton’s Law for the Viscous Liquid

On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.

A Discrete Newton's Method for Gain Based Predistorter

Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.

Ring-opening Polymerization ofε-Caprolactone Using Lanthanide Tris(4-tert-butylphenolate)s as a Single-component Initiator

The ring-opening polymerization of e-caprolactone (CL) initiated by novel single lanthanide tris(4-tert-butylphenolate)s [Ln(OTBP)3] is reported. Single-component La(OTBP)3 can effectively prepare polycaprolactone (PCL) with over 90% yield and viscosity average molecular weight about 60 x 10 under quite mild conditions: molar ratio of CL to initiator is 1000, 60 C, 2 h in toluene. Mechanism study indicates that the monomer inserts into the growing chain via the break of acyl-oxygen bond of CL.

Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, qpl, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where ζ(3) equals Apery’s constant, 1.202 …, and, n+(0)=n_(0), is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, n+(0) equals, 7.848E54 m-3, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, l+(0)=l_(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, g=9.81m/s2, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

Newton Did Not Invent or Use the So-Called Newton’s Gravitational Constant;G, It Has Mainly Caused Confusion

Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass;namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength.

Kantorovich’s theorem for Newton’s method on Lie groups

The convergence criterion of Newton’s method to find the zeros of a map f from a Lie group to its corresponding Lie algebra is established under the assumption that f satisfies the classical Lipschitz condition, and that the radius of convergence ball is also obtained. Furthermore, the radii of the uniqueness balls of the zeros of f are estimated. Owren and Welfert (2000) stated that if the initial point is close sufficiently to a zero of f, then Newton’s method on Lie group converges to the zero; while this paper provides a Kantorovich’s criterion for the convergence of Newton’s method, not requiring the existence of a zero as a priori.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

ON AMODIFIED NEWTON'S METHOD AND CONVERGENCE

In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(21/2) and a sharp error estimate is given about the iterative sequence.

Implementation of LDA+ Gutzwiller with Newton's method

In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA＋Gutzwiller method with Newton＇s method. The self-consistence process, efficiency and convergence of calculation are improved dramatically by using Newton＇s method with golden section search and other improvement approaches.We compare the calculated results by applying the previous linear mix method and Newton＇s method. We have applied our code to study the electronic structure of several typical strong correlated materials, including SrVO3, LaCoO3, and La2O3Fe2Se2. Our results fit quite well with the previous studies.