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.

Some Implications of the Gessel Identity

We generalize the congruences of Friedmann-Tamarkine (1909), Lehmer (1938), and Ernvall-Metsänkyla (1991) on the sums of powers of integers weighted by powers of the Fermat quotients to the next Fermat quotient power, namely to the third power of the Fermat quotient. Using this result and the Gessel identity (2005) combined with our past work (2021), we are able to relate residues of some truncated convolutions of Bernoulli numbers with some Ernvall-Metsänkyla residues to residues of some full convolutions of the same kind. We also establish some congruences concerning other related weighted sums of powers of integers when these sums are weighted by some analogs of the Teichmüller characters.

Newton identities的初等证明及应用

Newton identities是一个在初等数学领域中非常重要的恒定式,灵活巧妙地应用Newton identities及推论,可以使一些较为困难的问题迎刃而解。该文在对Newton identities及推论进行初等证明的基础上,论述了它在高师院校数学学院专业课程初等数论、竞赛数学、初等代数研究选讲中的应用。

Cultural Identity and Translator's Style: Case Study of Translation of Tea Relevant Acts in Hong Lou Meng

From the methodological perspective, the thesis summarized leisure tea act, judging-time tea act to map translator's style. Through investigations on all these, the thesis succeeded in confirming the translator's styles and pinpointing cultural identity as essential factors influencing their styles. Hopefully, this could help to provide a new angle of view to make research on translator's style. Moreover, the thesis wishes that with analysis of tea culture in Hong Lou Meng the translation of tea relevant acts receive greater priority in the Chinese Classics Translation.

The quadratic-form identity for constructing Hamiltonian structures of the Guo hierarchy

The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and （2＋l）-dimensional Guo hierarchy are obtained by the quadraticform identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.

Not Relying on the Newton Gravitational Constant Gives More Accurate Gravitational Predictions

The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.

Identity Issue and Mysterious Images in the Bonesetter's Daughter

This paper is going to do a research on the book The Bonesetter's Daughter and will make an analysis of mysterious images appear in the novel which can be considered as symbols that reflect the culture of orient. And it also looks into the identity issue of Chinese American women from postcolonial perspective.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

The Three Principles of Institutional Safeguards for Women's Participation in Legislation in China

The participation of women in legislation is an important aspect and means of safeguarding women’s rights.Feminist theory,based on criticism of both the“citizenship identity theory as rights”and the“citizenship identity theory as responsibilities,”proposes the“citizenship identity theory as subjectivity.”Observing the current practice of women’s participation in legislation in China,two institutional safeguard principles can be summarized:the“minimum proportion”and the“influence evaluation.”However,each of these principles has its inherent limitations.Therefore,it is necessary to supplement them with the principle of“subjective participation”in a reflective manner.This principle requires women to participate substantively in the legislative process as subjects,express women’s needs and demands,input women’s perspectives and experiences,and reconstruct the distribution of rights and responsibilities in the existing legislation.The three principles complement each other and work together to comprehensively constitute the institutional structure of women’s participation in legislation,thereby promoting the reproduction of corresponding action structures.

Translator's Identity in the English Translation of Wenxin Diaolong

In the article Owen’s and Yang Guobin’s English versions of Wenxin Diaolong are compared from the perspective of a translator’s identity.Owen is a translator of A-merican origin while Yang Guobin is of Chinese origin.Their multiple identity as a reader,author,creator and cultural communicator differs much from each other,which produces important influences upon the selection of the strategy of translation.Owen prefers foreignizing translation while Yang favors domesticating translation.The English translation of Wenxin Diaolong provides much value for the research on the translation of Chinese classic literature.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

The Enclosed Personal Space and Female Identity Construction in A. S. Byatt's Possession

From the perspective of feminism, by analyzing single intellectual women's living states in enclosed personal spaces, andcomparing their different spatial changes triggered by external intrusions, this essay intends to explore Byatt's ambivalent attitudestowards the feminists' pursuit for a room of one's own, and point out the significance of harmonious co-existence between men andwomen to female identity construction.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Negative Evaluation and Author’s Identity Construction in Chinese and English Academic Book Reviews

Evaluation,especially negative evaluation,is an important element in academic book reviews.Unfortunately,previous studies on evaluation strategies in Chinese and English book reviews are still limited in number.Recently,identity construction has been a hot research issue in various fields of social science.However,few studies have ever been conducted on how book reviewers construct various identities with the use of evaluation strategies.As such,this thesis tries to investigate how the negative evaluation,the most direct face-threatening evaluation,are linked closely to author’ s identity construction in Chinese and English book reviews,how the Chinese and English book reviewers make salient their appropriate identities with the skillful use of discourse strategies so as to avoid possible face-threatening.The present study collects fifteen Chinese and fifteen English academic book reviews as research data.An analysis of the data indicates that while there are similarities,there are also distinctive differences in the use of negative evaluation strategies and author’ s identity construction in Chinese and English book reviews.Specifically,with the use of negative evaluation,four important identities are constructed,namely,the author’ s identities as an authoritative writer,a polite and friendly evaluator,a responsible opinion holder and a kind academic ally.

Constructing Writer Identity in Developing Second Language Writer's Academic Writing

Writer identity in academic writing has long been ignored by developing L2 writers.Moreover,research has much focused on the reader in shaping writing,and treated the role of the writer as unproblematic.In this essay,the construction of writer identity in developing writers’academic writing practice will be explored through a review of some relevant literature research and gain insights for the development of writer apprentices and writing instruction.

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.

Soil Parameter Identification for Wheel-terrain Interaction Dynamics and Traversability Prediction

This paper presents a novel technique for identifying soil parameters for a wheeled vehicle traversing unknown terrain. The identified soil parameters are required for predicting vehicle drawbar pull and wheel drive torque, which in turn can be used for traversability prediction, traction control, and performance optimization of a wheeled vehicle on unknown terrain. The proposed technique is based on the Newton Raphson method. An approximated form of a wheel-soil interaction model based on Composite Simpson＇s Rule is employed for this purpose. The key soil parameters to be identified are internal friction angle, shear deformation modulus, and lumped pressure-sinkage coefficient. The fourth parameter, cohesion, is not too relevant to vehicle drawbar pull, and is assigned an average value during the identification process. Identified parameters are compared with known values, and shown to be in agreement. The identification method is relatively fast and robust. The identified soil parameters can effectively be used to predict drawbar pull and wheel drive torque with good accuracy. The use of identified soil parameters to design a traversability criterion for wheeled vehicles traversing unknown terrain is presented.

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.

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.