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.

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.

Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

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.

Ubiquitous Computing Identity Authentication Mechanism Based on D-S Evidence Theory and Extended SPKI/SDSI

Ubiquitous computing systems typically have lots of security problems in the area of identity authentication by means of classical PKI methods. The limited computing resources, the disconnection network, the classification requirements of identity authentication, the requirement of trust transfer and cross identity authentication, the bi-directional identity authentication, the security delegation and the simple privacy protection etc are all these unsolved problems. In this paper, a new novel ubiquitous computing identity authentication mechanism, named UCIAMdess, is presented. It is based on D-S Evidence Theory and extended SPKI/SDSI. D-S Evidence Theory is used in UCIAMdess to compute the trust value from the ubiquitous computing environment to the principal or between the different ubiquitous computing environments. SPKI-based authorization is expanded by adding the trust certificate in UCIAMdess to solve above problems in the ubiquitous computing environments. The identity authentication mechanism and the algorithm of certificate reduction are given in the paper to solve the multi-levels trust-correlative identity authentication problems. The performance analyses show that UCIAMdess is a suitable security mechanism in solving the complex ubiquitous computing problems.

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.

A Tentative Analysis Of Samuel Johnson's Definition To Metaphysical School In English Literature

The metaphysical poetry,as a rather influential literary school,plays a momentous andpredominant part in eariy seventeenth century English literature.The marked quality ofmetaphysical poetry,as practiced by Donne and his successors,is their philosophical subtlety orintellectual rigor,while the quintessence of which consists in its peculiar blend of thought andpassion of realistic violence and meditative refinements.Doctor Johnson accused the

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.

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.

Second Note on the Definition of S₁-Convexity

In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.

First Note on the Definition of s<i>1</i>-Convexity

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

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.

Unification of Gravitational and Electromagnetic Fields in Curved Space-Time Using Gauge Symmetry of Bianchi Identities

This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.

Algorithms and Identities for(q, h)-Bernstein Polynomials and(q, h)-Bézier Curves–A Non-Blossoming Approach

We establish several fundamental identities, including recurrence relations, degree elevation formulas, partition of unity and Marsden identity, for quantum Bernstein bases and quantum Bezier curves. We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bezier curves. Our proofs use standard mathematical induction and other elementary techniques.

GENERALIZED BIANCHI'S IDENTITIES FOR VARIANT CONSTRAINED SYSTEM

In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed.

Scheduling Multiple Orders per Job with Multiple Constraints on Identical Parallel Machines

With a comprehensive consideration of multiple product types,past-sequence-dependent(p-s-d) setup times,and deterioration effects constraints in processes of wafer fabrication systems,a novel scheduling model of multiple orders per job(MOJ)on identical parallel machines was developed and an immune genetic algorithm(IGA) was applied to solving the scheduling problem.A scheduling problem domain was described.A non-linear mathematical programming model was also set up with an objective function of minimizing total weighted earliness-tardiness penalties of the system.On the basis of the mathematical model,IGA was put forward.Based on the genetic algorithm(GA),the proposed algorithm(IGA) can generate feasible solutions and ensure the diversity of antibodies.In the process of immunization programming,to guarantee the algorithm's convergence performance,the modified rule of apparent tardiness cost with setups(ATCS) was presented.Finally,simulation experiments were designed,and the results indicated that the algorithm had good adaptability when the values of the constraints' characteristic parameters were changed and it verified the validity of the algorithm.

A Novel Fusion System Based on Iris and Ear Biometrics for E-exams

With the rapid spread of the coronavirus epidemic all over the world,educational and other institutions are heading towards digitization.In the era of digitization,identifying educational e-platform users using ear and iris based multi-modal biometric systems constitutes an urgent and interesting research topic to pre-serve enterprise security,particularly with wearing a face mask as a precaution against the new coronavirus epidemic.This study proposes a multimodal system based on ear and iris biometrics at the feature fusion level to identify students in electronic examinations(E-exams)during the COVID-19 pandemic.The proposed system comprises four steps.Thefirst step is image preprocessing,which includes enhancing,segmenting,and extracting the regions of interest.The second step is feature extraction,where the Haralick texture and shape methods are used to extract the features of ear images,whereas Tamura texture and color histogram methods are used to extract the features of iris images.The third step is feature fusion,where the extracted features of the ear and iris images are combined into one sequential fused vector.The fourth step is the matching,which is executed using the City Block Dis-tance(CTB)for student identification.Thefindings of the study indicate that the system’s recognition accuracy is 97%,with a 2%False Acceptance Rate(FAR),a 4%False Rejection Rate(FRR),a 94%Correct Recognition Rate(CRR),and a 96%Genuine Acceptance Rate(GAR).In addition,the proposed recognition sys-tem achieved higher accuracy than other related systems.

定积分在两点展开的渐近公式

对于具有m+n阶连续导数的被积函数的定积分,通过多次分部积分给出了在积分上限和积分下限两点处同时展开的定积分的渐近展开式,其余项类似于Taylor公式的积分型余项,这种展开式可看作是Taylor公式的一种推广.被积函数在积分上下限处的值有不同情形,展开式也会随之变化而具有多种形式.通过分析与举例也发现这种展开式的近似计算优于Taylor公式的近似计算,而且在某些积分不等式的证明中也体现了其快捷方便的优点.