SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE

In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by specializing certain parameters in the two transformations,four Rogers-Ramanujan type identities associated with moduli 20 are obtained.

Combinatorial Identities Concerning Harmonic Numbers

In this paper,we firstly establish a combinatorial identity with a free parameter x,and then by means of derivative operation,several summation formulae concerning classical and generalized harmonic numbers,as well as binomial coefficients are derived.

Analysis on Bicultural Identities of Chinese Americans Based on Acculturation Theory

In the context of globalization,the communication between countries is gradually enhanced and the immigration is increasing.Chinese Americans,as a unique ethnic group,are easy to fall into the difficult problem of self-identity construction when facing the bicultural identity conflict between Chinese and American.This paper selects the film The Farewell created by a Chinese American director as the research object,analyzes the cultural identity crisis of Chinese Americans,introduces the cultural adaption strategy adopted by Chinese Americans from the perspective of Acculturation Theory,and provides reference for Chinese Americans about how to realize the bicultural identities in the cultural diaspora.

State,Communal,and Individual Identities in Iran

Cultural identity in Iran is comprised of four primary elements,each of which have proven to be highly resonant in the country political history.The vexing issue of modernity,and where individuals and collectivities are placed in relation to it,has been one of the most prominent of these elements of Iranian identity.A second constitutive factor has been the role of the state as a deliberate crafter of cultural,in turn directly influencing the salience,interpretation,extent,and direction of modernity,or its antithesis,in Iran.Equally defining has been the role and significance of religion,which has emerged as a marker of individual and collective,as well as political,identities.Nationalism,and its compelling impulse across Iranian society especially from the early 1900s and continuing until today,has also emerged as an integral and inseparable feature of Iranian identity.Together,these four elements―modernity,a culturally intrusive state,religion and religiosity,and nationalism―constitute fluid yet constant,sometimes complementary and sometimes competing,dimensions of Iranian identity.

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。

Female Identities in Translated Literature and the Development of Native Sense

In the formation of native sense,many factors play important roles,such as native culture,literature,and social circumstances and so on.This thesis focuses on the construction of female identities and their importance in the formation of native sense.Due to their different cultural backgrounds and cultural identities,the constructions of female identities in translated literature are different,which own unique features.

CALCULATION OF HAMILTONIAN CONSTRAINT AND MANDELSTAM IDENTITIES OVER EXTENDED KNOT FAMILIES {ψ_i}_2~2, {ψ_i}_4~3 and {ψ_i}_6~4

The actions of the Hamiltonian constraint onto the members of the extended knot families {φi}2^2, {φi}3^4 and {φi}4^6, and the check of their invariance under the Mandelstam identities are given in the extended loop representation of loop quantum gravity.

Attachment&Abandonment——The Analysis of Dual Identities in Sylvia Plath' s Daddy

The interpretation of Sylvia Plath' s representative work Daddy is always being controversial.The poem involves many social and historical issues and various images,among which the image " Daddy" is the key to the interpretation of the poem as well as the poet ess' feminist consciousness of anti-patriarchy.

SOME SPATIALLY INTEGRATED TIME-AVERAGED IDENTITIES FOR FLUIDS

This paper deals with the derivation of a series of seemingly simple but ignored relations, and presents several identities for fluids never obtained before (relations of integrals over different sets of independent variables and connected by an invertible mapping). These identities are based on mass conservation and a mathematical transform with no restriction on dynamics. They are, however, crucial to some fundamental concepts and the interpretation of results from dynamics. The identity for momentum is of most importance and, when averaged over time, yields a relationship between the spatially integrated and time averaged Lagrangian momentum and the spatially integrated and time averaged Eulerian momentum. For a constant density fluid, the averaged identity reduces to a relation between the integrated mean displacement of the particles and the integrated mean Eulerian velocity. For an exactly oscillatory flow in an Eulerian description this identity yields a zero integrated mean displacement of particles. In the case of a progressive surface gravity wave, which is periodic but not exactly oscillatory in an Eulerian description such that there are no particles above the trough during part of the period, the mean momentum identity ensures that the integrated mean Eulerian momentum is equal to the integrated mean momentum of the particles. Therefore, there is essentially no superiority as to which description gives a better estimate of the total momentum or total transport at the same order of approximation. The widely used relation, that the Lagrangian velocity equals the Eulerian velocity plus the Stokes velocity, is not based on a 1 to 1 invertible mapping and is therefore ambiguous. This relation is not valid where there is a discontinuity, particularly above the wave trough. It can therefore give an incorrect result on the Lagrangian velocity. The Generalized Lagrangian Mean (GLM) theory uses a mapping between the mean positions of particles and the particles themselves and apparently avoids the non invertibility. However, this mapping is actually not invertible in general because different particles may have the same mean position.

HURWITZ-HODGE INTEGRAL IDENTITIES FROM THE ORBIFOLD MARIO-VAFA FORMULA

In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral （TbL λgλ1）ag.

New Operator Identities and Combinatorics Studied by Virtue of IWOP Technique

Using the coherent state representation we derive some new operator identities and study some mathematical relations in comblnatorics. The technique of integral within an ordered product （IWOP） of operators plays an essential role in realizing our goal.

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

Complex Spacetime Frame: Four-Vector Identities and Tensors

This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.

On Certain Theta Function Identities Analogous to Ramanujan’s <i>P-Q</i>Eta Function Identities

The purpose of this paper is to provide direct proofs of certain theta function identities analogous to Ramanujan’s P-Q eta functions identities.

The q _ultraspherical Polynomials and Some Identities of the Rogers-Ramanujan Type

In this paper, we give two transformation formulas for q _series using two simple properties of q _ultraspherical polynomials. Using these transformations and the well_known Rogers_Ramanujan identities, we provide simple proofs of some identities of the Rogers_Ramanujan type.

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.

Identities of Symmetry for q-Euler Polynomials

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the p-adic integral expression of the generating function for the q -Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q -analogue of alternating power sums.

Symmetric Identities from an Invariant in Partition Conjugation and Their Applications in <i>q</i>-Series

For every partition and its conjugation , there is an important invariant , which denotes the number of different parts. That is , . We will derive a series of symmetric q-identities from the invariant in partition conjugation by studying modified Durfee rectangles. The extensive applications of the several symmetric q-identities in q-series ?[1] will also be discussed. Without too much effort one can obtain much well-known knowledge as well as new formulas by proper substitutions and elementary calculations, such as symmetric identities, mock theta functions, a two-variable reciprocity theorem, identities from Ramanujan’s Lost Notebook and so on.

ON THE LATTICE PATH METHOD IN CONVOLUTION-TYPE COMBINATORIAL IDENTITIES(Ⅱ)—THE WEIGHTED COUNTING FUNCTION METHOD ON LATTICE PATHS

An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.

Cultural Identities and Integration of the Hakkas in Buu Long （Bien Hoa, Vietnam） Through the Transformation of the Clan Worships

East Asia during 17th to early 20th century witnessed many mass migration flows of South Chinese into Southeast Asia and other parts of the world, including Vietnam. They are the Cantonese, Hokkiens, Hainanese, Chiuchow Hoklo Clan, and Hakkas. Over the course of long history and with the impact of the natural environment and historical-social backgrounds of each country in Southeast Asia, the South Chinese communities have settled and created their livings under different forms. This long process includes the obvious ＂fossilization＂ of immigrant culture and the interesting cultural transformation to achieve harmonious and sustainable development. The Hakkas in Buu Long （Bien Hoa, Dong Nai, and Vietnam） migrated from the Stone-Carfting Prefecture of Huiyang, Guangdong Province （South China） to live preferably in Buu Long granite mountain area to continue their traditional professions and maintain their migrant culture. They brought to Vietnam the cult of three Professional Masters： Gods of stone-crafting, carpenter, and Blacksmithing. However, under the strong impacts of French colonial policies and local social movement in the early 20th century, the Hakkas changed the form of the cult of three Professional Masters into the cult of Goddess Tian Hou in order to attain the full integration with the other Chinese communities and with the local Vietnamese, socially and economically. Throughout the cultural shift, both the continuity and the change have been proven as the inevitable way to balance two opposite poles： Cultural identities and social integration.