Inverse Pairs Research Articles

The Comprehensive Analysis to the High Precipitation Supercell Affecting Guangxi

From 31 May to 1 June 2010, serious super high precipitation multi-cells caused convectional rainstorm in central region of Guangxi. The heaviest hour rainfall was 92mm, the heaviest rainfall for 48 hours was 503.9mm. The storms developed in the southwest warm moist wind and moved rightly. The radar reflectivity displayed several bow echoes moving from west to east along the 850hPa shear line. A line echo wave pattern developed. At 2.4°elevation angle, the maximum radar reflectivity of supercell reached 69dBz. The cross section of reflectivity showed that the 40dBz reflectivity core reached 9km in height, indicating a deep updraft. The radial velocity imagery showed with the mesocyclone features such as inverse wind area, the positive and negative velocity pairs. The VAD profile showed the deep warm-wet layer before the storm occurred. The 12m/s southwest wind reached 8km in depth. About 2 hours before the rainstorm, the VAD profile showed double dry region. When the double dry region appeared half hour later, the first rainstorm occurred. The numerical simulation analysis results indicated that the high precipitation multi-cell storms was produced and moved along the vortex path.

Profile of microRNAs following rat sciatic nerve injury by deep sequencing: implication for mechanisms of nerve regeneration.

Unlike the central nervous system, peripheral nerves can regenerate when damaged. MicroRNA (miRNA) is a novel class of small, non-coding RNA that regulates gene expression at the post-transcriptional level. Here, we report regular alterations of miRNA expression following rat sciatic nerve injury using deep sequencing. We harvested dorsal root ganglia tissues and the proximal stumps of the nerve, and identified 201 and 225 known miRNAs with significant expression variance at five time points in these tissues after sciatic nerve transaction, respectively. Subsequently, hierarchical clustering, miRNA expression pattern and co-expression network were performed. We screened out specific miRNAs and further obtained the intersection genes through target analysis software (Targetscan and miRanda). Moreover, GO and KEGG enrichment analyses of these intersection genes were performed. The bioinformatics analysis indicated that the potential targets for these miRNAs were involved in nerve regeneration, including neurogenesis, neuron differentiation, vesicle-mediated transport, homophilic cell adhesion and negative regulation of programmed cell death that were known to play important roles in regulating nerve repair. Finally, we combined differentially expressed mRNA with the predicted targets for selecting inverse miRNA-target pairs. Our results show that the abnormal expression of miRNA may contribute to illustrate the molecular mechanisms of nerve regeneration and that miRNAs are potential targets for therapeutic interventions and may enhance intrinsic regenerative ability.

Applications of the operator H(α,β) to the Humbert double hypergeometric functions

By making use of some techniques based upon certain new inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Humbert hypergeometric functions Φ1, Φ2, Φ3, Ψ1, Ψ2, Ξ1 and Ξ2. These operational representations are constructed and applied in order to derive the corresponding decomposition formulas. With the help of these inverse pairs of symbolic operators, as many as 34 decomposition formulas are found. Euler type integrals connected with Humbert functions are also presented.

SOME DECOMPOSITION FORMULAS ASSOCIATED WITH THE SARAN FUNCTION FE

With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function <TEX>$F_E$</TEX> in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function <TEX>$F_E$</TEX>.

Special Function Inverse Series Pairs

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type and , where 0, 1, 2,. Here , denote special polynomial functions, and , denote coefficients found by use of the orthogonal properties of and , or by skillful series manipulations. Typically and , the n-th Legendre polynomial. We give a collection of inverse series pairs of the type if and only if , each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

Inverse Relations and the Products of Bernoulli Polynomials

In this paper, we give two inverse pairs of identities involving products of the Bernoulli polynomials and the Bernoulli polynomials of the second kind.

A Study on the Aspects of Inverse Morphemes words pairs in the Chinese Characters of Korean Languages

동소역순 한자어는 이음절 한자합성어 중에 어소 순서가 도치되어 단어를 형성하는 어소도치 한자어를 지칭하는 것인데 이 두 한자어를 구성하는 어소는 반드시 동일해야 한다. ‘來往－往來, 施設－設施’는 이것이다. ≪표준국어대사전≫에서 등재된 어소도치 한자어는 약 4600쌍이 있는데 ＜현대 국어 사용 빈도 조사＞에 의하면 ‘AB’와 ‘BA’중에 어느 한 쪽 빈도수만 나타나는 한자어가 약 1,661쌍이고, 양쪽의 빈도수가 하나도 없고 거의 쓰이지 않는 한자어가 약 2,939쌍이 된다. 그런데 약 4600쌍의 어소도치 한자어 중에 ‘故事－事故, 社會－會社, 科學－學科…’과 같이 동일하지 않은 두 어소로 이루어진 어휘들, ‘冬季－季冬, 景致－致景, 電球－球電…’ 등에서 밑줄친 부분과 같이 한자어 조어법과 어긋나는 어휘들, 그리고 ‘角面－面角, 客火－火客, 粉水ㅡ水粉 …’처럼 언중들에게 잘 알려지지 않은 낯선 어휘들 등 어순도치 한자어가 될 수 없는 어휘들도 많다. 본고는 어소도치 한자어의 생성 원인 및 구조 양상을 통해서 기존된 어소도치 한자어에 대한 정의와 범주를 재설정해 보고, 다시 어소도치 한자어 형성의 제약을 제시해 보는 데 그 목적이 있다.

DECOMPOSITION FORMULAS FOR THE GENERALIZID HYPERGEOMETRIC4F3FUNCTION

By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities in- volving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric 4F3 function are then given. Fur- thermore, the integral representations associated with generalized hypergeometric functions are also presented.

Decomposition formulas for Srivastava’s hypergeometric function [formula omitted] on Saran functions

By using some techniques based upon certain inverse pairs of symbolic operators, the author investigates several decomposition formulas associated with Srivastava’s hypergeometric function H A in three variables. The operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities, as many as ten decomposition formulas are then found, which are expressed through the aforementioned triple hypergeometric function in terms of Saran’s hypergeometric functions.

J1601-1-6 事前知識を用いた強化学習の効率的学習(メカニカルシステムとその知能化)

Learning time is always a critical issue in Reinforcement Learning, especially when Recurrent Neural Networks are used to predict Q values in a Partially Observable Markov Decision Process (POMDP) environment. In this paper, we propose a new efficient learning method using domain knowledge of an environment. Our method generates undo-free episodes from recorded episodes by eliminating all action and inverse action pairs. Then recorded episodes and undo-free episodes are replayed after each learning epoch. We compare our method with the standard online reinforcement learning, and reinforcement learning using experience replay in a large scale state space problem. The results show the potential of our approach.

Decomposition formulas associated with the Lauricella multivariable hypergeometric functions

By making use of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Lauricella’s hypergeometric functions F B ( r ) , F C ( r ) , and F D ( r ) in r variables. In the three-variable case when r = 3 , some of these operational representations are constructed and applied in order to derive the corresponding decomposition formulas. With the help of these inverse pairs of symbolic operators, a total of 15 decomposition formulas are found, which are expressed as products of hypergeometric functions of the Gauss and Appell types.

Decomposition formulas for some triple hypergeometric functions

With the help of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Srivastava's hypergeometric functions H A , H B and H C in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities, as many as 15 decomposition formulas are then found, which express the aforementioned triple hypergeometric functions in terms of such simpler functions as the products of the Gauss and Appell hypergeometric functions. Other closely-related results are also considered briefly.

Some decomposition formulas associated with the Lauricella function [formula omitted] and other multiple hypergeometric functions

By making use of some rather elementary techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Lauricella’s hypergeometric function F A ( r ) in r variables ( r = 2 , 3 , 4 , … ) and also with other multiple hypergeometric functions. Alternative derivations of some of these decomposition formulas by means of (for example) integral representations are also indicated.

Description of deformation in shape memory alloys from DO 3 austenite to 18R martensite by group theory

This paper provides a clear and simple group theory description of deformation in shape memory alloys (SMAs) from DO 3 austenite to 18 R martensite. The 24 elements in the point group of austenite P 24 correspond to 24 martensite habit plane variants. After one pair of vectors (the normal vector of the habit plane and the corresponding shape strain vector) are obtained, the other 47 pairs (including the inverse pairs) can be produced by operations of P 24 and inverse through centre I ̃ on the original pair. As point group P 4 is a subgroup of P 24, operations of P 4 and I ̃ on one pair of vectors results in 8 pairs of vectors, which belong to the same basal plane. Point group P 2 is a regular subgroup of P 24. Phase transformation eigenstrain C is invariant in the operation of group P 2. There are 12 elements in L 12, which is the left co-set of P 2 in P 24, and they correspond to 12 different phase transformation eigenstrains in 18 R Martensite. The point group S 4 is also a subgroup of P 24, and stands for the self-accommodation group in 18 R Martensite. 4 pairs of vectors in this self-accommodation group S 4 cluster along direction i 1− i 2 / 2 . All 48 pairs of vectors can be generated by applied left co-set operations and I ̃ on these clustered pairs.

DETECTING STEM AND SHAPE OF PEARS USING FOURIER TRANSFORMATION AND AN ARTIFICIAL NEURAL NETWORK

Huanghua pear is an important fruit in China. The shape and condition of the stems are important indices forclassifying Huanghua pears. Images of Huanghua pears were acquired with a machine vision system. Using templates withdifferent sizes, an algorithm for judging the presence of stems was developed. Meanwhile, the stem head and the joint pointbetween the stem and the pear body were labeled. After calculating slopes of the approximate tangential lines of the stem atthe head and bottom positions, the included angle of these two lines was obtained. It was found that the included angle ofa broken stem was smaller than that of a good stem. Based on this feature, good stems can be distinguished from broken stems.Results of a test on 53 pear images showed that the accuracy for judging the presence and integrity of the stems reached 100%and 93%, respectively. A method for describing the irregular shapes of Huanghua pears was also studied. Fouriertransformation and Fourier inverse transformation pairs were used as the shape descriptors. The first 16 harmoniccomponents of the Fourier descriptor were found sufficient to represent the primary shapes of Huanghua pears. Thesecomponents were used as the inputs to an artificial neural network (ANN) to classify Huanghua pears. The classificationaccuracy reached 90%.

The Distribution of Reciprocal Pairs Modulo Polynomials over a Finite Field

AbstractGiven a finite field Fq of order q, a fixed polynomial g in –Fq[X] of positive degree, and two elements u and v in the ring of polynomials in R = Fq [X]/gFq[X], the question arises: How many pairs (a, 6) are there in R × R so that ab  1 mod g and so that a is close to u while b is close to v ? The answer is, about as many as one would expect. That is, there are no favored regions in R × R where inverse pairs cluster. The error term is quite sharp in most cases, being comparable to what would happen with random distribution of pairs. The proof uses Kloosterman sums and counting arguments. The exceptional cases involve fields of characteristic 2 and composite values of g. Even then the error term obtained is nontrivial. There is no computational evidence that inverses are in fact less evenly distributed in this case, however.

A new 3-D transform using a ternary product

We introduce a 3-D discrete transform that depends on the choice of a certain pair of 3-D arrays called inverse pairs. Many choices of inverse pairs are possible, and each choice gives a new 3-D transform. A number of new 2-D and 1-D transforms are also derived.

Stability of mutually inverse rational 2-D digital transfer functions

This brief considers the open problem concerning the BIBO stability of mutually inverse 2-D digital filters in the presence of nonessential singularities of the second kind on T/sup 2/. Necessary and sufficient conditions are obtained for the BIBO stability of mutually inverse pairs of 2-D digital filters having such singularities on T/sup 2/. Several illustrative examples are considered. >

A Ternary Algebra Arising from Association Schemes on Triples

A ternary algebra formed by three-dimensional arrays with entries from an arbitrary field is investigated. The three-dimensional adjacency arrays of a combinatorial structure called an "association scheme on triples" (AST), developed by the authors earlier, form such an algebra, a generalization of the "Bose-Mesner algebra" of the classical association schemes. We define the notion of identity pair and inverse pair and develop methods for finding inverse pairs. For the ternary sub-algebras generated by the adjacency matrices of the nontrivial relations of ASTs constructed from the the groups PSL(2, q), AGL(1, q), and also by 2-designs, it is shown that there is an abundance of inverse pairs.

Isospectral Hamiltonians from inverse scattering: I. Transformations in a united framework

The authors investigate possible transformations producing isospectral Hamiltonians under one united framework-the application of the commutation formula through the inverse scattering formulation. Four cases of such transformations are discussed. Two of the transformations are new. They produce different reflection coefficients for left and right incidence. These four transformations are illustrated to be inverse pairs and happen to include, by suitable compositions, all isospectral transformations previously introduced under the title of supersymmetric quantum mechanics.