In this study, we consider the Hermite-Hadamard type of unitary Carlsson?s orthogonality (UHH-C-orthogonality) to characterize real inner product spaces. We give a necessary and sufficient condition weaker than homogeneity symmetric HH-C-orthogonalities which characterizes spaces among normed linear dimension at least three. conclusion, some more characterizations are provided.

Application of Random Indexing (RI) to extractive text summarization has already been proposed in literature. RI is an approximating technique to deal with high-dimensionality problem of Word Space Models (WSMs). However, the distinguishing feature of RI from other WSMs (e.g. Latent Semantic Analysis (LSA)) is the near-orthogonality of the word vectors (index vectors). The near-orthogonality pr...

Using the direct relation between Gegenbauer polynomials C λn (x) and Ferrers function of first kind P μν (x), we compute interrelations certain Jacobi polynomials, Meixner functions second kind. We then Rodrigues-type, standard integral orthogonality Sobolev relations for kinds. In remainder paper using derive connection linearization relations, some definite series expansions, Christoffel-Dar...

1 Dirichlet’s theorem — set up Dirichlet’s famous theorem from 1837 asserts that if k is a positive integer and a is an integer coprime to k, then there are infinitely many primes p with p ≡ a (mod k). In this unit we will prove the stronger assertion that the sum of the reciprocals of the primes p ≡ a (mod k) is divergent. Important in the proof is the use of the orthogonality relations for th...

In most commercial wideband code division multiple access systems, the transmitted signal in the downlink channel is spread by orthogonal codes to accommodate different users. However, frequency selective fading destroys the orthogonality and causes multiple access interference. Application of a chip level decision feedback equaliser with the Alamouti transmit diversity scheme is proposed to re...

We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of Lp-norm of a subordinated one via the same norm of a dominating one. In this setting this was done by Burkholder in [Bu1]–[Bu8]. If one of the martingales is orthogonal, the constant should drop. This was demonstrated in [BaJ1], when the orthogona...

______________________________________________ Abstract: A major challenge in organic synthesis is the selective reaction of a functional group in the presence of others. This can be achieved by using an appropriate reagent, tuned to react exclusively at the desired centre. An alternate approach would be to use a single reagent, and to transmit from the outside the information as to where it sh...

This paper considers several tests of orthogonality conditions in linear models where stochastic errors may be heteroskedastic or autocorrelated. It is shown that these tests can be performed with Wald statistics obtained from simple auxiliary regressions. JEL Classification Number: C20 Word Count: 1460 Address for correspondence: Seung Chan Ahn, Department of Economics, Arizona State Universit...

When deriving the estimates on integral operators one often uses the Almost Orthogonality principle of M. Cotlar and E.M. Stein, first proved by M. Cotlar in [Cot55]. This result is classical; our excuse for formulating it once again is a need to have its weighted form which sometimes allows to reduce the number of integrations by parts in half (hereby weakening smoothness requirements), and al...

Learning embeddings of words and knowledge base elements is a promising approach for open domain question answering. Based on the remark that relations and entities are distinct object types lying in the same embedding space, we analyze the benefit of adding a regularizer favoring the embeddings of entities to be orthogonal to those of relations. The main motivation comes from the observation t...