Lattices are discrete mathematical objects with widespread applications to integer programs as well as modern cryptography. A fundamental problem in both domains is the Closest Vector Problem (popularly known as CVP). It is well-known that CVP can be easily solved in lattices that have an orthogonal basis if the orthogonal basis is specified. This motivates the orthogonality decision problem: v...

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.  

in this paper  we give newresults on the best approximation  in the hausdorff topological vectorspace and  consider relationship  with orthogonality. also we determined under  what conditions the map $p_{k,f}$ is upper semicontinous.

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...

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...

______________________________________________ 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...