Let A be a subset of Z/N Z and let R be the set of large Fourier coefficients of A. Properties of R have been studied in works of M.– C. Chang and B. Green. Our result is the following : the number of quadruples (r 1 , r 2 , r 3 , r 4) ∈ R 4 such that r 1 + r 2 = r 3 + r 4 is at least |R| 2+ǫ , ǫ > 0. This statement shows that the set R is highly structured. We also discuss some of the generali...

A cube design of order v, or a CUBE(v), is a decomposition of all cyclicly oriented quadruples of a v-set into oriented cubes. A CUBE(v) design is unoriented if its cubes can be paired so that the cubes in each pair are related by reflection through the center. A cube design is degenerate if it has repeated points on one of its cubes, otherwise it is nondegenerate. We show that a nondegenerate ...

In the paper we apply progressive waveletcorrelation using Fourier methods to locate objects in aJPEG image. The image is searched step by step. Thesearching consists of three incremental steps, each ofwhich quadruples the number of correlation points. Theprocess can be halted at any stage if the intermediateresults indicate that the correlation will not result in am...

Base sequences BS m,n are quadruples A;B;C;D of {±1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a δfunction. Normal sequences NS n are base sequences A;B;C;D ∈ BS n, n such that A B. We introduce a definition of equivalence for normal sequences NS n and construct a canonical form. By using this canonical form,...

Four points ordered in the positive order on unit circle determine vertices of a quadrilateral, which is considered either as euclidean or hyperbolic quadrilateral depending whether lines connecting are lines. In case lines, this type quadrilaterals called ideal quadrilaterals. Our main result gives counterpart an earlier distances between opposite sides The proof based computations involving g...

The aspect-category-opinion-sentiment (ACOS) quadruples play an essential role in implicit sentiment analysis. Considering the distances between aspects and opinions sentences, a novel Distance-Extract-Classify-ACOS quadruple extraction method with distance information is proposed. Compared Double-Propagation-ACOS, JET-BERT-ACOS Extract-Classify-ACOS models, recall F1 scores of model respective...

Let F be a family of sets in Rd (always d≥2). A set M⊂Rd is called F-convex, if for any pair distinct points x,y∈M, there F∈F, such that x,y∈F and F⊂M. four {w,x,y,z}⊂Rd rectangular quadruple, conv{w,x,y,z} non-degenerate rectangle. If the all quadruples, then we obtain right quadruple convexity, abbreviated as rq-convexity. In this paper focus on rq-convexity complements, taken most cases ball...

Using the coupled-cluster method, we have examined the contributions from the connected quadruple and quintuple virtual excitations to the harmonic vibrational frequencies and equilibrium bond distances of HF, N(2), F(2), and CO. Whereas the largest quadruples contributions are -18.8 cm(-1) to the harmonic frequency of N(2) and 0.43 pm to the bond distance of F(2), the largest quintuples contri...