Given n vectors {~ αi}i=1 ∈ [0, 1), consider a random walk on the ddimensional torus T = R/Z generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q) between the k-th step distribution of the walk and Haar measure is bounded below byD(Q) ≥ C1k, where C1 =...

For 2 (?1; 1), let Q (R n) be the space of all measurable functions with supp`(I)] 2?n Z I Z I jf(x) ? f(y)j 2 jx ? yj n+2 dx dy < 1; where the supremum is taken over all cubes I with the edge length`(I) and the edges parellel to the coordinate axes in R n. If 2 (?1; 0), then Q (R n) = BMO(R n), and if 2 1; 1), then Q (R n) = fconstantsg. In the present paper, we discuss the case 2 0; 1). These...

It is proved that a code L(q) which monomially equivalent to the Pless symmetry C(q) of length $$2q+2$$ contains (0,1)-incidence matrix Hadamard 3- $$(2q+2,q+1,(q-1)/2)$$ design D(q) associated with Paley–Hadamard type II. Similarly, any ternary extended quadratic residue incidence 3-design I. If $$q=5, 11, 17, 23$$ , then full permutation automorphism group coincides D(q), and similar result h...

An optimized three-lead ECG hierarchial decision-tree type of classification system for myocardial infarction is presented. For selection of the best threshold values for each criterion and the best association of features, we developed a procedure based on "receiver operating characteristic" (ROC) curve data analysis and information theory. Optimization was obtained through maximization of inf...

Let $GP(q,d)$ be the $d$-Paley graph defined on finite field $\mathbb{F}_q$. It is notoriously difficult to improve trivial upper bound $\sqrt{q}$ clique number of $GP(q,d)$. In this paper, we investigate connection between Gauss sums over a and maximum cliques their corresponding generalized Paley graphs. We show that tight if only $d \mid (\sqrt{q}+1)$, which strengthens previous related resu...

A quasi-kernel of a digraph D is an independent set Q⊆V(D) such that for every vertex v∈V(D)﹨Q, there exists directed path with one or two arcs from v to u∈Q. In 1974, Chvátal and Lovász proved has quasi-kernel. 1976, Erdős Székely conjectured sink-free D=(V(D),A(D)) size at most |V(D)|/2. this paper, we give new method show the conjecture holds generalization anti-claw-free digraphs. For any o...