Given positive integers h and k, denote by r(h, k) the smallest integer n such that in any k-coloring of the edges of a tournament on more than n vertices there is a monochromatic copy of every oriented tree on h vertices. We prove that r(h, k) = (h− 1) for all k sufficiently large (k = Θ(h log h) suffices). The bound (h − 1) is tight. The related parameter r∗(h, k) where some color contains al...

Let P1, P2, . . . , Pd+1 be pairwise disjoint n-element point sets in general position in d-space. It is shown that there exist a point O and suitable subsets Qi ⊆ Pi (i = 1, 2, . . . , d + 1) such that |Qi| ≥ cd|Pi|, and every d-dimensional simplex with exactly one vertex in each Qi contains O in its interior. Here cd is a positive constant depending only on d.

A highly sensitive and selective method for amplified electrochemical detection for hairpin-stem-loop structured target sequences was developed based on the temperature regulation of DNA hybrids on a sandwich-type electrochemical DNA sensor. Multistep hybridization was applied to promote the hybridization efficiency of each section of sandwich structure. The results showed that both multistep a...

In the seminal work [4] L. Lovász introduced the concept of an orthonormal representation of a graph, and also a related value, now popularly known as the Lovász number of the graph. One of the remarkable properties of the Lovász number is that it lies sandwiched between the stability number and the complementer chromatic number. This fact is called the sandwich theorem. In this paper, using ne...

The reaction between [XW(9)O(34)](9-) (X = As, P) and [RuC(6)H(6)Cl(2)](2) in aqueous buffer solution (pH 6.0) leads to the isolation of two pseudo-sandwich-type heteropolytungstates KNa(6)[(RuC(6)H(6))AsW(9)O(34)] x 17 H(2)O (As-1) and Na(7)[(RuC(6)H(6))PW(9)O(34)] x 14 H(2)O (P-2). Single-crystal X-ray diffraction analyses reveal that the two compounds have the following features: (1) in two ...

We consider anti-Ramsey type results. For a given coloring ∆ of the k-element subsets of an n-element set X, where two k-element sets with nonempty intersection are colored differently, let inj∆(k, n) be the largest size of a subset Y ⊆ X, such that the k-element subsets of Y are colored pairwise differently. Taking the minimum over all colorings, i.e. inj(k, n) = min∆ {inj∆(k, n)}, it is shown...

We prove that for every fixed k and ` ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2`. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, i.e., have the property that for every k, any k-edge coloring of a sufficiently large...

In this paper, we obtain a direct result and Voronovskaya type asymptotic formula for the exponential-type operators in simultaneous approximation with polynomial growth. In the end, we obtain the recurrence formulae for the central moments, direct results and Voronovskaya type asymptotic formulae for the various mixed summation-integral type operators. 2000 AMS Subject Classification. 41A28, 4...