The total number of noncrossing partitions of type Ψ is equal to the nth Catalan number 1 n+1 ( 2n n ) when Ψ = An−1, and to the corresponding binomial coefficient ( 2n n ) when Ψ = Bn or Cn. These numbers coincide with the corresponding number of nonnesting partitions. For type A, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each...

Cyanoborane adducts of the Lewis acids B(CN)3, BF(CN)2, and BH(CN)2 with pyridine 4-cyanopyridine have been obtained in high yields. The syntheses were accomplished by oxidation readily available potassium salts cyano(hydrido)borate anions [BH(CN)3]− (MHB), [BFH(CN)2]− (FHB), [BH2(CN)2]− (DHB) bromine presence respective derivative C5H5N or 4-CN-C5H4N as starting material. All six cyanoborane c...

A new fast and reliable reversed-phase high-performance liquid chromatographic method is proposed for quantifying all the major casein fractions during cheese proteolysis as an alternative to more complex methodologies. Excellent separation of caseins, para-κ-casein (ρ-κ-CN), αs1-casein (αs1-CN), αs1-I-casein (αs1-I-CN), αs2-casein (αs2-CN), β-casein (β-CN) was achieved, in terms linearity, rep...

the main goal of this paper is to propose a new practical method for hydrologic soil group estimation in surface runoff process based on geomorphology facieses and slop. the determination of cn based on this method can reduce the time and cost of project. in this research the upstream rivers of glinak watershed have been used as a case study to examine the efficiency of proposed method with a c...

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdős conjectured that when L is the cycle Cn on n vertices, R(Cn, Cn, Cn) = 4n − 3 for every odd n > 3. Luczak proved that if n is odd, then R(Cn, Cn, Cn) = 4n + o(n), as n → ∞, and Kohayakawa, Simonovits and Skokan confirmed...

The colorless salts [C5H10NH2][Au (CN)2], [C4H8NH2][Au (CN)2], [Ph2NNH3][Au (CN)2] H2O and [(n-C3H7)4N][Au(CN)2] H2O have been prepared by evaporation of aqueous solutions of potassium dicyanoaurate and the chloride salt of the appropriate cation. Hydrogen bonding between the cations and the cyano groups of the anions facilitates the formation of structures with strong aurophilic interactions b...