Stephan-Yl ~n Solomon Let L be a lan~'uage over m vocmb~Ja~y V ~nd let de~ot~. by E (V) the s,t of ml! enuSv~lence relmtlon~ (partitions) on V. If ~ ~ E (V) and x ~ V then we sb~ll denote by ~(v) the cell of ~ containing the elmment 7. Defini%ion I. A p~rtition ~GE(V) is s~id to be smturated ev~-VY i (I ~imn) there exlst such elements x~ Our purpose i.,~ to find (in the cese of m finite vocebu-...

Recently, polymeric carbon nitride (g-C3N4) as a proficient photo-catalyst has been effectively employed in photocatalysis for energy conversion, storage, and pollutants degradation due to its low cost, robustness, environmentally friendly nature. The critical review summarized the recent development, fundamentals, nanostructures design, advantages, challenges of g-C3N4 (CN), potential future p...

Bovine αS1-casein (αS1-CN) is the main allergen in cow's milk, and immunoglobulin E (IgE) epitopes are material basis to trigger allergic reactions. Thus, IgE could be as key targets for precise αS1-CN detection allergenicity assessment. Here, we designed a tandem containing nine linear of (tαS1-CN), expressed recombinant tαS1-CN Escherichia coli, prepared rabbit polyclonal antibody against (pA...

A biomolecule-assisted pyrolysis method has been developed to synthesize sulfur-doped graphitic carbon nitride (CNS) nanosheets. During the synthesis, sulfur could be introduced as a dopant into the lattice of carbon nitride (CN). Sulfur doping changed the texture as well as relative band positions of CN. By growing CN on preformed sulfur-doped CN nanosheets, composite CN/CNS heterojunction nan...

A special relational structure, called genealogical tree, is introduced; its social interpretation and geometrical realizations are discussed. The numbers Cn,k of all abstract genealogical trees with exactly n+1 nodes and k leaves is found by means of enumeration of code words. For each n, the Cn,k form a partition of the n-th Catalan numer Cn, that means Cn,1 + Cn,2 + · · ·+ Cn,n = Cn.

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The preparation and X-ray crystal structures of (CyNC)Au(I)CN, (n-BuNC)Au(I)CN, and (i-PrNC)Au(I)CN.0.5CH(2)Cl(2) are reported and compared with those of (MeNC)Au(I)CN and (t-BuNC)Au(I)CN, which were previously described. These linear molecules are all organized through aurophilic interactions into three structural classes: simple chains ((CyNC)Au(I)CN and (t-BuNC)Au(I)CN), side-by-side chains ...

In the present article we study the asymptotic behavior of the sums n≤x cn+1 pn+1 − cn pn and n≤x pn+1 cn+1 − pn cn , and of the series ∞ n=1 cn+1 pn+1 − cn pn α , where p n denotes the n-th prime number while c n stands for the n-th composed number.