Combinatorial methodologies were used for the synthesis and screening of mixed metal oxide heterogeneous catalysts. Primary screening at low reactant conversions at a throughput of greater than 10,000 catalyst compositions per month was performed by using simultaneous MS and photothermal def lection spectroscopy on spatially separated thick film catalysts with Ϸ200 g per catalyst prepared by using automated liquid dispensing. Secondary screening under realistic operating conditions was performed at a throughput of greater than 3,000 catalyst compositions per month on Ϸ50 mg of catalyst in an array of fixed bed microreactors with gas chromatograph detection. The approach was validated by the discovery of catalysts with superior performance to those previously described for the oxidative dehydrogenation of ethane to ethylene. We show the full implementation and integration of combinatorial methodologies for synthesis, screening, discovery, and optimization of multicomponent heterogeneous catalysts.Although combinatorial methodologies are practiced routinely for drug discovery (1, 2), this general approach is compelling in other fields where predictive abilities also are restricted. Recently, combinatorial methods have been applied within several different areas of materials science, where increasing compositional or structural complexity often results in unique or otherwise improved properties (1-12). Structural and compositional complexity may result in systems consisting of several components functioning cooperatively. In these combinations, the synergy of the multicomponent system results in performance characteristics that are particularly difficult to predict à priori. Presently, the vast majority of complex inorganic solids and multicomponent materials remain unexplored (13), in part because composition-structure-property relationships for such systems are limited. The utility of combinatorial chemistry, i.e., the ability both to prepare and to screen vast numbers of compounds in a rapid fashion, may be most productively realized within such systems. Here, we describe an integrated combinatorial program that has resulted in the discovery of improved multicomponent heterogeneous catalysts for the oxidative dehydrogenation of ethane to ethylene. Bringing combinatorial methodologies to bear on this application is particularly appealing because catalyst discovery has relied traditionally on an iterative trial-and-error synthesis and characterization strategy that is both tedious and time consuming.The parallel synthesis of catalytic materials by the use of automation and miniaturization techniques is most efficient when preparing very small quantities (Ͻ1 mg) of catalysts. The characterization of such small amounts of catalytic materials frequently is hindered by the lack of sensitive high throughput screening methodologies, particularly for reactions of low probability such as the partial oxidation of hydrocarbons. These obstacles have been overcome in our laboratories, and an integrated combinatorial d...

A ring R with center C is said to be centrally essential if the module R C is an essential extension of the module C C . In the paper, we study groups whose group algebras over fields are centrally essential rings. We focus on the centrally essential modular group algebras of finite groups over fields of nonzero characteristic.V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.

A general method for the synthesis of N,N-disubstituted 3-amino-1,2,4-triazoles 5 from di(benzotriazolyl)methanimines 1 and 1¢, hydrazine and substituted hydrazines is developed. The desired compounds were prepared regioselectively under mild conditions by simple procedures in yields of up to 95%.

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A code of length n over an alphabet of q > 2 elements is called a full ^-recursive code if it consists of all segments of length π of a recurring sequence that satisfies some fixed (nonlinear in general) recursivity law f(x\ , . . . , jty) of order k < n. Let n r (k, q) be the maximal number n such that there exists such a code with distance n -k+ 1 (MDS-code). The condition n r (k,q) > n means that the function / together with its n -k -1 sequential recursive derivatives forms an orthogonal system of fc-quasigroups. We prove that if q £ {2,6, 14, 18,26,42}, then n r (2,q) > 4. The proof is reduced to constructing some special pairs of orthogonal Latin squares.

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A full m-recursive code of length n > m over an alphabet of q > 2 elements is the set of all segments of length n of the recurring sequences that satisfy some fixed recursivity law f(x v , . . . , jc m ). We investigate the conditions under which there exist such codes with distance n -m + 1 (recursive MDS-codes). Let v r (/n, q) be the maximum of the numbers n for which a full m-recursive code exists. In our previous paper, it was noted that the condition v r (m>q) > n means that there exists an mquasigroup /, which together with its n -m -1 sequential recursive derivatives forms an orthogonal system of m-quasigroups (of Latin squares for m = 2). It was proved that v r (w,#) > 4 for all values q € N except possibly six of them. Here we strengthen this estimate for a series of values q < 100 and give some lower bounds for v r (m,q) for m > 2. In particular, we prove that v r (m,q) > q + 1 for all primary q and m -1, . . . ,q and v r (2' -1,2') = 2* +2 for / = 2,3,4. Moreover, we prove that there exists a linear recursive [6,3,4]-MDS-code over the group 7^ Θ^» but ^e re * s no suc^ coc^e over *h e field F 4 .

A ring R with center C is said to be centrally essential if the module R C is an essential extension of the module C C . We describe centrally essential exterior algebras of finitely generated free modules over not necessary commutative rings and study properties of semi-Artinian centrally essential rings.V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A. Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.