Thiadiazolo-Azaacenes

This work reports the synthesis and characterization of bis- and tetrakis(thiadiazolo)-appended di- and tetraazaacenes, displaying up to seven catenated benzene/pyrazine rings. The targets are obtained by condensation of benzo-bis(thiadiazole)-4,5-dione with aromatic di- and tetraamines. The condensation products—up to a heptacene-like species—are stable but can be insoluble. Soluble derivatives are readily processible, but do not show enhanced electron affinities, as the two or four attached benzothiadiazole units are effectively resonance-separated from the acene body, maximizing the number of Clar-sextets.     

The Forgotten Pyrazines: Exploring the Dakin–West Reaction

Pyrazines are an underreported class of N-heterocycles available from nitrogen-rich biomass presenting an interesting functional alternative for current aromatics. In this work, access to pyrazines obtained from amino acids by using the 90 year old Dakin–West reaction was explored. After a qualitative screening several functional proteinogenic amino acids proved good substrates for this reaction, which were successfully scaled to multigram scale synthesis of the corresponding intermediate α-acetamido ketones. Subsequently, the conditions towards pyrazine formation using δ-amino-levulinic acid were optimized, and these were employed to synthesize a relevant set of five functional dimethylpyrazines in high purity. These pyrazines can be considered a versatile toolbox of aromatic building blocks for a wide range of applications, such as in the synthesis of polymers or metal–organic frameworks.     

3-Fluoroalkyl (CF3, CHF2, CH2F) Cyclobutane-Derived Building Blocks for Medicinal Chemistry: Synthesis and Physicochemical Properties

Synthesis and physicochemical characterization of all possible cis- and trans-1,3-disubstituted cyclobutane-derived amines and carboxylic acids bearing mono-, di- and trifluoromethyl groups at the C-3 position is disclosed. Tetramethylammonium fluoride (TMAF)- or morpholinosulfur trifluoride (Morph-DAST)-mediated nucleophilic fluorination of appropriate cis- and trans-diastereomeric substrates was used as the key step for the preparation of CH₂F- and CHF₂-substituted derivatives. To obtain the corresponding cis- and trans-isomeric CF₃-substituted derivatives, resolution of known 3-(trifluoromethyl)cyclobutanecarboxylic acid (obtained as a mixture of diastereomers) was applied. The proposed procedures were suitable for the preparation of corresponding fluoroalkyl-substituted cyclobutane-derived amines and carboxylic acids on up to 50 g scale. All 12 building blocks obtained were characterized by measuring dissociation constants (pK_a) and lipophilicities (LogP, for model derivatives) to evaluate the effect of the fluoroalkyl substituents on their physicochemical properties relevant to further drug discovery applications.     

Multigram Synthesis of α- and γ-((Hetera)cyclo)alkylpyridines through α-Arylation of (Hetero)aliphatic Nitriles

A systematic study on the S_nAr reaction of halogenated fluoropyridines and (hetero)aliphatic nitrile anions as an approach to the synthesis of functionalized pyridines bearing a (cyclo)alkyl or saturated heterocyclic substituent by is described. The scope of the method was demonstrated on a wide range of (hetero)aliphatic nitriles (including three- to six-membered cycloalkane derivatives and N-, O-, S-containing saturated heterocycles) and all isomeric halogenated 2-and 4-fluoropyridines. High chemo- and regioselectivity (i. e., exclusive substitution of the fluorine atom), as well as excellent scalability of the proposed reaction sequence were demonstrated (up to 450 g for the arylation step or up to 77 g of cycloalkylpyridine over two steps in a single run). The utility of the synthesized products was illustrated in the additional functional group transformations resulting in synthetically valuable pyridine-containing building blocks.     

Universal deformation rings and Klein four defect groups

In this paper, the universal deformation rings of certain modular representations of a finite group are determined. The representations under consideration are those which are associated to blocks with Klein four defect groups and whose stable endomorphisms are given by scalars. It turns out that these universal deformation rings are always subquotient rings of the group ring of a Klein four group over the ring of Witt vectors.

     

A new algorithm for decomposition of graphical models

In this paper, we combine Leimer’s algorithm with MCS-M algorithm to decompose graphical models into marginal models on prime blocks. It is shown by experiments that our method has an easier and faster implementation than Leimer’s algorithm.     

On an asymptotic behavior of elements of order in irreducible representations of the classical algebraic groups with large enough highest weights

The behavior of the images of a fixed element of order in irreducible representations of a classical algebraic group in characteristic with highest weights large enough with respect to and this element is investigated. More precisely, let be a classical algebraic group of rank over an algebraically closed field of characteristic 2$">. Assume that an element of order is conjugate to that of an algebraic group of the same type and rank naturally embedded into . Next, an integer function on the set of dominant weights of and a constant that depend only upon , and a polynomial of degree one are defined. It is proved that the image of in the irreducible representation of with highest weight contains more than Jordan blocks of size if and are not too small and .

     

THE EXISTENCE OF CONNECTING ORBITS

In this paper,using the notion of an isolating block and Conley's attractor theory,an existence criterion of trajectories connecting a pair of invariant sets of ordinary differential equations is given.     

一致极小对,一致有界性及有穷基定理

本文使用最小板块的思想，揭示了泛代数领域中任一分配簇的任一代数都具有两个性质；（１）投射意义下一致极小对是存在的。（２）存在相对于整个族而言的极小对投射的一致上界。用以上的结果，给出了著名的有穷基定理的一个简单的、构造性的证明。