The partially ordered monoid generated by the operators H, S, P u , P f on classes of algebras

Let I, H, S, P _u , P _f denote the following operators on classes of algebras of the same type: I, H for isomorphic and homomorphic images of algebras, S for subalgebras and P _u , P _f for ultra and filtered products, respectively. In this paper, the monoid generated by the operators H, S, P _u , P _f with I as an identity is described. It turns out that there are 44 different operators such that every composite of H, S, P _u , P _f coincides with one of them (including the empty composite, the identity operator).     

Uncovering an oxide ion substitution for the OH− + CH3F reaction

Theoretical investigations on chemical reactions allow us to understand the dynamics of the possible pathways and identify new unexpected routes. Here, we develop a global analytical potential energy surface (PES) for the OH⁻ + CH₃F reaction in order to perform high-level dynamics simulations. Besides bimolecular nucleophilic substitution (S_N2) and proton abstraction, our quasi-classical trajectory computations reveal a novel oxide ion substitution leading to the HF + CH₃O⁻ products. This exothermic reaction pathway occurs via the CH₃OH⋯F⁻ deep potential well of the S_N2 product channel as a result of a proton abstraction from the hydroxyl group by the fluoride ion. The present detailed dynamics study of the OH⁻ + CH₃F reaction focusing on the surprising oxide ion substitution demonstrates how incomplete our knowledge is of fundamental chemical reactions.

Reaction dynamics simulations on a high-level ab initio analytical potential energy surface reveal a novel oxide ion substitution channel for the OH⁻ + CH₃F reaction.     

An easy ABD→ABCD strategy to indolo[2,3-a]quinolizin-4-one. Synthesis of deplancheine and yohimbane

The efficient synthesis of indolo[2,3-a]quinolizin-4-ones 2 is described in two steps via formal [3+3] cycloaddition reaction of α-sulfonyl tryptaminylacetamide 4 with various α,β-unsaturated esters 5 and the regioselective reduction of the resulting glutarimides 3 with sodium borohydride then sequent further dehydrated cyclization in the presence of boron trifluoride etherate. The useful building block is applied to synthesize deplancheine (1a) and yohimbane (1b).     

Quantum algebraic–combinatoric study of the conformational properties of n‐alkanes. I

Based on quantum chemical calculation results, four rules were previously derived for the numbers and the sequences of the conformers of free alkane molecules. This paper builds up first an algebra to handle the conformational problem of alkanes. Partitioning the set of all sequences, the whole problem is then subdivided into three independent subcases. With the help of an equivalence relation, the sequences can be classified. According to the quantum chemical rules, certain equivalence classes do not represent conformers. A welldefined subcase of the whole problem is solved.     

Synthesis and characterization of open-framework niobium silicates: Rb2(Nb2O4)(Si2O6).H2O and the dehydrated phase Rb2(Nb2O4)(Si2O6)

A new niobium(V) silicate, Rb(2)(Nb(2)O(4))(Si(2)O(6)).H(2)O, has been synthesized by a high-temperature, high-pressure hydrothermal method and characterized by single-crystal X-ray diffraction, thermogravimetric analysis, and solid-state NMR spectroscopy. It crystallizes in the tetragonal space group P4(3)22 (No. 95) with a = 7.3431(2) A, c = 38.911(3) A, and Z = 8. Its structure contains tetrameric units of the composition Nb(4)O(18), which share corners to form a layer of niobium oxide. The Nb-O layer is a slice of the pyrochlore structure. Neighboring Nb-O layers are linked by vierer single-ring silicates generating eight-ring and six-ring channels running parallel to <100> directions, in which the Rb(+) cations and water molecules reside. The tantalum analogue was prepared and characterized by powder X-ray diffraction. Upon heating to 500 degrees C, Rb(2)(Nb(2)O(4))(Si(2)O(6)).H(2)O loses lattice water molecules, while the framework structure is retained to give the anhydrous compound Rb(2)(Nb(2)O(4))(Si(2)O(6)), whose structure was also characterized by single-crystal X-ray diffraction. The dehydrated sample absorbs water reversibly, as indicated by powder X-ray diffraction. Rb(2)(Nb(2)O(4))(Si(2)O(6)) crystallizes in the tetragonal space group I4(1) (No. 80) with a = 10.2395(6) A, c = 38.832(3) A, and Z = 16.     

Shape-Selective Alkylation of Isopropylnaphthalene over HM Zeolite. A Theoretical Study

A first principle quantum chemical method for determining the shape of molecules has been elaborated and its value in interpreting the experimentally found shape selectivity in isopropylation of isopropylnaphthalene on H-mordenite zeolite is demonstrated. In line with experimental results, it is found that 2,6-diisopropylnaphthalene is the most feasible product since it diffuses through the main channels of mordenite the easiest among the possible isomers.     

Representations of generalized inverses via full-rank QDR decomposition

Numerical Algorithms - In this paper, novel representations of generalized inverses of rational matrices are developed. Therefore, a unified approach for the computation of {1,2,3} and {1,2,4}...     

Effect of the naphthalene moiety on the mesogenic properties of ferroelectric liquid crystals containing diastereomeric propionic acids

Two ferroelectric liquid crystals containing the naphthalene moiety were synthesized from 2(S)-[2(R)-methylhexyloxy]propionic acid and its (S, S)-diastereomer. Their mesogenic properties are compared with those of the analogous mesogens containing the biphenyl ring.     

Traceless polymer-supported divergent synthesis of quinoxalinones by microwave irradiation

A novel protocol for rapid assemble of quinoxalinones framework has been demonstrated. This method incorporated with soluble polymer support provides a convenient approach for diversification of heterocyclic compounds and for easy purification via facile precipitation from reaction matrix. The key transformation of this study involves in situ reduction of aromatic nitro compound, tandem lactamization concomitant with traceless cleavage of the polymer support under microwave irradiation in a one-pot fashion. Moreover, forward synthetic routes were introduced to maximize complexity of the master intermediate on which further chemical elaboration was applied. The strategy is envisaged to apply for establishment of drug-like small-molecule libraries for high-throughput screening.