Monogenic pseudo‐complex power functions and their applications

The use of a non‐commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of different types of polynomials. In this sense, the present paper investigates the intrinsic relationship between two different types of monogenic Appell polynomials. Several authors payed attention to the construction of complete sets of monogenic Appell polynomials, orthogonal with respect to a certain inner product, and used them advantageously for the study of problems in 3D‐elasticity and other problems. Our goal is to show that, as consequence of the binomial nature of those generalized Appell polynomials, their inner structure is determined by interesting combinatorial relations in which the central binomial coefficients play a special role. As a byproduct of own interest, a Riordan–Sofo type binomial identity is also proved. Copyright © 2013 John Wiley & Sons, Ltd.     

Controllability for systems governed by semilinear evolution inclusions without compactness

In this paper we study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation.     

Coordination Compounds of Palladium(II) and 4‐Amino‐1,2,4‐triazole

Mononuclear coordination compounds of the type [Pd(NH₂trz)₄]²⁺ with the counterions chloride, nitrate, trifluoromethanesulfonate, and methanesulfonate were synthesized and their structures identified with single‐crystal X‐ray diffraction. In case of the synthesis with methanesulfonate as the counterion the dominant product was of the generic formula [Pd₂(NH₂trz)₃](CH₃SO₃)₄, and the complex [Pd(NH₂trz)₄](CH₃SO₃)₂ only emerged as a byproduct. While the structure of the byproduct could be analyzed by single‐crystal X‐ray diffraction, suitable crystals of the main product [Pd₂(NH₂trz)₃](CH₃SO₃)₄ could not be obtained. However, stoichiometry implies a polynuclear nature with NH₂trz present in the rare μ₃‐η¹:η¹:η¹ coordination type, i.e. with NH₂trz molecules coordinating to three palladium atoms. Accordingly, identification of solids by single‐crystal analysis alone can be misleading in particular with NH₂trz as a ligand due to its versatile coordination behavior. Finally, analysis by differential scanning calorimetry (DSC) revealed that the complexes were thermally stable (the onset of decomposition well above 100 °C), with [Pd₂(NH₂trz)₃](CH₃SO₃)₄ being the most stable compound (onset of decomposition at 204 °C).     

High-density lipoproteins contribute to the alpha-1-globulin zone in capillary electrophoresis of human serum proteins

Alpha-1-antitrypsin (AAT) and alpha-1-acid glycoprotein (AAG) are reported to be the main proteins contributing to the alpha-1-globulin capillary zone electrophoresis (CZE) zone, but the sum (AAT + AAG) showed lower than the alpha-1-globulin. We investigated the role of high-density lipoprotein (HDL), an additional protein migrating in the alpha-1-globulin zone, as a possible cause for such a gap. In a set of 98 sera we measured the alpha-1-globulin with a dedicated clinical capillary electrophoresis system, and AAT, AAG and apolipoprotein A-1 (ApoA) by immunonephelometry. The alpha-1-globulin were consistently higher than the sum (AAT + AAG), by (mean value +/- standard deviation) 1.70 +/- 0.88 g/L in 49 sera with low ApoA, and by 3.59 +/- 0.75 g/L in 49 sera with high ApoA. Corresponding figures in the comparison alpha-1-globulin/(AAT + AAG + ApoA) were reduced to 1.08 +/- 0.77 g/L and 1.67 +/- 0.70 g/L. It is concluded that HDL significantly contribute to the CZE alpha-1-globulin zone, but do not completely explain the differences between the electrophoretic and the immunochemical measurements. However, CZE alpha-1-globulin measurements give information about increases of the two major acute phase proteins comparable to specific protein measurements.     

Novel antibiotics: second generation macrocyclic peptides designed to trap Holliday junctions

Described are the syntheses of 15 macrocyclic peptides designed to trap Holliday junctions (HJs) in bacteria during site-specific and homologous recombination. This leads to inhibiting bacterial growth. These second generation macrocycles were based on the C-2 symmetrical HJ. They were synthesized using a strategy that permits elucidation of the amino acid role in binding HJs. The syntheses of these macrocycles are an important step in the development of a new class of antibiotics.     

Intramolecular cyclopropanation of unsaturated terminal epoxides and chlorohydrins

Lithium 2,2,6,6-tetramethylpiperidide (LTMP)-induced intramolecular cyclopropanation of unsaturated terminal epoxides provides an efficient and completely stereoselective entry to bicyclo[3.1.0]hexan-2-ols and bicyclo[4.1.0]heptan-2-ols. Further elaboration of C-5 and C-6 stannyl-substituted bicyclo[3.1.0]hexan-2-ols via Sn-Li exchange/electrophile trapping or Stille coupling generates a range of substituted bicyclic cyclopropanes. An alternative straightforward cyclopropanation protocol using a catalytic amount of 2,2,6,6-tetramethylpiperidine (TMP) allows for a convenient (1 g-7.5 kg) synthesis of bicyclo[3.1.0]hexan-2-ol and other bicyclic adducts. The synthetic utility of this chemistry has been demonstrated in a concise asymmetric synthesis of (+)-beta-cuparenone. The related unsaturated chlorohydrins also undergo intramolecular cyclopropanation via in situ epoxide formation.     

Über ebene affine Inzidenzgruppen

For a translation plane P with respect to f we consider the group of collineations generated by all elations fixing f and a point F of f. All subgroups or are determined which operate regularly on the points of the affine plane P. Group-theoretic and operating properties of the groups are stated especially for the finite and the Desarguesian cases. In the latter case the companion NL-near modules are constructed. Finally we characterize the groups within PGL(3, K) with commutative field K of finite characteristic.     

Water-Assisted Concerted Proton-Electron Transfer at Co(II)-Aquo Sites in Polyoxotungstates With Photogenerated RuIII(bpy)33+ Oxidant

The cobalt substituted polyoxotungstate [Co₆(H₂O)₂(α-B-PW₉O₃₄)₂(PW₆O₂₆)]¹⁷⁻ ( Co6 ) displays fast electron transfer (ET) kinetics to photogenerated Ru^III(bpy)₃³⁺, 4 to 5 orders of magnitude faster than the corresponding ET observed for cobalt oxide nanoparticles. Mechanistic evidence has been acquired indicating that: (i) the one-electron oxidation of Co6 involves Co(II) aquo or Co(II) hydroxo groups (abbreviated as Co6(II) −OH ₂ and Co6(II) −OH, respectively, whose speciation in aqueous solution is associated to a pK_a of 7.6), and generates a Co(III)−OH moiety ( Co6(III) −OH), as proven by transient absorption spectroscopy; (ii) at pH>pK_a, the Co6(II) −OH→Ru^III(bpy)₃³⁺ ET occurs via bimolecular kinetics, with a rate constant k close to the diffusion limit and dependent on the ionic strength of the medium, consistent with reaction between charged species; (iii) at pH <pK_a, the process involves Co6(II) − OH₂ → Co6(III)−OH transformation and proceeds via a multiple-site, concerted proton electron transfer (CPET) where water assists the transfer of the proton, as proven by the absence of effect of buffer base concentrations on the rate of the ET and by a H/D kinetic isotope in a range of 1.2–1.4. The reactivity of water is ascribed to its organization on the surface of the polyanionic scaffold through hydrogen bond networking involving the Co(II)−OH₂ group.     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

Transformations of polycyclic musks AHTN and HHCB upon disinfection with hypochlorite: two new chlorinated disinfection by-products (CDBP) of AHTN and a possible source for HHCB-lactone

In this work, the behavior of the polycyclic musks 6-acetyl-1,1,2,4,4,7-hexamethyltetraline (AHTN) and 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexamethylcyclopenta-γ-2-benzopyran (HHCB) was investigated upon disinfection by using sodium hypochlorite as disinfectant in a model disinfection basin in order to find new disinfection by-products (DBP). In the case of AHTN, the carboxylic acid 3,5,5,6,8,8-hexamethyl-5,6,7,8-tetrahydronaphthalene-2-carboxylic acid (AHTN-COOH) was generated by a haloform reaction, being the origin for two new chlorinated DBPs. In the case of HHCB, disinfection via hypochlorite led to the HHCB-lactone. All reaction products and intermediates were synthesized and isolated. The relevant degradation mechanisms are discussed in detail.