Spectrum control in linear systems with incomplete feedback

For a linear stationary control system closed by a linear incomplete feedback, we obtain necessary and sufficient conditions for the solvability of the spectrum control problem in the case of coefficients of special form.     

Crystal packing in the structures of diethanolamine derivatives

Four distinct hydrogen‐bonding topologies were observed in the structures of six diethanolamine ligands. These compounds are (1R*,2R*)‐2‐[(2‐hydroxyethyl)(methyl)amino]‐1,2‐diphenylethanol, C₁₇H₂₁NO₂, (I), 1‐[(2S)‐2‐(hydroxydiphenylmethyl)pyrrolidin‐1‐yl]‐2‐methylpropan‐2‐ol, C₂₁H₂₇NO₂, (II), 2‐[(2‐hydroxyethyl)(methyl)amino]‐1,1‐diphenylethanol, C₁₇H₂₁NO₂, (III), 1‐{(2‐hydroxy‐2‐methylpropyl)[(1S)‐1‐phenylethyl]amino}‐2‐methylpropan‐2‐ol, C₁₆H₂₇NO₂, (IV), 1‐{[(2R)‐2‐hydroxy‐2‐phenylethyl][(1S)‐1‐phenylethyl]amino}‐2‐methylpropan‐2‐ol, C₂₀H₂₇NO₂, (V), and (1R*,2S*)‐2‐[(2‐hydroxyethyl)(methyl)amino]‐1,2‐diphenylethanol, C₁₇H₂₁NO₂, (VI). In each compound, all `active' hydroxy H atoms are engaged in hydrogen bonding, but the N atoms are not involved in intermolecular hydrogen bonding. In the structures of (I), (II) and (IV)–(VI), molecules are linked into chains by intermolecular O—H...O interactions. These chains are organized in such a way as to hide the hydrophilic groups inside, and so the outer surfaces of the chains are hydrophobic. The structure of (VI) contains two distinct non‐equivalent systems of intermolecular O—H...O hydrogen bonds formed by disordered hydroxy H atoms.     

Two polymorphs of morpholin‐4‐ium 2‐(5‐methyl‐1H‐1,2,4‐triazol‐3‐ylsulfanyl)acetate

Two polymorphs of the title organic salt (a very effective medicinal preparation with the commercial name thiotriazoline), C₄H₁₀NO⁺·C₅H₆N₃O₂S⁻, were obtained. The cations and anions are connected by hydrogen bonds and extend into two‐dimensional networks. The main packing motifs are an R₄⁴(12) cluster in the monoclinic form and a chain in the orthorhombic form.     

Planar graphs without 4‐cycles adjacent to 3‐cycles are list vertex 2‐arborable

It is known that not all planar graphs are 4‐choosable; neither all of them are vertex 2‐arborable. However, planar graphs without 4‐cycles and even those without 4‐cycles adjacent to 3‐cycles are known to be 4‐choosable. We extend this last result in terms of covering the vertices of a graph by induced subgraphs of variable degeneracy. In particular, we prove that every planar graph without 4‐cycles adjacent to 3‐cycles can be covered by two induced forests. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 234–240, 2009     

Anti‐Ramsey numbers of doubly edge‐critical graphs

Given a graph H and a positive integer n, Anti‐Ramsey number AR(n, H) is the maximum number of colors in an edge‐coloring of K_n that contains no polychromatic copy of H. The anti‐Ramsey numbers were introduced in the 1970s by Erd?s, Simonovits, and Sós, who among other things, determined this function for cliques. In general, few exact values of AR(n, H) are known. Let us call a graph H doubly edge‐critical if χ(H?e)≥p+ 1 for each edge e∈E(H) and there exist two edges e₁, e₂ of H for which χ(H?e₁?e₂)=p. Here, we obtain the exact value of AR(n, H) for any doubly edge‐critical H when n?n₀(H) is sufficiently large. A main ingredient of our proof is the stability theorem of Erd?s and Simonovits for the Turán problem. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 210–218, 2009     

Modeling of flow separation of assist gas as applied to laser cutting of thick sheet metal

The present paper describes the results of mathematical modeling of supersonic flows of a viscous compressible gas, obtained by numerically solving three-dimensional full Navier–Stokes equations, and also the results of experiments with visualization of gas jet flows in channels geometrically similar to the laser cut. Separation of the gas flow from the cut front is predicted numerically and then validated by experiments on a model setup. The gas flow structure arising in a narrow channel behind a sonic (conical) or supersonic nozzle is described. Specific features of originating in the flow separation on a smooth surface in a narrow channel are examined, and mechanisms controlling the separation are proposed. Flow separation directly affects the changes in the shape and structure of striations and is the one of main reason for the worse quality of the laser cut surface. It is shown that the changes in the structures of striations over the thickness of the sheet being cut are closely related to aerodynamic features of jet flows of the assisting gas in the cut channel.     

Improved CO oxidation activity in the presence and absence of hydrogen over cluster-derived PtFe/SiO2 catalysts

The catalytic performance of cluster-derived PtFe/SiO(2) bimetallic catalysts for the oxidation of CO has been examined in the absence and presence of H(2) (PROX) and compared to that of Pt/SiO(2). PtFe(2)/SiO(2) and Pt(5)Fe(2)/SiO(2) samples were prepared from PtFe(2)(COD)(CO)(8) and Pt(5)Fe(2)(COD)(2)(CO)(12) organometallic cluster precursors, respectively. FTIR data indicate that both clusters can be deposited intact on the SiO(2) support. The clusters remained weakly bonded to the SiO(2) surface and could be extracted with CH(2)Cl(2) without any significant changes in their structure. Subsequent heating in H(2) led to complete decarbonylation of the supported clusters at approximately 350 degrees C and the formation of Pt-Fe nanoparticles with sizes in the 1-2 nm range, as indicated by HRTEM imaging. A few larger nanoparticles enriched in Pt were also observed, indicating that a small fraction of the deposited clusters were segregated to the individual components following the hydrogen treatment. A higher degree of metal dispersion and more homogeneous mixing of the two metals were observed during HRTEM/XEDS analysis with the cluster-derived samples, as compared to a PtFe/SiO(2) catalyst prepared through a conventional impregnation route. Furthermore, the cluster-derived PtFe(2)/SiO(2) and Pt(5)Fe(2)/SiO(2) samples were more active than Pt/SiO(2) and the conventionally prepared PtFe/SiO(2) sample for the oxidation of CO in air. However, substantial deactivation was also observed, indicating that the properties of the Pt-Fe bimetallic sites in the cluster-derived samples were altered by exposure to the reactants. The Pt(5)Fe(2)/SiO(2) sample was also more active than Pt/SiO(2) for PROX with a selectivity of approximately 92% at 50 degrees C. In this case, the deactivation with time on stream was substantially slower, indicating that the highly reducing environment under the PROX conditions helps maintain the properties of the active Pt-Fe bimetallic sites.     

Solid-state NMR and EXAFS spectroscopic characterization of polycrystalline copper(I) O,O'-dialkyldithiophosphate cluster compounds: Formation of copper(I) O,O'-diisobutyldithiophosphate compounds on the surface of synthetic chalcocite

A number of polycrystalline copper(I) O,O'-dialkyldithiophosphate cluster compounds with Cu4, Cu6, and Cu8 cores were synthesized and characterized by using extended X-ray absorption fine-structure (EXAFS) spectroscopy. The structural relationship of these compounds is discussed. The polycrystalline copper(I) O,O'-diisobutyldithiophosphate cluster compounds, [Cu8{S2P(OiBu)2}6(S)] and [Cu6{S2P(OiBu)2}6], were also characterized by using 31P CP/MAS NMR (CP = cross polarization, MAS = magic-angle spinning) and static 65Cu NMR spectroscopies (at different magnetic fields) and powder X-ray diffraction (XRD) analysis. Comparative analyses of the 31P chemical-shift tensor, and the 65Cu chemical shift and quadrupolar-splitting parameters, estimated from the experimental NMR spectra of the polycrystalline copper(I) cluster compounds, are presented. The adsorption mechanism of the potassium O,O'-diisobutyldithiophosphate collector, K[S2P(OiBu)2], at the surface of synthetic chalcocite (Cu2S) was studied by means of solid-state 31P CP/MAS NMR spectroscopy and scanning electron microscopy (SEM). 31P NMR resonance lines from collector-treated chalcocite surfaces were assigned to a mixture of [Cu8{S2P(OiBu)2}6(S)] and [Cu6{S2P(OiBu)2}6] compounds.     

Logic gates and elementary computing by enzymes

Different selected enzymes, glucose oxidase (GOx), catalase (Cat), glucose dehydrogenase (GDH), horseradish peroxidase (HRP), and formaldehyde dehydrogenase (FDH), are used alone or coupled to construct eight different logic gates. The added substrates for the respective enzymes, glucose and H(2)O(2), act as the gate inputs, while the biocatalytically generated gluconic acid or NADH are the output signals that follow the operation of the gates. Different enzyme-based gates are XOR, INHIBIT A, INHIBIT B, AND, OR, NOR, Identity and Inverter gates. By combining the AND and XOR or the XOR and INHIBIT A gates, the half-adder and half-subtractor are constructed, respectively, opening the way to elementary computing by the use of enzymes.     

Photodissociation of HBr. 1. Electronic structure, photodissociation dynamics, and vector correlation coefficients

Ab initio potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P(1/2)), and the lowest order anisotropy parameters, beta, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[a1(3) (parallel, perpendicular)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.