A Higher-Dimensional Version of the Brody Reparametrization Lemma

We prove a generalization of the Brody reparametrization lemma.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1369 – 1377, October, 2004.     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Nonequilibrium synthesis and assembly of hybrid inorganic-protein nanostructures using an engineered DNA binding protein

We show that a protein with no intrinsic inorganic synthesis activity can be endowed with the ability to control the formation of inorganic nanostructures under thermodynamically unfavorable (nonequilibrium) conditions, reproducing a key feature of biological hard-tissue growth and assembly. The nonequilibrium synthesis of Cu(2)O nanoparticles is accomplished using an engineered derivative of the DNA-binding protein TraI in a room-temperature precursor electrolyte. The functional TraI derivative (TraIi1753::CN225) is engineered to possess a cysteine-constrained 12-residue Cu(2)O binding sequence, designated CN225, that is inserted into a permissive site in TraI. When TraIi1753::CN225 is included in the precursor electrolyte, stable Cu(2)O nanoparticles form, even though the concentrations of [Cu(+)] and [OH(-)] are at 5% of the solubility product (K(sp,Cu2O)). Negative control experiments verify that Cu(2)O formation is controlled by inclusion of the CN225 binding sequence. Transmission electron microscopy and electron diffraction reveal a core-shell structure for the nonequilibrium nanoparticles: a 2 nm Cu(2)O core is surrounded by an adsorbed protein shell. Quantitative protein adsorption studies show that the unexpected stability of Cu(2)O is imparted by the nanomolar surface binding affinity of TraIi1753::CN225 for Cu(2)O (K(d) = 1.2 x 10(-)(8) M), which provides favorable interfacial energetics (-45 kJ/mol) for the core-shell configuration. The protein shell retains the DNA-binding traits of TraI, as evidenced by the spontaneous organization of nanoparticles onto circular double-stranded DNA.     

Conformations of luteoskyrin and rugulosin in solution

The pigments Luteoskyrin (Ls) and Rugulosin (Rg) might adopt a priori two extreme conformations, a planar and an angular one. To determine the predominant conformation in solution, the nature of the lowest energy transition of the chromophores and the presence of intramolecular H-bonding have been investigated. The solvent effects on electronic absorption and CD spectra indicated the π-π* nature of the lowest energy transition. Treatments of the electronic absorption results according to McRae and Kosower relations, IR absorption and PMR spectra suggested the presence of strong intra-molecular H-bonds. From these results it was concluded that Ls and Rg adopted in a variety of solvents the most planar conformation.     

Action d'organolithiens sur la méthyl-2 quinoxaline. Etude de la réactivité des adduits

The action of organolithium reagents such as phenyllithium or n-bulyllithium on 2-methylquinoxaline gave lithiation of the methyl group which upon reaction with electtropholesphiles produce side chain alkenyl derivatives. On the other hand organolithium reagents react with the quinoxaline azomethine bond to give I-lithio-2-alkyl)or ary-1)-3 methylquinoxalines which can be further loithiated on the methyl group to give 2-alkyl(or aryl)-3-alkenylquinoxaline derivatives. The adducts can be condensed with clectrophiles such as benzonitrile or methlyl benzoate but only methyl benzoate leads to N condensed derivatives. Furthermore substituted 1,2,3,4-terahydroqinoxalines are available via the above lithio intermediates.     

Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso

Journal of Optimization Theory and Applications - In the previous paper Bello-Cruz et al. (J Optim Theory Appl 188:378–401, 2021), we showed that the quadratic growth condition plays a key...     

Rh(II) and Rh(I) two-legged piano-stool complexes: structure,reactivity, and electronic properties

The ligand 1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene, 3, was used to synthesize a mononuclear Rh(II) complex [(eta(1):eta(6):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh][PF(6)](2), 6+, in a two-legged piano-stool geometry. The structural and electronic properties of this novel complex including a single-crystal EPR analysis are reported. The complex can be cleanly interconverted with its Rh(I) form, allowing for a comparison of the structural properties and reactivity of both oxidation states. The Rh(I) form 6 reacts with CO, tert-butyl isocyanide, and acetonitrile to form a series of 15-membered mononuclear cyclophanes [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(3)][PF(6)] (8), [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CNC(CH(3))(3))(2)][PF(6)] (10), and [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(CH(3)CN)][PF(6)] (11). The Rh(II) complex 6+ reacts with the same small molecules, but over shorter periods of time, to form the same Rh(I) products. In addition, a model two-legged piano-stool complex [(eta(1):eta(6):eta(1)-1,4-bis[3-(diphenylphosphino)propoxy]-2,3,5,6-tetramethylbenzene)Rh][B(C(6)F(5))(4)], 5, has been synthesized and characterized for comparison purposes. The solid-state structures of complexes 5, 6, 6+, and 11 are reported. Structure data for 5: triclinic; P(-)1; a = 10.1587(7) A; b = 11.5228(8) A; c = 17.2381(12) A; alpha = 96.4379(13) degrees; beta = 91.1870(12) degrees; gamma = 106.1470(13) degrees; Z = 2. 6: triclinic; P(-)1; a = 11.1934(5) A; b = 12.4807(6) A; c = 16.1771(7) A; alpha = 81.935(7) degrees; beta = 89.943(1) degrees; gamma = 78.292(1) degrees; Z = 2. 6+: monoclinic; P2(1)/n; a = 11.9371(18) A; b = 32.401(5) A; c = 12.782(2) A; beta = 102.890(3) degrees; Z = 4. 11: triclinic; P(-)1; a = 13.5476(7) A; b = 13.8306(7) A; c = 14.9948(8) A; alpha = 74.551(1) degrees; beta = 73.895(1) degrees; gamma = 66.046(1) degrees; Z = 2.     

Simple mimetics of a nuclear localization signal (NLS)

[reaction: see text] Molecular modeling was used to design mimetics of the HIV-1 matrix protein nuclear localization signal (NLS) in which a scaffold of two resorcinol units joined by a diamide linker presents 3-aminopropyl ethers in place of lysine side chains. Prospective mimetics with linkers of 6, 8, 10, or 12 atoms were synthesized and compared in a competition assay for binding to the nuclear import receptor subunit karyopherin alpha, showing the 10-atom linker to be best and shorter ones ineffective.     

Effect of diffusion on rates and molecular weights in graft polymerization

A theoretical analysis has been made of the graft polymerization process in terms of the quantitative interrelationship between the initiation rate R_i, the k_p/k_t^1/ ratio of the monomer, the equilibrium solubility M of the monomer in the polymer, the polymer film thickness L, and the diffusivity D of the monomer in the polymer. It is shown how the values of these parameters in any grafting system interact to lead to diffusion-controlled graft polymerization. Whether graft polymerization is diffusion-free or diffusion-controlled depends on the values of K_p, d, k_p/k_p^1/2, and L as gathered in the parameter A = [(K_p/k_t^1/2)R_i, D,/^1/2] L/2. When the values of the various terms are such that A is less than 0.1 (i.e., D is large while R_i, k_p, and L are small), the reaction is diffusion-free. When A is greater than 3 (i.e., D is small while R_i, k_p, and L are large), the reaction is diffusion-controlled. The derived equations showing the relationship between kinetic and diffusional parameters are theoretically applicable to all grafting systems, i.e., for all monomer-polymer combinations under all conditions of reaction temperature, radiation intensity and polymer film thickness. The theoretical analysis has been verified for the rate and degree of polymerization for the radiation-induced graft polymerization of styrene to polyethylene.     

The effect of the “Inert” support on relative photocatalytic activity in the oxidative decomposition of alcohols on irradiated titanium dioxide composites

Reduced quantum efficiencies for the photocatalytic degradation of cyclohexanol, cyclododecanol, 2-hexanol, and benzyl alcohol are observed on TiO₂ particles included within small pore zeolitic supports suspended in acetonitrile. A modest reduction in photocatalytic activity observed with TiO₂ included within large pore zeolites and pillared clays is attributed to reflective and refractive losses of incident light. No appreciable substrate size selectivity could be observed in this series of supported TiO₂ composites. TS-1, a titanium-containing zeolite with Ti in tetrahedral lattice sites, was photoactive, although ETS-10, a titanium-containing zeolite with Ti in octahedral lattice sites, was less so. The low quantum yield residual photoactivity observed with these alcoholic substrates on unmodified zeolites may derive from surface charge transfer complexation, as suggested by diffuse reflectance absorption measurements.