Linear and nonlinear nonlocal boundary value problems for differential-operator equations

This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal L_p -regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.     

Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.     

Quiesent Crystallization Kinetics of Nucleated Metallocene and ZN Isotactic Polypropylenes

Crystallization kinetics and thermodynamic properties of nucleated isotactic polypropylene (PP) are analyzed using Hoffman—Lauritzen crystallization theory to determine the mechanistic effects of the nucleators. Calorimetric data provides quantitative comparisons between nucleating efficiences of the (Millad) and (NJSTAR) nucleator in Metallocene (M) and Ziegler—Natta (ZN) PP. The two types of PP without nucleators showed similar crystallization behavior though the T°_m for ZN-iPP was about 10°C higher than M-iPP. Both nucleators show significant improvement in crystallization rate in both types of PP. In addition, Millad outperforms NJSTAR. The magnitude of the kinetic response is,however, different and both the nucleators appear to function better in ZN than in Metallocene PP. nucleated PP shows predominantly the form. The amount of the form is thermal history dependent and changes with supercooling (T=T°_m–T_c). Similar equilibrium melting temperature (T°_m) in the nucleated and control PPs indicates the lack of any thermodynamic effect of the nucleator. All nucleated PPs show a much lower secondary nucleation rate constant, K_g.This revised version was published online in November 2005 with corrections to the Cover Date.     

Synthesis, Characterization and Antibacterial Activity of Some Transition Metal cis-3,7-dimethyl-2,6-octadiensemicarbazone Complexes

The synthesis and characterization of some transition metal cis-3,7-dimethyl-2,6-octadiensemicarbazone (CDOSC) complexes are reported. The ligand CDOSC yields: [ML₂ Cl₂] and [ML₂ Cl₂] Cl type complexes, where M = Cr^III, Mn^II, Fe^III, Co^II, Ni^II, Cu^II, Zn^II, Cd^II and Hg^II, L = CDOSC. Structures of the complexes were determined using elemental analysis, molar conductivity, magnetic measurements, i.r. and electronic, as well as n.m.r spectra. CDOSC acts as a bidentate ligand in all the complexes. All the newly synthesized metal complexes, as well as the ligand, were screened for their antibacterial activity. All the complexes exhibit strong inhibitory action against Gram (+) bacteria Staphylococcus aureus and Gram (−) bacteria Escherichia coli. The antibacterial activities of the complexes are stronger than those of the ligand CDOSC itself.     

High resolution 1H detected 1H,13C correlation spectra in MAS solid-state NMR using deuterated proteins with selective 1H,2H isotopic labeling of methyl groups

MAS solid-state NMR experiments applied to biological solids are still hampered by low sensitivity and resolution. In this work, we employ a deuteration scheme in which individual methyl groups are selectively protonated. This labeling scheme allows the acquisition of proton carbon correlation spectra with a resolution comparable to that in solution-state NMR experiments. We observe an increase in resolution by a factor of 10-15 compared to standard heteronuclear correlation experiments using PMLG for 1H,1H dipolar decoupling in the indirect dimension. At the same time, the full sensitivity of the proton-based experiment is retained. In comparison to the heteronuclear detected version of the experiment, a gain in sensitivity of a factor of approximately 4.7 is achieved.     

A simple extrusion method for the synthesis of aligned silica nanowires using the template of a rigid surfactant mesophase

Long range alignment of silica nanowires has been accomplished by extrusion of a novel surfactant mesophase prior to silica synthesis.     

Circular logic: nonribosomal peptide-like macrocyclization with a ribosomal peptide catalyst

A protease from ribosomal peptide biosynthesis macrocyclizes diverse substrates, including those resembling nonribosomal peptide and hybrid polyketide-peptide products. The proposed mechanism is analogous to thioesterase-catalyzed chemistry, but the substrates are amide bonds rather than thioesters.     

Simulating infrared spectra and hydrogen bonding in cellulose Iβ at elevated temperatures

We have modeled the transformation of cellulose Iβ to a high temperature (550 K) structure, which is considered to be the first step in cellulose pyrolysis. We have performed molecular dynamics simulations at constant pressure using the GROMOS 45a4 united atom forcefield. To test the forcefield, we computed the density, thermal expansion coefficient, total dipole moment, and dielectric constant of cellulose Iβ, finding broad agreement with experimental results. We computed infrared (IR) spectra of cellulose Iβ over the range 300-550 K as a probe of hydrogen bonding. Computed IR spectra were found to agree semi-quantitatively with experiment, especially in the O-H stretching region. We assigned O-H stretches using a novel synthesis of normal mode analysis and power spectrum methods. Simulated IR spectra at elevated temperatures suggest a structural transformation above 450 K, a result in agreement with experimental IR results. The low-temperature (300-400 K) structure of cellulose Iβ is dominated by intrachain hydrogen bonds, whereas in the high-temperature structure (450-550 K), many of these transform to longer, weaker interchain hydrogen bonds. A three-dimensional hydrogen bonding network emerges at high temperatures due to formation of new interchain hydrogen bonds, which may explain the stability of the cellulose structure at such high temperatures.