Exponential Stability and Uniform Boundedness of Solutions for Nonautonomous Periodic Abstract Cauchy Problems. An Evolution Semigroup Approach

Let u _{μ, x, s} (., 0) be the solution of the following well-posed inhomogeneous Cauchy Problem on a complex Banach space X $$\left \{\begin{array}{ll}\dot{u}(t) = A(t)u(t) + e^{i\mu t}x, \quad t > s \\ u(s) = 0. \end{array} \right.$$ Here, x is a vector in X,?μ is a real number, q is a positive real number and A(·) is a q-periodic linear operator valued function. Under some natural assumptions on the evolution family ${\mathcal{U} = \{U(t, s): t \geq s\}}$ generated by the family {A(t)}, we prove that if for each?μ, each s?≥ 0 and every x the solution u _{μ, x, s} (·, 0) is bounded on R ₊ by a positive constant, depending only on x, then the family ${\mathcal{U}}$ is uniformly exponentially stable. The approach is based on the theory of evolution semigroups.     

New method for determining size of critical nucleus of fibril formation of polypeptide chains

A new method for determining the size of critical nucleus of fibril formation of polypeptide chains is proposed. Based on the hypothesis that the fibril grows by addition of a nascent peptide to the preformed template, the nucleus size N(c) is defined as the number of forming template peptides above which the time to add a new monomer becomes independent of the template size. Using lattice models one can show that our method and the standard method which is based on calculation of the free energy, provide the same result for N(c).     

Synthesis and NMR Spectroscopic Characteristics of a Series of Hydrazide‐Hydrazones Containing Furoxan Ring Derived from Isoeugenoxyacetic Acid

A novel hydrazide, 2‐methoxy‐4‐(3‐methyfuroxan‐4‐yl)‐5‐nitrophenoxyacetylhydrazine, was prepared from isoeugenoxyacetic acid. The hydrazide was condensed with aromatic aldehydes to give a series of 20 hydrazide‐hydrazones incorporating the furoxan ring. The structure of obtained compounds was determined by analytical and spectral data. It was demonstrated that the two sets of resonance signals in the ¹H‐NMR and ¹³C‐NMR spectra of the examined hydrazide‐hydrazones are caused by E_N–C(O) and Z_N–C(O) conformers. The energy barriers for the conformation exchange were determined by ¹H‐NMR‐measurement at various temperatures. Among seven tested hydrazide‐hydrazones, four compounds exhibit inhibition activities in vitro on human epidermis carcinoma (KB‐cell) with IC₅₀ = 47, 68, 79, and 103 μg/mL.     

Synthesis of 4-substituted chlorophthalazines, dihydrobenzoazepinediones, 2-pyrazolylbenzoic acid, and 2-pyrazolylbenzohydrazide via 3-substituted 3-hydroxyisoindolin-1-ones

Herein we describe a general three-step synthesis of 4-substituted chlorophthalazines in good overall yields. In the key step, N,N-dimethylaminophthalimide (8a) directs the selective monoaddition of alkyl, aryl, and heteroaryl organometallic reagents to afford 3-substituted 3-hydroxyisoindolinones 9b, 9i-9am. Many of these hydroxyisoindolinones are converted to chlorophthalazines 1b-1v via reaction with hydrazine, followed by chlorination with POCl(3). We have also discovered two novel transformations of 3-vinyl- and 3-alkynyl-3-hydroxyisoindolinones. Addition of vinyl organometallic reagents to N,N-dimethylaminophthalimide (8a) provided dihydrobenzoazepinediones 15a-15c via the proposed ring expansion of 3-vinyl-3-hydroxyisoindolinone intermediates. 3-Alkynyl-3-hydroxyisoindolinones react with hydrazine and substituted hydrazines to afford 2-pyrazolyl benzoic acids 16a-16d and 2-pyrazolyl benzohydrazides 17a-17g rather than the expected alkynyl phthalazinones.     

Implementation of a genetically tuned neural platform in optimizing fluorescence from receptor-ligand binding interactions on microchips

This paper describes the use of a genetically tuned neural network platform to optimize the fluorescence realized upon binding 5-carboxyfluorescein-D-Ala-D-Ala-D-Ala (5-FAM-(D-Ala)(3) ) (1) to the antibiotic teicoplanin from Actinoplanes teichomyceticus electrostatically attached to a microfluidic channel originally modified with 3-aminopropyltriethoxysilane. Here, three parameters: (i) the length of time teicoplanin was in the microchannel; (ii) the length of time 1 was in the microchannel, thereby, in equilibrium with teicoplanin, and; (iii) the amount of time buffer was flushed through the microchannel to wash out any unbound 1 remaining in the channel, are examined at a constant concentration of 1, with neural network methodology applied to optimize fluorescence. Optimal neural structure provided a best fit model, both for the training set (r(2) = 0.985) and testing set (r(2) = 0.967) data. Simulated results were experimentally validated demonstrating efficiency of the neural network approach and proved superior to the use of multiple linear regression and neural networks using standard back propagation.     

Electronic structure and thermochemical properties of silicon-doped lithium clusters Li(n)Si0/+, n = 1-8: new insights on their stability

A theoretical investigation on small silicon-doped lithium clusters Li(n)Si with n = 1-8, in both neutral and cationic states is performed using the high accuracy CCSD(T)/complete basis set (CBS) method. Location of the global minima is carried out using a stochastic search method and the growth pattern of the clusters emerges as follows: (i) the species Li(n)Si with n ≤ 6 are formed by directly binding one Li to a Si of the smaller cluster Li(n-1)Si, (ii) the structures tend to have an as high as possible symmetry and to maximize the coordination number of silicon. The first three-dimensional global minimum is found for Li(4)Si, and (iii) for Li(7)Si and Li(8)Si, the global minima are formed by capping Li atoms on triangular faces of Li(6)Si (O(h)). A maximum coordination number of silicon is found to be 6 for the global minima, and structures with higher coordination of silicon exist but are less stable. Heats of formation at 0 K (Δ(f)H(0)) and 298 K (Δ(f)H(298)), average binding energies (E(b)), adiabatic (AIE) and vertical (VIE) ionization energies, dissociation energies (D(e)), and second-order difference in total energy (Δ(2)E) of the clusters in both neutral and cationic states are calculated from the CCSD(T)/CBS energies and used to evaluate the relative stability of clusters. The species Li(4)Si, Li(6)Si, and Li(5)Si(+) are the more stable systems with large HOMO-LUMO gaps, E(b), and Δ(2)E. Their enhanced stability can be rationalized using a modified phenomenological shell model, which includes the effects of additional factors such as geometrical symmetry and coordination number of the dopant. The new model is subsequently applied with consistency to other impure clusters Li(n)X with X = B, Al, C, Si, Ge, and Sn.     

Singly and doubly lithium doped silicon clusters: geometrical and electronic structures and ionization energies

The geometric structures of neutral and cationic Si(n)Li(m)(0/+) clusters with n = 2-11 and m = 1, 2 are investigated using combined experimental and computational methods. The adiabatic ionization energy and vertical ionization energy (VIE) of Si(n)Li(m) clusters are determined using quantum chemical methods (B3LYP/6-311+G(d), G3B3, and CCSD(T)/aug-cc-pVxZ with x = D,T), whereas experimental values are derived from threshold photoionization experiments in the 4.68-6.24 eV range. Among the investigated cluster sizes, only Si(6)Li(2), Si(7)Li, Si(10)Li, and Si(11)Li have ionization thresholds below 6.24 eV and could be measured accurately. The ionization threshold and VIE obtained from the experimental photoionization efficiency curves agree well with the computed values. The growth mechanism of the lithium doped silicon clusters follows some simple rules: (1) neutral singly doped Si(n)Li clusters favor the Li atom addition on an edge or a face of the structure of the corresponding Si(n)(-) anion, while the cationic Si(n)Li(+) binds with one Si atom of the bare Si(n) cluster or adds on one of its edges, and (2) for doubly doped Si(n)Li(2)(0/+) clusters, the neutrals have the shape of the Si(n+1) counterparts with an additional Li atom added on an edge or a face of it, while the cations have both Li atoms added on edges or faces of the Si(n)(-) clusters.     

Fourteen-electron ring model and the anomalous magnetic circular dichroism of meso-triarylsubporphyrins

The MCD spectra of meso-triarylsubporphyrins show a sign anomaly which is correlated with the acceptor properties of the aryl substituent. From the spectra, magnetic moments of the excited states are determined. In the context of a simplified orbital model, the sign change is attributed to the quenching of the magnetic moment of the LUMO by acceptor orbitals of the substituent. The actual calculation of this moment presents a major challenge to computational methods. It is shown that wave function techniques based on CASSCF underestimate the covalency effects that are responsible for the quenching. In contrast, a CI method based on DFT orbitals yields excellent results, which fully support the orbital model.     

Generalized Cauchy problems involving nonlocal and impulsive conditions

We study the abstract Cauchy problem involving a class of nonlinear differential inclusions, with impulsive and nonlocal conditions. By using MNC estimates, the existence result and continuous dependence on initial data of the solution set are proved.     

Photochemical effects of KrF excimer excitation in laser-induced fluorescence measurements of OH in combustion environments

This paper presents experimental evidence that using the KrF excimer laser for quantitative laser-induced fluorescence (LIF) studies of the OH A-X (3,0) system is highly problematic if the effects of both photobleaching and photochemistry are not included for laser spectral irradiances greater than 20 MW/cm² cm^-1. Pump-probe and time-resolved measurements of the OH LIF signal in an atmospheric pressure, premixed CH₄-air flame at low- and high-laser-spectral-irradiance conditions show that a significant amount of OH is produced from photofragments resulting from the simultaneous 2-photon predissociation of H₂O molecules in the C-X system. A 5+2-level rate-equation model that includes the effects of both photobleaching and photochemical OH production is shown to satisfactorily predict the data using a single adjustable parameter given by the effective, spectrally integrated 2-photon cross-section of H₂O near 248 nm. The time-integrated OH LIF signal was found to depend on both the laser spectral irradiance and the local concentration of H₂O. Additionally, use of the KrF excimer laser for 2-line rotational thermometry can produce temperature errors as great as +550 K at high laser-pulse energies. Received: 21 August 2000 / Revised version: 30 October 2000 / Published online: 21 February 2001