Fourier-Galerkin numerical technique for solitary waves of fifth order Korteweg-de Vries equation

The present paper is aimed to display the performance of the Fourier-Galerkin technique developed earlier by the authors for numerical treatment of localized solutions in ²(-∞, ∞) for higher-order equations. The solitary-wave solution of the Kortweg-de Vries fifth order equation is obtained numerically and compared with approximate results of other authors.     

Ultrabroadband laser using prism-based “spatially-dispersive” resonator

An ultrabroadband (up to 35 nm FWHM) generation by a pulsed dye laser is reported. The principle of laser operation is based on a recently proposed cavity configuration, which we have termed spatially-dispersive resonator. By means of a prism pair this spreads the various spectral components into different spatial areas in the active medium and thus reduces the competition between them. A generation of a spectrum containing a number of equally spaced lines is also demonstrated.     

Effects of excited-state absorption and stimulated emission in UV dyes on the shortening of laser pulses interacting with saturable absorbers

Saturation properties of the dyes in the presence of excited-state absorption and amplified spontaneous emission in the dye are studied theoretically. In the analysis the above two effects are included separately and it is shown that they are deleterious to the pulse-shortening capabilities of the dyes. It is also shown that in the conventional single-pass shortening of laser pulses with saturable dyes large pulse shortening ratios (20) may be expected if the dye saturation is combined with a properly delayed dye generation.     

Thermodynamic simulation of four-component carnallite type systems

Summary The standard method ofPitzer for predicting the solubility isotherms of systems in which solid phases with a constant composition crystallize is applied to cases when mixed crystals are formed. The four-component carnallite type systems RbCl-CsCl-MgCl₂-H₂O, RbCl-KCl-MgCl₂-H₂O, and RbCl-RbBr-MgCl₂-MgBr₂-H₂O and the corresponding subsystems are thermodynamically simulated at 25°C. It is established that the solubility diagrams consist of crystallization regions of the simple saltsMX,MX, MgX ₂·6H₂O, and MgX₂·6H₂O and of the corresponding carnallite type double salts with the composition 1:1:6. A method of calculation of the integralGibbs energy of mixingG ^mix(s) of crystals formed in water-salt systems has been proposed. The results on the systems RbCl-KCl-H₂O, RbCl-RbBr-H₂O, and MgCl₂-MgBr₂-H₂O are compared with experimental data from the literature and with values calculated using various models.

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Thermodynamische Simulation von Vierkomponentensystemen des Carnallit-Types

Zusammenfassung DiePitzer-Methode zur Voraussage der Löslichkeitsisothermen in Mehrstoffsystemen, in welchen feste Phasen mit konstanter Zusammensetzung auskristallisieren, wurde auch für Fälle angewendet, bei denen sich Mischkristalle bilden. Die Vierstoffsysteme RbCl-CsCl-MgCl₂-H₂O, RbCl-KCl-MgCl₂-H₂O und RbCl-RbBr-MgCl₂-MgBr₂-H₂O, aus welchen Carnallit-Typ-Mischkristalle auskristallisieren, und die dazugehörigen Dreistoff-Randsysteme wurden bei 25°C simuliert. Man stellt fest, daß die Löslichkeitsdiagramme sowohl Kristallisationsbereiche der einfachen SalzeMX,M'X, MgX ₂·6H₂O und MgX ₂·6H₂O als auch der entsprechenden carnallitartigen Doppelsalze mit der Zuzammensetzung 1:1:6 umfassen. Eine Methode zur Berechnung derGibbs-EnergieG ^mix(s) für die in Wasser-Salz-Systemen gebildeten Mischkristalle wird vorgeschlagen. Die für die Systeme RbCl-KCl-H₂O, RbCl-RbBr-H₂O und MgCl₂-MgBr₂-H₂O erhaltenen Ergebnisse werden mit experimentellen Literaturdaten und Resultaten von Berechnungen aufgrund verschiedener Modelle verglichen.

     

Optical detection of triggered atherosclerotic plaque disruption by fluorescence emission analysis

Fluorescence emission analysis (FEA) has proven to be very sensitive for the detection of elastin, collagen and lipids, which are recognized as the major sources of autofluorescence in vascular tissues. FEA has also been reported to detect venous thromboemboli. In this paper we have tested the hypothesis that FEA can reproducibly detect in vivo and in vitro triggered plaque disruption and thrombosis in a rabbit model. Fluorescence emission (FE) spectra, recorded in vivo, detected Russell's viper venom (RVV)-induced transformation of atherosclerotic plaque. FE intensity at 410-490 nm 4 weeks after angioplasty was significantly lower (P < 0.0033 by analysis of variance) in RVV-treated rabbits when compared to control animals with stable plaque. FE spectral profile analyses also demonstrated a significant change in curve shape as demonstrated by polynomial regression analysis (R2 from 0.980 to 0.997). We have also demonstrated an excellent correlation between changes in FE intensity and the structural characteristics detected at different stages of "unstable atherosclerotic plaque" development using multiple regression analysis (R2 = 0.989). Thus, FEA applied in vivo is a sensitive and highly informative diagnostic technique for detection of triggered atherosclerotic plaque disruption and related structural changes, associated with plaque transformation, in a rabbit model.     

Effect of temperature on the solubility of carnallite type double salts

A method based on Pitzer's model has been used for calculation of the solubilities of carnallite type double salts crystallizing in the systems MeX–MgX₂–H₂O (Me=Li, NH₄, K, Rb, Cs; X=Cl, Br). The solubility of congruently soluble double salts was also determined experimentally at 25–75°C. The results from studies of the solubility diagrams of ternary carnallite type water-salt systems over a wide temperature range are summarized. It is found that the width of the crystallization region for each of the salts can be explained by the relative differences in the solubilities of the ternary solution components (MeX, MgX₂·6H₂O and MeX·MgX₂·6H₂O) and by a change of temperature, and by the effect of temperature on the solubility. A method is proposed for calculating Pitzer's ternary parameters of interionic interaction (_MN and _MNX) on the basis of experimental data for the solubility in water of the double salts crystallizing in the corresponding ternary water-salt systems.     

An algorithm for determination of the copolymer molecular weight distribution by Markov chain simulation

A simple and general algorithm, convenient for computer implementation, for calculation of the copolymer molecular weight distribution (MWD), its moments, copolymer composition, etc. from standard data has been developed describing copolymerization as a Markovian process. The algorithm is applicable for simulations of multimonomer copolymerization with monomolecular, bimolecular and mixed termination. It can be used for calculating the MWD of copolymers prepared under non-stationary conditions. Explicit formulae have been derived for the above parameters. They are exact even for low-molecular-weight oligomers. The calculation procedure involves nothing but plain matrix operations as matrix multiplication and inversion. For high-molecular-weight copolymers, even simpler dependencies that resemble those used for homopolymers can be used. A very simple numerical test has been proposed for checking their correctness.     

Conformational Dynamics Underlies Different Functions of Human KDM7 Histone Demethylases

The human KDM7 subfamily histone H3 Nϵ-methyl lysine demethylases PHF8 (KDM7B) and KIAA1718 (KDM7A) have different substrate selectivities and are linked to genetic diseases and cancer. We describe experimentally based computational studies revealing that flexibility of the region linking the PHD finger and JmjC domains in PHF8 and KIAA1718 regulates interdomain interactions, the nature of correlated motions, and ultimately H3 binding and demethylation site selectivity. F279S an X-linked mental retardation mutation in PHF8 is involved in correlated motions with the iron ligands and second sphere residues. The calculations reveal key roles of a flexible protein environment in productive formation of enzyme-substrate complexes and suggest targeting the flexible KDM7 linker region is of interest from a medicinal chemistry perspective.