Stability of the motion of linear large-scale oscillating systems

A method for setting up a time-periodic Lyapunov function for a linear system with periodic coefficients based on an auxiliary matrix-valued function is proposed and developed. New sufficient conditions for the stability of large-scale periodic systems decomposed into an even number of subsystems are formulated     

Stability of the stationary motion of a double pendulum interacting with a string

The equation of in-plane vertical motion of a double pendulum suspended at some point of a horizontal elastic string is derived using a hybrid model of this mechanical system. The conditions for the asymptotic stability of the stationary motion of the pendulum interacting with the string are established     

Application of DSC, IST, and FTIR study in the compatibility testing of nateglinide with different pharmaceutical excipients

Experiments were done to assess the compatibility of nateglinide (NTG) with selected excipients in the development of immediate release tablets of NTG by thermal and isothermal stress testing (IST) techniques. To evaluate the drug excipient compatibility, different techniques such as differential scanning calorimetric (DSC) study, infrared (IR) spectrophotometric study, and IST were adopted. The results of DSC study showed that magnesium stearate exhibited some interaction with NTG. However, the results of IR and IST studies showed that all the excipients used in the formula were compatible with NTG. The optimized formulation developed using the compatible excipients were found to be stable after 3 months of accelerated stability studies (40 ± 2 °C and 75 ± 5% RH). Overall, compatibility of excipients with NTG was successfully evaluated using the combination of thermal and IST methods and the formulations developed using the compatible excipients was found to be stable.     

Quantum Entanglement and Reduced Density Matrices

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.     

Separation and identification of parathion and its metabolites in autopsy tissues by thin layer chromatography

Summary Thin-layer chromatography on magnesium oxide/starch with 4% ethanol in fusel oil will distinguish parathion and its metabolitep-nitrophenol from malathion, diazinon andm-systox in autopsy fluids and tissues. As little as 1g of parathion can be detected on the thin-layer plate with Rhodamine B.

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Zusammenfassung Dünnschiohtchromatographie auf Magnesiumoxid/ Stärkepulver mit Amylalkohol und 4% Ä hanol eignet sich zur Unterscheidung von Parathion und dessen Metaboliten p-Nitrophenol von Malathion, Diazinon und Metasystox in Körperflüssigkeiten und Geweben. 1g Parathion kann auf der Dünnschichtplatte noch mit Rhodamin B nachgewiesen werden.

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Paper read on 19. March 1969 at the Winter School of Forensic Science held at Nangal Dam.     

Inhibition of unwanted proteolysis during sample preparation: evaluation of its efficiency in challenge experiments

Measures to counteract proteolysis during sample preparation are widely used; among them, protein extraction at a basic pH (Tris pH 11.0), sample boiling in sodium dodecyl sulfate (SDS), extraction in denaturing lysis solutions and the use of proteinase inhibitors combined with some of these approaches. Here, we tested their efficiency under stringent conditions using a high proteinase (trypsin and a mixture of pancreatic proteinases) contamination and as substrate, streptokinase, a protein highly sensitive to proteolytic degradation. Total degradation was observed in Tris pH 11.0. There was an efficient inhibition for the pancreatic proteinases after boiling in 1% SDS, 1% dithiothreitol (DTT), while trypsin inhibition was dependent on the enzyme-to-substrate ratio. A panel of 21 lysis solutions with variable concentrations of urea, thiourea and detergents was essayed for the ability to counteract proteolysis. In all solutions containing 7-9 M urea, detergents and proteinase inhibitors but not containing thiourea, there was a strong proteolysis. However, in all samples containing 2 M thiourea, proteolysis was inhibited. Moreover, inhibition was dependent on the thiourea concentration. According to these results, we are prompted to consider that the well-known benefits of incorporating thiourea into the lysis solution are a result of two factors, its efficiency in solubilizing proteins and the inhibition of the proteolysis of sensitive substrates; both contributing to the detection of a higher number of species in two-dimensional electrophoresis (2-DE) gels.     

Wiener–Ingham type inequality for Vilenkin groups and its application to harmonic analysis

An important trigonometric inequality essentially due to Wiener but later on made precise by Ingham concerning the lacunary trigonometric sums \(f(x)=\sum A_ke^{in_kx}\), where \(A_k\)’s are complex numbers, \(n_{-k}=-n_k\) and \(\{n_k\}\) satisfies the small gap condition \((n_{k+1}-n_k)\ge q\ge 1\) for \(k=0,1,2,\ldots \), says that if I is any subinterval of \([-\pi ,\pi ]\) of length \(|I|=2\pi (1+\delta )/q>2\pi /q\) then \(\sum |A_k|^2\le A_{\delta }|I|^{-1}\int _I|f|^2\), \(|A_k|\le A_{\delta }|I|^{-1}\int _I|f|\), wherein \(A_{\delta }\) depends only on \(\delta \). Such an inequality is proved here in the setting of the Vilenkin groups G. The inequality is then applied to generalize the Bernstěin, Szász and Ste?hkin type results concerning the absolute convergence of Fourier series on G.     

Cross-strand split tetra-Cys motifs as structure sensors in a beta-sheet protein

We have designed "split tetra-Cys motifs" that bind the biarsenical fluorescein dye 4',5'-bis(1,3,2-dithioarsolan-2-yl)fluorescein (FlAsH) across strands of a model beta-rich protein. Our strategy was to divide the linear FlAsH binding tetra-Cys sequence such that dye could be fully liganded only when the strands were arranged in space correctly by native protein conformational proximities. We introduced pairs of alternating cysteines on adjacent beta strands of cellular retinoic acid binding protein to create FlAsH binding sites in the native structure. Selective labeling occurred both in vitro and in vivo relative to sites with fewer than four Cys or with inappropriate geometry. Interestingly, two of the split tetra-Cys motif-carrying proteins bound FlAsH whether native or urea unfolded, while one was capable of binding FlAsH only when native. This latter design exemplifies the potential of split motifs as structure sensors.     

Synthesis,characterization, and compatibility study of acetylated starch with lamivudine

In this study, highly substituted starch acetate was prepared by reaction with native moth bean starch and acetic anhydride. Physicochemical characterization of this modified starch was done using scanning electron microscopy, X-ray diffraction, and thermogravimetric analysis. Their formation was confirmed by titrimetric analysis and highest degree of substitution was observed with a value of 2.35. The synthesized modified starch was further studied for compatibility with model drug lamivudine using differential scanning calorimetry and isothermal stress testing for its controlled release tablet formulation.