Chaotic Vibrations of a Cylindrical Shell-Panel with an In-Plane Elastic-Support at Boundary

This paper presents numerical results on chaotic vibrations of a shallow cylindrical shell-panel under harmonic lateral excitation. The shell, with a rectangular boundary, is simply supported for deflection and the shell is constrained elastically in an in-plane direction. Using the Donnell--Mushtari--Vlasov equation, modified with an inertia force, the basic equation is reduced to a nonlinear differential equation of a multiple-degree-of-freedom system by the Galerkin procedure. To estimate regions of the chaos, first, nonlinear responses of steady state vibration are calculated by the harmonic balance method. Next, time progresses of the chaotic response are obtained numerically by the Runge--Kutta--Gill method. The chaos accompanied with a dynamic snap-through of the shell is identified both by the Lyapunov exponent and the Poincaré projection onto the phase space. The Lyapunov dimension is carefully examined by increasing the assumed modes of vibration. The effects of the in-plane elastic constraint on the chaos of the shell are discussed.     

Baseline noise and measurement uncertainty in liquid chromatography.

The stochastic properties of baseline noise in HPLC systems with a UV photo-diode array, photo-multiplier and gamma-ray detector were examined by dividing the noise into auto-correlated random process (Markov process) and an independent process (white noise). The present work focused on the effect of the stochastic noise properties on a theoretical estimation of the standard deviation (SD) of area measurements in instrumental analyses. An estimation theory, called FUMI theory (Function of Mutual Information), was taken as an example. A computer simulation of noise was also used. It was shown that the reliability (confidence intervals) of theoretical SD estimates mainly depends on the following factors: the ratio of the white noise and Markov process occurring in the baselines; the number of data points used for the estimation; the width of a target peak for which the SD is estimated.     

Minkowski’s Second Theorem over a Simple Algebra

We generalize the notion of successive minima, Minkowski’s second theorem and Siegel’s lemma to a free module over a simple algebra whose center is a global field.     

A note on asymptotic solutions for heat transfer in laminar forced flow against a non-isothermal rotating disk

Exact asymptotic expansions for heat transfer in laminar forced flow against a non-isothermal rotating disk are obtained for large and small Prandtl numbers using a perturbation method. The surface temperature of the disk is assumed to vary according to a power law with the radial distance. The results point out the erroneous terms in the existing asymptotic solutions and give the further higher order corrections to them.

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Zusammenfassung Mit Hilfe einer Störungsmethode werden exakte asymptotische Entwicklungen für den Wärmeübergang in laminarer Zwangskonvektion gegen eine nichtisotherme rotierende Scheibe für kleine und große Prandtl-Zahlen erhalten. Die Oberflächentemperatur soll nach einem Potenzgesetz vom Radius abhängen. Die Ergebnisse zeigen die Fehler in den bisherigen Lösungen auf und geben die Korrekturen höherer Ordnung.

     

Glycyl-alanyl-histidine protects PC12 cells against hydrogen peroxide toxicity

Background

Peptides with cytoprotective functions, including antioxidants and anti-infectives, could be useful therapeutics. Carnosine, β-alanine-histidine, is a dipeptide with anti-oxidant properties. Tripeptides of Ala-His-Lys, Pro-His-His, or Tyr-His-Tyr are also of interest in this respect.

Results

We synthesized several histidine-containing peptides including glycine or alanine, and tested their cytoprotective effects on hydrogen peroxide toxicity for PC12 cells. Of all these peptides (Gly-His-His, Ala-His-His, Ala-His-Ala, Ala-Ala-His, Ala-Gly-His, Gly-Ala-His (GAH), Ala-His-Gly, His-Ala-Gly, His-His-His, Gly-His-Ala, and Gly-Gly-His), GAH was found to have the strongest cytoprotective activity. GAH decreased lactate dehydrogenase (LDH) leakage, apoptosis, morphological changes, and nuclear membrane permeability changes against hydrogen peroxide toxicity in PC12 cells. The cytoprotective activity of GAH was superior to that of carnosine against hydrogen peroxide toxicity in PC12 cells. GAH also protected PC12 cells against damage caused by actinomycin D and staurosporine. Additionally, it was found that GAH also protected SH-SY5Y and Jurkat cells from damage caused by hydrogen peroxide, as assessed by LDH leakage.

Conclusion

Thus, a novel tripeptide, GAH, has been identified as having broad cytoprotective effects against hydrogen peroxide-induced cell damage.

     

Effect of Acid Treatment of Montmorillonite on “Support‐Activator” Performance to Support Metallocene for Propylene Polymerization Catalyst

This work is focused on montmorillonite (MMT)‐based “support‐activators” (S‐As) for the metallocene‐catalyzed propylene polymerization. This catalyst was previously industrialized; however, for further technological advances, the activation mechanism is investigated. The chemical and morphological requirements of the S‐A are surveyed using both commercially available raw clay minerals (non‐acid‐treated) and acid‐treated clay minerals. The S‐A possessing strong‐acid sites (pK a < ?8.2) gives a highly active catalyst. Acid treatment of MMT induces morphological changes as well as the formation of strong acid sites. Based on pore size distribution analysis and atomic force microscopy observations, it is concluded that the strong acid sites are located in the small pores around the edge of the clay mineral (not in the interlayer), where the structure is disordered by the acid treatment.

     

Multi-poly-Bernoulli numbers and polynomials with a <Emphasis Type="Italic">q</Emphasis> parameter

We introduce themulti-poly-Bernoulli numbers and polynomialswith a q parameter, which are generalizations of the poly-Bernoulli numbers and polynomials with a q parameter, respectively.We give several combinatorial identities and properties of these new numbers and polynomials.     

Complementary Euler numbers

For an integer k, define poly-Euler numbers of the second kind \(\widehat{E}_n^{(k)}\) (\(n=0,1,\ldots \)) by

$$\begin{aligned} \frac{{\mathrm{Li}}_k(1-e^{-4 t})}{4\sinh t}=\sum _{n=0}^\infty \widehat{E}_n^{(k)}\frac{t^n}{n!}. \end{aligned}$$

When \(k=1\), \(\widehat{E}_n=\widehat{E}_n^{(1)}\) are Euler numbers of the second kind or complimentary Euler numbers defined by

$$\begin{aligned} \frac{t}{\sinh t}=\sum _{n=0}^\infty \widehat{E}_n\frac{t^n}{n!}. \end{aligned}$$

Euler numbers of the second kind were introduced as special cases of hypergeometric Euler numbers of the second kind in Komatsu and Zhu (Hypergeometric Euler numbers, 2016, arXiv:1612.06210), so that they would supplement hypergeometric Euler numbers. In this paper, we study generalized Euler numbers of the second kind and give several properties and applications.