Study of Heat Transport in Bénard-Darcy Convection with g-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids

The effects of temperature-dependent viscosity, gravity modulation and thermo-mechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg–Landau model. The effect of gravity modulation is to decrease the Nusselt number, Nu and variable viscosity leads to increase in Nu. The thermo-mechanical anisotropies have opposite effect on Nu with thermal anisotropy decreasing the heat transport.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

On <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">r</Emphasis></Superscript>-closing for flows on orientable and non-orientable 2-manifolds

We provide an affirmative answer to the C ^r -Closing Lemma, r ≥ 2, for a large class of flows defined on every closed surface.     

Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c ₂(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.     

Synthesis of nanoplate bismuth oxychloride—a visible light active material

We have synthesized bismuth oxychloride (BiOCl) by wet chemical route. Characterization of the synthesized samples has been carried out using XRD, SEM with EDAX, HRTEM, FT-IR, Raman Spectroscopy, PL and UV. XRD and SEM analysis confirms crystallite size varying from 20–40 nm. FTIR spectrum indicates that the prepared material is highly pure and there is no water molecule present. Raman and photoluminescence spectrum of the bismuth oxychloridenanoplate demonstrated strong blue light emission which brings them in a special class of materials which work under visible light exposure. UV-Vis spectroscopy shows very less charge carriers transit time under visible light thus confirming excellent photocatalytic properties of material.     

On cutting sequences of the <Emphasis Type="Italic">L</Emphasis>-shaped translation surface tiled by three squares

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.     

Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, \({f \in \mathcal{A}(\bar{\mathbb{C}} \setminus A)}\), \({\# A< \infty}\). J. Nuttall has put forward the important relation between the maximal domain of f where the function has a single-valued branch and the domain of convergence of the diagonal Padé approximants for f. The Padé approximants, which are rational functions and thus single-valued, approximate a holomorphic branch of f in the domain of their convergence. At the same time most of their poles tend to the boundary of the domain of convergence and the support of their limiting distribution models the system of cuts that makes the function f single-valued. Nuttall has conjectured (and proved for many important special cases) that this system of cuts has minimal logarithmic capacity among all other systems converting the function f to a single-valued branch. Thus the domain of convergence corresponds to the maximal (in the sense of minimal boundary) domain of single-valued holomorphy for the analytic function \({f\in\mathcal{A}(\bar{\mathbb{C}} \setminus A)}\). The complete proof of Nuttall’s conjecture (even in a more general setting where the set A has logarithmic capacity 0) was obtained by H. Stahl. In this work, we derive strong asymptotics for the denominators of the diagonal Padé approximants for this problem in a rather general setting. We assume that A is a finite set of branch points of f which have the algebro-logarithmic character and which are placed in a generic position. The last restriction means that we exclude from our consideration some degenerated “constellations” of the branch points.     

Simulation of oxidative stress of guanosine and 8-oxo-7,8-dihydroguanosine by electrochemically assisted injection–capillary electrophoresis–mass spectrometry

Oxidative stress plays a crucial role in DNA and RNA damage within biological cells. As a consequence, mutations of DNA can occur, leading to disorders like cancer and neurodegenerative and cardiovascular diseases. The oxidative attack of guanosine and 8-oxo-7,8-dihydroguanosine is simulated by electrochemistry coupled to capillary electrophoresis–mass spectrometry. The electrochemical conversion of the compound of interest is implemented in the injection protocol termed electrochemically assisted injection (EAI). In this way, oxidation products of guanosine can be generated electrochemically, separated by capillary electrophoresis, and detected by electrospray ionization time-of-flight mass spectrometry (EAI–CE–MS). A fully automated laboratory-made EAI cell with an integrated buffer reservoir and a compartment holding screen-printed electrodes is used for the injection. In this study, parameters like pH of the sample solution and the redox potential applied during the injection were investigated in terms of corresponding formation of well-known markers of DNA damage. The important product species, 8-oxo-7,8-dihydroguanosine, was investigated in a separate study to distinguish between primary and secondary oxidation products. A comparison of product species formed under alkaline, neutral, and acidic conditions is presented. To compare real biological systems with an analytical approach for simulation of oxidative stress, it is desirable to have a well-defined control over the redox potential and to use solutions, which are close to physiological conditions. In contrast to typical HPLC–MS protocols, the hyphenation of EAI, CE, and MS enables the generation and separation of species involved without the use of organic solvents. Thus, information of the electrochemical behavior of the nucleoside guanosine as well as the primary oxidation product 8-oxo-7,8-dihydroguanosine can be characterized under conditions close to the physiological situation. In addition, the migration behavior found in CE separations of product species can be used to identify compounds if several possible species have the same mass-to-charge values determined by MS detection.

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