Lehmer -tuples

Generalizing a classical problem of Lehmer, in this paper we provide an asymptotic result for the number of Lehmer -tuples.

     

Capillary electrophoretic separation of inorganic sulfur-sulfide, polysulfides, and sulfur-oxygen species

A CE protocol was developed for the identification and separation of inorganic polysulfides simultaneously with other inorganic sulfur-bearing species coexisting in aqueous hydrosulfide/sulfur solutions. The electrophoretic separation of thiosulfate, sulfate, hydrosulfide, sulfite, tetrathionate, and polysulfides was achieved at pH values between 8.2 and 12.2. The peaks attributed to the polysulfide species were strongly sensitive to pH. CE analysis of hydrosulfide/sulfur solutions at different pH values permitted possible identification of two forms of polysulfides: S4(2-) and S3(2-). Upon exposure to air at ambient temperature, thiosulfate was the main oxidation product of hydrosulfide/sulfur solutions mainly in the first 60 min, when hydrosulfide was rapidly consumed. Analysis of the oxidation reaction products provided retrospectively tentative evidence that the peaks separated and identified as tri- and tetrasulfide may be ascribed to polysulfides.     

Coding of geodesics on some modular surfaces and applications to odd and even continued fractions

The connection between geodesics on the modular surface $PSL(2,\mathbb{Z})?\mathbb{H}$ and regular continued fractions, established by Series, is extended to a connection between geodesics on $\Gamma ?\mathbb{H}$ and odd and grotesque continued fractions, where $\Gamma ?{\mathbb{Z}}_{3}1{\mathbb{Z}}_3$ is the index two subgroup of $PSL(2,\mathbb{Z})$ generated by the order three elements $\left(\begin{array}{cc}\hfill 0\hfill & \hfill ?1\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right)$ and $\left(\begin{array}{cc}\hfill 0\hfill & \hfill 1\hfill \\ \hfill ?1\hfill & \hfill 1\hfill \end{array}\right)$, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on $\Theta ?\mathbb{H}$ and even continued fractions is discussed in our framework, where $\Theta$ denotes the Theta subgroup of $PSL(2,\mathbb{Z})$ generated by $\left(\begin{array}{cc}\hfill 0\hfill & \hfill ?1\hfill \\ \hfill 1\hfill & \hfill 0\hfill \end{array}\right)$ and $\left(\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right)$.     

Adjoint Sensitivity Analysis of a Fluid-Structure Interaction Problem

A fluid-structure mathematical model usually includes parameters whose actual values are known only approximately or can vary around some reference values. The objective of the sensitivity analysis is to determine quantitatively the behavior of the responses of a fluid-structure system locally around a chosen point of the trajectory in the phase-space of parameters and dependent variables. In this work, the response considered is the total mechanical energy of the structure. The sensitivities with respect to all the parameters the fluid-structure system depends on are useful in many situations as well as for optimization purposes. We present the theoretical developments necessary for the application of the adjoint sensitivity analysis methods (ASAM) for the fully coupled governing equations of an aeroelastic system. The algorithm is general and can be applied for any kind of fluid-structure interaction problems. Illustrative numerical examples are presented for the case of typical section with two degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of an Euler implicit‐mixed finite element scheme for reactive solute transport in porous media

In this article, we analyze an Euler implicit‐mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, a model for subsurface fluid flow. We prove the convergence of the scheme by estimating the error in terms of the discretization parameters. In doing so we take into account the numerical error occurring in the approximation of the fluid flow. The article, is concluded by numerical experiments, which are in good agreement with the theoretical estimates. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

On the restricted partition function

For a vector \(\mathbf a = (a_1,\ldots ,a_r)\) of positive integers, we prove formulas for the restricted partition function \(p_{\mathbf a}(n): = \) the number of integer solutions \((x_1,\dots ,x_r)\) to \(\sum _{j=1}^r a_jx_j=n\) with \(x_1\ge 0, \ldots , x_r\ge 0\) and its polynomial part.     

Enzyme-catalyzed synthesis of (R)- and (S)-3-heteroaryl-3-hydroxy-propanoic acids and their derivatives

Starting from the racemic 3-benzofuranyl- and 3-benzo[b]thiophenyl-3-hydroxypropanoic acid ethyl esters as substrates, various multistep enzymatic procedures were developed for the efficient synthesis of the corresponding highly enantiomerically enriched (R)- and (S)-3-heteroaryl-3-hydroxypropanoic acids.