Optimal Error Estimate of the Penalty Finite Element Method for the Micropolar Fluid Equations

We present an optimal error estimate of the numerical velocity, pressure, and angular velocity for the fully discrete penalty finite element method of the micropolar equations when the parameters ?, Δ t, and h are sufficiently small. In order to obtain this estimate, we present the time discretization of the penalty micropolar equation that is based on the backward Euler scheme; the spatial discretization of the time discretized penalty micropolar equation is based on a finite elements space pair (X _h , M _h ) that satisfies some approximations properties.     

On the moments of Kloosterman sums and fibre products of Kloosterman curves

Let q=p^r with p=3 and r2. We give a recursion formula for the moments of a Kloosterman sum over the finite field , which utilizes known weight formulae for the ternary Melas code M of length q−1. The method is illustrated by giving explicit formulae for the moments up to the tenth moment. As an application for the formulae, and for their analogues obtained earlier in case p=2, we get the exact number of rational points on fibre products of certain Kloosterman curves. As a corollary we obtain identities between Ramanujan's tau-function, Kronecker class numbers, and Dickson polynomials.     

A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

This paper presents a novel method of multi-objective optimization by learning automata (MOLA) to solve complex multi-objective optimization problems. MOLA consists of multiple automata which perform sequential search in the solution domain. Each automaton undertakes dimensional search in the selected dimension of the solution domain, and each dimension is divided into a certain number of cells. Each automaton performs a continuous search action, instead of discrete actions, within cells. The merits of MOLA have been demonstrated, in comparison with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and non-dominated sorting genetic algorithm II (NSGA-II), on eleven multi-objective benchmark functions and an optimal problem in the midwestern American electric power system which is integrated with wind power, respectively. The simulation results have shown that MOLA can obtain more accurate and evenly distributed Pareto fronts, in comparison with MOEA/D and NSGA-II.     

Asymptotic analysis of the nonsteady micropolar fluid flow through a curved pipe

ABSTRACT

We consider the nonsteady flow of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. Germano's reference system is employed to describe the pipe's geometry. After writing the governing equations in curvilinear coordinates, we construct the asymptotic expansion up to a second order. Obtained in the explicit form, the asymptotic approximation clearly demonstrates the effects of pipe's distortion, micropolarity and the time derivative. A detailed study of the boundary layers in space is provided as well as the construction of the divergence correction. Finally, a rigorous justification of the proposed effective model is given by proving the error estimates.     

Dynamic Analysis of Human Gait Disorder and Metabolical Cost Estimation

For the design and improvement of orthotic and prosthetic devices the biomechanical effort is an important criterion to obtain a more comfortable and natural gait of humans with gait disorders. In the first part of the paper the inverse dynamic analysis based on measurements of the human gait for subjects with different kinds of disorders is presented. The second part is devoted to a method to estimate the energy expenditure for human motions. This approach allows the computation of metabolical cost for human locomotion using Hill-type muscle models.     

Electronic Olfactory Sensor Based on A. mellifera Odorant‐Binding Protein 14 on a Reduced Graphene Oxide Field‐Effect Transistor

An olfactory biosensor based on a reduced graphene oxide (rGO) field‐effect transistor (FET), functionalized by the odorant‐binding protein 14 (OBP14) from the honey bee (Apis mellifera) has been designed for the in situ and real‐time monitoring of a broad spectrum of odorants in aqueous solutions known to be attractants for bees. The electrical measurements of the binding of all tested odorants are shown to follow the Langmuir model for ligand–receptor interactions. The results demonstrate that OBP14 is able to bind odorants even after immobilization on rGO and can discriminate between ligands binding within a range of dissociation constants from K_d=4 μM to K_d=3.3 mM . The strongest ligands, such as homovanillic acid, eugenol, and methyl vanillate all contain a hydroxy group which is apparently important for the strong interaction with the protein.     

Ammonium ion mediated resorcarene capsules: ESI-FTICRMS study on gas-phase structure and ammonium ion affinity of tetraethyl resorcarene and its per-methylated derivative

The ammonium ion binding affinities of tetraethyl resorcarene (1) and its per-methylated derivative (2) were studied by electrospray ionization Fourier transform ion cyclotron resonance (ESI-FTICR) mass spectrometry. Ten different ammonium ions were tested as guests for the resorcarenes. A strong tendency for complex formation was observed with all ammonium ions of size and charge distribution suitable for noncovalent interactions with the cavities of the resorcarene hosts 1 and 2. Although differences in ammonium ion affinities were observed between 1 and 2 due to the dissimilar conformations, the overall tendency was that increase in the degree of substitution and the length of carbon chain of the ammonium cation facilitated the complex formation until the sterical hindrance impeded the complexation. Dimeric as well as monomeric ammonium ion complexes were formed with resorcarene 1, but resorcarene 2 was unable to form the dimeric capsules because of the lack of H-bond donor possibilities. The nature of binding of the guest was further investigated with ion-molecule reactions and by determination of the single crystal X-ray structure of host 1 complexed with tetramethyl ammonium bromide.