Discrepancy of Fractions with Divisibility Constraints

We provide bounds for the absolute discrepancy of sequences of fractions with denominators streaming in a given arithmetic progression and satisfying divisibility constraints. Supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.     

Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide

The propagation of electromagnetic surface waves along a radially inhomogeneous dielectric waveguide is investigated. The problem is formulated in terms of differential equations to be satisfied by the radially dependent parts of the electromagnetic field vectors. The dielectric waveguide is assumed to consist of a homogeneous cladding of infinite extent and a radially inhomogeneous core of higher permittivity. Numerical solutions of the differential equations in the core are obtained by two different methods, viz. by direct numerical integration and by substitution of an appropriate power series expansion. In the cladding the field is expressed in terms of modified Bessel functions. Imposing the boundary conditions at the interface of core and cladding, an equation for the unknown propagation coefficient is obtained. From this equation the propagation coefficients for the lower order modes are computed numerically. Numerical results are presented for some permittivity profiles of practical interest in single-mode transmission along optical fibres.Nomenclature a radius of the core - a _q vector coefficient in the power series expansion off() - A _i constants - A square matrix - b _q coefficient in the power series expansion of _r() - B square matrix - C square matrix - c _n unknown constant - d _n unknown constant - D() fundamental matrix - E,E _r,,z electric field vector and components - E,e _r,,z radially dependent parts ofe _r,,z - f solution vector - G _q square matrix - H,H _r,,z magnetic field vector and components - h _r,,z radially dependent parts ofE _r,,z - h reduced wavenumber - i radial mode number - j imaginary unit - k _0,m wave number - K _n modified Bessel function of the second kind and order n - n azimuthal mode number - t time - U normalized propagation constant - Z _m plane wave impedance of the cladding - r, , z cylindrical co-ordinates - p, q, s integers - propagation coefficient - increment - _0,m,r permittivity - normalized radiusr - ₀ wavelength in free space - ₀ permeability - angular frequency - d _r, differentiation with respect tor, Engineering and Professor H. J. Frankena of the Physics Department for their valuable discussions.     

Structural properties of Dirichlet series with harmonic coefficients

An infinite family of functional equations in the complex plane is obtained for Dirichlet series involving harmonic numbers. Trigonometric series whose coefficients are linear forms with rational coefficients in hyperharmonic numbers up to any order are evaluated via Bernoulli polynomials, Gauss sums, and special values of L-functions subject to the parity obstruction. This in turn leads to new representations of Catalan’s constant, odd values of the Riemann zeta function, and polylogarithmic quantities. Consequently, a dichotomy result is deduced on the transcendentality of Catalan’s constant and a series with hyperharmonic terms. Moreover, making use of integrals of smooth functions, we establish Diophantine-type approximations of real numbers by values of an infinite family of Dirichlet series built from representations of harmonic numbers.     

Generalized Hyperbolic Octonion Formulation for the Fields of Massive Dyons and Gravito-Dyons

The close analogy between electromagnetic theory and linear gravity is discussed by the hyperbolic (split) octonion formalism. Using the similarities between the relevant field equations of massive dyons in electromagnetic theory and gravito-dyons in linear gravity, a new mathematical model is proposed to formulate these fields in a compact and simple form. The generalized wave equation including both massive dyon and monopole terms is derived. Similarly, the most generalized form of hyperbolic octonionic Klein–Gordon equation is obtained for the hypothetical particle carrying simultaneously both electromagnetic and gravitational charges (masses).     

The stress state of a plastic layer with a variable yield strength under a flat deformation

We study the stress state of a plastic layer with a variable yield strength in a strip under a flat deformation with a tensile load. We approximately calculate the first integrals of the system of plastic equilibrium equations, obtain an analog of the first Hencky theorem, and solve the conjugation problem for stresses on the contact boundary.     

A novel amperometric glucose biosensor based on reconstitution of glucose oxidase on thiophene-3-boronic acid polymer layer

The biosensor was constructed for determination of glucose by using glucose oxidase enzyme immobilized on poly(thiophene-3-boronic acid) (PTBA). Boronic acid functionalized polythiophene layer was obtained by electrochemical polymerization of Thiophene (Th) and thiophene-3-boronic acid (TBA) with different monomer rations. The reconstitution of the apo-glucose oxidase (apo-GOx) on a complexed flavin adenine dinucleotide (FAD) linked to polythiophene boronic acid (PTBA) monolayer yields an electrically contacted enzyme monolayer. The GOx-reconstituted enzyme electrode exhibited excellent electrocatalytic activities toward the reduction and oxidation of hydrogen peroxide as well. The PTBA/FAD/GOx biosensor shows an excellent performance for glucose at +0.4 V with a high sensitivity (2.14 μA/mM) and lower response time (～5 s) in a wide concentration range of 0.5–18 mM (correlation coefficient of 0.9952). Furthermore, the effects of applied potential, pH, temperature, electroactive interference, stability and reusability of the biosensors were discussed.     

Influence of tungsten doping concentration on the electronic and optical properties of anatase TiO2

The structural, electronic and optical properties of tungsten-doped TiO₂ have been investigated using density functional theory with plane wave basis sets and ultrasoft pseuodopotential. Substitutional W doping at Ti sites create W 5d states just below the conduction band minimum while interstitial W doping gives isolated W 5d states in the middle of forbidden region. Averaged bond lengths show that W doping at Ti sites produce minimum structural distortion as compared to the interstitial W-doped TiO₂. Substitutional W-doped TiO₂ has better visible light absorption compared to interstitial W-doped TiO₂ and has stable configuration which provide reasonable explanation for the experimental findings. Tungsten doping in TiO₂ with different doping concentrations is investigated as an enabling concept for enhancing the visible light absorption. Optical properties show that optimal W doping concentration would improve the visible light absorption. 2.08% W doping concentration gives strong visible and ultraviolet light absorption among all doped models found consistent with experiments.     

Experimental investigation of mixed convection heat transfer of nanofluids in a circular microchannel with different inclination angles

Journal of Thermal Analysis and Calorimetry - In this study, the characteristics of mixed convection heat transfer of nanofluids in circular microchannels with 500 μm diameter were...     

Electrochemical Iodine-Mediated Oxidation of Enamino-Esters to 2H-Azirine-2-Carboxylates Supported by Design of Experiments

An electrochemical iodine-mediated transformation of enamino-esters for the synthesis of 2H-azirine-2-carboxylates is presented. In addition, a thermic conversion of azirines to 4-carboxy-oxazoles in quantitative yield without purification was described. Both classes 2H-azirines-2-carboxylates and the 4-carboxy-oxazoles are substructures in natural products and therefore are of considerable interest for synthetic and pharmaceutical chemists. The optimization was not performed in a conventional manner with a one-factor-at-a-time process but with a Design of Experiments (DoE) approach. Beside a broad substrate scope the reaction was also employed to a robustness screen, a sensitivity assessment, and complemented with mechanistic considerations from cyclic voltammetry experiments.     

Optimal learning for sequential sampling with non-parametric beliefs

We propose a sequential learning policy for ranking and selection problems, where we use a non-parametric procedure for estimating the value of a policy. Our estimation approach aggregates over a set of kernel functions in order to achieve a more consistent estimator. Each element in the kernel estimation set uses a different bandwidth to achieve better aggregation. The final estimate uses a weighting scheme with the inverse mean square errors of the kernel estimators as weights. This weighting scheme is shown to be optimal under independent kernel estimators. For choosing the measurement, we employ the knowledge gradient policy that relies on predictive distributions to calculate the optimal sampling point. Our method allows a setting where the beliefs are expected to be correlated but the correlation structure is unknown beforehand. Moreover, the proposed policy is shown to be asymptotically optimal.