Trigonometric approximation in reflexive Orlicz spaces

The Lipschitz classes Lip(α, M) , 0 α≤ 1 are defined for Orlicz space generated by the Young function M, and the degree of approximation by matrix transforms of f ∈ Lip (α, M) is estimated by n-α .     

Khayyam with Cabri: experiences of pre-service mathematics teachers with Khayyam's solution of cubic equations in dynamic geometry environment

The study reported in this article deals with the observed actionsof Turkish pre-service mathematics teachers in dynamic geometryenvironment (DGE) as they were learning Khayyam's method forsolving cubic equations formed as x³ + ax = b. Having learnedthe method, modelled it in DGE and verified the correctnessof the solution, students generated their own methods for solvingdifferent types of cubic equations such as x³ + ax² = b andx³ + a = bx in the light of Khayyam's method. With the presentedteaching experiment, students realized that Khayyam's mathematicsis different from theirs. We consider that this gave them anopportunity to have an insight about the cultural and socialaspects of mathematics. In addition, the teaching experimentshowed that dynamic geometry software is an excellent tool fordoing mathematics because of their dynamic nature and accurateconstructions. And, it can be easily concluded that the historyof mathematics is useful resource for enriching mathematicslearning environment.     

Three 1,2,4‐triazole derivatives containing subtituted benzyl and benzyl­amino groups

The title compounds, 4‐benzyl­amino‐3‐(4‐methyl­benzyl)‐1H‐1,2,4‐triazol‐5(4H)‐one, C₁₇H₁₈N₄O, (I), 3‐(4‐methyl­benzyl)‐4‐(4‐methyl­benzyl­amino)‐1H‐1,2,4‐tri­azol‐5(4H)‐one, C₁₈H₂₀N₄O, (II), and 3‐(4‐chloro­benzyl)‐4‐(4‐methyl­benzyl­amino)‐1H‐1,2,4‐triazol‐5(4H)‐one, C₁₇H₁₇ClN₄O, (III), were obtained from the corresponding Schiff base in the presence of diglyme and NaBH₄. Each compound contains a 1,2,4‐triazole ring and two benzene rings, which are essentially planar. The molecules are linked by a combination of intermolecular N—H⋯O and N—H⋯N hydrogen bonds. Additionally, there is a weak π–π stacking interaction in (I), involving the benzene ring of the amino­benzyl group and the partially aromatic 1,2,4‐triazole moiety, with a centroid–centroid distance of 3.7397 (10) Å.     

Conical defects in growing sheets

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle phi(e) at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if phi(e)0. We construct these states in the regime where bending dominates and determine their energies and how stress is distributed in them. For each state a critical value of phi(e) is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.     

Elastica hypoarealis

We examine the equilibria of a rigid loop in the plane, characterized by an energy functional quadratic in the curvature, subject to the constraints of fixed length and fixed enclosed area. Whereas the only non self-intersecting equilibrium corresponding to the fixed length constraint is the circle, the area constraint gives rise to distinct equilibria labeled by an integer. These configurations exhibit self-intersections and bifurcations as the area is reduced. In addition, not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but the embedding itself can be expressed as a local function of the curvature. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. Analytical expressions for the energy as a function of the area are obtained in the limiting regimes. Received 18 October 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: capo@fis.cinvestav.mx RID="b" ID="b"e-mail: chryss@nuclecu.unam.mx RID="c" ID="c"e-mail: jemal@nuclecu.unam.mx     

Solid-state Electrochemical Sensor Based on a Cross-linked Copper(II)-doped Copolymer and Carbon Nanotube Material for Selective and Sensitive Detection of Monohydrogen Phosphate

A novel solid-state electrochemical sensor based on a newly synthesized cross-linked copper(II) doped-copolymer and carbon nanotube material was developed for the direct determination of monohydrogen phosphate ions (HPO₄²⁻). The synthesized copolymers were characterized by FTIR, XPS, TG/DTG-DTA and SEM techniques. The sensor had a Nernstian slope:-30.7±0.4 mV/decade, linear concentrations range: 1.0×10⁻⁶ - 1.0×10⁻¹ M, detection limit: 6.5×10⁻⁷ M, response time: 4 s and life time: 17 weeks. The sensor displayed constant potentials in the pH range 7.0-9.5. The sensor was successfully used as an indicator electrode in potentiometric titration and the direct determination of HPO₄ ²⁻ in water samples.     

User behavior modeling of voice communications: an empirical study

In this study, analysis and modeling of arrival and service processes are presented in a comprehensive fashion in order to determine statistical properties of voice traffic from end‐user perspective in accordance with the queueing theory. For the first time in the literature, we introduce a user centric approach and examine these services considering both flow directions of voice traffic, the uplink and the downlink as opposed to existing studies with the network centric approach. In our study, we use experimental data composed of actual phone calls collected from 2G/3G networks. To achieve this, we designed and implemented a data collection system for mobile users and compared the results by using data from an operational cellular network. In order to determine the time correlation of voice calls, Hurst parameter estimation methods are used. On the basis of the outcomes, independency of call arrivals is shown. Additionally, it is shown that calls acquired from user and network centric approaches are both Poisson distributed. Next, looking at the problem from service process perspective, thorough analyses are performed to determine mathematical models that can best characterize call holding times. Maximum likelihood estimation and expectation maximization algorithm are used, and it is shown that the optimum mathematical model for the characterization of call holding times is the lognormal distribution family. Copyright © 2014 John Wiley & Sons, Ltd.     

Solvothermal synthesis and characterization of coordination polymers of cobalt(II) and zinc(II) with succinic acid

The complexes [Co(C₄H₄O₄)]_n (1) and [Zn(im)₂(C₄H₄O₄)]_n (2) (C₄H₄O₄ = succinate dianion, suc; im = imidazole) have been synthesized solvothermally and characterized by elemental analysis, IR, TG–DTA, and single-crystal X-ray diffraction techniques. Complex 1 is the first anhydrous member of the cobalt succinate family and has high thermal stability under a static air atmosphere, up to 425 °C, and complex 2 is a 1D coordination polymer. In addition, a new synthesis method and some properties of the known [Co(HCOO)₂·2H₂O]_n (3) complex are reported. After in situ synthesis of 3 via decomposition of DMF at 140 °C, it was found that complex 3 can adsorb some solvents repeatedly and is selective for H₂O.     

Barrier height enhancement of metal/semiconductor contact by an enzyme biofilm interlayer

A metal/interlayer/semiconductor (Al/enzyme/p-Si) MIS device was fabricated using α-amylase enzyme as a thin biofilm interlayer. It was observed that the device showed an excellent rectifying behavior and the barrier height value of 0.78?eV for Al/α-amylase/p-Si was meaningfully larger than the one of 0.58?eV for conventional Al/p-Si metal/semiconductor (MS) contact. Enhancement of the interfacial potential barrier of Al/p-Si MS diode was realized using enzyme interlayer by influencing the space charge region of Si semiconductor. The electrical properties of the structure were executed by the help of current–voltage and capacitance–voltage measurements. The photovoltaic properties of the structure were executed under a solar simulator with AM1.5 global filter between 40 and 100?mW/cm² illumination conditions. It was also reported that the α-amylase enzyme produced from Bacillus licheniformis had a 3.65?eV band gap value obtained from optical method.