Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs

A general class of multi-step iterative methods for finding approximate real or complex solutions of nonlinear systems is presented. The well-known technique of undetermined coefficients is used to construct the first method of the class while the higher order schemes will be attained by a frozen Jacobian. The point of attraction theory will be taken into account to prove the convergence behavior of the main proposed iterative method. Then, it will be observed that an m-step method converges with 2m-order. A discussion of the computational efficiency index alongside numerical comparisons with the existing methods will be given. Finally, we illustrate the application of the new schemes in solving nonlinear partial differential equations.     

Electrocatalytic properties of a dinuclear cobalt(III) coordination compound in molecular oxygen reduction reaction

A new dinuclear cobalt(III) coordination compound, [Co₂L(μ‐N₃)(N₃)₂]·CH₃OH ( 1 ), was synthesized and characterized by elemental analysis, spectroscopic methods, and single‐crystal X‐ray analysis in which H₃L is a heptadentate ligand obtained by the condensation of triethylenetetramine with 5‐bromo‐2‐hydroxybenzaldehyde. X‐ray analysis revealed that two cobalt(III) ions have distorted octahedral geometry and are connected together by a phenoxy and an azide bridging ligand. The catalytic activity of compound 1 for oxygen (O₂) reduction reaction was investigated. Compound 1 can efficiently catalyze the reduction of O₂ by a weak electron donor, ferrocene (Fc), at the polarized water–1,2‐dichloroethane interface. It was found that compound 1 can catalyze O₂ reduction to H₂O₂, whereas in the presence of Fc, it can catalyze the reduction of O₂ to water.     

Zn/MCM-41-catalyzed unsymmetrical Hantzsch reaction and the evaluation of optical properties and anti-cancer activities of the polyhydroquinoline products

The three-component Hantzsch condensation of various aryl aldehydes, dimedone, and methyl 3-aminocrotonate was investigated in the presence of MCM-41-supported ZnNO3. The polyhydroquinoline products which were obtained under mild conditions and very easy workup were evaluated for anti-cancer activities against MCF-7, SK-BR-3, and HT-29 of breast and colon cancer cells. The fluorescence emission of some products was also studied and their optical parameters were reported.     

Welch bound analysis on generic code division multiple access codes with interference free windows

Code-division multiple access (CDMA) technology has been applied to many wireless communication systems. CDMA system suffers from both multiple access interference (MAI) and inter-symbol interference (ISI) over a multipath channel. To suppress MAI and ISI, this paper proposes the spreading codes with interference free windows. In particular, we will develop several upper bounds on the efficiency of generalized spreading codes (for both unitary and complementary codes) in terms of the width of their interference free windows.     

An extension of weighted generalized cumulative past measure of information

Ricerche di Matematica - In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative...     

A rigorous proof of MIMO channel capacity＇s increase with antenna number

It is well known that adding more antennas at the transmitter or at the receiver may offer larger channel capacity in the multiple-input multiple-output(MIMO) communication systems.In this letter,a simple proof is presented for the fact that the channel capacity increases with an increase in the number of receiving antennas.The proof is based on the famous capacity formula of Foschini and Gans with matrix theory.     

An Efficient Nearest Neighbor Search Method

A simple, but efficient, nearest neighbor search algorithm is proposed and simulation results demonstrating its effectiveness in the case of vector quantization for a given source are presented. The simulation results indicate that use of this approach reduces the number of multiplications and additions to as low as 9 percent of those required for the conventional full search method. The reduction in the number of subtractions is also considerable. The increase in the number of comparisons is moderate, and therefore, the total number of operations can be as low as 28 percent of those required by the full search method. An additional advantage of the described algorithm is the fact that it requires no precomputations and/or extra memory.     

A note on the capacity of discrete noiseless channels

Zusammenfassung Diese Mitteilung gibt einen mathematischen Beweis einer Darstellung vonShannon, betreffend die Kanalkapazität einer Klasse von einfachen Kanälen ohne Gedächtnis.     

A fast MMSE encoding technique for vector quantization

The authors present a very efficient minimum mean-squared error (MMSE) encoding method useful for vector quantization. Using this method results in a considerable reduction in the number of multiplications and additions. The increase in the number of comparisons is moderate, and therefore the overall saving in the number of operations is still considerable. Very little precomputation and extra storage is required     

Synthesis of Bilayer Surfactant-Coated Magnetic Nanoparticles for Application in Magnetic Fluid Hyperthermia

Nanocrystalline La_0.73Sr_0.27MnO₃ perovskite oxides with an average particle size of 26 nm were synthesized using the sol-gel method. To make water based magnetic fluid, the obtained nanoparticles were coated by self-organized bilayer surfactant containing oleic acid and sodium dodecyl sulfate as inner and outer layer, respectively. The bare and coated nanoparticles were characterized by x-ray powder diffraction, Fourier transform infrared spectroscopy, thermogravimetry, and transmission electron microscopy analyses. Calorimetric analysis was used to determine the heat generation efficiency of the prepared magnetic fluid under various alternating magnetic fields. The obtained results revealed that the maximum temperature achieved by the nanoparticles is in the therapeutic temperature range which enables these materials to be used as self-controlled heating agents in magnetic hyperthermia therapy.