A simultaneous approach to inverse source problem by Green's function

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation u_t = u_xx + F(t) and u₀(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Fréchet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Fréchet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd.     

Pure uterine lipoma

Lipomatous tumors of the uterus are unusual, benign neoplasms seen in postmenopausal women. Although many of the mixed-type cases such as lipoleiomyoma and fibrolipoma have been reported, pure uterine lipomas are extremely rare. In the literature, a few cases with pure uterine lipoma have been reported. We first present the advanced magnetic resonance findings of pure uterine lipoma, followed by those of ultrasonography (US) and computed tomography (CT). We markedly detected lipid peaks on the magnetic resonance spectroscopy (MRS) and the apparent diffusion coefficient value to be 0.00 due to chemical-shift effects with diffusion-weighted imaging (DWI). Although pelvic lipomatous tumors can be diagnosed with US and CT, in some cases, further workup may be required to localize the lesion. MRI may yield more valuable data for differential diagnosis. MRS and DWI findings provide additional clues on the nature of the lesion.     

A Bifunctional B,N-Based Asymmetric Catalytic Nitrostyrene-Michael Addition Acting through a 10-Membered Ring Cyclic Transition State

The B,N-bifunctional catalyst homoboroproline has been applied to a catalytic asymmetric nitroalkene-Michael addition to β-nitrostyrene analogues, showing broad substrate tolerance, high conversions and moderate to good asymmetric induction. The ability of homoboroproline to act as an efficient catalyst based on enamine-formation of the secondary amine, coupled with intramolecular Lewis-acid chelation of the nitro function, in a non-FLP manner, to effect efficient and enantioselective catalysis via a proposed large 10-membered ring transition state is remarkable and reinforced by theoretical calculations.     

Electrochemical Determination of Homocysteine at Disposable Graphite Electrodes

In the case of disruption of Hcy metabolism, the blood level of Hcy increases and it causes particularly the cardiovascular diseases, cancer, dementia and Parkinson’s disease. Thus, the sensitive analysis of Hcy levels in biological fluids is very important. Hcy analysis was performed herein using very practical and cost‐effective protocol using differential pulse voltammetry and graphite electrode. Detection limit of Hcy was found to be 1.21 µM in the linear range from 2 µM to 20 µM. The electrochemical Hcy detection in artificial urine medium was also successfully performed even in the presence of L ‐Cysteine, L ‐Methionine and Glutathione.     

Synthesis and Assembly of Zinc Oxide Microcrystals by a Low-Temperature Dissolution–Reprecipitation Process: Lessons Learned About Twin Formation in Heterogeneous Reactions

Cobalt-doped zinc oxide single crystals with the shape of hexagonal platelets were synthesized by thermohydrolysis of zinc acetate, cobalt acetate, and hexamethylenetetramine (HMTA) in mixtures of ethanol and water. The mineralization proceeds by a low-temperature dissolution–reprecipitation process from the liquid phase by the formation of basic cobalt zinc salts as intermediates. The crystal shape as well as twin formation of the resulting oxide phase can be influenced by careful choice of the solvent mixture and the amount of doping. An understanding of the course of the reaction was achieved by comprehensive employment of analytical techniques (i.e., SEM, XRD, IR) including an in-depth HRTEM study of precipitates from various reaction stages. In addition, EPR as well as UV/Vis spectroscopic measurements provide information about the insertion of the cobalt dopant into the zincite lattice. The Langmuir–Blodgett (LB) technique is shown to be suitable for depositing coatings of the platelets on glass substrates functionalized with polyelectrolyte multilayers and hence is applied for the formation of monolayers containing domains with ordered tessellation. No major differences are found between deposits on substrates with anionic or cationic surface modification. The adherence to the substrates is sufficient to determine the absolute orientation of the deposited polar single crystals by piezoresponse force microscopy (PFM) and Kelvin probe force microscopy (KPFM) studies.     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

The removal of heavy metal cations by natural zeolites

In this study, the adsorption behavior of natural (clinoptilolite) zeolites with respect to Co²⁺, Cu²⁺, Zn²⁺, and Mn²⁺ has been studied in order to consider its application to purity metal finishing wastewaters. The batch method has been employed, using metal concentrations in solution ranging from 100 to 400 mg/l. The percentage adsorption and distribution coefficients (K_d) were determined for the adsorption system as a function of sorbate concentration. In the ion exchange evaluation part of the study, it is determined that in every concentration range, adsorption ratios of clinoptilolite metal cations match to Langmuir, Freundlich, and Dubinin–Kaganer–Radushkevich (DKR) adsorption isotherm data, adding to that every cation exchange capacity metals has been calculated. It was found that the adsorption phenomena depend on charge density and hydrated ion diameter. According to the equilibrium studies, the selectivity sequence can be given as Co²⁺ > Cu²⁺ > Zn²⁺ > Mn²⁺. These results show that natural zeolites hold great potential to remove cationic heavy metal species from industrial wastewater.     

Fermion families and chirality through extra dimensions

We give a simple model to explain the origin of fermion families and chirality through the use of a domain wall-anti-domain wall pair placed in a five dimensional space-time. Received: 14 March 2002 / Revised version: 3 July 2002 / Published online: 27 September 2002 RID="a" ID="a" e-mail: erdem@likya.iyte.edu.tr