Group of units of group algebras

By a right (left resp.) S_2n-polynomial we mean a multilinear polynomial f(X₁,…, X_t) over the ring of integers with noncommuting in-determinates X_isuch that for any prime ring R if f( X₁,…, X _t) is a PI of some nonzero right (left resp.) ideal of R, then R satisfies S_2nthe standard identity of degree 2n. In this paper we prove the theorem:Let R be a prime ring, d a nonzero derivation of R, L a noncommutative Lie ideal of R and f(X₁,…, X_t) a right or left S_2n-polynomial. Suppose that f(d( u₁)ⁿ¹,…,d(u_t)^nt)=0 for all u_iu,_i[d] L, where n₁,…,n_tare fixed positive integers. Then R satisfies S_2n+2. Also, the one-sided version of the theorem is given.     

Highly Sensitive and Selective Voltammetric Sensor Fullerene Modified Glassy Carbon Electrode for Determination of Cefitizoxime in Solubilized System

The usefulness of fullerene modified glassy carbon electrode in mediating the reduction of cefitizoxime in solubilized system has been demonstrated. Due to the unique structure and extraordinary properties, fullerene shows higher catalytic efficiency towards cefitizoxime reduction. The kinetic parameters, electron transfer coefficient (α) and rate constant (K₀) across the modified electrode are 0.37 and 0.1081/s respectively. The proposed square‐wave voltammetric method is linear over the concentration range 1.2–10.3 µg/mL. The limit of detection (LOD) is found 0.27 ng/mL. High sensitivity and selectivity together with low detection limit of the electrode response make it suitable for the determination of cefitizoxime.     

EPR and Optical Absorption Studies of Cu2+-Doped Bis(l-Asparaginato)Mg(II)

The electron paramagnetic resonance study of Cu²⁺-doped bis(l-asparaginato)Mg(II) is performed at room temperature. Two magnetically non-equivalent sites for Cu²⁺ are observed. The spin-Hamiltonian parameters evaluated by fitting spectra to the crystalline field of rhombic symmetry are as follows: g _x  = 2.0420 ± 0.0002, g _y  = 2.0808 ± 0.0002, g _z  = 2.3600 ± 0.0002, A _x  = (99 ± 2) × 10⁻⁴ cm⁻¹, A _y  = (108 ± 2) × 10⁻⁴ cm⁻¹, A _z  = (140 ± 2) × 10⁻⁴ cm⁻¹. The ground state wave function of Cu²⁺ is also determined. The g-anisotropy is estimated and compared with the experimental value. Further, with the help of optical study the nature of bonding of a metal ion with different ligands in the complex is discussed.     

Substrate assisted electrochemical deposition of patterned cobalt thin films

The patterned Co layers deposited on the scratched Cu surfaces were investigated with the use of the scanning electron microscopy. Patterned cobalt thin films were electrochemically deposited from the cobalt sulfate bath at room temperature. Pattering of cobalt was carried out by simple means of substrate scratching. Gentle scratching induces a direct pattering of cobalt from vertical to horizontal. The prepared pattered films were characterized for their structural, surface morphological and compositional properties by means of X-ray diffraction, scanning electron microscopy and energy dispersive spectroscopy. X-ray diffraction studies reveal that the films are of cobalt. From the SEM images fabrication of patterns of cobalt is apparent. This work demonstrates a novel approach for obtaining patterned cobalt for many technological applications.     

A simple and convenient method for the synthesis of 1‐dialkylaminocarbothioic acid S‐[(2,3‐epithio)propyl] esters

A simple and convenient method for the synthesis of 1‐dialkylaminocarbothioic acid S‐[(2,3‐epithio)propyl] ester was developed by the reaction of 1‐dialkylaminocarbodithioic acid‐sodium salt with 1‐chloro‐2,3‐epoxypropane in water‐methanol mixture at room temperature. An intermediate was isolated and characterized, based on which a possible mechanism was proposed.     

Efficient Elemental Iodine Catalyzed One-Pot Synthesis of 2,4,5-Triarylimidazoles

Summary. Elemental iodine is used as an efficient catalyst for the synthesis of 2,4,5-triarylimidazoles in excellent yields via condensation of benzoin, ammonium acetate, and aromatic aldehydes. This is a simple, one-pot, high yielding technique using cheap, non-toxic iodine in catalytic amounts.     

A Characterization of Nash Equilibrium for the Games with Random Payoffs

We consider a two-player random bimatrix game where each player is interested in the payoffs which can be obtained with certain confidence. The payoff function of each player is defined using a chance constraint. We consider the case where the entries of the random payoff matrix of each player jointly follow a multivariate elliptically symmetric distribution. We show an equivalence between the Nash equilibrium problem and the global maximization of a certain mathematical program. The case where the entries of the payoff matrices are independent normal/Cauchy random variables is also considered. The case of independent normally distributed random payoffs can be viewed as a special case of a multivariate elliptically symmetric distributed random payoffs. As for Cauchy distribution, we show that the Nash equilibrium problem is equivalent to the global maximization of a certain quadratic program. Our theoretical results are illustrated by considering randomly generated instances of the game.     

On the hypergeometric matrix functions of two variables

We introduce the generalized hypergeometric function with matrix parameters. We also define two variable Appell matrix functions and find their regions of convergence as well as integral representations.     

Efficient Elemental Iodine Catalyzed One-Pot Synthesis of 2,4,5-Triarylimidazoles

Elemental iodine is used as an efficient catalyst for the synthesis of 2,4,5-triarylimidazoles in excellent yields via condensation of benzoin, ammonium acetate, and aromatic aldehydes. This is a simple, one-pot, high yielding technique using cheap, non-toxic iodine in catalytic amounts.     

Electrochemical studies on surfactant-modified cellulose acetate membrane

The possibility of electrochemical modification of cellulose acetate membrane upon immobilization of the anionic surfactant (SDS) has been explored on the basis of membrane potential studies. Surface tension measurements with and without cellulose acetate membrane were carried out to ascertain the extent of immobilization of the surfactant. Cellulose acetate membrane practically does not exhibit any ion selectivity. However, modified membrane exhibits cation selectivity which varies with concentration of the surfactant till its critical micelle concentration is reached. An attempt has also been made to demonstrate correspondence between the immobilized surfactant and the permselectivity of the membrane.