Vanishing Derivations and Co-Centralizing Generalized Derivations on Multilinear Polynomials in Prime Rings

Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x₁,…, x_n) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) ? f(r)G(f(r))) = 0 for all r = (r₁,…, r_n) ∈ Rⁿ, then one of the following holds:

1. There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a ? q] = 0 and f(x₁,…, x_n)² is central valued on R;

2. There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;

3. There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa ? bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;

4. R satisfies s₄ and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa ? bx and G(x) = ax + xb for all x ∈ R;

5. There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb ? δ(x), G(x) = bx + δ(x) and d(x) = [c, x] for all x ∈ R, with [c, a′] = 0 and f(x₁,…, x_n)² is central valued on R.

     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

An electrochemical chiral sensor based on electrochemically modified electrode for the enantioselective discrimination of D-/L-tryptophan

Journal of Solid State Electrochemistry - Chirality is a universal characteristic of natural systems and discrimination of enantiomers of a chiral molecule plays a major role particularly in...     

Platinum (II) N‐heterocyclic carbene complexes: Synthesis,characterization and cytotoxic properties

Platinum (II) complexes bearing N‐heterocyclic carbene (NHC) ligands have been widely used in catalytic chemistry, but there are very few reports of biological properties of this type of complexes. A series of [PtCl₂(NHC)(PEt₃)] complexes were synthesized. The structures of all compounds were characterized by ¹H‐NMR, ¹³C‐NMR, IR and elemental analysis techniques, which supported the proposed structures. The single crystal structures of complexes 1a and 1e were determined. The title complexes show slightly distorted square‐planar coordination around the platinum (II) metal center. The cytotoxic properties of the platinum (II)–NHC complexes have been assessed in various human cancer lines, including cisplatin‐sensitive and resistant cells. IC₅₀ values of these four complexes were determined by the MTS‐based assay on three human cell lines—brain (SHSY5Y), colon (HTC116) and liver (HEP3B). These complexes have been highlighted cancer therapeutic agent with unique structures and functions.     

Spectroscopic and computational investigation of second-sphere contributions to redox tuning in Escherichia coli iron superoxide dismutase

In Fe- and Mn-dependent superoxide dismutases (SODs), second-sphere residues have been implicated in precisely tuning the metal ion reduction potential to maximize catalytic activity (Vance, C. K.; Miller, A.-F. J. Am. Chem. Soc. 1998, 120, 461-467). In the present study, spectroscopic and computational methods were used to characterize three distinct Fe-bound SOD species that possess different second-coordination spheres and, consequently, Fe(3+/2+)reduction potentials that vary by approximately 1 V, namely, FeSOD, Fe-substituted MnSOD (Fe(Mn)SOD), and the Q69E FeSOD mutant. Despite having markedly different metal ion reduction potentials, FeSOD, Fe(Mn)SOD, and Q69E FeSOD exhibit virtually identical electronic absorption, circular dichroism, and magnetic circular dichroism (MCD) spectra in both their oxidized and reduced states. Likewise, variable-temperature, variable-field MCD data obtained for the oxidized and reduced species do not reveal any significant electronic, and thus geometric, variations within the Fe ligand environment. To gain insight into the mechanism of metal ion redox tuning, complete enzyme models for the oxidized and reduced states of all three Fe-bound SOD species were generated using combined quantum mechanics/molecular mechanics (QM/MM) geometry optimizations. Consistent with our spectroscopic data, density functional theory computations performed on the corresponding active-site models predict that the three SOD species share similar active-site electronic structures in both their oxidized and reduced states. By using the QM/MM-optimized active-site models in conjunction with the conductor-like screening model to calculate the proton-coupled Fe(3+/2+) reduction potentials, we found that different hydrogen-bonding interactions with the conserved second-sphere Gln (changed to Glu in Q69E FeSOD) greatly perturb the p K of the Fe-bound solvent ligand and, thus, drastically affect the proton-coupled metal ion reduction potential.     

Application of full factorial design for the preconcentration of chromium by solid phase extraction with Amberlyst 36 resin

The preconcentration of chromium(III) by solid phase extraction and its determination from aqueous solutions by flame atomic absorption spectrometry (FAAS) is investigated by applying an experimental design. The optimization of the preconcentration variables such as pH of the sample solution, flow rate of the sample solution and concentration of elution solution was carried out using 2³ full factorial design. The most important parameter affecting the preconcentration of chromium is the concentration of eluent. In the established experimental conditions, chromium can be determined with a relative standard deviation of 2.0% (N = 7) for a chromium concentration of 100 μg L⁻¹. The detection limit for chromium was 1 μg L⁻¹ (N = 20). The adsorption capacity of Amberlyst 36 is found to be 90.9 mg g⁻¹ for chromium. Effect of other ions on the procedure was also evaluated. The method was validated by the analysis of certified reference materials (tea leaves GBW 07605 and fish tissue IAEA-407). The method was applied to the determination of chromium in waste water, dam water, carrot, parsley and lettuce. Correspondence: Ali Rehber Türker, Department of Chemistry, Faculty of Science and Arts, Gazi University, TR-06500 Ankara, Turkey     

Some relationships among quasidifferential,weak subdifferential and exhausters

In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. Moreover, under some assumptions weak subdifferentiability of a quasidifferentiable function is proved and the weak subdifferential is obtained by using the quasidifferential. Under some assumptions, it is proved that a positively homogeneous and lower semicontinuous function is quasidifferentiable. It is also shown that directional differentiability and weak subdifferentiability imply quasidifferentiability. Furthermore, a method to evaluate the quasidifferential is given by using reduced weak lower exhausters.     

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N,N'-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II)

N,N'-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV-vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities (beta) and the electric dipole moments (mu) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero beta values, and it might have microscopic NLO behaviour.     

Electrochemical Investigation of Heavy Metal Ion Transfer Across the Water/1,2‐Dichloroethane Interface Assisted by 9‐Ethyl‐3‐Carbazolecarboxaldehyde‐Thiosemicarbazone

The transfer of heavy metal ions across the polarized water/1,2‐dichloroethane (1,2‐DCE) interface assisted by 9‐ethyl‐3‐carbazolecarboxaldehyde‐thiosemicarbazone (ECCAT) in the 1,2‐DCE phase has been studied by cyclic voltammetry. Voltammetric waves of Pb(II) and Cd(II) ions were reversible and quasi‐reversible, respectively, whereas that of Hg(II) and Zn(II) ion were irreversible. The voltammogram of Cu(II) ion showed a two‐step wave, however the nature of the transfer could not be satisfactorily evaluated by analyzing the cyclic voltammetric data. When Ni(II) and Co(II) was used no peak was visible under the experimental conditions used in this study. The dependence of the half‐wave potentials of Pb(II) and Cd(II) ions on the ligand concentration reveals that their ion‐transfer is assisted by the formation of 1:3 metal‐ECCAT complex in 1,2‐DCE. The over‐all association constants of [Pb(ECCAT)₃]²⁺ and [Cd(ECCAT)₃]²⁺ complexes in DCE‐phase have been determined to be log β =14.03 and log β =15.44, respectively.