Synthesis, structure and magnetic properties of chiral and nonchiral transition-metal malates

Carboxylate-bridged complexes of transition metals, M(II)=Mn(II), Fe(II), Co(II), Ni(II), Zn(II), were synthesised by reaction of M(II) salts with dl-malate and L-malate under hydrothermal conditions. These complexes form four series of compounds, which have been fully characterised structurally, thermally and magnetically. The crystal structures of the new chiral compounds, [Mn(L-mal)(H(2)O)] (1), [Fe(L-mal)(H(2)O)] (2), [Co(L-mal)(H(2)O)] (3) and [Zn(L-mal)(H(2)O)] (4) as well as those of the bimetallic analogues [Mn(0.63)Co(0.37)(L-mal)(H(2)O)] (5) and [Mn(0.79)Ni(0.21)(L-mal)(H(2)O)] (6) have been solved by single-crystal X-ray diffraction. The six L-malate monohydrates crystallise in the chiral space group P2(1)2(1)2(1) and consist in a three-dimensional network of metal(II) centres in octahedral sites formed by oxygen atoms. These structures were compared to those of the chiral trihydrate compounds [Co(L-mal)(H(2)O)]2 H(2)O (7), [Ni(L-mal)(H(2)O)]2 H(2)O (8) and [Co(0.52)Ni(0.48)(L-mal)(H(2)O)]2 H(2)O (9), which exhibit helical chains of M(II) centres, and those of dl-malate dihydrates [Co(dl-mal)(H(2)O)]H(2)O (10) and [Ni(dl-mal)(H(2)O)H(2)O (11) and trihydrate [Mn(L-mal)(H(2)O)]2 H(2)O (12) highlighting the great flexibility of the coordination by the malate ligand. UV/Vis spectroscopic results are consistent with octahedral coordination geometry of high-spin transition-metal centres. Extensive magnetic characterisation of each homologous series indicates rather weak coupling interaction between paramagnetic centres linked through carboxylate bridges. Curie-like paramagnetic, antiferromagnetic, ferromagnetic or weak ferromagnetic behaviour is observed and discussed on the basis of the structural features. The bimetallic compounds 5 and 6 represent new examples of chiral magnets.     

Synthesis and X-ray crystal structure of pyrrolo[1,2-a]benzimidazoles

Reaction of nitrilimines 1 with 2-cyanomethylbenzimidazole 2 gave the 3-arylazo-2-methylpyrrolo[1,2-a]benzimidazole 4a rather than the reported 2-arylazo-3-methylpyrrolo[1,2-a]benzimidazole 3a. The correct structure of the product was determined using X-ray crystal structure analysis. The similar reaction of nitrilimines with 2-aminobenzimidazole 5 gave the acyclic nucleophilic addition product 6.     

Dynamics of a close-loop controlled MEMS resonator

The dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated. The parameter space of the resonator actuation voltage is investigated to determine the optimal operating regions. Bifurcation diagrams of the resonator response are obtained at five different actuation voltage levels. The resonator exhibits bi-stability with two coexisting stable equilibrium points located inside a lower and an upper potential wells. Steady-state chaotic attractors develop inside each of the potential wells and around both wells. The optimal region in the parameter space for mass sensing purposes is determined. In that region, steady-state chaotic attractors develop and spend most of the time in the safe lower well while occasionally visiting the upper well. The robustness of the chaotic attractors in that region is demonstrated by studying their basins of attraction. Further, regions of large dynamic amplification are also identified in the parameter space. In these regions, the resonator can be used as an efficient long-stroke actuator.     

Corrigendum of “Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate” [International Journal of Non-Linear Mechanics 38 (2003) 513–520]

The problem of steady, laminar mixed convection heat and mass transfer past a semi-infinite vertical plate in the presence of Hall current has been studied. The governing partial differential equations describing the problem are transformed to a system of non-linear ordinary differential equations with appropriate boundary conditions using Lie's method of infinitesimal transformation groups. The non-linear ordinary differential equations are solved numerically using Chebyshev spectral method. The effects of various parameters on the velocity profiles, temperature and concentration profiles are presented and discussed. This work is an extension and correction for the paper by Megahed et al. [1], published in International Journal of Non-Linear Mechanics 38 (2003) 513–520.     

Total domination in inflated graphs

The inflation $G_I$ of a graph $G$ is obtained from $G$ by replacing every vertex $x$ of degree $d\left(x\right)$ by a clique $X=K_{d\left(x\right)}$ and each edge $xy$ by an edge between two vertices of the corresponding cliques $X$ and $Y$ of $G_I$ in such a way that the edges of $G_I$ which come from the edges of $G$ form a matching of $G_I$. A set $S$ of vertices in a graph $G$ is a total dominating set, abbreviated TDS, of $G$ if every vertex of $G$ is adjacent to a vertex in $S$. The minimum cardinality of a TDS of $G$ is the total domination number ${\gamma }_t\left(G\right)$ of $G$. In this paper, we investigate total domination in inflated graphs. We provide an upper bound on the total domination number of an inflated graph in terms of its order and matching number. We show that if $G$ is a connected graph of order $n\ge 2$, then ${\gamma }_t\left(G_I\right)\ge 2n/3$, and we characterize the graphs achieving equality in this bound. Further, if we restrict the minimum degree of $G$ to be at least $2$, then we show that ${\gamma }_t\left(G_I\right)\ge n$, with equality if and only if $G$ has a perfect matching. If we increase the minimum degree requirement of $G$ to be at least $3$, then we show ${\gamma }_t\left(G_I\right)\ge n$, with equality if and only if every minimum TDS of $G_I$ is a perfect total dominating set of $G_I$, where a perfect total dominating set is a TDS with the property that every vertex is adjacent to precisely one vertex of the set.     

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.     

Phase behaviour of tri-n-butylmethylammonium chloride hydrates in the presence of carbon dioxide

The phase behaviour of the system water?Ctri-n-butylmethylammonium chloride (TBMAC)?CCO₂ was investigated by pressure-controlled differential scanning calorimetry in the range 0?C10?mol% TBMAC in water and at CO₂ pressures ranging from 0 to 1.5?MPa. In the absence of CO₂, an incongruent melting hydrate, which estimated composition corresponds to TBMAC·30H₂O, crystallizes at temperatures below ?13.6?°C and forms with ice a peritectic phase at approximately 3.9?mol% TBMAC. In the presence of CO₂ at pressures as low as 0.5?MPa, curves evidenced the presence of an additional phase exhibiting congruent melting at temperatures that are strongly pressure dependent and significantly higher than those of hydrates obtained without CO₂. This new phase, whose enthalpy of dissociation and CO₂ content increase slightly with CO₂ pressure, was identified as a mixed semi-clathrate hydrate of TBMAC and CO₂ of general formula: (TBMAC?+?xCO₂)·30H₂O.     

A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions

We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary as well as sufficient optimality conditions of controls for relaxed controls, who are a measure-valued processes.     

A general decomposition approach for multi-criteria decision trees

In this paper, we address the dynamic and multi-criteria decision-making problems under uncertainty, generally represented by multi-criteria decision trees. Decision-making consists of choosing, at each period, a decision that maximizes the decision-maker outcomes. These outcomes should often be measured against a set of heterogeneous and conflicting criteria. Generating the set of non-dominated solutions is a common approach considered in the literature to solve the multi-criteria decision trees, but it becomes very challenging for large problems. We propose a new approach to solve multi-criteria decision trees without generating the set of all non-dominated solutions, which should reduce the computation time and the cardinality of the solution set. In particular, the proposed approach combines the advantages of decomposition with the application of multi-criteria decision aid (MCDA) methods at each decision node. A generalization of the Bellman’s principle of decomposition to the multi-criteria context is put forward. A decomposition theorem is therefore proposed. Under the sufficient conditions stated by the theorem, the principle of decomposition will generate the set of best compromise strategies. Seven MCDA methods are then characterized (lexicographic, weighted sum, multi-attribute value theory, TOPSIS, ELECTRE III, and PROMETHEE II) against the conditions of the theorem of decomposition and against other properties (neutrality, anonymous, fidelity, dominance, independency), in order to confirm or infirm their applicability with the proposed decomposition principle. Moreover, the relationship between independency and temporal consistence is discussed as well as the effects of incomparableness, rank reversals, and use of thresholds. Two conjectures resulted from this characterization.