Degree-equipartite graphs

A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A?V\left(G\right)$, the degree sequences of the induced subgraphs $G\left[A\right]$ and $G[V\left(G\right)?A]$ are the same. In this paper, we characterize all degree-equipartite graphs. This answers Problem 1 in the paper by Grünbaum et al. [B. Grünbaum, T. Kaiser, D. Král, and M. Rosenfeld, Equipartite graphs, Israel J. Math. 168 (2008) 431–444].     

Calculation of Density for Mixtures of Carbon Dioxide with Nitrogen and Methane from the ISM Equation of State

In this paper the analytical equation of state (EoS) proposed by Ihm‐Song‐Mason was applied to calculate molar volume of mixtures of carbon dioxide with nitrogen and methane. The pair interaction potential has been used to evaluate the second virial coefficients and the ISM EoS parameters (i.e. α and b). The calculated values of the aforesaid quantities were applied to predict the molar volumes for mixtures of carbon dioxide with nitrogen and methane. Agreement with experiment was excellent for both mixtures.     

Highly Efficient,Four Component,One-pot Synthesis of Tetrasubstituted Imidazoles Using a Catalytic Amount of FeCl<Subscript>3</Subscript> · 6H<Subscript>2</Subscript>O

Summary. An efficient and improved procedure for the synthesis of tetrasubstituted imidazoles by FeCl₃ · 6H₂O catalyzed four-component one-pot synthesis in refluxing ethanol is described.     

A generalization of Eagon–Reiner’s theorem and a characterization of bi-CMt bipartite and chordal graphs

We give a generalization of Eagon-Reiner’s theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CM_t property of its Alexander dual. Then we characterize bi-CM_t bipartite graphs and bi-CM_t chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.     

Concurrence and Quantum Discord in the Eigenstates of Chaotic and Integrable Spin Chains

There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.     

Vibrational control of mechanical systems with piecewise linear damping and high-frequency inputs

Nonlinear Dynamics - This paper discusses averaging and vibrational control of mechanical control-affine systems with piecewise linear damping and high-frequency inputs. The results are used for...     

A comparative study on the catalytic performance of heme and non‐heme catalysts: Metal porphyrins versus metal Schiff bases

Catalytic activity and oxidative stability of a series of iron and manganese porphyrins with 2‐chlorophenyl, phenyl and 4‐methoxyphenyl at the meso positions and metallosalens (Mn‐ and Fe‐salens) including N,N′‐bis(salicylidene)ethylenediamine, N,N′‐bis(5‐ chlorosalicylidene)ethylenediamine and N,N′‐bis(2,4‐dihydroxysalicylidene)ethylenediamine for the oxidation of olefins with tetra‐n‐butylammonium periodate (TBAP) and tetra‐n‐butyl‐ammonium Oxone (TBAO) have been investigated and compared. Although the metalloporphyrins showed an increased catalytic activity relative to the Schiff base complexes, the former provided no significant catalytic advantage over the latter. Also, a comparable or slightly higher oxidative stability was observed for the Schiff base complexes under the reaction conditions. Furthermore, in spite of large difference between the oxidizing ability of TBAO and TBAP, similar patterns were observed for the order of catalytic activity and oxidative stability of the used heme and non‐heme catalysts. The introduction of a methyl group at the ɑ position of styrene led to an increase in its reactivity, indicating the dominance of electronic effects over the steric ones in these catalytic systems.     

Preparation,characterization, DFT calculations and ethylene oligomerization studies of iron(II) complexes bearing 2-(1H-benzimidazol-2-yl)-phenol derivatives

Five 2-(1H-benzimidazol-2-yl)-phenol derivatives including 1H (HL₁), 5-chloro-(HL₂), 5-methyl-(HL₃), 5,6-dichloro-(HL₄), and 5,6-dimethyl-(HL₅) were synthesized by the reaction of their corresponding benzene-1,2-diamine precursors and 2-hydroxybenzaldehyde which subsequently was employed in complexation with Fe(II) to prepare complexes C1–C5, respectively. Indeed, in all complexes, the ligands were coordinated as bidentate, via the C=N nitrogen and hydroxy oxygen atom of benzimidazole moiety and phenol ring, respectively. The compounds were characterized by FTIR, UV–vis, ¹H- and ¹³C-NMR spectropscopy, ICP, and elemental analysis (C, H, and N). The purity of these compounds was determined by melting point (m.p )and TLC. The synthesized ligands and complexes were geometrically optimized by Gaussian09 software at B3LYP/TZVP level of theory and satisfactory theoretical–experimental agreement was achieved for analysis of IR data of the compounds. Catalytic behavior of the iron(II) complexes was investigated for ethylene reactivity. On activation with diethylaluminum chloride (Et₂AlCl), iron(II) complex (C4) showed the highest activity (1686 kg oligomers.mol^?1(Fe).h^?1) for ethylene oligomerization when it contains chlorine substituents and exhibits good selectivity for linear 1-butene. The steric and electronic effects of ligands were investigated in detail on the influence of their catalytic activities.     

Development of a Henry’s constant correlation and solubility measurements of n-pentane,i-pentane,cyclopentane, n-hexane,and toluene in water

In this communication, we report new experimental data on n-pentane, i-pentane, cyclopentane, n-hexane, and toluene solubility in water at low temperature (below 298.15 K) and atmospheric pressure conditions. The new experimental data together with those reported in the literature have been used in developing a new equation for Henry’s constants of normal alkanes (methane to decane), BETEX compounds, and acid gases in aqueous phase over a wide range of temperature (typically from 273.15 K to 373.15 K). The new equation is based on a thermodynamic model, which uses the Peng–Robinson equation of state combined with the classical quadratic mixing rules for modelling non-aqueous phases, while the NRTL model is used to calculate the water activity.The predictions of the developed thermodynamic model are compared to the experimental data and the results of a thermodynamic approach, which uses the Valderrama modification of the Patel–Teja equation of state and non-density dependent mixing rules for modelling all fluid phases. Good agreement is observed between the experimental data and the model predictions.