One-sided invertibility of discrete operators and their applications

For \(p\in [1,\infty ]\), we establish criteria for the one-sided invertibility of binomial discrete difference operators \({{\mathcal {A}}}=aI-bV\) on the space \(l^p=l^p(\mathbb {Z})\), where \(a,b\in l^\infty \), I is the identity operator and the isometric shift operator V is given on functions \(f\in l^p\) by \((Vf)(n)=f(n+1)\) for all \(n\in \mathbb {Z}\). Applying these criteria, we obtain criteria for the one-sided invertibility of binomial functional operators \(A=aI-bU_\alpha \) on the Lebesgue space \(L^p(\mathbb {R}_+)\) for every \(p\in [1,\infty ]\), where \(a,b\in L^\infty (\mathbb {R}_+)\), \(\alpha \) is an orientation-preserving bi-Lipschitz homeomorphism of \([0,+\infty ]\) onto itself with only two fixed points 0 and \(\infty \), and \(U_\alpha \) is the isometric weighted shift operator on \(L^p(\mathbb {R}_+)\) given by \(U_\alpha f= (\alpha ^\prime )^{1/p}(f\circ \alpha )\). Applications of binomial discrete operators to interpolation theory are given.     

Stabilization of von Kármán plate in the presence of thermal effects in a subsonic potential flow of gas

We discuss the problem of nonlinear oscillations of a clamped plate in the presence of thermal effects in a subsonic gas flow. The dynamics of the plate is described by von Kármán system in the presence of thermal effects, in which rotational inertia is accounted for. To describe influence of the gas flow we apply the linearized theory of potential flows. Our main result states that each weak solution of the problem considered tends to the set of the stationary points of the problem.     

Preemptive scheduling of two uniform parallel machines to minimize total tardiness

We consider the problem of preemptive scheduling n jobs on two uniform parallel machines. All jobs have equal processing requirements. For each job we are given its due date. The objective is to find a schedule minimizing total tardiness ∑T_i. We suggest an O(n log n) algorithm to solve this problem.     

A system for priority routing and capacity assignment in packet switched networks

A model and its associated solution procedure for the problem of concurrent flow and capacity assignment in a packet switched network are presented. The distinguishing feature of the model lies in the fact that a user defined priority level is associated with each message in the network. Different service requirements and message characteristics are associated with each message class. An algorithm that generates good feasible solutions to the model, together with tight lower bounds on the value of the objective function, is developed. Results of numerical experiments using several network topologies are reported.     

Ranking fuzzy choice functions by their rationality indicators

In this paper we study two rationality indicators and two normality indicators of a fuzzy choice function. They express the degree of rationality or normality of this fuzzy choice function. This way we can establish a hierarchy in a given family of fuzzy choice functions with respect to their degree of rationality.     

Kinetics and mechanism of the growth of gold nanoparticles by reduction of tetrachloroauric acid by hydrazine in Triton N-42 reverse micelles

The kinetics of the growth of gold nanoparticles during the reduction of tetrachloroauric acid by hydrazine in dispersed aqueous solution encapsulated by reverse micelles of Triton N-42 surfactant (with decane as dispersion medium) was studied by means of spectrophotometry. According to DLS data, at a set value of solubilization capacity V _s/V _o = 0.005 initial micelles have an aqueous core hydrodynamic diameter d _c = 3.6±0.2 nm. The final particles obtained after full reduction of Au^III have a metallic core of defect-free single-crystalline gold with a narrow size distribution and average core diameter d _Au = 7.7 ± 1.4 nm as shown by TEM. The rate of the particle growth is limited by the rate of gold reduction. The process kinetics corresponds to the model consisting of two stages of reduction Au^III → Au^I → Au⁰. The stages involve the formation and redox decay of the intermediate complexes Au(N₂H₄)Cl₃ and Au(N₂H₄)Cl, and each stage proceeds via two routes: (1) homogeneous in the dispersed aqueous phase, and (2) heterogeneous on the particle surfaces. Reactions taking route (2) are autocatalytic because they proceed with participation of the surface atoms of particles as the final products of Au^III reduction. The dependencies of observed rate constants on reagent concentrations, temperature, and solubilization capacity of the micellar solution are studied.     

Trifluoromethanesulfonamide: X‐ray single‐crystal determination and quantum chemical calculations

The X‐ray single‐crystal structure of 1,1,1‐trifluoromethanesulfonamide (triflamide) CF₃SO₂NH₂, which is the ancestor of a large family of its derivatives, has been determined. The crystal structure is composed of infinite layers with an interlayer distance of 3.4 Å. Geometry optimization at the Møller‐Plesset (MP2) and density functional theory (DFT) level showed the calculated bond distances to be, as a rule, longer than the experimental ones. A trial to simulate crystal packing effect on the geometrical parameters by calculating the dimer of triflamide in the gas phase failed – the starting X‐ray geometry of the ‘dimeric’ unit with one NH···O=S H‐bond – was optimized to the cyclic dimer with two H‐bonds. However, when the external (crystal) field effect was simulated using the polarizable continuum model, the experimental geometry of the ‘dimeric’ fragment was satisfactorily reproduced. Calculations of the heptamer cluster having the structure of the hexagon with six triflamide molecules in vertices and one in the middle nicely reproduce the X‐ray structure and brings the geometrical parameters closer to the experiment. Copyright © 2015 John Wiley & Sons, Ltd.     

Stabilization of stochastic cycles and control of noise-induced chaos

We study the robustness of symmetrically coupled and clustering-based weighted heterogeneous inter-connected networks with respect to load-failure-induced cascades. This is done under the assumption that the flow dynamics are governed by global redistribution of loads based on weighted betweenness centrality. Our results indicate that no weighting bias should be assigned to inter-links when calculating shortest path between node pairs under the clustering-based weighting scheme; i.e., inter-links shall be treated no differently than intra-links. In contrast with local load redistribution cases, we show that increasing connectivity is preferred for the robustness against global load redistribution-based cascading failures in clustering-based weighted inter-connected networks. Furthermore, comparisons among weighting schemes reveal that, both the clustering-based and degree-based schemes outperform the random one in the sense of requiring lower initial and total investments required to ensure robustness. We also find that clustering-based scheme outperforms degree-based one in terms of requiring lower initial investments. Except in a limited range where weighting is heavily suppressed, clustering-based scheme is shown to outperform degree-based one in terms of total investments. Finally, when there exists a hard investment budget constraint, clustering-based weighting scheme would be a better choice against a two-nodes-induced failure than the degree-based weighting, and the clustering-based scheme is more stable than degree-based scheme against one-or-two-nodes-induced failure. We expect our findings to be significantly useful in designing real-world weighted inter-connected networks that are robust against load-failure-induced cascades.     

Synthesis of new tetrahydropyrido[1,2-a]benzimidazoles based on recyclization of N-arylitaconimides with 2-cyanomethylbenzimidazole

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Magnetite-based highly dispersed materials for the sorption of asphaltenes

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