Farkas-Type Theorems and Applications: From IPH Functions to ICR Functions

Abstract

Some versions of Farkas-type theorems for systems of inequalities consisting of Increasing and Positively Homogeneous (IPH) functions are established. Applying these results, we establish Farkas-type theorems for the systems involving Increasing and Coradiant (ICR) functions as well. As an application, we apply these results to solve constrained IPH and ICR optimization problems with unconstrained counterparts.     

Modulation of electronic couplings within Ru2-polyyne frameworks

Dimers of [Ru(2)(Xap)(4)] bridged by 1,3,5-hexatriyn-diyl (Xap are 2-anilinopyridinate and its aniline substituted derivatives), [Ru(2)(Xap)(4)](2)(μ-C(6)) (1), were prepared. Compounds 1 reacted with 1 equiv of tetracyanoethene (TCNE) to yield the cyclo-addition/insertion products [Ru(2)(Xap)(4)](2){μ-C≡CC(C(CN)(2))-C(C(CN)(2))C≡C} (2) and 1 equiv of Co(2)(dppm)(CO)(6) to yield the η(2)-Co(2) adducts to the middle C≡C bond, [Ru(2)(Xap)(4)](2)(μ-C(6))(Co(2)(dppm)(CO)(4)) (3). Voltammetric and spectroelectrochemical studies revealed that (i) two Ru(2) termini in 1 are sufficiently coupled with the monoanion (1(-)) as a Robin-Day class II/III mixed valence species; (ii) the coupling between two Ru(2) is still significant but somewhat weakened in 3; and (iii) the coupling between two Ru(2) is completely removed by the insertion of TCNE in 2. The attenuation of electronic couplings in 2 and 3 was further explored with both the X-ray diffraction study of representative compounds and spin-unrestricted DFT calculations.     

An adaptive quality of service channel borrowing algorithm for cellular networks

A multimedia call consists of three main sub‐streams (i.e. video, audio and data) each with its own distinct quality of service (QoS) requirements (e.g. packet loss rate, delay tolerance, and jitter). These requirements constitute a specific fixed QoS level. In contrast to static approaches, we propose an adaptive QoS platform in which each sub‐stream declares a preset range of acceptable QoS levels (e.g. maximum, acceptable, minimum) instead of just a single level. This range of QoS levels is pre‐defined in a user‐defined profile (UDP). In this paper, we propose a channel borrowing algorithm based on such adaptive QoS platform. In our proposed algorithm, an acceptor cell that has used all its channels can borrow from any neighbouring (donor) cell as long as this donor cell has some channels available after satisfying a minimum QoS (minQ) level defined in the UDP. A donor cell that is assigning QoS levels (to calls under its coverage) higher than the minQ levels will declare those channels as available for borrowing by other acceptor cells. The criteria for choosing the free channel include not only the number of free channels, but also the QoS levels in the donor cell. The criteria are also extended to include the effect of channel locking on the number of free channels, and the QoS levels on the locked cells. The algorithm is not triggered unless it does not cause any call dropping in either the donor cell, or the cells affected by call blocking. In the meantime, the call blocking rate is significantly decreased while the offered load increases. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermochemistry is not a lower bound to the activation energy of endothermic reactions: a kinetic study of the gas-phase reaction of atomic chlorine with ammonia

The rate constant for Cl + NH3 --> HCl + NH2 has been measured over 290-570 K by the time-resolved resonance fluorescence technique. Ground-state Cl atoms were generated by 193 nm excimer laser photolysis of CCl4 and reacted under pseudo-first-order conditions with excess NH3. The forward rate constant was fit by the expression k1 = (1.08 +/- 0.05) x 10(-11) exp(-11.47 +/- 0.16 kJ mol(-1)/RT) cm3 molecule(-1) s(-1), where the uncertainties in the Arrhenius parameters are +/-1 sigma and the 95% confidence limits for k1 are +/-11%. To rationalize the activation energy, which is 7.4 kJ mol(-1) below the endothermicity in the middle of the 1/T range, the potential energy surface was characterized with MPWB1K/6-31++G(2df,2p) theory. The products NH2 + HCl form a hydrogen-bonded adduct, separated from Cl + NH3 by a transition state lower in energy than the products. The rate constant for the reverse process k(-1) was derived via modified transition state theory, and the computed k(-1) exhibits a negative activation energy, which in combination with the experimental equilibrium constant yields k1 in fair accord with experiment.     

Sampling free and particle‐bound chemicals using solid‐phase microextraction and needle trap device simultaneously

The possibility of sampling the free and particle‐bound concentrations of organic compounds was studied using two different sampling techniques at the same time: needle trap device (NTD) and solid‐phase microextraction (SPME). In this study, a mosquito coil was used to produce gaseous (free) and particle‐bound compounds. Allethrin, the active ingredient in mosquito coils, was chosen as the target analyte. Under the same sampling conditions, the amount of allethrin extracted from the mosquito‐coil smoke was higher for the NTD compared to the SPME fiber, while the extracted amounts were almost the same for both devices when sampling gaseous samples of allethrin. These results can be explained by the fact that the SPME fiber can only extract free molecules (based on diffusion), whereas the NTD, an exhaustive sampling device, collects both free and particle‐bound allethrin. Breakthrough for NTD and carryover for both NTD and SPME were negligible under the given sampling and desorption conditions.     

Copper Catalyzed Synthesis of Thiomorpholine Derivatives: A New Entry of Multicomponent Reaction Between Terminal Alkynes,Isothiocyanates, and Aziridines

Copper acetylide was reacted with isothiocyanate and aziridines to form 1,4‐thiomorpholine derivatives. Reaction outcome depends highly on the reaction conditions and the particular solvent employed. Optimum conditions are developed using copper iodide in hexafluoro‐2‐isopropanol at 60°C. Both the alkyl‐substituted and aryl‐substituted aziridines and terminal alkynes were studied.     

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell–Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.     

Application of the Complementary Derivatives Method in the ADI-FDTD Solution of Maxwell's Equations

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is well suited for simulating structures with large aspect ratios or problems with large gradient fields where different grid sizes can be used to yield greater computational efficiency. However, using different grid sizes increases the truncation error at the interface between domains having different grid sizes. The truncation error is manifested as a spurious reflection from the grid boundary, thus decreasing the simulation accuracy. In this paper, we apply the complementary derivatives method (CDM) to reduce the spurious reflections arising from the use of different grid size domains when using the ADI-FDTD method. It is shown that, the CDM guarantees uniform second-order accuracy throughout the computational domain. When the CDM is implemented in the ADI-FDTD method, the implicit updating equations cannot be written in a tri-diagonal matrix and the computational efficiency of the ADI-FDTD method is not preserved. By employing the Sherman-Morrison formula, we retain the numerical efficiency of the conventional ADI-FDTD. A representative numerical example is presented to demonstrate the accuracy of CDM in the ADI-FDTD simulations.