Conformational stability, the spectroscopic (FT-IR and UV), first order hyperpolarizability, NBO analysis, HOMO and LUMO analysis of 6,8-diphenylimidazo[1,2-α]pyrazine molecule by ab initio HF and density functional methods

The conformational analysis of 6,8-diphenylimidazo[1,2-α]pyrazine molecule (abbreviated as 68DIP) was performed by using B3LYP/6-31G(d) level of theory to find the most stable form. Two staggered stable conformers were observed on the torsional potential energy surface. The equilibrium geometry, bonding features and vibrational frequencies of 68DIP have been investigated by using the DFT (B3LYP) and HF methods for the lowest energy conformer. The first order hyperpolarizability (β(total)) of this molecular system and related properties (β, μ, <α> and Δα) are calculated using HF/6-311++G(d,p) and B3LYP/6-311++G(d,p) methods based on the finite-field approach. Stability of the molecule arising from hyperconjugative interactions, charge delocalization and C-H?N intramolecular hydrogen-bond-like weak interaction has been analyzed using natural bond orbital (NBO) analysis by using B3LYP/6-311++G(d,p) method. The results show that electron density (ED) in the σ* and π* antibonding orbitals and second order delocalization energies E((2)) confirm the occurrence of intramolecular charge transfer (ICT) within the molecule. UV-vis spectrum of the compound was recorded and electronic properties, such as HOMO, LUMO energies, excitation energies and wavelength were performed by TD-DFT/B3LYP, CIS and TD-HF methods by using 6-311++G(d,p) basis set. Finally, the calculation results were applied to simulated infrared spectra of the title compound which show good agreement with observed spectra.     

Implicit difference approximation for the time fractional heat equation with the nonlocal condition

In this work, a method for solving inhomogeneous nonlocal fractional heat equations is proposed. The method is based on the modified Gauss elimination method. It is proved by using matrix stability approach that the method is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of the proposed method.     

Value of supplier’s capacity information in a two-echelon supply chain

In traditional supply chain models it is generally assumed that full information is available to all parties involved. Although this seems reasonable, there are cases where chain members are independent agents and possess different levels of information. In this study, we analyze a two-echelon, single supplier-multiple retailers supply chain in a single-period setting where the capacity of the supplier is limited. Embedding the lack of information about the capacity of the supplier in the model, we aim to analyze the reaction of the retailers, compare it with the full-information case, and assess the value of information and the effects of information asymmetry using game theoretic analysis. In our numerical studies, we conclude that the value of information is highly dependent on the capacity conditions and estimates of the retailers, and having information is not necessarily beneficial to the retailers.     

The multi-terminal maximum-flow network-interdiction problem

This paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K ? 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the post-interdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E.     

New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller-Tucker-Zemlin constraints

Given an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topology-enforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991).     

Statistical ward continuity

Recently, it has been proved that a real-valued function defined on an interval $A$ of R, the set of real numbers, is uniformly continuous on $A$ if and only if it is defined on $A$ and preserves quasi-Cauchy sequences of points in $A$. In this paper we call a real-valued function statistically ward continuous if it preserves statistical quasi-Cauchy sequences where a sequence $\left({\alpha }_k\right)$ is defined to be statistically quasi-Cauchy if the sequence $\left(\Delta {\alpha }_k\right)$ is statistically convergent to 0. It turns out that any statistically ward continuous function on a statistically ward compact subset $A$ of R is uniformly continuous on $A$. We prove theorems related to statistical ward compactness, statistical compactness, continuity, statistical continuity, ward continuity, and uniform continuity.     

Tauberian conditions for Cesàro summability of integrals

In this paper we generalize some classical type Tauberian theorems given for Cesàro summability of integrals.     

Reduced charge transfer exciton recombination in organic semiconductor heterojunctions by molecular doping

We investigate the effect of molecular doping on the recombination of electrons and holes localized at conjugated-polymer-fullerene interfaces. We demonstrate that a low concentration of p-type dopant molecules (<4% weight) reduces the interfacial recombination via charge transfer excitons and results in a favored formation of separated carriers. This is observed by the ultrafast quenching of photoluminescence from charge transfer excitons and the increase in photoinduced polaron density by ~70%. The results are consistent with a reduced formation of emissive charge transfer excitons, induced by state filling of tail states.     

Preconversion phase modulation of input differential phase-shift-keying signals for wavelength conversion and multicasting applications using phase-modulated pumps

We demonstrate a method to use phase-modulated pumps for multicasting of return-to-zero differential phase-shift keying (RZ-DPSK) signals. The method uses phase modulation of the input signal along with the co-phase-modulated pumps prior to wavelength conversion. Nine copies of a 50?Gbit/s RZ-DPSK data signal are generated via four-wave mixing with an average conversion efficiency of ～0?dB. An average receiver sensitivity penalty of ～1.9?dB is observed at a bit-error rate of 10(-9) with a worst case of 2.3?dB. The effects of synchronization errors and phase-modulation frequencies up to 5?GHz are investigated.