Theoretical demonstration of the hybrid focusing points of sonic crystal flat lenses and possible applications

We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain (FDTD) simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.     

On Two Equivalent Dilation Theorems in VH-Spaces

We prove that a generalized version, essentially obtained by R.M. Loynes, of the B. Sz.-Nagy??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued (here ${\mathcal{H}}$ is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W.F. Stinespring??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued completely positive linear maps on B ^*-algebras. This equivalence result is a generalization of a theorem of F.H. Szafraniec, originally proved for the case of operator valued maps (that is, when ${\mathcal{H}}$ is a Hilbert space).     

Characterization of porous polar semiconductors by their optical spectra in the region of phonon and plasmon-phonon excitations

Optical properties of porous A ³ B ⁵ semiconductors (GaAs, InP, and GaP) in the far-infrared region, in particular, the specular reflection and attenuated total reflection, including the excitation regime of surface polaritons, are considered. Considering a porous material as a composite, we performed calculations in the context of the effective medium model using two modifications of it, Maxwell-Garnett and Bruggeman, which correspond to two different topologies of the composite material—matrix and statistical. The effect of porosity of the material and of such parameters as doping, anisotropy, and penetration depth of an electromagnetic wave to a porous material on optical spectra is analyzed. In addition, some experimental data are presented and the adequacy of the performed numerical simulation is demonstrated.     

Demand forecasting and sharing strategies to reduce fluctuations and the bullwhip effect in supply chains

Supply chain inventories are prone to fluctuations and instability. Known as the bullwhip effect, small variations in the end item demand create oscillations that amplify throughout the chain. By using system dynamics simulation, we investigate some of the structural sources of the bullwhip effect, and explore the effectiveness of information sharing to eliminate the undesirable fluctuations. Extensive simulation analysis is carried out on parameters of some standard ordering policies, as well as external demand and lead-time parameters. Simulation results show that (i) a major structural cause of the bullwhip effect is isolated demand forecasting performed at each echelon of the supply chain, and (ii) demand and forecast sharing strategies can significantly reduce the bullwhip effect, even though they cannot completely eliminate it. We specifically show how each policy is improved by demand and forecast sharing. Future research involves more advanced ordering and forecasting methods, modelling of other well-known sources of bullwhip, and more complex supply network structures.     

[1,2,5]thiadiazolo[3,4‐g]quinoxaline acceptor‐based donor–acceptor–donor‐type polymers: Effect of strength and size of donors on the band gap

Electrochromic polymers based on [1,2,5]thiadiazolo[3,4‐g]quinoxaline acceptor and thiophene, 3,4‐ethylenedioxythiophene and 3,3‐didecyl‐3,4‐proylenedioxythiophene donors, namely poly(6,7‐diphenyl‐4,9‐di(thiophen‐2‐yl)‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P1 ), poly(4‐(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)‐9‐(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐7‐yl)‐6,7‐diphenyl‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P2 ), and poly(4‐(3,3‐didecyl‐3,4‐dihydro‐2H‐thieno[3,4‐b][1,4]dioxepin‐6‐yl)‐9‐(3,3‐didecyl‐3,4‐dihydro‐2H‐thieno[3,4‐b][1,4]dioxepin‐8‐yl)‐6,7‐diphenyl‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P3 ), respectively, were electrochemically and/or chemically synthesized and characterized. Electrochemical and optical properties of the polymers were then investigated. The results, which were obtained electrochemically and optically, indicate that the polymers bearing the same acceptor and different donor units have a band gap range of 0.59–1.24 eV depending on the strength and size of the donor units and band gap determination method. A significant finding in this study was the phenomenon that when the acceptor is physically huge, the general rule that a weak donor would have a high band gap whereas a strong donor would have low band gap can be broken due to the torsional angles/steric hindrances involved with physically large donor molecules. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3483–3493     

Extensions and their Minimizations on the Sierpinski Gasket

We study the extension problem on the Sierpinski Gasket (SG). In the first part we consider minimizing the functional \(\mathcal {E}_{\lambda }(f) = \mathcal {E}(f,f) + \lambda \int f^{2} d \mu \) with prescribed values at a finite set of points where \(\mathcal {E}\) denotes the energy (the analog of \(\int |\nabla f|^{2}\) in Euclidean space) and μ denotes the standard self-similiar measure on SG. We explicitly construct the minimizer \(f(x) = \sum _{i} c_{i} G_{\lambda }(x_{i}, x)\) for some constants c _i , where G _λ is the resolvent for λ≥0. We minimize the energy over sets in SG by calculating the explicit quadratic form \(\mathcal {E}(f)\) of the minimizer f. We consider properties of this quadratic form for arbitrary sets and then analyze some specific sets. One such set we consider is the bottom row of a graph approximation of SG. We describe both the quadratic form and a discretized form in terms of Haar functions which corresponds to the continuous result established in a previous paper. In the second part, we study a similar problem this time minimizing \(\int _{SG} |\Delta f(x)|^{2} d \mu (x)\) for general measures. In both cases, by using standard methods we show the existence and uniqueness to the minimization problem. We then study properties of the unique minimizers.     

Study of Solution Polymerization of Styrene in the Presence of Poly(ethylene glycol)-RAFT Agents Possessing Benzoyl Xanthate Derivatives

In this work, Macro-Reversible addition fragmentation termination (RAFT) agents based on poly(ethylene glycol) (PEG) possessing different molecular weights and bearing benzoyl xanthate moieties were synthesized by the reaction of PEG potassium xanthate salts with benzoyl chloride, 4-methyl benzoyl chloride and 4-chloro benzoyl chloride. Controlled free radical polymerization of the styrene were carried out in the presence of these macro-RAFT agents using 2,2′-azobisizsobutyronitrile (AIBN) as an initiator to yield PS-b-PEG-b-PS block copolymers. The linear kinetic plot ln [M]_o/[M] vs. polymerization time indicated that was first order with reference to monomer concentration. The block copolymerization possessed controlled/living character. The controlled character of the RAFT polymerization of the styrene was confirmed by the formation of narrow polydispersity of the polymers, linear increases in the molecular weight with polymerization time and molecular weight of the products that agreed well with theoretical values. Polymers having relatively narrow molecular weight distributions and predetermined number average molecular weights were obtained by the RAFT polymerization of the styrene. However, molecular weights of the polymers deviated from the theoretical values when low molecular weight RAFT agents are used. The results indicate that PEG benzoyl xanthate RAFT agents can more efficiently control the polymerization comparing methyl or chlorobenzoyl derivatives. The block copolymers were characterized by spectroscopic and GPC methods.