A Technique for Stochastic Control Problems with Unbounded Control Set

We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function.     

Linear diacetylene polymers containing bis(dimethylsilyl) phenyl and/or bis-(tetramethyldisiloxane) carborane residues: Their synthesis,characterization and thermal and oxidative properties

A series of inorganic-organic linear diacetylenic hybrid polymers ( 5a–e ) were prepared by the polycondensation reaction of 1,4-dilithiobutadiyne with 1,4-bis(dimethylchlorosilyl)benzene and/or 1,7-bis(tetramethylchlorodisiloxane)-m-carborane. Their structures were characterized using FTIR, and ¹³C and ¹H NMR spectroscopies, and their thermal and oxidative properties were evaluated by DSC and TGA analyses. The hybrid polymers exhibited solubility in common organic solvents and were viscous liquids or low melting solids at room temperature. Broad prominent exotherms, attributed to reaction of the diacetylenic units, were observed by DSC in the 306°C to 354°C temperature range. When 5a–e were analyzed by TGA to 1000°C under nitrogen, weight retention between 79 and 86% were obtained. Ageing studies, performed at elevated temperatures in air on a thermoset and a ceramic obtained from polymer 5b , showed this system to have excellent thermal and oxidative stability. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2387–2391, 1997     

The Kolkata Paise Restaurant problem and resource utilization

We study the dynamics of the “Kolkata Paise Restaurant problem”. The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.     

Multiple dot-in-rod PbS/CdS heterostructures with high photoluminescence quantum yield in the near-infrared

Pb cations in PbS quantum rods made from CdS quantum rods by successive complete cationic exchange reactions are partially re-exchanged for Cd cations. Using STEM-HAADF, we show that this leads to the formation of unique multiple dot-in-rod PbS/CdS heteronanostructures, with a photoluminescence quantum yield of 45-55%. We argue that the formation of multiple dot-in-rods is related to the initial polycrystallinity of the PbS quantum rods, where each PbS crystallite transforms in a separate PbS/CdS dot-in-dot. Effective mass modeling indicates that electronic coupling between the different PbS conduction band states is feasible for the multiple dot-in-rod geometries obtained, while the hole states remain largely uncoupled.     

Preclusion of nano scale self-assembly in block-selective non-aqueous solvents for rod–coil and coil–rod–coil macromolecular surfactants based on perylene tetracarboxylic diimide

Self-assembly of amphiphilic molecules ranging from simple surfactants to block copolymers in a solvent depends on one part of the molecule (one block in block copolymers) being soluble, and the other not. The aggregation of the insoluble segment in the block-selective solvent leads to the self assembly. In this paper, we describe a system of amphiphilic rod–coil and coil–rod–coil molecules, which do not show self assembly in block-selective non-aqueous solvents. We prepared rod–coil molecules based on hydrophilic propylene oxide/ethylene oxide copolymer (PO–EO copolymer) (Jeffamine®) as the flexible segment and photo-conducting large aromatic perylenediimide (PTCDI) as the rod. PO–EO copolymer was attached either to one side of PTCDI (MJ–PTCDI) or both sides (DJ–PTCDI). The former can be considered an inverse macromolecular surfactant, since the tail is hydrophilic and the head is hydrophobic. The DJ–PTCDI is a pseudo Gemini surfactant. Because of the presence of the chromophore, UV–Vis and fluorescent spectra could be used to study the self assembly of these amphiphilic rod coil polymers in solution. PTCDI forms π-interaction mediated aggregates in aqueous solution and these are H-stacked in MJ–PTCDI and J-stacked in DJ–PTCDI. Variable temperature UV and NMR spectra show that the assembly is stable over a large temperature range in water. The aggregates are also stable up to a pH of 12. However, when a non-aqueous solvent is used, no aggregation occurs. This is attributed to the “solvation” of the π-system of the PTCDI. With the addition of water, such solvation seems to be interrupted and aggregation occurs when water becomes a major component. We find that the mole percentage of the aggregates in acetone/water mixtures increases almost linearly with the concentration of water, providing a route to control the extent of aggregation of the chromophores. Due to the long, waxy PO–EO copolymer, MJ–PTCDI and DJ–PTCDI do not show liquid crystalline behavior or nanorod morphology, which were seen with short side chains. The optical microscopy of the bulk material shows aggregated crystals of PTCDI in the waxy matrix, showing that even in the presence of PO–EO copolymer, the molecular assembly of PTCDI takes place in the bulk. Secondary assembly was seen, in that upon ageing of the aqueous solutions, the drop cast films show that the spherical aggregates one-dimensionally coalesced into long fibers. Although UV–Vis spectra indicated no aggregation in non-aqueous solvents, drop-cast films of these solutions show needle-like aggregates and Lego-like assemblies.     

An unexpected formation of benzoyl benzoin from benzil during the attempted Knoevenagel type condensation with dimethylmalonate (or malononitrile)

An unexpected product, 2-oxo-1,2-diphenylethyl benzoate (benzoyl benzoin), was isolated during the attempted Knoevenagel reaction of benzil and dimethylmalonate (or malononitrile) in the presence of potassium carbonate. The product was confirmed by spectral analysis as well as by single crystal studies and a mechanism is proposed to explain its formation.     

Natural Phytocompounds from Common Indian Spices for Identification of Three Potential Inhibitors of Breast Cancer: A Molecular Modelling Approach

Breast cancer is the second most common cancer-related cause of death for women throughout the globe. In spite of some effective measures, the main concerns with traditional anti-cancer chemotherapy are its low bioavailability, physical side effects, acquired resistance of cancer cells and non-specific targeting. Now researchers have taken the initiative to establish natural product-based therapy methods and to identify viable hits for future lead optimization in the development of breast cancer medication. Our study aims to identify the potent phytocompounds from five very popular Indian spices (Zingiber officinale Roscoe, Cuminum cyminum L., Piper nigrum L., Curcuma longa L., and Allium sativum L.). From these spices, a total of 200 phytocompounds were identified and screened against three target genes, namely, cyclin-dependent kinase 8 (CDK 8), progesterone receptor (PR) and epidermal growth factor receptor (EGFR), through structure-based virtual screening using iGEMDOCK 2.1 software. Based on the binding affinity score, the top three phytocompounds against each target protein (cynaroside (−149.66 Kcal/mol), apigetrin (−139.527 Kcal/mol) and curcumin (−138.149 Kcal/mol) against CDK8; apigetrin (−123.298 Kcal/mol), cynaroside (−118.635 Kcal/mol) and xyloglucan (−113.788 Kcal/mol) against PR; cynaroside (−119.18 Kcal/mol), apigetrin (−105.185 Kcal/mol) and xyloglucan (−105.106 Kcal/mol) against EGFR) were selected. Apigetrin, cynaroside, curcumin, and xyloglucan were finally identified for further docking analysis with the respective three target proteins. Autodock 4.2 was applied to screen the optimal binding position and to assess the relative intensity of binding interactions. In addition, the ADME/T property checks and bioactivity scores analysis of were performed to understand the suitability of these four phytocompounds to be potential candidates for developing effective and non-toxic anticancer agents. Based on this in silico analysis, we believe this study could contribute to current efforts to develop new drugs for treating breast cancer.     

Attenuation of Sommerfeld effect in an internally damped eccentric shaft-disk system via active magnetic bearings

Meccanica - Eccentric shaft-disk system with internal damping driven by a non-ideal power source exhibits Sommerfeld effect characterized by nonlinear jump phenomena of amplitude and rotor speed...     

Structure–property correlations of sulfonated polyimides. I. Effect of bridging groups on membrane properties

A series of six‐membered sulfonated polyimides were synthesized using 1,4,5,8‐naphthalenetetracarboxylic dianhydride, 4,4′‐diaminobiphenyl 2,2′‐disulfonic acid as the sulfonated diamine, and various nonsulfonated diamine monomers having different bridging groups. These bulky bridging groups have the capacity to increase hydrolytic stability and proton conductivity. Polyimides with bulky bridging groups showed increased solubility but exhibited lower thermal stability. The ion exchange capacity and water uptake reduced with increase in the bulkiness of the bridging group. This was attributed to the increase in the molecular weight of the repeating unit and hence effectively reduced the sulfonic acid content. In low temperatures, the conductivity was lower than Nafion®115 and, with increase in temperature, the conductivity rapidly increased and exhibited better conductivity than Nafion®115. Polyimides with bulky bridging groups 4‐amino phenyl sulfone, and 2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane showed higher conductivity than other polyimides and Nafion®115 despite low ion exchange capacity. The hydrolytic stability of the polyimides with bulky bridging groups was higher than the polyimides with less bulky atoms because of the imparted flexibility. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3612–3620, 2004     

Nanoindentation studies of polyimide thin films with various internal linkages in the diamine component

Polyimide thin films were synthesized from 3,3′,4,4′‐biphenyltetracarboxylic acid dianhydride (BPDA) and four different diamines (p‐phenylene diamine, 4,4′‐oxydiphenylene diamine, 4,4′‐biphenylene diamine, and 4,4′‐sulfonyldiphenylene diamine). The nanoindentation behavior of the resulting polyimides, namely, poly(p‐phenylene biphenyltetracarboximide) (BPDA‐PDA), poly(4,4′‐biphenylene biphenyltetracarboximide) (BPDA‐BZ), poly(4,4′‐oxydiphenylene biphenyltetracarboximide) (BPDA‐ODA), and poly(4,4′‐sulfonyldiphenylene biphenyltetracarboximide) (BPDA‐DDS), were investigated. Also, the morphological properties were characterized with a prism coupler and wide‐angle X‐ray diffraction and were correlated to the nanoindentation studies. The nanoindentation behavior and hardness varied quite significantly, depending on the changes in the chemical and morphological structures. The hardness of the polyimide thin films increased in the following order: BPDA‐DDS < BPDA‐ODA < BPDA‐BZ < BPDA‐PDA. For all the polyimide thin films, except that of BPDA‐BZ, the hardness decreased with an increase in the load. The birefringence, a measure of the molecular in‐plane orientation, increased in the following order: BPDA‐DDS < BPDA‐ODA < BPDA‐PDA < BPDA‐BZ. The X‐ray diffraction studies revealed that the crystallinity of the polyimide thin films varied with the changes in the chemical structure. The studies showed that the indentation response with an applied load and the hardness by nanoindentation for the BPDA‐based polyimides were closely related to the morphological structure. The nanoindentation and birefringence results revealed that the mechanical properties of the polyimide thin films were dependent on the crystallinity, which arose because of the chain order along the chain axis and the molecular packing order. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 861–870, 2004