A dynamic approach to the Shapley value based on associated games

We propose a dynamic process leading to the Shapley value of TU games or any solution satisfying Inessential Game (IG) and Continuity (CONT), based on a modified version of Hamiache's notion of an associated game. The authors are very grateful to William Thomson and two anonymous referees for valuable comments which much improve the paper. They provide better statements and proofs of several major results than the original ones.     

Influence of non-reactive solvent on optical performance, photopolymerization kinetics and morphology of nanoporous polymer gratings

A study of nanoporous polymer gratings, with controllable nanostructured porosity, as a function of grating performance, photopolymerization kinetics and morphology is presented. Modifying the standard holographic polymer dispersed liquid crystal (H-PDLC) system, by including a non-reactive solvent, results in a layered, nanoporous morphology and produces reflective optical elements with excellent optical performance of broadband reflection. The addition of the non-reactive solvent in the pre-polymer mixture results in a morphology typified by void/polymer layer-by-layer structures if sufficient optical energy is used during the holographic writing process. The duration and intensity of optical exposure necessary to form well-aligned nanoporous structures can only be obtained in the modified system by (a) illumination under longer time of holographic interference patterning (30 min) or (b) illumination under very short time of holographic interference patterning (30 s) and followed by post-curing using homogeneous optical exposure for 60 min. Comparatively, a typical H-PDLC is formed in less than 1 min. To further understand the differences in the formation of these two analogous materials, the temporal dynamics of the photoinitiation and polymerization (propagation) kinetics were examined. It is shown herein that the writing exposure gives a cross-linked polymer network that is denser in the bright regions. With 60% (or even 45%) acrylate conversion, almost no free monomer would be left after the writing. Continued exposure serves primarily to add cross-links. This has the tendency to collapse the network, especially the less dense portions, which in effect get glued down to the more dense parts. To the extent that the solvent increases the mobility of the polymer network, this process will be aided. Equally important, the size of the periodic nanopores can be varied from 10 to 50 nm by controlling either the LC concentration in the pre-polymer mixture or by controlling the time of the homogeneous post-cure.     

High temperature characteristics of ZnO-based MOS-FETs with a photochemical vapor deposition SiO2 gate dielectric

The authors report the fabrication of ZnO-based metal-oxide-semiconductor field effect transistors (MOSFETs) with a high quality SiO₂ gate dielectric by photochemical vapor deposition (photo-CVD) on a sapphire substrate. Compared with ZnO-based metal-semiconductor FETs (MESFETs), it was found that the gate leakage current was decreased to more than two orders of magnitude by inserting the photo-CVD SiO₂ gate dielectric between ZnO and gate metal. Besides, it was also found that the fabricated ZnO MOSFETs can achieve normal operation of FET, even operated at 150 °C. This could be attributed to the high quality of photo-CVD SiO₂ layer. With a 2 μm gate length, the saturated I_ds and maximum transconductance (G_m) were 61.1 mA/mm and 10.2 mS/mm for ZnO-based MOSFETs measured at room temperature, while 45.7 mA/mm and 7.67 mS/mm for that measured at 150 °C, respectively.     

Numerical inversion of laplace transform via wavelet in partial differential equations

This article presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that P is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulae of listing table (Chen et al., Journal of The Franklin Institute 303 (1977), 267–284) to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task. The operational method presented in this article owns the advantages of simpler computation as well as broad application. We still can obtain satisfying solution even under large matrix. Moreover, we do not have numerically unstable problems. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 536–549, 2014     

Predicting melting temperature directly from protein sequences

Proteins of both hyperthermophilic and mesophilic microorganisms generally constitute from the same 20 amino acids; however, the extent of thermal tolerance of any given protein is an inherent property of its amino acid sequence. The present study is the first to report a rapid method for predicting Tm (melting temperature), the temperature at which 50% of the protein is unfolded, directly from protein sequences (the Tm Index program is available at http://tm.life.nthu.edu.tw/). We examined 75 complete microbial genomes using the Tm Index, and the analysis clearly differentiated hyperthermophilic from mesophilic microorganisms on this global genomic basis. These results are consistent with the previous hypothesis that hyperthermophiles express a greater number of high Tm proteins compared with mesophiles. The Tm Index will be valuable for modifying existing proteins (enzymes, protein drugs and vaccines) or designing novel proteins having a desired melting temperature.     

Structure Evolution upon Uniaxial Drawing Skin‐ and Core‐Layers of Injection‐Molded Isotactic Polypropylene by In Situ Synchrotron X‐ray Scattering

The structure evolution of the oriented layer (skin) and unoriented layer (core) from injection‐molded isotactic polypropylene samples upon uniaxial drawing is probed by in situ synchrotron X‐ray scattering. The X‐ray data analysis approach, called “halo method”, is used to semiquantitatively identify the transformation process of crystal phase upon uniaxial drawing. The results verify the validation of the stress‐induced crystal fragmentation and recrystallization process in the deformation of the injection‐molded samples under different temperatures. Furthermore, the end of strain softening region in the engineering stress‐strain curves explicitly corresponds to the transition point from the stress‐induced crystal fragmentation to recrystallization process. Basically, the skin and core layers of the injection‐molded parts share the similar deformation mechanism as aforementioned. The stretching temperature which dramatically affects the relative strength between the entanglement‐induced tie chains and the adjacent crystalline lamellae determines the crystal structural evolution upon drawing. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1618–1631     

Crystallization behavior of isotactic propylene‐1‐hexene random copolymer revealed by time‐resolved SAXS/WAXD techniques

The crystallization behavior of isotactic propylene‐1‐hexene (PH) random copolymer having 5.7% mole fraction of hexene content was investigated using simultaneous time‐resolved small‐angle X‐ray scattering (SAXS) and wide‐angle X‐ray diffraction (WAXD) techniques. For this copolymer, the hexene component cannot be incorporated into the unit cell structure of isotactic polypropylene (iPP). Only α‐phase crystal form of iPP was observed when samples were melt crystallized at temperatures of 40 °C, 60 °C, 80 °C, and 100 °C. Comprehensive analysis of SAXS and WAXD profiles indicated that the crystalline morphology is correlated with crystallization temperature. At high temperatures (e.g., 100 °C) the dominant morphology is the lamellar structure; while at low temperatures (e.g., 40 °C) only highly disordered small crystal blocks can be formed. These morphologies are kinetically controlled. Under a small degree of supercooling (the corresponding iPP crystallization rate is slow), a segmental segregation between iPP and hexene components probably takes place, leading to the formation of iPP lamellar crystals with a higher degree of order. In contrast, under a large degree of supercooling (the corresponding iPP crystallization rate is fast), defective small crystal blocks are favored due to the large thermodynamic driving force and low chain mobility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 26–32, 2010     

Aligned and molecularly oriented semihollow ultrafine polymer fiber yarns by a facile method

In this work, aligned and molecularly oriented bone‐like PLLA semihollow fiber yarns were manufactured continuously from an optimized homogeneous polymer‐solvent‐nonsolvent system [PLLA, CH₂Cl₂, and dimethyl formamide (DMF)] by a single capillary electrospinning via self‐bundling technique. Here, it should be emphasized that the self‐bundling electrospinning technique, a very facile electrospinning technique with a grounded needle (which is to induce the self‐bundling of polymer nanofibers at the beginning of electrospinning process), is used for the alignment and molecular orientation of the polymer fiber, and the take‐up speed of the rotating drum for the electrospun fiber yarn collection is very low (0.5 m/s). PLLA can be dissolved in DMF and CH₂Cl₂ mixed solvent with different ratios. By varying the ratios of mixed solvent system, PLLA electrospun semihollow fiber with the porous inner structure and compact shell wall could be formed, the thickness of the shell and the size of inner pores could be adjusted. The results of polarized FTIR and wide angle X‐ray diffraction investigations verified that as‐prepared PLLA semihollow fiber yarns were well‐aligned and molecularly oriented. Both the formation mechanism of semihollow fibers with core‐shell structure and the orientation mechanism of polymer chains within the polymer fibers were all discussed. The as‐prepared self‐bundling electrospun PLLA fiber yarns possessed enhanced mechanical performance compared with the corresponding conventional electrospun PLLA fibrous nonwoven membranes. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1118–1125, 2010