On the uniqueness of the Shapley value

L.S. Shapley [1953] showed that there is a unique value defined on the classD of all superadditive cooperative games in characteristic function form (over a finite player setN) which satisfies certain intuitively plausible axioms. Moreover, he raised the question whether an axiomatic foundation could be obtained for a value (not necessarily theShapley value) in the context of the subclassC (respectivelyC′, C″) of simple (respectively simple monotonic, simple superadditive) gamesalone. This paper shows that it is possible to do this. Theorem I gives a new simple proof ofShapley's theorem for the classG ofall games (not necessarily superadditive) overN. The proof contains a procedure for showing that the axioms also uniquely specify theShapley value when they are restricted to certain subclasses ofG, e.g.,C. In addition it provides insight intoShapley's theorem forD itself. Restricted toC′ orC″, Shapley's axioms donot specify a unique value. However it is shown in theorem II that, with a reasonable variant of one of his axioms, a unique value is obtained and, fortunately, it is just theShapley value again.     

Diffusion-induced modulational instability in magnetised semiconductor plasmas: effect of carrier heating

The present paper is aimed to the exploration of modulational amplification in transversely magnetised diffusive semiconductors. By considering that the origin of modulational interaction lies in the third-order optical susceptibility c⁽³⁾\chi^{(3)} arising from the nonlinear diffusion current density and using coupled mode theory, an analytical investigation of frequency modulational interaction between co-propagating laser beams and internally generated acoustic mode is presented. We have studied the steady state and transient amplification characteristics of modulated waves arising in the transversely magnetised semiconductor plasmas. The effect of carrier heating adds new dimensions to the present study. The heating effect reduces the required threshold amplitude of wave and enhances steady-state as well as transient gain of the generated acoustic mode.     

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.     

Coherence characteristics of light-emitting diodes

We report the measurement of coherence characteristics of light-emitting diodes (LEDs). Experiments were performed using red and green color LEDs directly illuminating the Young's double slit kept in the far-zone. Fourier transform fringe analysis technique was used for the measurement of the visibility of interference fringes from which the modulus of degree of spectral coherence was determined. Low degree of spectral coherence, typically 0.4 for red and 0.2 for green LED with double-slit separation of 400 μm was observed. A variable slit was then kept in front of the LEDs and the double slit was illuminated with the light coming out of the slit. Experiments were performed with various slit sizes and the visibility of the interference fringes was observed. It was found that visibility of the interference fringes changes drastically in presence of variable slit kept in front of LEDs and a high degree of spectral coherence, typically 0.85 for red and 0.8 for green LED with double-slit separation of 400 μm and rectangular slit opening of 500 μm was observed. The experimental results are compared with the theoretical counterparts. Coherence lengths of both the LEDs were also determined and it was obtained 5.8±2 and 24±4 μm for green and red LEDs, respectively.     

Low dissipative entropy stable schemes using third order WENO and TVD reconstructions

A low dissipative framework is given to construct high order entropy stable flux by addition of suitable numerical diffusion operator into entropy conservative flux. The framework is robust in the sense that it allows the use of high order reconstructions which satisfy the sign property only across the discontinuities. The third order weighted essentially non-oscillatory (WENO) interpolations and high order total variation diminishing (TVD) reconstructions are shown to satisfy the sign property across discontinuities. Third order accurate entropy stable schemes are constructed by using third order WENO and high order TVD reconstructions procedures in the diffusion operator. These schemes are efficient and less diffusive since the diffusion is actuated only in the sign stability region of the used reconstruction which includes discontinuities. Numerical results with constructed schemes for various test problems are given which show the third order accuracy and less dissipative nature of the schemes.     

Effects of silicon negative ion implantation in semi-insulating gallium arsenide

ABSTRACT

In the present work, effects of silicon negative ion implantation into semi-insulating gallium arsenide (GaAs) samples with fluences varying between 1?×?10¹⁵ and 4?×?10¹⁷?ions?cm^?2 at 100?keV have been described. Atomic force microscopic images obtained from samples implanted with fluence up to 1?×?10¹⁷?ion?cm^?2 showed the formation of GaAs clusters on the surface of the sample. The shape, size and density of these clusters were found to depend on ion fluence. Whereas sample implanted at higher fluence of 4?×?10¹⁷?ions?cm^?2 showed bump of arbitrary shapes due to cumulative effect of multiple silicon ion impact with GaAs on the same place. GXRD study revealed formation of silicon crystallites in the gallium arsenide sample after implantation. The silicon crystallite size estimated from the full width at half maxima of silicon (111) XRD peak using Debye-Scherrer formula was found to vary between 1.72 and 1.87?nm with respect to ion fluence. Hall measurement revealed the formation of n-type layer in gallium arsenide samples. The current–voltage measurement of the sample implanted with different fluences exhibited the diode like behavior.     

Analytical modeling and simulation of subthreshold characteristics of back-gated SSGOI and SSOI MOSFETs: A comparative study

The Silicon–Germanium-on-Insulator (SGOI) and Silicon-on-Insulator (SOI) based MOS structures are spearheading the strained-Si technology. The present work compares the subthreshold characteristics of two short-channel back-gated (BG) strained-Si-on-SGOI (SSGOI) and BG strained-Si-on-Insulator (SSOI) MOSFETs, and provides some solutions to overcome the degradation in subthreshold characteristics with the unrelenting downscaling of the devices. Subthreshold behaviors of the MOS structures are based on surface potential model which is determined by solving the 2D Poisson's equation with suitable boundary conditions by evanescent mode analysis for both of the MOS structures. The closed form expressions for threshold voltage, subthreshold current and subthreshold swing have been derived for symmetrical as well as independent gate operation (IGO). In addition, the Electrostatic integrity (EI) factors for SSOI and SSGOI MOS structures have been estimated and compared with Double-Gate (DG) MOSFET. The numerical simulation results, obtained by ATLAS?, a 2D device simulator from Silvaco, have been used to assess the validity of the models.     

An Efficient One‐pot Three‐component Method for the Synthesis of 5‐Amino‐3‐(2‐oxo‐2H‐chromen‐3‐yl)‐7‐aryl‐7H‐thiazolo[3,2‐a]pyridine‐6,8‐dicarbonitriles

A facile, convenient, and adequate method has been developed for the synthesis of novel 5‐amino‐3‐(2‐oxo‐2H‐chromen‐3‐yl)‐7‐aryl‐7H‐thiazolo[3,2‐a]pyridine‐6,8‐dicarbonitriles ( 6 ) by employing 2‐(4‐(2‐oxo‐2H‐chromen‐3‐yl)thiazol‐2‐yl)acetonitrile ( 3 ) as an important precursor. Initially, we have synthesized the target compounds in a stepwise manner and then approached a tandem method to examine the feasibility of one‐pot method. Subsequently, one‐pot three‐component protocol has been established for the synthesis of title compounds by the reaction of 3 with benzaldehyde and malononitrile in refluxing ethanol engender a new six‐membered thiazolo[3,2‐a] pyridine as a hybrid scaffold. Reaction conditions were optimized for this reaction and a broad substrate scope with various aryl and heteroaryl aldehydes make this protocol very practical, attractive, and worthy. Mechanistic aspects for the formation of these compounds were outlined comprehensively. Characterization of these newly synthesized compounds was achieved by means of IR, ¹H NMR, ¹³C NMR, and HRMS.