The Cartan,Choquet and Kellogg properties for the fine topology on metric spaces

We prove the Cartan and Choquet properties for the fine topology on a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We apply these key tools to establish a fine version of the Kellogg property, characterize finely continuous functions by means of quasicontinuous functions, and show that capacitary measures associated with Cheeger supersolutions are supported by the fine boundary of the set.     

Actualism and Modal Semantics

According to actualism, modal reality is constructed out of valuations (combinations of truth values for all propositions). According to possibilism, modal reality consists in a set of possible worlds, conceived as independent objects that assign truth values to propositions. According to possibilism, accounts of modal reality can intelligibly disagree with each other even if they agree on which valuations are contained in modal reality. According to actualism, these disagreements (possibilist disagreements) are completely unintelligible. An essentially actualist semantics for modal propositional logic specifies which sets of valuations are compatible with the meanings of the truth-functional connectives and modal operators without drawing on formal resources that would enable us to represent possibilist disagreements. The paper discusses the availability of an essentially actualist semantics for modal propositional logic. I argue that the standard Kripkean semantics is not essentially actualist and that other extant approaches also fail to provide a satisfactory essentially actualist semantics. I end by describing an essentialist actualist semantics for modal propositional logic.     

Continuous approximation of linear impulsive systems and a new form of robust stability

The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive system can be affected by replacing the impulse effect with a continuous (as opposed to discontinuous, impulsive) perturbation, producing what is known as an impulse extension equation. Theoretical properties related to the existence of the time-scale tolerance are given for periodic systems, as are algorithms to compute them. Some methods are presented for general, aperiodic systems. Additionally, sufficient conditions for the convergence of solutions of impulse extension equations to the solutions of their associated impulsive differential equation are proven. Counterexamples are provided.     

Mössbauer study of the magnetocaloric compound AlFe<Subscript>2</Subscript><Emphasis Type="Bold">B</Emphasis><Subscript>2</Subscript>

Mössbauer spectroscopy in the ferromagnetic AlFe₂ B ₂ reveals T_c=299 K and shows good agreement with magnetic measurements. The crystals are plate-shaped. The flakes are found from X-ray diffraction to be in the crystallographic ac-plane in the orthorhombic system. The axes of the principle electric field gradient tensor are, by symmetry, colinear with the crystal a-, b- and c-axes. By using information about the quadrupole splitting and line asymmetry in the paramagnetic regime together with the quadrupole shift of the resonance lines in the ferromagnetic regime the magnetic hyperfine field direction is found to be in the ab-plane having an angle =40^° to the b-axis.     

Quantum Authencryption with Two-Photon Entangled States for Off-Line Communicants

In this paper, a quantum authencryption protocol is proposed by using the two-photon entangled states as the quantum resource. Two communicants Alice and Bob share two private keys in advance, which determine the generation of two-photon entangled states. The sender Alice sends the two-photon entangled state sequence encoded with her classical bits to the receiver Bob in the manner of one-step quantum transmission. Upon receiving the encoded quantum state sequence, Bob decodes out Alice’s classical bits with the two-photon joint measurements and authenticates the integrity of Alice’s secret with the help of one-way hash function. The proposed protocol only uses the one-step quantum transmission and needs neither a public discussion nor a trusted third party. As a result, the proposed protocol can be adapted to the case where the receiver is off-line, such as the quantum E-mail systems. Moreover, the proposed protocol provides the message authentication to one bit level with the help of one-way hash function and has an information-theoretical efficiency equal to 100 %.     

Quantum Games under Decoherence

Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.     

Nonlinear Spinor Fields in Bianchi type-III Spacetime

Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In this case the spacetime remains locally rotationally symmetric and anisotropic all the time. It is found that depending on the sign of nonlinearity the models allows both accelerated and oscillatory modes of expansion. The non-diagonal components of energy-momentum tensor though impose some restrictions on metric functions and components of spinor field, unlike Bianchi type I, V and V I ₀ cases, they do not lead to vanishing mass and nonlinear terms of the spinor field.     

Tunneling Radiation of Vector Particles in Four and Five Dimensional Black Holes

Recent research shows that the WKB approximation and the Hamilton-Jacobi method has been succeed in studying the tunneling radiation of vector particles. In view of this, our main aim in this letter is to study the Proca equation and the vector particles tunneling radiation in the 4-dimensional and 5-dimensional black holes. And finally, the results here show that the temperature of vector particle is the same as Dirac particle’s and other particle’s.     

A high-voltage lithium-ion battery prepared using a Sn-decorated reduced graphene oxide anode and a LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.5</Subscript>O<Subscript>4</Subscript> cathode

This paper describes the preparation and characterization of a high-voltage lithium-ion battery based on Sn-decorated reduced graphene oxide and LiNi_0.5Mn_1.5O₄ as the anode and cathode active materials, respectively. The Sn-decorated reduced graphene oxide is prepared using a microwave-assisted hydrothermal synthesis method followed by reduction at high temperature of a mixture of (C₆H₅)₂SnCl₂ and graphene oxide. The so-obtained anode material is characterized by thermogravimetric analysis, X-ray diffraction, scanning electron microscopy, and electron diffraction spectroscopy. The LiNi_0.5Mn_1.5O₄ is a commercially available product. The two materials are used to prepare composite electrodes, and their electrochemical properties are investigated by galvanostatic charge/discharge cycles at various current densities in lithium cells. The electrodes are then used to assemble a high-voltage lithium-ion cell, and the cell is tested to evaluate its performance as a function of discharge rate and cycle number.     

A combined analytical approach applied to Medieval wall paintings from Puglia (Italy): The study of painting techniques and its conservation state

A combined analytical approach has been applied to the wall paintings, dated from 10th to 14th centuries, of the Santi Stefani crypt at Vaste (Lecce, Southern Italy). These paintings are a precious testimony of Medieval art in Southern Italy. However, the church shows problems of damp as well as clear evidences of flora, fungi and mold presence, and there is little knowledge of the pictorial methodologies used. Raman spectroscopy allowed to determine the palette and to reconstruct the worksite and the chronological sequence of the various paint layers. Kaolinite, calcite, carbon black, hematite, massicot, goethite, indigo and azurite were identified as pigments along with synthetic pigments, like phthalocyanine blue and chrome yellow. Attenuated total reflectance‐Fourier transform infrared spectroscopy suggested the presence of egg as a binder in some pictorial layers. The conservation state of the crypt is poor, and detachments of pigmented layers are frequent because of the presence of subflorescence and efflorescence: nitrate, sulfate and chloride salts have been identified spectroscopically and quantified by ion chromatography. The extensive use of kaolinite in Santi Stefani, actually not uncommon in Medieval art, is observed for the first time in a crypt of Puglia: its use to stabilize some pigments and to improve their adhesion on substrate is proposed. Copyright © 2015 John Wiley & Sons, Ltd.