Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.     

Formation of low-temperature deformation-induced segregations of nickel in Fe–Ni-based austenitic alloys

ABSTRACT

The authors present the results of an investigation in Fe–Ni-Cr austenitic alloys of the low-temperature deformation-induced segregations of nickel that form in the micro regions being (i) located close to grain- and subgrain boundaries and (ii) characteristic of the concentration and magnetic inhomogeneities indicated by the appearance of a dark diffraction contrast at the electron diffraction patterns taken from these regions typical (at the same time) of an enhanced value of Curie temperature. The observed effects were connected with the micro distortions caused by the local change of lattice parameter because of an increase in nickel concentration, as well as in the result of a magnetostriction dilatation. Using methods of the X-ray energy dispersive spectroscopy (XEDS) and atomic-probe body-section radiography (tomography – APT) has made it possible to determine the borders of those regions of austenite that were characteristic of an enhanced concentration of nickel in the fields of the localisation of a deformation-induced segregation of nickel in the vicinity of grain (subgrain) boundaries of austenitic alloys of the types Fe–13Cr–30Ni and Fe–37Ni–3Ti.     

Microstructural stability and age-hardening behavior of Re-added dual two-phase Ni3Al and Ni3V intermetallic alloys

The effect of Re addition on the microstructure and hardening behaviour of the dual two-phase Ni₃Al (L1₂) and Ni₃V (D0₂₂) intermetallic alloy was investigated by scanning electron microscopy, transmission electron microscopy and Vickers hardness test. The two-phase eutectoid microstructure accompanying the Re-rich precipitates were observed in the channel region of the alloys in which Re substituted for Ni but not in those in which Re substituted for Al and V. The concomitant addition of Nb (or Ta) with Re more stabilized the two-phase eutectoid microstructure and consequently more induced the fine precipitates in the channel region. The annealing at temperatures below the eutectoid temperature was necessary to induce the fine precipitates in the channel region and thereby result in the precipitation hardening. The fine precipitation in the channel region and related hardening was attributed to the alloying feature so that Re is soluble in the A1 (fcc) phase at high temperatures and becomes less soluble in the two intermetallic phases decomposed from the A1 phase at low temperatures.     

Experimental and Theoretical Mechanistic Study on the Thermal Decomposition of 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline

The present paper is a continuation of comprehensive study regarding to synthesis and properties of pyrazoles and their derivatives. In its framework an experimental and theoretical studies of thermal decomposition of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline were performed. It was found, that the decompositions of the mentioned pyrazoline system in the solution and at the melted state proceed via completely different molecular mechanisms. These mechanisms have been explained in the framework of the Molecular Electron Density Theory (MEDT) with the computational level of B3LYP/6-31G(d). A Bonding Evolution Theory (BET) examination of dehydrochlorination of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline permits elucidation of the molecular mechanism. It was found, that on the contrary for most known HCl extrusion processes in solution, this reaction is realised via single-step mechanism.     

Design of organophosphorus materials for organic electronics and bio-applications

π-Extended molecules are key components for the development of materials science. In fact, polyaromatic structures are fundamental for the scientific and technological progress of fields such as organic electronics and bio-applications. Beneficial properties of π-extended structures are absorption in the visible region, often luminescence, high electron mobilities and stability. Common approaches to adjust the properties of polyaromatic structures to functional setups involve changes in shape and size at the molecular level. Recently, incorporating hetero-elements emerged as successful approach. In this regard, organophosphorus conjugated molecules are new materials holding great promise for potential applications. In this review, we comprehensively discuss the design/development of polyaromatic phosphorus materials and their applicability. We establish structure/property/applicability relationships to provide key guidelines for the engineering of newer, future applications. This article thus provides a source of information for the further development of this rapidly evolving field of research.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.