Generalized Γ Calculus and Application to Interacting Particles on a Graph

Potential Analysis - The classical Bakry-Émery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as...     

The Newton–Wigner Problem in the Relativistic Quantum Mechanics of Free Particles

We discuss the old Newton–Wigner problem, which is understood as the problem of a correct coordinate interpretation of the relativistic quantum mechanics of free particles. This problem is still relevant for quantum field theory because the S-matrix approach assumes that asymptotic fields describe relativistic free quantum-mechanical particles. From the modern standpoint, the original solution of this problem by Newton and Wigner already cannot be considered sufficient because it admits the smearing of wave packets with a superlight velocity. We discuss a possibility of overcoming this difficulty. This possibility is connected with relativistic deformations of the standard Heisenberg algebra. We describe situations in which a sort of desingularization of the effective free Hamiltonian occurs for some special deformations, which possibly allows preserving sublight velocity in the theory.     

Four-Operator Splitting via a Forward–Backward–Half-Forward Algorithm with Line Search

In this article, we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward–backward–half-forward splitting and the Tseng’s algorithm with line search. At each iteration, our algorithm defines the step size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving nonlinearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a nonlinearly constrained least-square problem and we compare its performance with available methods in the literature.

     

Optimal business policies for a supplier–transporter–buyer channel with a price-sensitive demand

As the third party logistics partners (carriers) taking a more and more significant role in supply chain practices and customer service performance improvement, there is an emerging need for the studies on optimal channel coordination policies for business processes involving not only supplier and buyer (retailer), but also transportation partners. In this paper, we explicitly add a transportation partner with concave cost functions into the analysis for supplier–buyer channel coordination policies, and analyse the impact of coordination and pricing policies on supply chain profitability. The market demand is assumed to be a decreasing convex function of buyer's selling price (x), D(x)=d/x². Under this assumption, we quantify the improvement on total supply chain profitability when moving from a non-cooperative environment to a fully cooperative environment, and show that the joint annual profit of three partners in a cooperative environment can be at least twice of what may be achieved by three independently operated companies in a leader–follower business game. While in a real-world business environment, a perfect collaboration is hard to achieve, this result can be used to provide a quick estimation on the upper bound on the budget for profit sharing or discount offers among the supply chain partners.     

The ‘electromagnetic’ Wigner equation for an electron with spin

We derive and analyse the three-dimensional quantum Liouville equation for an electron with spin in an external electromagnetic field. By using methods of semigroup theory, we prove existence and uniqueness of the initial value problem. Expanding the solution into a series of pure states, we derive the existence of a generalized particle density and anL -estimate on the solution. The last section is devoted to an analysis of the classical and electrostatic limits.

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Zusammenfassung Die drei-dimensionale Quanten-Liouville Gleichung für ein Elektron mit Spin in einem äueren elektromagnetischen Feld wird hergeleitet und analysiert. Mit Hilfe der Halbgruppen-Theorie werden Existenz und Eindeutigkeit des Anfangswertproblems bewiesen. Aus der Entwicklung der Lösung in eine Reihe von reinen Zuständen schließen wir die Existenz einer verallgemeinerten Teilchendichte und erhalten eineL -Abschätzung für die Lösung. Im letzten Kapitel werden der klassische und elektrostatische Limes untersucht.

     

Unitary Representations of the Wigner Group ISL(2, ℂ) and A Two-Spinor Description of Massive Particles With An Arbitrary Spin

Based on Wigner unitary representations for the covering group ISL(2,?) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with an arbitrary spin that satisfy the Dirac–Pauli–Fierz equations. In the framework of a two-spinor formalism, we construct spin-polarization vectors and obtain conditions that fix the corresponding density matrices (the Behrends–Fronsdal projection operators) determining the numerators in the propagators of the fields of such particles. Using these conditions, we find explicit expressions for the particle density matrices with integer (Behrends–Fronsdal projection operators) and half-integer spin. We obtain a generalization of the Behrends–Fronsdal projection operators to the case of an arbitrary number D of space–time dimensions.     

Blow-up for a reaction–diffusion equation with variable coefficient

We study the blow-up behavior for positive solutions of a reaction–diffusion equation with nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point.     

Traveling fronts for a delayed reaction–diffusion system with a quiescent stage

In this paper, we study the traveling wave fronts of a delayed reaction–diffusion system with a quiescent stage for a single species population with two separate mobile and stationary states. By transforming the corresponding wave system into a scalar delayed differential equation with an integral term, we establish the existence of the minimal wave speed c_min, and the asymptotic behavior, monotonicity and uniqueness (up to a translation) of the traveling wave fronts. In particular, the effects of the delay and transfer rates on the minimal wave speed are studied.     

A Refinement of the Robertson–Schrödinger Uncertainty Principle and a Hirschman–Shannon Inequality for Wigner Distributions

Journal of Fourier Analysis and Applications - We propose a refinement of the Robertson–Schrödinger uncertainty principle (RSUP) using Wigner distributions. This new principle is...     

Berry-Esséen Bounds for Long Memory Moving Averages via Stein's Method and Malliavin Calculus

Using the Stein method on Wiener chaos introduced in Nourdin and Peccati [10], we prove Berry-Esséen bounds for long memory moving averages.     

Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations

In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational–hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational–hemivariational inequality and give some conditions under which the variational–hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational–hemivariational inequality and the well-posedness of corresponding inclusion problem.     

Random attractors for a Ginzburg–Landau equation with additive noise

The existence of a compact random attractor for the random dynamical system generated by the complex Ginzburg–Landau equation with additive white noise has been proved. And a precise estimate of the upper bound of the Hausdorff dimension of the random attractor is obtained.     

Extinction times for a birth–death process with weak competition

We consider a birth–death process with birth rates iλ and death rates iμ+i(i?1)θ, where i is the current state of the process. A positive competition rate θ is assumed to be small. In the supercritical case where λ > μ, this process can be viewed as a demographic model for a population with high carrying capacity around (λ?μ)/θ. The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as θ → 0. All three reproduction regimes λ > μ, λ < μ, and λ = μ are studied.