Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

A Closed Metallomolecular Cage that can Open its Aperture by Disulfide Exchange

A closed metallomolecular cage based on the tris(saloph) framework, in which its aperture can be opened by disulfide exchange, was designed. At the apertures of the molecular cage, bridging diamine ligands having a disulfide bond were introduced to close the cage structure. These bridging ligands efficiently blocked the uptake of a guest, Cs⁺, but the presence of a thiolate anion significantly accelerated the guest uptake. This clearly means that this cage complex became open by the addition of the thiolate anion, because the cage closure becomes more dynamic due to the disulfide exchange reaction.     

A calibrated model of local food system of Hawaii: What are the economic implications of the state's food goals and policies?

We develop a fully calibrated positive mathematical programming model for Hawaii's local food systems—which captures the production and the consumer sides of the market. Then we use the model to assess two proposed policies—a general excise tax (GET) exemption on locally produced foods, and an investment in agricultural infrastructure. For the GET exemption case, our results indicate an economic gain of $118 per $100 cost. On the other hand, an investment in 1,200 acres of land injected to support local production may generate an economic gain of up to $357 per $100 annual cost of the investment. However, these estimates should be considered preliminary, and thus viewed with caution. Although the model is used to capture Hawaii's local food systems, we believe that our model is generalizable and can be adopted by other economies to assess their respective food localization policies. Recommendations for Resource Managers

• Local food policies need to be based on quantitative terms instead of mere armchair speculation because often their potential outcomes may vary significantly.

• The current modeling framework demonstrates the potential of using positive mathematical programming (PMP) in capturing the intricacies of local food systems. However, this exploratory exercise should be viewed as preliminary in nature and the ensuing results were taken with caution because many important factors such as labor availability may have been left out.

• Thus, further model refinements are necessary to better capture the complexities of local food systems such as farm heterogeneity, availability of farm labor, water availability, and interisland transportation of farm products in the case of Hawaii.

     

Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.     

G2-manifolds and the ADM formalism

In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold M and prove the orbits of the constrained Hamiltonian dynamical system correspond to $G_2$-manifolds foliated by hypersurfaces diffeomorphic to $M\times \mathrm{SO}(3)$.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.