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Mechanical allodynia impinges on the life quality of patients. Hen Egg Lysozyme (HEL) is a substance extracted from eggs that is commonly used to inhibit bacterial activity. The role of HEL in regulating and treating pain is unclear. Here, we find that HEL selectively attenuates static mechanical allodynia of mice induced by complete Freund's adjuvant (CFA), spinal nerve ligation (SNL) and chemotherapeutic agent. RNA-seq screening reveals that CFA significantly reduces the expression of Parkin in dorsal root ganglion (DRG) neurons of mice, while pre-administration of HEL increases the expression of Parkin and remits the static mechanical allodynia induced by Parkin-siRNA. Moreover, HEL increases the interaction between nuclear respiratory factor 1 (NRF1) and histone acetyltransferase P300 and then enhances the NRF1 mediated histone acetylation in prkn promoter region in DRGs of mice. Further, Parkin interacts with mechanotransducing ion channel TACAN (Tmem120a) and knockdown of Parkin significantly increases the membrane trafficking of TACAN in sensory neurons of mice. While pre-administration of HEL inhibits the increased membrane trafficking of TACAN in sensory neurons of mice induced by Parkin-siRNA. In addition, pre-given of HEL also significantly attenuates the static mechanical allodynia induced by overexpression of TACAN in mice, and the effect of HEL can be blocked by Parkin-siRNA. This indicates that HEL increases the expression of Parkin through epigenetic mechanisms and then decreases TACAN membrane trafficking in sensory neurons to relieve static mechanical hypersensitivity. Therefore, we reveal a novel function of HEL, which is a potential substance for the treatment of static mechanical pain.

With the global express delivery industry growing rapidly, the service that uses high-speed rail (HSR) passenger trains to carry parcels has been introduced in China, signaling that the competition between HSR and air transport is no longer limited to the passenger sector. In this paper, we build a simple model to study the competition between air and rail in both the passenger market and the cargo market. We consider the transport operators face passengers directly but they rely on a forwarder at the downstream for the cargo service. Three scenarios are investigated: 1) both the passenger and the cargo sectors are only served by air transport; 2) the passenger sector is served by both air transport and HSR while the cargo sector is only served by air transport; and 3) both sectors are served by both transport modes. We find that when airlines use aircraft belly to transport cargo while the belly capacity is limited, it is possible that introducing HSR as a competitor in the passenger sector is social welfare deteriorating. However, social welfare will always be improved if HSR enters not only the passenger sector but also the cargo sector.

This paper sets up an integrated economic model to analyze an optimal public-private partnership (PPP) in financing a high-speed rail (HSR) project. The model considers the HSR's spillover onto the regional economy, which is uncertain in terms of both the direction (i.e., benefiting or harming the regional economy) and magnitude. The optimal private ownership is found to increase with the expected value of the marginal economic spillover of HSR traffic. In view of the risk sharing, the government also raises the private ownership when there is a higher uncertainty concerning the marginal spillover. However, when either the expected value of the marginal spillover or its uncertainty gets too high, the government may choose not to adopt PPP, but rather to entirely finance HSR projects with public funds. Essentially, in this case, PPP would require too much private ownership and as a result, seriously reduce social welfare. Finally, we apply our analytical results to offer an explanation for why China has so far implemented PPP for HSR construction only in its eastern/coastal regions.

"In this paper we present a unified theory of convergence results in the study of abstract problems. To this end we introduce a new mathematical object, the so-called Tykhonov triple $\cT=(I,\Omega,\cC)$, constructed by using a set of parameters $I$, a multivalued function $\Omega$ and a set of sequences $\cC$. Given a problem $\cP$ and a Tykhonov triple $\cT$, we introduce the notion of well-posedness of problem $\cP$ with respect to $\cT$ and provide several preliminary results, in the framework of metric spaces. Then we show how these abstract results can be used to obtain various convergences in the study of a nonlinear equation in reflexive Banach spaces. "

We model the vertical investment of a container shipping line in the port capacity in a two-port system. Our analytical and numerical analyss suggests that the relative scale of the capacity invest...

In this paper, we prove the weak convergence of a modified extragradient algorithm for solving a variational inequality problem involving a pseudomonotone operator in an infinite dimensional Hilbert space. Moreover, we establish further the R-linear rate of the convergence of the proposed algorithm with the assumption of error bound. Several numerical experiments are performed to illustrate the convergence behaviour of the new algorithm in comparisons with others. The results obtained in the paper have extended some recent results in the literature.

We consider a mixed variational problem governed by a nonlinear operator and a set of constraints. Existence, uniqueness and convergence results for this problem havealreadybeen obtained in the literature. In this current paper we complete these results by proving the well-posedness of the problem, in the sense of Tykhonov. To this end we introduce a family of approximating problems for which we state and prove various equivalence and convergence results. We illustrate these abstract results in the study of a frictionless contact model with elastic materials. The process is assumed to be static and the contact is with unilateral constraints. We derive a weak formulation of the model which is in the form of a mixed variational problem with unknowns being the displacement field and the Lagrange multiplier. Then, we prove various results on the corresponding mixed problem, including its well-posedness in the sense of Tykhonov, under various assumptions on the data. Finally, we provide mechanical interpretation of our results.

In this study, we propose nonemptiness and boundedness of the solution set for a bifunction variational inequality problem with P-strict feasibility in reflexive Banach spaces. As a novel concept, P-strict feasibility for a bifunction variational inequality is introduced. Moreover, it is proved that a pseudomonotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is P-strictly feasible in reflexive Banach spaces. Finally, some examples are given to illustrate the validity of the main results.

The overarching goal of this paper is to introduce and investigate a new nonlinear system driven by a nonlinear differential equation, a history-dependent quasivariational inequality, and a parabolic variational inequality in Banach spaces. Such a system can be used to model quasistatic frictional contact problems for viscoelastic materials with long memory, damage and wear. By using the Banach fixed point theorem, we prove an existence and uniqueness theorem of solution for such a system under some mild conditions. As a novel application, we obtain a unique solvability of a quasistatic viscoelastic frictional contact problem with long memory, damage and wear.

We consider a history-dependent variational–hemivariational inequality with unilateral constraints in a reflexive Banach space. The unique solvability of the inequality follows from an existence and uniqueness result obtained in Sofonea and Migórski (2016, 2018). In this current paper we introduce and study a generalized penalty method associated to the inequality. To this end we consider a sequence of generalized penalty problems, governed by a parameter and an operator . We prove the unique solvability of the penalty problems as well as the convergence of corresponding solutions sequence to the solution of original problem. These results extend the previous results in Sofonea etal. (2018) and Xiao and Sofonea (2019). Finally, we illustrate them in the study of a history-dependent problem with unilateral boundary conditions which describes the quasistatic evolution of a rod–spring system under the action of given applied force.

We consider an initial and boundary value problem \begin{document}$ {{\mathcal{P}}} $\end{document} which describes the frictionless contact of a viscoplastic body with an obstacle made of a rigid body covered by a layer of elastic material. The process is quasistatic and the time of interest is \begin{document}$ \mathbb{R}_+ = [0,+\infty) $\end{document} . We list the assumptions on the data and derive a variational formulation \begin{document}${{\mathcal{P}}}_V $\end{document} of the problem, in a form of a system coupling an implicit differential equation with a time-dependent variational-hemivariational inequality, which has a unique solution. We introduce the concept of Tykhonov triple \begin{document}$ {{\mathcal{T}}} = (I,\Omega, {{\mathcal{C}}}) $\end{document} where \begin{document}$ I $\end{document} is set of parameters, \begin{document}$ \Omega $\end{document} represents a family of approximating sets and \begin{document}${{\mathcal{C} }} $\end{document} is a set of sequences, then we define the well-posedness of Problem \begin{document}${{\mathcal{P}}}_V $\end{document} with respect to \begin{document}$ {{\mathcal{T}}}$\end{document} . Our main result is Theorem 3.4, which provides sufficient conditions guaranteeing the well-posedness of \begin{document}$ {{\mathcal{P} }}_V $\end{document} with respect to a specific Tykhonov triple. We use this theorem in order to provide the continuous dependence of the solution with respect to the data. Finally, we state and prove additional convergence results which show that the weak solution to problem \begin{document}$ {{\mathcal{P}}} $\end{document} can be approached by the weak solutions of different contact problems. Moreover, we provide the mechanical interpretation of these convergence results.

In this paper, we are denoted to introducing the strict feasibility of a variational inclusion problem as a novel notion. After proving a new equivalent characterization for the nonemptiness and boundedness of the solution set for the variational inclusion problem under consideration, it is proved that the nonemptiness and boundedness of the solution set for the variational inclusion problem with a maximal monotone mapping is equivalent to its strict feasibility in reflexive Banach spaces.

In this paper, we focus on distributionally robust chance constrained problems (DRCCPs) under general moments information sets. By convex analysis, we obtain an equivalent convex programming form for DRCCP under assumptions that the first and second order moments belong to corresponding convex and compact sets respectively. We give some examples of support functions about matrix sets to show the tractability of the equivalent convex programming and obtain the closed form solution for the worst case VaR optimization problem. Then, we present an equivalent convex programming form for DRCCP under assumptions that the first order moment set and the support subsets are convex and compact. We also give an equivalent form for distributionally robust nonlinear chance constrained problem under assumptions that the first order moment set and the support set are convex and compact. Moreover, we provide illustrative examples to show our results.