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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.

Fuzzy variational inequalities (FVIs) are modeling tools used to characterize a variety of fuzzy decision making problems arising in mathematical optimization, control theory, operations research, and game theory. Fractional order delay differential equations are also finding applications in all disciplines including chemistry, physics, and finance. The aim of this paper is to introduce and study a new dynamical fuzzy system, named the fractional differential fuzzy variational inequality (FDFVI) with delay, which bridges these two areas of research and broadens the class of problems amenable to be studied under the fuzzy environments. By using the KKM theorem and monotonicity arguments, we show that the solution set of the FVI is nonempty, convex and compact. We also establish the upper semicontinuity of the solution mapping U of the FVI involved in the FDFVI with delay. Moreover, we obtain an existence of the mild solution for the FDFVI with delay by employing Bohnenblust-Karlin's fixed point theorem. In addition, we provide an approximating algorithm to find a solution of the FDFVI with delay. Finally, we give two numerical examples to illustrate our main results.

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. "

The main goal of this paper is to study a class of differential nonlinear system involving parabolic variational and history-dependent hemivariational inequalities in Banach spaces by using the penalty method. We first construct a penalized problem for such a nonlinear system and then derive the existence and uniqueness of its solution to obtain an approximating sequence for the nonlinear system. Moreover, we prove the strong convergence of the obtained approximating sequence to the solution of the original nonlinear system when the penalty parameter converges to zero. Finally, we apply the obtained convergence result to a long-memory elastic frictional contact problem with wear and damage in mechanics. First part title: Introduction Second part title: Preliminaries Third part title: Convergence result for (1.1) Fourth part title: An application

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.

The present paper is devoted to building degree theory for a generalized mixed quasi-variational inequality in finite dimensional spaces. Then, by employing the obtained results, we prove the existence and stability of solutions to the considered generalized mixed quasi-variational inequality.

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.

This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense of Pareto to a class of multi-objective discrete optimal control problems with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order optimality conditions for a multi-objective mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a multi-objective discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.

This paper introduces a class of differential fuzzy variational inequalities, the model provides an efficient approach for solving many dynamic multi-objective optimization problems in fuzzy environments. An existence theorem of the Caratheodory weak solution for the model is established under some suitable assumptions. An algorithm, supported by the convergence analysis, is developed to find the solution. In addition, some examples are given to illustrate the application and the algorithm.

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.

In this paper, we propose two inertial algorithms with new stepsize rule for solving a monotone and Lipschitz variational inequality in a Hilbert space and prove some weak and strong convergence th...

We consider a frictionless contact problem, Problem [Formula: see text], for elastic materials. The process is assumed to be static and the contact is modelled with unilateral constraints. We list the assumptions on the data and derive a variational formulation of the problem, Problem [Formula: see text]. Then we consider a perturbation of Problem [Formula: see text], which could be frictional, governed by a small parameter [Formula: see text]. This perturbation leads in a natural way to a family of sets [Formula: see text]. We prove that Problem [Formula: see text] is well-posed in the sense of Tykhonov with respect to the family [Formula: see text]. The proof is based on arguments of monotonicity, pseudomonotonicity and various estimates. We extend these results to a time-dependent version of Problem [Formula: see text]. Finally, we provide examples and mechanical interpretation of our well-posedness results, which, in particular, allow us to establish the link between the weak solutions of different contact models.

In this paper, we introduce a new algorithm for solving a variational inequality problem in a Hilbert space. The algorithm originates from an explicit discretization of a dynamical system in time. ...

In this paper, we introduce two golden ratio algorithms with new stepsize rules for solving pseudomonotone and Lipschitz variational inequalities in finite dimensional Hilbert spaces. The presented stepsize rules allow the resulting algorithms to work without the prior knowledge of the Lipschitz constant of operator. The first algorithm uses a sequence of stepsizes which is previously chosen, diminishing and non-summable. While the stepsizes in the second one are updated at each iteration and by a simple computation. A special point is that the sequence of stepsizes generated by the second algorithm is separated from zero. The convergence as well as the convergence rate of the proposed algorithms are established under some standard conditions. Also, we give several numerical results to show the behavior of the algorithms in comparisons with other algorithms.

We consider a mathematical model which describes the equilibrium of an elastic body in contact with a foundation. The contact is frictionless and is modeled with a nonsmooth interface law which involves unilateral constraints and subdifferential conditions. The weak formulation of the model is in the form of an elliptic hemivariational inequality governed by a number of parameters. We prove the unique weak solvability of the problem, then we state and prove a continuous dependence result of the solution with respect to the data and parameters. Next, we formulate a boundary optimal control problem for which we prove the existence of optimal pairs. We also study the dependence of the optimal pairs with respect to the data and parameters and prove a convergence result. The proofs are based on arguments of monotonicity, lower semicontinuity and Clarke subdifferential calculus.

In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint qualifications of Zangwill type, Abadie type and Mangasarian–Fromovitz type as well as a regularity condition of Abadie type are proposed in a nonsmooth setting. The connections between these proposed conditions are established. They are applied to develop second-order Karush–Kuhn–Tucker necessary optimality conditions for local (weak, Geoffrion properly) efficient solutions to the considered problem. Examples are also given to illustrate the obtained results.

We expand the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of the nonlinear ill-posed problem presented in Jin and Hou (Numer Math 83:139–159, 1999) by weakening the conditions needed in Jin and Hou [13]. Using a center-type Lipschitz condition instead of a Lipschitz-type condition used in Jin and Hou [13], Scherzer et al. (SIAM J Numer Anal 30:1796–1838, 1993), we obtain a tighter convergence analysis. Numerical examples are presented to show that our results apply but earlier ones do not apply to solve equations.

Effective treatments for patients suffering from heat hypersensitivity are lacking, mostly due to our limited understanding of the pathogenic mechanisms underlying this disorder. In the nervous system, activating transcription factor 4 (ATF4) is involved in the regulation of synaptic plasticity and memory formation. Here, we show that ATF4 plays an important role in heat nociception. Indeed, loss of ATF4 in mouse dorsal root ganglion (DRG) neurons selectively impairs heat sensitivity. Mechanistically, we show that ATF4 interacts with transient receptor potential cation channel subfamily M member-3 (TRPM3) and mediates the membrane trafficking of TRPM3 in DRG neurons in response to heat. Loss of ATF4 also significantly decreases the current and KIF17-mediated trafficking of TRPM3, suggesting that the KIF17/ATF4/TRPM3 complex is required for the neuronal response to heat stimuli. Our findings unveil the non-transcriptional role of ATF4 in the response to heat stimuli in DRG neurons., The molecular mechanisms mediating nociception are unclear. Here, the authors show that the Activating Transcription Factor 4 (ATF4) is important for the response to heat nociception in mice and ATF4 role in mediating protein trafficking in dorsal root ganglion neurons.

Consider an abstract Problem P in a metric space (X; d) assumed to have a unique solution u. The aim of this paper is to compare two convergence results u'n → u and u''n → u, both in X, and to construct a relevant example of convergence result un → u such that the two convergences above represent particular cases of this third convergence. To this end, we use the concept of Tykhonov triple. We illustrate the use of this new and nonstandard mathematical tool in the particular case of hemivariational inequalities in reflexive Banach space. This allows us to obtain and to compare various convergence results for such inequalities. We also specify these convergences in the study of a mathematical model, which describes the contact of an elastic body with a foundation and provide the corresponding mechanical interpretations.

We consider an abstract minimization problem in reflexive Banach spaces together with a specific family of approximating sets, constructed by perturbing the cost functional and the set of constraints. For this problem, we state and prove various well-posedness results in the sense of Tykhonov, under different assumptions on the data. The proofs are based on arguments of lower semicontinuity, compactness and Mosco convergence of sets. Our results are useful in the study of various mathematical models in contact mechanics. To provide examples, we introduce 2 models, which describe the equilibrium of an elastic body in contact with a rigid body covered by a rigid-plastic and an elastic material, respectively. The weak formulation of each model is in the form of a minimization problem for the displacement field. We use our abstract well-posedness results in the study of these minimization problems. In this way, we obtain existence, uniqueness and convergence results, and moreover, we provide their mechanical interpretations.

We consider an elliptic variational–hemivariational inequality with constraints in a reflexive Banach space, denoted $$\mathcal{P}$$ , to which we associate a sequence of inequalities $$\{\mathcal{P}_n\}$$ . For each $$n\in \mathbb {N}$$ , $$\mathcal{P}_n$$ is a variational–hemivariational inequality without constraints, governed by a penalty parameter $$\lambda _n$$ and an operator $$P_n$$ . Such inequalities are more general than the penalty inequalities usually considered in literature which are constructed by using a fixed penalty operator associated to the set of constraints of $$\mathcal{P}$$ . We provide the unique solvability of inequality $$\mathcal{P}_n$$ . Then, under appropriate conditions on operators $$P_n$$ , we state and prove the convergence of the solution of $$\mathcal{P}_n$$ to the solution of $$\mathcal{P}$$ . This convergence result extends the results previously obtained in the literature. Its generality allows us to apply it in various situations which we present as examples and particular cases. Finally, we consider a variational–hemivariational inequality with unilateral constraints which arises in Contact Mechanics. We illustrate the applicability of our abstract convergence result in the study of this inequality and provide the corresponding mechanical interpretations.

We consider a general mathematical model which describes the quasistatic contact of a deformable body with an obstacle, the so-called foundation. The material’s behaviour is modeled with a visco-elastic-type constitutive law and the contact is described with a general interface law associated to a version of Coulomb’s law of dry friction. We list the assumptions on the data and provide relevant examples of constitutive laws and boundary conditions. Then, we derive two different variational formulations of the model in which the unknowns are the displacement and the strain field, respectively. We prove the equivalence of these formulations. Finally, we use recent arguments of sweeping process in order to obtain the existence of a unique weak solution to the contact model.

Adults are more likely to suffer from chronic pain than minors, and its underlying mechanism remains unclear. SIRT1 an important age-related protein with function of lifespan extension; whether SIRT1 plays a role in the different pain vulnerability of adult and juvenile remains unclear. Here, we found that the expression level of SIRT1 in dorsal root ganglia (DRG) was related to the pain vulnerability. After nerve injury, the expression of SIRT1 in DRG was decreased in adult rodents whereas increased in juvenile rodents. Differential manipulation of SIRT1 abolished the different pain vulnerability between adult and juvenile rodents. Furthermore, SIRT1 interacted with ClC-3 channel and mediated ClC-3 membrane trafficking and Cl- current in DRG neurons. Differential manipulation of ClC-3 also abolished the difference in pain vulnerability between adult and juvenile rodents. The different anti-inflammatory ability determined the different change trends of SIRT1 and ClC-3 trafficking contributed to the different pain vulnerability in adult and juvenile rodents. In addition, the serum SIRT1 level was negatively correlated with the pain score in patients with chronic pain. These findings revealed the mechanism of the difference in pain vulnerability between adult and juvenile rodents and provided evidence for age-specific treatment of chronic pain.

In this paper, we introduce a new Tykhonov-type well-posedness concept for elliptic hemivariational inequalities, governed by an approximating function h. We characterize the well-posedness in terms of the metric properties of the family of approximating sets, under various assumptions on h. Then, we use the well-posedness properties in order to obtain convergence results of the solution with respect to the data. The proofs are based on arguments of monotonicity combined with the properties of the Clarke directional derivative. Our results provide mathematical tools in the study of a large number of static problems in Contact Mechanics. To provide an example, we consider a mathematical model which describes the equilibrium of a rod–spring system with unilateral constraints. We prove the unique weak solvability of the model, and then we illustrate our abstract convergence results in the study of this contact problem and provide the corresponding mechanical interpretations.

In (J. Optim. Theory Appl. 183:139–157, 2019) we introduced and studied the concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces. Our aim of this current paper is to extend the results in (J. Optim. Theory Appl. 183:139–157, 2019) to a system which consists of two independent problems denoted by P and Q, coupled by a nonlinear equation. Following the terminology used in literature we refer to such a system as a split problem. We introduce the concept of well-posedness for the abstract split problem and provide its characterization in terms of metric properties for a family of approximating sets and in terms of the well-posedness for the problems P and Q, as well. Then we illustrate the applicability of our results in the study of three relevant particular cases: a split variational–hemivariational inequality, an elliptic variational inequality and a history-dependent variational inequality. We describe each split problem and clearly indicate the family of approximating sets. We provide necessary and sufficient conditions which guarantee the well-posedness of the split variational–hemivariational inequality. Moreover, under appropriate assumptions on the data, we prove the well-posedness of the split elliptic variational inequality as well as the well-posedness of the split history-dependent variational inequality. We illustrate our abstract results with various examples, part of them arising in contact mechanics.

In this paper, we introduce and study a class of nonsmooth Stackelberg equilibrium problems with differential revenue functions and nonsmooth cost functions. First, we describe the best response set of the follower and the best strategy set of the leader for the considered nonsmooth Stackelberg equilibrium problem via mixed variational inequalities. Then, by using the resolvent operator method and the Banach fixed point theorem, we show the existence and uniqueness of its solution.

To evaluate the comparative therapeutic efficacy of radiofrequency ablation (RFA) and hepatic resection (HR) for breast cancer liver metastases (BCLMs). Studies that had examined the outcomes for both RFA and HR for BCLM were identified by searching the electronic databases PubMed, EMBASE, and the Cochrane Library. Pooled analyzes of the overall survival (OS), disease-free survival (DFS), and short-term outcomes of BCLM were performed. Patients with BCLM gained many more survival benefits from HR than from RFA with regard to the 3-year OS rate (combined odds ratio (OR) 0.41, 95% confidence interval (CI) 0.29–0.59, P

To investigate airlines’ incentives in operational fuel efficiency improvement, it might be important to consider financial hedge as its substitute. In this paper, we build a simple theoretical model to compare the implications of fuel financial hedge and operational fuel efficiency improvement on airlines’ expected profit. We find that financial hedge is more efficient in reducing airlines’ profit volatility/risk exposure, while operational improvement will generate a higher expected profit level when its effectiveness is sufficiently high. With market competition, operational improvement will be less prevalent. Furthermore, a fuel/carbon tax makes financial hedge less attractive and operational improvement more attractive.

In this paper, we introduce some new algorithms for solving the equilibrium problem in a Hilbert space which are constructed around the proximal-like mapping and inertial effect. Also, some...

The prognosis for patients with liver metastases from gastric cancer is very poor. Nevertheless, standard therapeutic strategies have not been established yet. The impact of hepatic surgical treatment on survival of patients with metachronous liver metastases from gastric cancer still remains controversial. We conducted a retrospective analysis on records of 436 patients who received radical gastrectomy (with D2 lymphadenectomy, regardless of hepatic surgical treatment) for gastric cancer with metachronous (≥ 3 months after gastrectomy) liver metastases in our center between 2001 and 2016. All patients were followed until 2017/10/31 or withdrawn from the follow-up because of death. The median interval for non-hepatic metastases of the 436 patients who underwent radical gastrectomy is 14 months. T (P = 0.041), N (P = 0.023) and lymphovascular invasion (P

This study identifies the key drivers for China's international trade delivered by air with an augmented gravity model, and investigates the country's air freight network using complex network analysis. Gravity model estimation suggests that income elasticity for airborne trade at country level is 1.1, whereas the values for the three major economic zones are significantly higher. More importantly, we found that for China's international trade by air, the composition of economy is a more important driver than the size of economy. These results suggest that the Chinese air cargo sector will outpace the overall economic growth, with leading airports in the economic zones well-positioned to grow into major freight gateways. Air cargo demand in China was not as high as past GDP numbers suggested in the past, but is likely to experience sustained growth in the years to come. Network analysis suggests that cargo traffic volumes are concentrated in the catchments of metropolitan regions, where passenger hubs also serve as air cargo bases. However, domestic air freights currently mainly flow through a relatively small point-to-point network, suggesting that the leading airports are yet to become cargo gateway hubs despite their significant growth potential.

In the present paper, we focus on a class of multivalued variational–hemivariational inequalities with pseudomonotone operator and constraint set in Hilbert spaces. By employing the penalty method and the Moreau–Yosida approximation technique, we construct an approximating problem for the original multivalued variational–hemivariational inequality under consideration. The main result in the paper shows that every weak cluster of the solution sequence for the approximating problem is always a solution of the original problem. Moreover, based on the obtained weak convergence result, another two strong convergence results are obtained when the condition of pseudomonotonicity is reinforced. Finally, we illustrate the application of our abstract results in the study of a frictionless contact problem in mechanics with unilateral constraint.

In this paper, we consider a class of Stackelberg quasi-equilibrium problem with two players in finite dimensional spaces. Existence and location of the Stackelberg quasi-equilibrium is discussed by employing the quasivariational inequality techniques and the fixed point arguments. The results presented in this paper generalize some corresponding ones due to Nagy [Nagy, S., Stackelberg equilibia via variational inequalities and projections, J. Global Optim., 57 (2013), 821–828].

In the present paper, we investigate a generalized differential mixed quasi-variational inequality consisting of a system of an ordinary differential equation and a generalized mixed quasi-variational inequality. By using an important result concerning the measurable selection, we prove the existence of Caratheodory weak solution to ´ the generalized differential mixed quasi-variational inequality. Then, with the existence result, we establish two stability results for the generalized differential mixed quasi-variational inequality under different conditions, i.e., upper semicontinuity and lower semicontinuity of the Caratheodory weak solution with respect to the ´ parameter, which is a perturbation of some mappings in the generalized mixed quasi-variational inequality.