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The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

The authors establish a result concerning the L²-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L²-convergence rate is established.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

Due to unceasing declination in environment, sustainable agro-food supply chains have become a topic of concern to business, government organizations and customers. The purpose of this study is to examine a problem associated with sustainable network design in context of Indian agro-food grain supply chain.

A mixed integer nonlinear programming (MINLP) model is suggested to apprehend the major complications related with two-echelon food grain supply chain along with sustainability aspects (carbon emissions). Genetic algorithm (GA) and quantum-based genetic algorithm (Q-GA), two meta-heuristic algorithms and LINGO 18 (traditional approach) are employed to establish the vehicle allocation and selection of orders set.

The model minimizes the total transportation cost and carbon emission tax in gathering food grains from farmers to the hubs and later to the selected demand points (warehouses). The simulated data are adopted to test and validate the suggested model. The computational experiments concede that the performance of LINGO is superior than meta-heuristic algorithms (GA and Q-GA) in terms of solution obtained, but there is trade-off with respect to computational time.

In literature, inadequate study has been perceived on defining environmental sustainable issues connected with agro-food supply chain from farmer to final distribution centers. A MINLP model has been formulated as practical scenario for central part of India that captures all the major complexities to make the system more efficient. This study is regulated to agro-food Indian industries.

The suggested network design problem is an innovative approach to design distribution systems from farmers to the hubs and later to the selected warehouses. This study considerably assists the organizations to design their distribution network more efficiently.

The author investigates realized comoments that overcome the drawback of conventional ones and derive the following findings. First, the author proves that (even generalized) geometric implied lower-order comoments yield neither geometric realized third comoment nor fourth moment. This is in contrast to previous studies that produce geometric realized third moment and arithmetic realized higher-order moments through lower-order implied moments. Second, arithmetic realized joint cumulants are obtained through complete Bell polynomials of lower-order joint cumulants. This study’s realized measures are unbiased estimators and they can, therefore, overcome the drawbacks of conventional realized measures.

The purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.

The paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.

The geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.

All results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

The purpose of this paper is to improve the tactical planning of the stakeholders of the midstream liquefied natural gas (LNG) supply chain, using an optimisation approach. The results can contribute to enhance the proactivity on significant investment decisions.

A decision support tool (DST) is proposed to minimise the operational cost of a fleet of vessels. Mixed integer linear programming (MILP) used to perform contract assignment combined with a genetic algorithm solution are the foundations of the DST. The aforementioned methods present a formulation of the maritime transportation problem from the scope of tramp shipping companies.

The validation of the DST through a realistic case study illustrates its potential in generating quantitative data about the cost of the midstream LNG supply chain and the annual operations schedule for a fleet of LNG vessels.

The LNG transportation scenarios included assumptions, which were required for resource reasons, such as omission of stochasticity. Notwithstanding the assumptions made, it is to the authors’ belief that the paper meets its objectives as described above.

Potential practitioners may exploit the results to make informed decisions on the operation of LNG vessels, charter rate quotes and/or redeployment of existing fleet.

The research has a novel approach as it combines the creation of practical management tool, with a comprehensive mathematical modelling, for the midstream LNG supply chain. Quantifying future fleet costs is an alternative approach, which may improve the planning procedure of a tramp shipping company.

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.