The paper considers issues on the theoretical substantiation of options for choosing an optimal strategy to integrate an agricultural enterprise into the wholesale market by using methodological tools of the non-cooperative game theory. We have proposed modeling the behavior of an agrarian enterprise in the market by achieving a Nash equilibrium under various scenarios of competitors’ activities and volumes of information on market conditions. The methodology has been substantiated to apply the iterative algorithms to calculate equilibria in a general class of non-quadratic convex polyhedra in order to form the methodologies and construct algorithms for a behavior of agricultural enterprises in market activity. It was determined that decision-making occurs in parallel to the real conditions of activity of an agricultural enterprise in the wholesale market. The comprehensive application of numerical methods based on solving the optimization problems provides a smooth approach to the Nash equilibrium. A game can have multiple isolated Nash equilibria if players have non-quadratic payment functions when solving such problems. Based on the above, the results were determined of local convergence, since global results have strong constraints in non-quadratic problems. However, there is a connection with semi-global practical asymptotic stability if players have quadratic payoff functions. It has been shown that there is a shift in the convergence in proportion to the amplitudes of disturbance signals and the third derivative of payoff functions for non-quadratic payoff functions. This shift in the convergence corresponds to the shift in a numerical example. It has been determined that the learning strategy developed in accordance with the main provisions of the theory of games remains attractive if one has partial information on the state of the market. Application of the indicated action strategy provides a company with a possibility to improve its initial position by measuring its own payoff values only and not using estimates of potentially uncertain parameters. It has been proposed to use applied tools from the game theory to determine an optimal action strategy for an agricultural enterprise for its integration into the wholesale market of vegetable products

/pdf/optimizing-the-strategy-of-activities-using-numerical-1oqocrlqy5.pdf

Optimizing the Strategy of Activities Using Numerical Methods for Determining Equilibrium

In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a Ambrosetti-Rabinowitz-type condition. The interaction of the nonlinearities with the spectrum of the fractional operator will used to study the existence and multiplicity of solutions. The main technical result proves that a local minimum in $C_{s}^0(\overline{\Omega})$ is also a local minimum in $W^{s,p}_0$ for nonlinearities with exponential growth.

Critical fractional elliptic equations with exponential growth without Ambrosetti-Rabinowitz type condition

In this paper we establish, using variational methods combined with the Moser–Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a Ambrosetti–Rabinowitz-type condition. The interaction of the nonlinearities with the spectrum of the fractional operator will be used to study the existence and multiplicity of solutions. The main technical result proves that a local minimum in $$C_{s}^0 (\overline{\Omega })$$
 is also a local minimum in $$W^{s,p}_0$$
 for exponentially growing nonlinearities.

Critical fractional elliptic equations with exponential growth

Flexible/stretchable electronics constitute a class of prospective technology incorporating stretchable/bendable/twistable components such that unprecedented properties superior to those of conventional rigid/brittle electronics are realized over [...].

Editorial for the Special Issue on Structural Analyses and Designs for Flexible/Stretchable Electronics

This paper introduces a chip-level oven-controlled system for improving the temperature stability of MEMS resonators wherein we designed the resonator and the micro-hotplate using MEMS technology, then bounding them in a package shell at the chip level. The resonator is transduced by AlN film, and its temperature is monitored by temperature-sensing resistors on both sides. The designed micro-hotplate is placed at the bottom of the resonator chip as a heater and insulated by airgel. The PID pulse width modulation (PWM) circuit controls the heater according to the temperature detection result to provide a constant temperature for the resonator. The proposed oven-controlled MEMS resonator (OCMR) exhibits a frequency drift of 3.5 ppm. Compared with the previously reported similar methods, first, the OCMR structure using airgel combined with a micro-hotplate is proposed for the first time, and the working temperature is extended from 85 °C to 125 °C. Second, our work does not require redesign or additional constraints on the MEMS resonator, so the proposed structure is more general and can be practically applied to other MEMS devices that require temperature control.

/pdf/a-micro-hotplate-based-oven-controlled-system-used-to-3kc52nqr.pdf

A Micro-Hotplate-Based Oven-Controlled System Used to Improve the Frequency Stability of MEMS Resonators

We consider the following fractional p-Laplacian equation: , where , , , is the fractional -Laplacian, and and for a.e. . has the subcritical growth but higher than ; however, the nonlinearity may change sign. If is coercive, we investigate the existence of ground state solutions for p-Laplacian equation.

/pdf/non-nehari-manifold-method-for-fractional-p-laplacian-4w199o0iao.pdf

Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity

With the development of flexible electronics, flexible microheaters have been applied in many areas. Low power consumption and fast response microheaters have attracted much attention. In this work, systematic thermal and mechanical analyses were conducted for a kind of flexible microheater with two different wire structures. The microheater consisted of polyethylene terephthalate (PET) substrate and copper electric wire with graphene thin film as the middle layer. The steady-state average temperature and heating efficiency for the two structures were compared and it was shown that the S-shaped wire structure was better for voltage-controlled microheater other than circular-shaped structure. In addition, the maximum thermal stress for both structures was from the boundary of microheaters, which indicated that not only the wire structure but also the shape of micro heaters should be considered to reduce the damage caused by thermal stress. The influence resulting from the thickness of graphene thin film also has been discussed. In all, the heating efficiency for flexible microheaters can be up to 135 °C/W. With the proposed PID voltage control system, the response time for the designed microheater was less than 10 s. Moreover, a feasible fabrication process flow for these proposed structures combing thermal analysis results in this work can provide some clues for flexible microheaters design and fabrication in other application areas.

/pdf/design-and-thermal-analysis-of-flexible-microheaters-193oi9bp.pdf

Design and Thermal Analysis of Flexible Microheaters

As a powerful tool in scientific research and industrial technologies, the cold atom absolute gravity sensor (CAGS) based on cold atom interferometry has been proven to be the most promising new generation high-precision absolute gravity sensor. However, large size, heavy weight, and high–power consumption are still the main restriction factors of CAGS being applied for practical applications on mobile platforms. Combined with cold atom chips, it is possible to drastically reduce the complexity, weight, and size of CAGS. In this review, we started from the basic theory of atom chips to chart a clear development path to related technologies. Several related technologies including micro-magnetic traps, micro magneto–optical traps, material selection, fabrication, and packaging methods have been discussed. This review gives an overview of the current developments in a variety of cold atom chips, and some actual CAGS systems based on atom chips are also discussed. We summarize by listing some of the challenges and possible directions for further development in this area.

/pdf/review-of-atom-chips-for-absolute-gravity-sensors-ippx7kpd.pdf

Wenfeng He

Papers

Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity

Design and Thermal Analysis of Flexible Microheaters

Review of Atom Chips for Absolute Gravity Sensors