A Nash equilibrium solution in an oligopoly market: The search for Nash equilibrium solutions with replicator equations derived from the gradient dynamics of a simplex algorithm

The present analysis applies continuous time replicator dynamics to the analysis of oligopoly markets. In the present paper, we discuss continuous game problems in which decision-making variables for each player are bounded on a simplex by equalities and non-negative constraints. Several types of problems are considered under conditions of normalized constraints and non-negative constraints. These problems can be classified into two types based on their constraints. For one type, the simplex constraint applies to the variables for each player independently, such as in a product allocation problem. For the other type, the simplex constraint applies to interference among all players, creating a market share problem. In the present paper, we consider a game problem under the constraints of allocation of product and market share simultaneously. We assume that a Nash equilibrium solution can be applied and derive the gradient system dynamics that attain the Nash equilibrium solution without violating the simplex constraints. Models assume that three or more firms exist in a market. Firms behave to maximize their profits, as defined by the difference between their sales and cost functions with conjectural variations. The effectiveness of the derived dynamics is demonstrated using simple data. The present approach facilitates understanding the process of attaining equilibrium in an oligopoly market.     

Mechano-Optical Sensors Fabricated with Multilayered Liquid Crystal Elastomers Exhibiting Tunable Deformation Recovery

Advances in tuning the mechanoresponsive behavior of liquid crystal elastomers have facilitated the development of next-generation applications such as reconfigurable photonic/electronic materials, energy-harvesting devices, and flexible sensors. However, the molecular-level control of mechanical responses remains difficult, with limited tunability achieved for recovery processes after stimulus removal. Herein, a design concept is proposed for facilely tuning the recovery of both the macroscopic deformation and molecular orientation change of liquid crystal elastomers using layered materials that exhibit the desired mechanoresponsive behavior. Changing the layering materials (a polydimethylsiloxane film with elastic response to a polymethylpenten film with plastic response) alters the relaxation time from <1 s to >6 months. To demonstrate this concept, highly sensitive, stretchable mechano-optical sensors with fast and ultraslow recovery times are developed that enable an applied strain to be quantitatively detected in real time or memorized with high spatial resolution, even with a conventional camera. This material design concept for arbitrarily controlling the recovery response can provide a platform for stimuli-responsive applications.     

Renal cell carcinoma sharply captured by imaging technology at an early stage in a hemodialysis patient: Usefulness of noninvasive monochrome superb microvascular imaging

It has been drawing much attention that type 2 diabetes mellitus is closely associated with increased incidence of numerous cancers and their poor prognosis. Consequently, malignancy has been recently recognized as one of diabetic complications in addition to various conventional complications. Furthermore, it is well known that the prevalence of renal cell carcinoma (RCC) is drastically increased in hemodialysis (HD) patients. Therefore, screening of RCCs in HD patients is a very important and urgent issue as there are no highly sensitive tumor markers for RCCs. Monochrome superb microvascular imaging (mSMI) is a relatively new Doppler ultrasound technique and is useful especially when evaluating very slow blood flow state, because this allows for imaging microvessels with low velocity in the absence of a contrast agent. Thus, mSMI might be also useful when contrast enhancement is not obvious on CT and/or contrast-enhanced ultrasonography using perflubutane or contrast agents are contraindicated. Moreover, it has been reported that mSMI could effectively detect vascularity of renal malignant tumor than benign renal mass in nondialysis patients. We propose that mSMI of ultrasonography could become one of the very useful methods for detecting RCCs at an early stage with high sensitivity in HD patients.     

Development of microparticle counting sensor based on structural and spectroscopic properties of metal mesh device

A microparticle counter based on a metal mesh device was developed. The metal mesh device had a lattice-shaped structure with well-regulated holes of 1.8 μm. The collection percentages of differently sized microparticles using the metal mesh device were determined by flow cytometry. The cut-off point and hole size of the metal mesh device were identical. Polystyrene microparticles were detected from changes in the spectroscopic properties of the metal mesh device. When microparticles were trapped on the holes of the metal mesh device, the transmittance in the infrared spectra decreased. Microparticles smaller than the holes were not detected by the metal mesh device, whereas 2 and 3 μm microparticles were detected. Polystyrene and silica microparticles could be counted using the metal mesh device via calibration curves between the concentration of microparticles and the change level in the transmittance of the metal mesh device. The separation of microparticles from a mixture suspension using the metal mesh device was evaluated. Unlike a microfiber filter, only 2 μm microparticles were collected from coexisting 1 μm microparticles by the metal mesh device. Owing to its high separation ability, the metal mesh device selectively detected 2 μm microparticles in coexisting 10-equivalence 1 μm microparticles.     

Fabrication of calcite-core/Mg-calcite-shell nanorods for better thermal stability

Calcite-core/Mg-calcite (Mg_xCa_1?xCO₃)-shell nanorods were synthesized by bubbling CO₂ gas into Ca(OH)₂ aqueous slurry with Mg²⁺ doping. The thermal stability of the resulting particles in the forms of aqueous slurry and dry powder was investigated, and the nanorods doped with higher Mg²⁺ concentrations were found to have excellent thermal stability both in water and air. The microscopic structures of the nanorods were characterized in detail by XRD and TEM, and the Mg-calcite nanoclusters that almost fully covered the particle surface were deduced to be responsible for the improvement of particle morphology stability. Facile fabrication of 1D anisotropic nanoparticles with better thermal stability can widen the industrial application of calcite.     

Evaluating the fatigue limit of metals having surface compressive residual stress and exhibiting shakedown

The objective of the study described in this article is to evaluate the effect of shakedown of surface compressive residual stresses introduced by shot peening on fatigue limit of stainless steel. First, the tension‐compression fatigue tests were conducted on ASTM CA6NM specimens under controlled load and displacement conditions to acquire a fatigue limit diagram under various compressive mean stress. The results showed that shakedown of negative mean stress occurs under controlled displacement. We then carried out in‐plane–bending fatigue tests under controlled load conditions on welded ASTM 309 stainless steel specimens with surface compressive residual stress introduced by ultrasonic shot peening. The results provide a fatigue limit of 415 MPa, which agrees with the value of 404 MPa calculated based on a modified Goodman line considering shakedown. Therefore, it is suggested that the surface layer is restricted by the internal bulk that creates controlled displacement conditions and the shakedown of surface compressive residual stress occurs.     

Tip-sample distance control using photothermal actuation of a small cantilever for high-speed atomic force microscopy

We have applied photothermal bending of a cantilever induced by an intensity-modulated infrared laser to control the tip-surface distance in atomic force microscopy. The slow response of the photothermal expansion effect is eliminated by inverse transfer function compensation. By regulating the laser power and regulating the cantilever deflection, the tip-sample distance is controlled; this enables much faster imaging than that in the conventional piezoactuator-based z scanners because of the considerably higher resonant frequency of small cantilevers. Using this control together with other devices optimized for high-speed scanning, video-rate imaging of protein molecules in liquids is achieved.