Intertemporal Optimization Model of Entrepreneurs Behavior

The intertemporal problem of consumer’s behavior is the basis of modern models. The interest in this kind of problems is determined by the attempt to widen the range of directions within which it is possible to conduct additional mathematical research in the theory of consumption. The article considers the problem of maximizing discounted utility derived from an entrepreneur’s consumption due to optimal allocation of monetary means which he gets as profit from his production company and interest on assets. The difference of this problem from the basic dynamic problem of consumer’s behavior lies in the fact that an entrepreneur as an individual acts in two roles: as a consumer and as a manufacturer. Furthermore, the problem is characterized by two peculiarities: a distinctive budget limitation which includes production function and reveals an irregular differential relation and also by the presence of mixed boundary conditions on the value of capital and assets. Formalization of the problem as a dynamic optimization model is given. It was studied with the use of mathematical analysis and the means of the optimal control theory. According to parameter correlations of the model, two strategies were identified which can be recommended for an entrepreneur as the most optimal ones. The model that was developed in the course of research can serve as a tool for taking decisions because it suggests optimal strategies of allocation of financial means in an enterprise which leads to maximization of consumption utility.

Anisotropic compact stars in f(R) gravity

We derive a new interior solution for stellar compact objects in $$f\mathcal {(R)}$$ f ( R ) gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $$f\mathcal {(R)}$$ f ( R ) . After, the time component of the metric potential and the form of $$f({\mathcal {R}})$$ f ( R ) function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter C which has to be $$C=2GM/Rc^2<<0.5$$ C = 2 G M / R c 2 < < 0.5 for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman–Oppenheimer–Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.

On one extremal problem for nonlinear Cauchy-Riemann-Beltrami systems

The study of nonlinear Cauchy--Riemann--Beltrami systems is conditioned study of certain problems of hydrodynamics and gas dynamics, in which there is an inhomogeneity of media and a certain singularity. The paper considers a nonlinear Cauchy--Riemann--Beltrami type system in the polar coordinate system in which the radial derivative is expressed through the complex coefficient, the angular derivative and its m-degree module. In particular, if m is equal to zero, then this system of equations is reduced to the ordinary linear system of Beltrami equations. Note that general first-order systems were used by M.А. Lavrentyev to define quasiconformal mappings on the plane, see \cite{L}. The problem of area distortion under quasi-conformal mappings is due to the work of B. Boyarsky, see \cite{Bo}. For the first time, the upper estimate of the area of the disk image under quasi-conformal mappings was obtained by M.А. Lavrentyev, see \cite{L}. A refinement of the Lavrentyev inequality in terms of the angular dilatation was obtained in the monograph \cite{BGMR}, see Proposition 3.7. In the present paper, it is found an exact upper estimate of the area of the image of the disk, which is analogous to the known result by Lavrentyev. Also, we find here a mapping on which the estimate is achieved. Thus, the work solves the extreme problem for the area functional of the image of disks under a certain class of regular homeomorphic solutions of nonlinear systems of the Cauchy--Riemann--Beltrami type with generalized derivatives integrated with a square. The work uses p-angular dilatation. In the conformal case, angular dilatation is important in the theory of quasi-conformal mappings and nondegenerate Beltrami equations. Proof of the main result of the article is based on the differential relation for the area function of the image of disks of arbitrary radii, which was established in the previous work of the authors for regular homeomorphisms with Luzin's N-property.

Entropy driven transformations of statistical hypersurfaces

Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface is explored through a differential relation for the variables, and connections with the replicator dynamics for Gibbs’ weights are highlighted. Ideal and super-ideal cases are analyzed, while considering their integral characteristics.

Inhibitory Processes and Fluid Intelligence: a Performance at Early Years of Schooling

Inhibition constitutes one of the main executive functions and it is important to more complex skills such as fluid intelligence. Actually, there is an agreement on distinguishing three inhibitory types: perceptual, cognitive and response inhibition. Several studies show the differential engagement of these inhibitory types in different skills. However, there is no registered evidence about the differential relation of inhibitory types with fluid intelligence. This inquiry is especially important during the first school years, since in this stage, inhibitory processes would already be differentiated, and inhibitory processes and fluid intelligence are linked to the performance of children in the school setting. For these reasons, the goal of this work is to study the relation and contribution of perceptual, cognitive, and response inhibition with fluid intelligence, in children in the first years of primary school. For that purpose, a sample of children from six to eight years old (N = 178) was tested with a perceptual inhibition task (perception of similarities and differences task); a cognitive inhibition task (proactive interference task); a response inhibition task (stop signal task); and a fluid intelligence task (progressive matrices task). We observed significant correlations between perceptual and response inhibition and fluid intelligence (controlling for age), but only perceptual inhibition explains significantly part of the performance in the fluid intelligence task. This study provides data about the specific contribution, during childhood, of an inhibitory type to fluid intelligence and contributes empirical evidence in support of the non-unitary approach of inhibition.