Annotasiya

Annotasiya.Azrbaycan xalqnn milli-mnvi irsi zngin tarixi, mdni v mnvi dyrlr saslanan, nsillrdn-nsl trln bir xzindir.Bu irs xalqn kimliyini

This work deals with two mathematical aspects of subsurface flow problems within aquifer systems, namely Mathematical Modeling and Theoretical Analysis. Concerning the Mathematical Modeling, the classical challenges for this class of problems are a rigorous description of diverse interactions that may take place between different involved aquifers. Recall that the main challenge at this stage is a realistic description of the flows from one aquifer to another passing necessarily through an aquitard which is a porous layer with small permeability coefficient and small thickness (compared with the mean thickness of involved aquifers. In the same way as most of flow phenomena, the governing equations of subsurface flows are based upon conservation laws.) To address the mathematical modeling of water exchange between different aquifers separated by aquitards we expose a mathematical approach based upon the Taylor expansion. Introducing the concept of observers located inside the aquitard and the neighboring aquifers, the mass conservation law has been applied and has led to one mass balance equation for each aquifer. Thanks to this original approach we have recovered the well-known mass balance equations exposed in the literature for flow problems in aquifer systems. Due to the assumptions of small thickness and homogeneity of the absolute permeability of aquitards for our framework the water flow is supposed vertical in aquitards and so we deal with one-dimensional flows there. This is the reason why the Taylor expansion deployed there concerns only the vertical space variable. The flux continuity has been applied to get the coupling of flow equations in the two aquifers. Since the flows in aquifers are supposed horizontal it is clear that the interface aquitard/aquifer flux acts as an additional source-term for each aquifer (and not a boundary term). Concerning the Theoretical Analysis of the global system of elliptic equations (as the flow is supposed to be submitted to a steady state) the Schauder Fixed Point Theorem has been applied for facing the nonlinearity of the right-hand sides of the system. This is the way we have got the existence of a solution to the system, but not the uniqueness. Thanks to a monotonicy assumption on the right-hand side vector-function we get the uniqueness of the solution. Finally the stability of that solution has been established under appropriate conditions.

This paper examines the influence of monetary policy on corporate economies, focusing on whether supply fluctuations affect the decisions of economic agents or whether money is neutral under specific conditions. To investigate this, we develop a two-period general equilibrium model with incomplete and production financial markets, capturing frictions and asymmetries typical of real financial systems. The model is then applied to a corporate finance context, analyzing a capital structure with a single owner. The findings show that monetary policy is generally not neutral when markets are incomplete. Neutrality of money emerges only as a special case when markets are fully complete and efficient, conditions rarely observed in practice. The equilibrium model demonstrates that monetary policy is not neutral or generally does not occur unless markets are complete. For the case of a single owner in a capital structure, Fisher’s separation theorem is valid, reinforcing the non-neutrality of money in this economy with markets and incomplete production.In other words, being in an incomplete exchange environment affects the path of consumption of economic agents, although it does not alter the firm âs operational framework. For future research, it would be relevant to extend the analysis time horizon, relax the assumption regarding currency carryover, incorporate private or public banks with fiscal policies into the model, and also consider the application of the Modigliani-Miller theorem

The emergence and spread of infectious diseases pose significant challenges to public health systems worldwide. Understanding the dynamics of epidemic outbreaks is crucial for effective intervention strategies. The goal of change point detection is to find time steps when the mean, standard deviation, or slope of the data changes from one value to another. This paper explores the concept of epidemic change points through the lens of Nash equilibrium. We propose a mathematical model that incorporates the dynamics of epidemic the change point's model into game theory. Game Theory refers to a language used to model choices made by purposive agents, where the outcomes of each player are influenced by the actions of other agents. Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that players should take to secure the best outcomes. This article is worth reading because it demonstrates the use of game theory in estimating change points. It studies interactive decision-making, where the outcome for each participant or player depends on the actions of all. And it is interesting that the Nash equilibrium points of the two actors and the researcher are for optimizing their utility functions (minimizing loss functions). We demonstrate the applicability of our approach through simulations of hypothetical epidemics, revealing how game-theoretic strategies can enhance decision-making processes in real-time.

This research proposal develops a systematic and efficient mathematical approach of solving the non-linear Boussinesq-Burger's equations system. The primary objective is to develop a scale-3 Haar wavelet-based numerical scheme. In order to authenticate the efficiency, the study investigates a range of numerical problems with different source terms. In order to tackle the intrinsic challenges of nonlinearity of the problems, quasi-linearization method is employed. Explicit analytical expressions for the integrals involved are also derived for both cases under consideration. Validity and accuracy of the proposed scheme are checked by solving problems whose exact solutions are known and by comparing the solutions with special values of parameters. The results show that the Haar scale-3 wavelet method is more efficient with higher accuracy compared to the Haar scale-2 method, as confirmed by comparisons with available studies in the literature.

Fractional differential inequalities have emerged as powerful tools for modeling and analyzing dynamic systems with fractional-order derivatives, offering a sophisticated framework to capture the complexities of real-world processes. Among the various analytical techniques, the comparison principle stands out as a fundamental approach in understanding the behavior of solutions to fractional differential inequalities. This study focuses on the development and analysis of comparison principles for some of the fractional differential inequalities involving the variable-order Caputo fractional derivative which is a generalization of the classical Caputo derivative that allows the order of differentiation to vary with respect to time or space. Such flexibility is important for modeling systems whose memory characteristics change over time or space. We formulate both weak and strong versions of the comparison principle with variable order Caputo fractional derivative. Our approach combines analytical techniques from fractional calculus and the theory of differential inequalities to establish some results. To have the applicability and relevance of our theoretical work, we provide an example demonstrating the effectiveness of the proposed comparison theorems. The findings of this paper not only contribute to the theoretical advancement of fractional differential inequalities with variable order but also applicable to systems where dynamic memory effects are prominent.