Stability on a cone in terms of two measures for impulsive differential equations with “supremum”

AbstractThe stability of nonlinear impulsive differential equations with “supremum” is studied. A special type of stability, combining two different measures and a dot product, is defined. The definition is a generalization of several types of stability known in the literature. Razumikhin’s method as well as a comparison method for scalar impulsive ordinary differential equations have been employed

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed

Nonlinear Bihari Type Integral Inequalities with Maxima

Some new nonlinear integral inequalities that involve the maximum of the unknown scalar function of one variable are solved. The considered inequalities are generalizations of the classical nonlinear integral inequality of Bihari. The importance of these integral inequalities is defined by their wide applications in qualitative investigations of differential equations with "maxima" and it is illustrated by some direct applications

Stability for Generalized Caputo Proportional Fractional Delay Integro-Differential Equations

A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included

INDIVIDUAL AND GROUP DECISION MAKING IN MACEDONIAN SMES

Management is principally a bundle of decision-making processes. Decision-making is the process of selecting the best alternative among various available courses of action. The managers of any organization are responsible for achieving the vision, mission and operational and financial goals in particular. All the functions like planning, organizing, coordinating and controlling are dependent on the quality of the decisions made. In companies, no matter of their size, decisions are made on all hierarchical levels. Structured decision-making process is important for large corporations, but not less important for small and medium enterprises. The innovation capacity that enables the competitive points of difference, utilization of market opportunities and potentials depend on the accuracy and timing of the decisions. This paper discusses the different methods used in individual and group decision-making processes and their application in the small and medium enterprises in North Macedonia. We conducted a research on a sample of SMEs from North Macedonia and analyzed the different decision-making methods applied and the role of individual and group decision-making methods from the perspective of managers (entrepreneurs) and employees including their roles and involvement

Existence and Ulam type stability for nonlinear Riemann-Liouville fractional differential equations with constant delay

A nonlinear Riemann–Liouville fractional differential equation with constant delay is studied. Initially, some existence results are proved. Three Ulam type stability concepts are defined and studied. Several sufficient conditions are obtained. Some of the obtained results are illustrated on fractional biological models

Stability of gene regulatory networks modeled by generalized proportional caputo fractional differential equations

A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium.publishe

Quadratic Lyapunov functions for stability of the generalized proportional fractional differential equations with applications to neural networks

A fractional model of the Hopfield neural network is considered in the case of the application of the generalized proportional Caputo fractional derivative. The stability analysis of this model is used to show the reliability of the processed information. An equilibrium is defined, which is generally not a constant (different than the case of ordinary derivatives and Caputo-type fractional derivatives). We define the exponential stability and the Mittag–Leffler stability of the equilibrium. For this, we extend the second method of Lyapunov in the fractional-order case and establish a useful inequality for the generalized proportional Caputo fractional derivative of the quadratic Lyapunov function. Several sufficient conditions are presented to guarantee these types of stability. Finally, two numerical examples are presented to illustrate the effectiveness of our theoretical results.publishe

Stability of delay Hopfield neural networks with generalized proportional Riemann-Liouville fractional derivative

The general delay Hopfield neural network is studied. It is considered the case of time-varying delay, continuously distributed delays, time varying coefficients and a special type of a Riemann-Liouville fractional derivative (GPRLFD) with an exponential kernel. The presence of delays and GPRLFD in the model require two special types of initial conditions. The applied GPRLFD also required a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. We use Razumikhin method and Lyapunov functions to study stability properties of the equilibrium of the model. We apply Lyapunov functions defined by absolute values as well as quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GPRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included

MANAGING TECHNOLOGY IN MACEDONIAN SMEs CONTEXT: PERCEPTIONS, PRACTICES AND CHALLENGES

Academicians and policy makers alike state that technology is the catalyst of growth for small medium businesses (SMEs). The review of past research reveals that the strategic upside of technology is the accomplishment of competitive advantage through their business strategies. The effective implementation of advanced technologies enables companies to achieve economies of scale and scope simultaneously. That is, investigating advanced technologies reduces the cost of future product innovation, allowing the company to increase its speed of response to market and competitive changes. Therefore, investment in advanced manufacturing technologies represents a strategic option. Despite the great importance of technology in small sized businesses, not many studies attempted to explore technology embraced by them, especially within the Macedonian context. The purpose of this paper is to gain an understanding of advanced technology knowledge and usage within the specific SME sector in the Republic of North Macedonia and to discover, if technology is used, whether it is seen as crucial to their competitive strategy. Moreover, the main research question is how advanced technology affects different aspects such as costs, sales and profitability, employee productivity, customer care, share of the e-market and competitiveness. Primary data were obtained through a questionnaire survey, carried out in small and medium sized businesses in the Republic of North Macedonia and evaluated using the tools of descriptive statistics and the methods of comparison, induction, deduction and synthesis. The research results indicate that advanced technology influences favorably the overall costs and also increases profitability. Likewise, the findings show that advanced technology leads to increase of productivity and sales. One of the conclusions of the paper is that small businesses find it important to invest in advanced technology in order to promote competitiveness. JEL Classification: M19; L19; O39