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The mathematical study of epidemics and their management has been performed for many years, however, in the last few years, new models have been published. Public health is considered very important and has to be monitored, as it is permanently under risk due to the appearance of even more types of microorganisms. Compartmental models, such as exponential models, SI, SIS, SIR, SEIRS, SEIAR, MESIR models, other generalized SIR models were and still are remarkable for studying the spread of an epidemic and for their simulations in software such as MATLAB, Maple, GLEAMviz, etc. The paper has two main objectives: a. to present new simulations in Maple and GLEAMviz for the spread of COVID-19; b. to suggest a generalization of the SIR model for analyzing the spread of COVID-19 and a simulation of it in GLEAMviz. The conclusions are that, generally, mathematical models show a value of a reproduction threshold, which can be used to forecast whether the pandemic is the increasing or decreasing phase, and that mathematical models and simulations in various programs facilitate the improvement of methods of analysis of an epidemic situation and the management of the public health system.

The tourism industry was one of the world’s greatest markets, until the world was affected by the COVID-19 pandemic. Now, tourism managers have to carefully assess the impact of epidemics on their businesses and develop new risk management methods to cope with the crisis. The current pandemic has created an opportunity for the development of rural tourism. This study aims to present a mathematical modeling of the entropy of rural tourism in the context of COVID-19 and a differential equation verified by this entropy. The model presented in this paper reflects the entropy of the preference for this type of tourism and a differential equation that models its variation. This paper aims to offer a tool to measure uncertainty regarding this topic. The model can be generalized and applied to any epidemic. The model could be used by specialists in quality management and mathematical modeling, managers of rural tourism organizations, local authorities, to estimate the entropy regarding how rural tourism has been and is still impacted by the COVID-19. The results obtained will help policy makers take necessary strategic and operational decisions, along with maximizing the profit of the rural tourism organization as well as the safety of the tourists

New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation. [ABSTRACT FROM AUTHOR]

In this article, we will solve optimization problems from the financial and economic field with constants, infinite-horizon iterative techniques and elements from fixed point theory. We will resort to C' iric' contractions in Banach space and the main result consists of the existence of a fixed point to solve an important class of infinite-horizon iterative schemes for optimization problems with state constraints for which the value function is merely lower semi-continuous. The developed tools allowed us to solve the stationary infinite-horizon optimization problems, especially for the maximization of the utility of households. We present some fixed point results that are fundamental for the development of our contributions: Notably, existence, monotonicity, attainability and results in the C' iric' contribution. We show the convergence in norm with probability for an iterative procedure defined for our problem under the stated assumptions. By using the C' iric' operator and the Reich-Rus type F-contraction, we prove the existence of the results of the optional cost function of an infinite horizon problem in a complete metric space. For a particular case, we realize a numerical simulation in C++. The conclusions are that the convergence, the existence and the uniqueness results of an optimal cost function of an infinite horizon problem in a Banach space can be treated by resorting to the C' iric' operator. [ABSTRACT FROM AUTHOR]

The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

It is known that for the scientific substantiation of quality management have been applied models that pertain to mathematical statistics, the probability theory, the information theory, fuzzy systems, graphic methods, time series, and algebraic and numerical methods.

In this paper, the author suggests a mathematical model for the entropy of the sustainable development of rural tourism organizations. The author uses the entropy formula defined by C. Shannon for each component of the sustainable development: the economic component, the sociocultural component, and the environmental component, applying the maximum of the entropies of these components. The model has the advantage that it can be easily understood and applied also by individuals who do not have a very strong mathematical background. The constants within this model can be chosen by the management of the organization according to the organization's specificity and objectives, and according to the managers' professional experience. The model suggested within the paper was applied for the entropy of the sustainable development of five rural tourism organizations from Sibiu County, Romania. The result can be compared with the result for the coming years, 2018, 2019, etc. or with the result calculated for other rural tourism organizations from other regions. [ABSTRACT FROM AUTHOR]

The evaluation of the quality and quantity of research results in higher education, both at an institutional and an individual level, has become a must in today’s competitive environment. Universities use sets of indicators validated at national or international level, in order to measure research results and to set goals, but sometimes they need specific systems that are more appropriate in order to reach their strategic objectives. Based on the system of evaluation used by a Romanian medium-sized university, in the first part of the case study from this article, it is mathematically proven that the measurement itself has a great impact on the research results’ dynamics because of the changing behaviour of the academic staff. The model could be applied and customized to any set of indicators used by different universities, and our results prove that a good set of indicators could be a useful tool to increase research performance and to achieve specific goals and strategic objectives in universities. In the second part of the case study, we tried to answer the following question: From a set of indicators used to quantify research activity in higher education, which ones are critical indicators? In order to find an answer to this question, we used the topic of hierarchization of the research indicators in higher-education as a multiple-criteria decision-making problem. The criteria used in the case study are funding from the state budget and from other sources, and national and international visibility of the research results. [ABSTRACT FROM AUTHOR]

The capital markets are in continuous development and change, which raises the question whether the market hypotheses are still relevant and statistically valid in the present times. Thus, this paper presents an analysis of the development and the current status of the capital market hypotheses. Moreover, the paper presents a summary of the tests used to assess form efficiency in a developing market, and of the research methods used to detect chaos in a financial time series. [ABSTRACT FROM AUTHOR]

The goal of the present study is to increase the intelligibility of macroeconomic phenomena triggered by governmental intervention in economy by means of fiscal policies. During cyclical movements, fiscal policy can play an important role in order to help stabilise the economy. But discretionary policy usually implies implementation lags and is not automatically reversed when economic conditions change. In contrast, automatic fiscal stabilisers (SFA) ensure a prompter, and self-correcting fiscal response. The present study aims to tackle the topic of discretionary vs nondiscretionary characteristic of fiscal stabilisers (SF). In this context, the scope of the research undertaking is to launch a scientific debate over the definitions of the concepts of non-automatic fiscal stabilisers (SfnA) and SFAs. We describe how we can quantify the discretionary and non-discretionary character of the fiscal policy, by the analysis of the structure of the conventional budget balance (SBc), budget balance associated with the current GDP. In the final part of this article, we propose a quantitative equilibrium model for establishing the mathematical prerequisites for an SF to become automatic. Likewise, on the basis of the proposed mathematical model we have performed a qualitative analysis of the influence factors. [ABSTRACT FROM PUBLISHER]

One of the themes that have been approached more and more within the specialised literature is being represented by economic cycles. The analysis of these is very useful in the long term predictions, in finding solutions for the economic raise and for detecting the economic crisis. At the same time, it is underlined in a lot of scientific and research papers, the importance of the sustainable development in the present and future society. In this paper we intend to bring contributions to the study of the cycles of a sustainable economy and we will analyse it having in mind the purpose of creating the sustainable economy. We will demonstrate the fact that curves that represent graphically all these, are not simple logistics anymore, bi-logistics or multilogistics curves, but curves in plan that are obtained by composing logistics functions with the function of the sustainable development or with the function that shapes the economic component of it mathematically. We will present an interpretation of mathematic models within the frame of the sustainable development. [ABSTRACT FROM AUTHOR]

The subject of entropy and its application of the management of quality has been approached by other authors as well [1], [2], [3], [4]. Through our transdisciplinary approach, we would like to contribute to the development of this subject. To extend the range of mathematical models applied for the scientific approach of quality and quality management, and simulated with programs such as Microsoft Excel, we brought a contribution by presenting our own results, as their authors or co-authors, published in specialty journals and works presented at conferences, among which: we defined quality entropy, we simulated it in Microsoft Excel, and we applied it for the analysis of key programs of study [5], [6]; we defined conditioned negentropy [7], and we applied it [8], [9]. This paper adds new results that use the concepts of entropy, conditioned negentropy of a tangible or intangible product's quality. The research methods used in the realization of this paper are the bibliographical research method and the creation of new models. The main conclusions are that mathematical models of entropy and negentropy is compatible with the epistemological simplicity required in the field of quality and quality management. [ABSTRACT FROM AUTHOR]

This paper aims to present a sequence of phases that can be used to create a schematic model of quality management of intellectual capital in industrial organizations and two mathematical models for the representation of these phases by using the fuzzy formalism, functional dependencies respectively. The mathematical models are similar to the ones I created for the management of the quality of life, of the education process, of the human resources training respectively, which were presented in the books mentioned in the references. I consider that the methods and techniques of modeling and simulation that have been used so far in traditional fields, such as manufacturing, accounting, finance, engineering, marketing etc., can be easily understood, can be extended and customized as quantitative methods and techniques for other fields, such as the one approached in this paper, in the field of quality and quality management of the intellectual capital in industrial organizations respectively. [ABSTRACT FROM AUTHOR]

Supply chain optimization is a modern subject, approached by many specialists in their papers [2,6,7,9 and others]. It is the application of processes and tools to ensure the optimal operation of a manufacturing and distribution supply chain. This often involves the application of mathematical modeling techniques using computer software. One of the papers related to supply chain optimization was published in 2007, by Ghodsypour and O'Brien, in an International Journal of Production Economics [8]. The paper focused in optimizing the whole supply chain and make it more effective and efficient by not just focusing on the buyer's cost but by examining costs from both the buyer and the seller. In this paper we formulated and introduced a discounted cost saving strategy to ensure that both actors (buyer and seller) benefit. Secondly, we included an out of stock and excess inventory costs and then formulated and implemented an optimized solution. The model has been solved by applying mixedinteger nonlinear programming using LINGO software. This paper compares the results with the original work using the same example and provides a win-win situation for both the actor to make the problem feasible even for decentralized situation. [ABSTRACT FROM AUTHOR]

The aim of the present study is to define quality entropy as well as to illustrate some of its properties. The simulation of the mathematical model for quality entropy shall be performed by means of specialized software for mathematical problem simulation, such as MicrosoftExcel that we have employed for this particular study. Our aim is to prove that quality entropy may be expanded to the notions of Markov source of quality and Bernoulli source of quality, by analogy with the Markov and Bernoulli sources employed in formation theory. Likewise, the present study delineates some aspects regarding tolerance to quality entropy. The subject of entropy and its application of the management of quality has been approached by other authors as well (Dinu, Ghe., Vodă, K Ghe.,2007; Dinu, Ghe.,2007; Georgescu-Roegen, Nicholas, 1979; Stamatiu, Al., 2000," Stamatiu, Al., 2002). Through our transdiscipIinary approach, we would like to contribute to the development of this subject. [ABSTRACT FROM AUTHOR]

In this paper we present an optimization problem solving, problem that is mathematically shaped as a linear programming problem. This is made with the purpose of finding an optimal solution which is also a sustainable one. In the present and future society, it is clear that nothing can be done honestly, but only in the sense of a professional and sustainable thinking (Konrad, C., 2011, pp.202-217, Petrescu, I., 2006, p.1). To think sustainable can also mean "to be calculated", in popular language "to choose wisely", all for achieving the proposed project, being careful to using non-renewable resources, to pollution, to protection for human resource, etc. Of course that the logical and precise language of Mathematics can help us formulate these issues as rigorous as possible. The problem addressed in this article was simulated in WinQSB software. [ABSTRACT FROM AUTHOR]

In the paper [8] from the bibliography, the authors presented a case study about photovoltaic cells embedded in curtain wall structures. The conclusions of the authors were that the investment, therefore, turns out to be profitable only for emerging organization rather than for the existing ones. The use of alternative energy for this purpose would be a profitable investment and consequently lead to the sustainable development of the organization. The costs entailed by an energetic capitalization of solar radiation are still very high. A profitable investment might be accomplished, though, running parallel to the classical system, by mounting photovoltaic panels in order to cover the necessary energy for the operation of small energophagous consumers: illumination, household hot water, office systems (computers, printers, etc.); therefore the preservation of the classical system for the highly energophagous technology. It is a prerequisite for the economic situation of any country to evince a strong connection with sustainable development. Profit can only be obtained under decent circumstances, given the connection among the three components of sustainable development, i.e. economic, social and environmental. The strategies aimed at environmental protection and resource management are considered as a major objective for any manager. The aim of this paper is to set forth a theoretical approach to environmental protection strategies by means of promoting investment in photovoltaic panels, as well as provinding a statistic analysis in SPSS 16. [ABSTRACT FROM AUTHOR]

Sustainable development is a relatively new theory and still emerging and finding shape, moreover the concept of sustainable development has found at a time when environmental issues are the subject of heated political debate. Initially though sustainable development was meant to provide a solution to the ecological crisis engendered by excessive industrial exploitation of resources and the continuous depletion of the environment as well as the preservation of the environmental quality; currently the concept has included the quality of life in its entire complexity, both economic and socially. The object of sustainable development is here and now, i.e. the preoccupation for fairness and equity among states, not only among generations. The present paper sets forth a synthesis of the relations among general principles such as: the principle of sustainable development [1, 9, 13], the principle of sustainable quality [8, 11, 12], the principle of qualitative communication [8, 11], the ethical principle [8]. [ABSTRACT FROM AUTHOR]