On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and GeoGebra, the exact and the approximate solution of the given numerical example are constructed, and their dependence on the initial condition and the fractional derivatives is shown graphically

New Model of Maximal Covering Location Problem with Fuzzy Conditions

The objective of Maximal Covering Location Problem is locating facilities such that they cover the maximal number of locations in a given radius or travel time. MCLP is applied in many different real-world problems with several modifications. In this paper a new model of MCLP with fuzzy conditions is presented. It uses two types of fuzzy numbers for describing two main parameters of MCLP - coverage radius and distances between locations. First, the model is defined, then Particle Swarm Optimization method for solving the problem is described and tested

The optimization of technological factors during production of hummus spread

The traditional hummus spread is obtained of cooked and grinded chickpeas, blended with susame paste (tahini), olive oil, lemon juice and spices. Hummus spread is a rich source of dietary fibers, polyunsaturated fatty acids, vitamins A, E and C, folate, minerals Mg, K and Fe. During production of such kind of spreadable food product, many factors can have influence on product behavior trough the all phases of production and to the final product quality. In this work, the influence of different technological factors on rheological, textural and sensory properties of hummus spreads made by certain recipes were examined, in the aim to achieve the maximum quality of final product. The way of preparation of raw materials, the composition of the spreads and the amount of water phase have been varied in the aim to define optimal rheological and textural parameters, to increase the production efficiency and in order to obtain desired sensory properties of final spread product

Usvajanje pojma/pojmova funkcije u programiranoj nastavi koja se izvodi u računalnom kabinetu

In teaching mathematics the concept/concepts of function are very important, but also difficult. Thus, they are gradually introduced in the teaching process depending on the students\u27 age. The development of mathematics and education technologies allows different approaches for introducing students to these concepts as well as testing of their acquisition by students. The paper outlines the possibility of acquiring the concepts of function through programmed instruction using the Cartesian method, in which the educational space is represented by “a point” with six components. One of the specified components is media, which are used for acquiring new content, and also for testing what students have acquired, for example, in the field of function. This approach ensures the presence of the direct and feedback loop, and the teaching of mathematics is organized as a manageable process. The above mentioned is effectively implemented in a computer classroom through programmed teaching using appropriate tools and Educational Computer Software (ECS).U nastavi matematike pojam/pojmovi funkcije vrlo su bitni, no također i vrlo zahtjevni. Stoga se postupno uvode u nastavni proces ovisno o dobi učenika. Razvoj matematike i obrazovne tehnologije omogućava raznolike pristupe pri upoznavanju učenika s tim pojmovima, kao i raznolike pristupe testiranju stupnja njihove usvojenosti od učenika. Ovaj rad navodi mogućnost usvajanja pojmova funkcije putem programirane nastave, primjenom kartezijanske metode, u kojoj se obrazovni prostor predstavlja „točkom“ koja se sastoji od šest komponenti. Jedna od tih navedenih komponenti su mediji, koji se koriste za usvajanje novoga nastavnog sadržaja, no i za testiranje onoga što su učenici uistinu usvojili, npr. u području funkcije. Ovaj pristup osigurava postojanje izravne petlje povratne veze, pa se nastava matematike organizira kao praktičan proces. Navedeno se učinkovito provodi u računalnom kabinetu putem programirane nastave i primjenom odgovarajućih alata i obrazovnoga računalnog softvera

Aversion to a sure loss: turning investors into gamblers

In situations where there is a lack of relevant information for proper decisionmaking, investors tend to be ambiguity-averse, opting for the probabilities with predictable outcomes. In cases where investors are faced with options without known probabilities, they tend to choose an option that will guarantee the most negligible loss. When faced with a diminutive loss, the investors will try to avoid these losses, even if that means exposing more resources to potential losses. Average down investment strategy can help to overcome losses faster while risking large amounts of resources, thus, showing investors’ propensity for loss-aversion. However, stock trading under ambiguity is not rational behavior, and is closer to gambling than investing, even when faced with losses. The choice of average down as investment strategy can explain the effect that dominates during investment decision-making process when losses occur due to ambiguity. This paper presents the results of a research conducted in order to determine if investors will use average down strategy when there is a lack of information on the market, and the size of the loss when they will be willing to use it. Obtained results show strong probability of average down usage among the subject group, thus proving aversion to a sure loss. The relation between risk aversion and aversion to a sure loss is tested. The results show that there is no influence of risk aversion on choice to use average down investment strategy. The results and possible applications of the research are thoroughly discussed

The optimization of technological factors during production of hummus spread

The traditional hummus spread is obtained of cooked and grinded chickpeas, blended with susame paste (tahini), olive oil, lemon juice and spices. Hummus spread is a rich source of dietary fibers, polyunsaturated fatty acids, vitamins A, E and C, folate, minerals Mg, K and Fe. During production of such kind of spreadable food product, many factors can have influence on product behavior trough the all phases of production and to the final product quality. In this work, the influence of different technological factors on rheological, textural and sensory properties of hummus spreads made by certain recipes were examined, in the aim to achieve the maximum quality of final product. The way of preparation of raw materials, the composition of the spreads and the amount of water phase have been varied in the aim to define optimal rheological and textural parameters, to increase the production efficiency and in order to obtain desired sensory properties of final spread product