INTERDISCIPLINARNOST MATEMATIKE I PRIRODE U GOSPODARSTVU

U radu će se pokazati interdisciplinarnost matematike, botanike, biologije, stočarstva, i tako dalje. Pokazat će se uloga Fibonaccijevih brojeva u rješavanju mnogih prirodnih fenomena. Ukazat će se na uporabu matematike za objašnjavanje zakonitosti prirode i utjecaj gospodarstva na razvoj matematike

Pythagora\u27s numbers and Pythagora\u27s equation

Jedna od najjednostavnijih kvadratnih diofantskih jednadžbi i odavno poznatih jednadžbi je Pitagorina jednadžba. U radu ćemo pokazati da su sve cjelobrojne Pitagorine trojke dane s (2 abt, (a^2-b^2)t, (a^2+b^2)t), pričemu su $a,b,t in Z$ i D(a,b)=1, gdje je D(a,b) najveći zajednički djelitelj brojeva a i b.One of the simplest quadratic Diophantine equations and homogeneous equations known from long time ago is Pythagora\u27s equation. In the paper it will be shown that all Pythagorean integer triples are given by (2 abt, (a^2-b^2)t, (a^2+b^2)t), where $a,b,t in Z$, D(a, b)=1

INTERDISCIPLINARNOST MATEMATIKE I PRIRODE U GOSPODARSTVU

U radu će se pokazati interdisciplinarnost matematike, botanike, biologije, stočarstva, i tako dalje. Pokazat će se uloga Fibonaccijevih brojeva u rješavanju mnogih prirodnih fenomena. Ukazat će se na uporabu matematike za objašnjavanje zakonitosti prirode i utjecaj gospodarstva na razvoj matematike

TRANSPORTNI PROBLEM U ŠUMARSTVU

U ovom radu ćemo teorijski i praktično riješiti jedan konkretan problem “Hrvatskih šuma“ koje u svom sastavu imaju dvije transportne jedinice koje prevoze drvni materijal od pomoćnog stovarišta (tvrda šumska cesta) do glavnog stovarišta (kraj željezničkog kolodvora). Rješava se transportni problem kao specijalni slučaj linearnog optimiranja.U radu ćemo koristiti analitičko rješenje

Some new results on the travelling salesman problem

The travelling salesman problem (or The sales representative problem) has been insufficiently explored so far. One of the first results on this issue was provided by Euler in 1759 (The problem of moving a knight on the chess board), Knight\u27s Tour Problem. Papers on this subject were written by A.T. Vandermonde (1771), T. P. Kirkman (1856) and many others. The sales representative problem is a major challenge due to the application in solving theoretical and practical problems such as the quality of algorithms and of optimization methods. This well-known optimization problem has been extensively studied from several aspects since 1930. In general form the study was started by Karl Menger, seeking the shortest route through all points of a finite set with known distances between every two points. Since then, there have been many formulations of the problem. In this paper we shall provide an analysis of the nature of the commercial representative problem, and highlight its complexity and some ways of its solution. We shall use graph theory, and pay particular attention to the search of Hamiltonian cycle of minimum weight in the weighted graph. During the paper development we were led by the following question: "How to minimize the total distance travelled by a sales representative in order to visit n given locations exactly once and return to the starting point?" Nowadays, there are many formulations of the commercial representative problem and we shall mention two equivalent formulations: a) A set of places that a sales representative has to visit exactly once and return to the starting point is determined, the distance between places being known. The question is in which order a sales representative should visit the places so that the total length of his tour is minimal b) A Hamiltonian cycle of minimum weight should be determined in the weighted graph. Note that the formulation of the problem is very simple, but finding solutions inflicts great difficulties. For a graph of n vertices there are n! maximum number of Hamiltonian cycles, thus the problem of factorial complexity occurs

Production Optimisation as a Decision Making Basis

U radu je dana interpretacija proizvodnje koja može poslužiti menadžmentu pri odlučivanju. Uz određene pretpostavke riješena je matematička interpretacija optimalne alokacije resursa i maksimizacija dohotka gospodarskog subjekta.This paper provides a production analysis which can help management in the decision making process. Given that certain assumptions are correct, the mathematical interpretation of the optimal resource allocation and the income maximisation of a certain economic entity can be solved

Pythagora\u27s numbers and Pythagora\u27s equation

Jedna od najjednostavnijih kvadratnih diofantskih jednadžbi i odavno poznatih jednadžbi je Pitagorina jednadžba. U radu ćemo pokazati da su sve cjelobrojne Pitagorine trojke dane s (2 abt, (a^2-b^2)t, (a^2+b^2)t), pričemu su $a,b,t in Z$ i D(a,b)=1, gdje je D(a,b) najveći zajednički djelitelj brojeva a i b.One of the simplest quadratic Diophantine equations and homogeneous equations known from long time ago is Pythagora\u27s equation. In the paper it will be shown that all Pythagorean integer triples are given by (2 abt, (a^2-b^2)t, (a^2+b^2)t), where $a,b,t in Z$, D(a, b)=1

An Approach to the Application of the Internet of Things in Logistics

The Internet of Things (IoT) is a technology of the future that is being widely applied in business environment. Companies around the world are starting to apply IoT technologies to ensure the most efficient business possible. The importance of the application of this technology has been particularly evident in improving logistics processes. This paper describes IoT applications in processes such as supply chain management, i.e. control of transport and storage of goods and materials. Examples of smart solutions offered by IoT technology are presented. Various technologies and standards are used in the implementation of the IoT. The scientific community is increasingly researching new technologies such as NB-IoT and 5G, which provide an even greater potential for IoT development. Therefore, this paper shows a comparison of these technologies and explains how IoT devices work with them

Training methods in municipal enterprises

The impact of change on the contemporary business is immense. Regardless of their position in an organisation, employees face changes every day. Change can cause uncertainty, anxiety and discouragement. Given that business processes are becoming increasingly specialised, businesses need to be able to adapt successfully to the demands of the market and changes in the business environment. Targeted and continuous training helps employees acquire skills and knowledge needed to respond to the challenges they face in the workplace. The main goal of a business is to create value. Increasingly, businesses are starting to realise that human resources are one of the most important resources in achieving that goal. In today’s business environment, the success of a company greatly depends on the competences and motivation of its employees. It is becoming increasingly difficult to maintain employee motivation and engagement, and achieve the desired business outcomes. Employee training is an important factor in meeting this challenge. The paper presents the results of a survey on employee training methods used by municipal service companies in the Republic of Croatia. An analysis is given of various training methods, explaining the importance and purpose of some of them

Analysis and Proposals for Improving Knowledge and Skills in Engineering Aimed at Reducing Unemployment

The aim of this paper is to assess the readiness of engineering students to enter the labour market and to make proposals for improving their knowledge and skills. Our research is based on the assumption that smart economic growth should be based on interdisciplinary knowledge including ICT, communication in foreign languages and economic knowledge. Results of the study conducted on a sample of 153 final-year engineering students point to the necessity of changing educational needs, and to the knowledge and skills desirable in the labour market, and this is supported by the respondents’ opinion on the conditions for knowledge acquisition at their tertiary education institutions but also by their willingness to acquire the necessary knowledge