Some Refinements of Formulae Involving Floor and Ceiling Functions

The floor and ceiling functions appear often in mathematics and manipulating sums involving floors and ceilings is a subtle game. Fortunately, the well-known textbook Concrete Mathematics provides a nice introduction with a number of techniques explained and a number of single or double sums treated as exercises. For two such double sums we provide their single-sum analogues. These closed-form identities are given in terms of a dual partition of the multiset (regarded as a partition) of all b-ary digits of a nonnegative integer. We also present the double- and single-sum analogues involving the fractional part function and the shifted fractional part function

ANALIZA PROVOĐENJA FAZE INICIJACIJE PROJEKTA NA PRIMJERU PROJEKTA REORGANIZACIJE STUDENTSKOG CENTRA SPLIT : završni rad

Pri izradi svakoga projekta najprije se formirala ideja i ciljevi. Na taj se način osiguravaju nužne smjernice za uspješno ostvarenje projektnih ciljeva. Projekt u fazi inicijacije mora biti sastavljen tako da svi parametri budu ostvarivi i realni i da su si međusobne protuteže, odnosno mora biti cjelovit i uravnotežen. U prvoj fazi definiranja potrebo je utvrditi sve ono što će se raditi na projektu uključivši i rizike kojima se izlaže. Nadalje tim projekta čine projektni menadžer te ostali članovi. Projektni menadžer ne mora imati ni najdulje stručno znanje, ni viziju ni brzinu, već mora imati onaj element koji povezuje, motivira i nadahnjuje tim te koji kvalitetno komunicira s naručiteljem i koji timu može osigurati potrebne resurse za rad. Mora prije svega dobro poznavati samoga sebe, odnosno svoje prednosti i nedostatke te mora davati osjećaj sigurnosti svome timu. Kod studije izvodivosti i selekcije projekta menadžer treba biti maksimalno objektivan i uzeti sve parametre u razmatranje. Projekt može biti pod raznim pritiscima i radi toga postaje u budućnosti upitan. Da bi se to spriječilo moramo u fazi inicijacije i drugim fazama dobro razraditi projekt i provesti više faza analize.Forming the idea and the goals is principal when conceiving a project. Thus the important guidelines to successfully achieve the project goals are ensured. In its initial phase, the project parameters have to be feasible and realistic and mutually counterbalanced, i.e. the project has to be thorough and balanced. In the first, defining phase, all project tasks have to be outlined, including the risks. Furthermore, the project team are the project manager and other members. It is not necessary for the project manager to be the most experienced, nor the quickest nor to have a vision, but he or she has to have the intertwining element and the ability to motivate and drive the team, to communicate effectively with the client and to provide the team with the necessary job resources. First and foremost, the project manager has to know himself/herself, his/her own advantages and faults and he/she has to provide its team with the sense of security. When it comes to the feasibility study and project selection, the manager has to be maximally objective and has to take all parameters into observation. There can be different types of pressure related to the project which can result in its future instability. In order to anticipate it, the project has to be fully elaborated in its initial and other phases, and numerous phases of analysis have to be completed

WPFantasy – waterpolo fantasy manager

Tema diplomskog rada je izrada sustava za vaterpolo fantasy manager. Sustav se sastoji od četiri dijela: NoSQL baza podataka realizirana pomoću MongoDB, RESTful API realiziran pomoću Express.js, Web aplikacija za administratore realizirana pomoću React.js, Mobilna aplikacija za korisnike realizirana pomoću React native. U prvom dijelu rada opisane su sve korištene tehnologije, a u ostatku rada su po poglavljima opisani svaki od dijelova sustava pojedinačno kao i korištenje aplikacija.The subject of thesis is development of waterpolo fantasy manager. Project consists of four parts: NoSQL database implemented using MongoDB, RESTful API implemented using Express.js, Web application for administrators implemented using React.js, Mobile application for users implemented using React native. In the first part of thesis all used technologies are described and in latter parts all components of project are described individualy as well as usage of applications