Besselovi nizovi i bazni okviri

Ovaj rad sastoji se od tri cjeline. Prva cjelina obuhvaća definicije i važne rezultate teorije normiranih prostora potrebne za opis Besselovih nizova i baznih okvira, što čini centralni dio ovog rada. U drugom poglavlju detaljno opisujemo Besselove nizove i bazne okvire iznoseći njihova svojstva i karakterizacije. Objašnjavamo pojam duala i dualnog baznog okvira te proučavamo osnovne rezultate vezane uz njih. Posebno izdvajamo usporedbu baza i baznih okvira te ističemo ekvivalenciju egzaktnih Parsevalovih baznih okvira i ortonormiranih baza Hilbertovog prostora. Naposljetku stavljamo naglasak na napete bazne okvire, ističući Parsevalove bazne okvire. Posebno je zanimljivo promotriti kada Besselov niz možemo s konačno mnogo elemenata nadopuniti do baznog okvira. U trećem poglavlju posvećujemo se razmatranju takvih situacija te iznosimo teoreme koji nam daju nužne i dovoljne uvjete da bi navedena nadopuna postojala. Također, navodimo i odgovarajući rezultat za nadopunu do Parsevalovog baznog okvira.This thesis consists of three parts. The first part contains definitions and important results of the theory of normed vector spaces which will be used to describe Bessel sequences and frames. In the second, central part of the thesis, we present properties and characterizations of Bessel sequences and frames. We describe duals and dual frames and show main results concerning them. Furthermore, we make a comparison of frames and bases and state the equivalence of exact, Parsel frames and orthonormal bases. Finally, we study tight frames and highlight Parsel frames. In chapter three we state necessary and sufficient condition under which a Bessel sequence can be extended to a frame by adding a finite sequence of vectors. In the same spirit, we provide necessary and sufficient condition for the existence of a finite extension of a Bessel sequence to a Parsel frame

Besselovi nizovi i bazni okviri

Ovaj rad sastoji se od tri cjeline. Prva cjelina obuhvaća definicije i važne rezultate teorije normiranih prostora potrebne za opis Besselovih nizova i baznih okvira, što čini centralni dio ovog rada. U drugom poglavlju detaljno opisujemo Besselove nizove i bazne okvire iznoseći njihova svojstva i karakterizacije. Objašnjavamo pojam duala i dualnog baznog okvira te proučavamo osnovne rezultate vezane uz njih. Posebno izdvajamo usporedbu baza i baznih okvira te ističemo ekvivalenciju egzaktnih Parsevalovih baznih okvira i ortonormiranih baza Hilbertovog prostora. Naposljetku stavljamo naglasak na napete bazne okvire, ističući Parsevalove bazne okvire. Posebno je zanimljivo promotriti kada Besselov niz možemo s konačno mnogo elemenata nadopuniti do baznog okvira. U trećem poglavlju posvećujemo se razmatranju takvih situacija te iznosimo teoreme koji nam daju nužne i dovoljne uvjete da bi navedena nadopuna postojala. Također, navodimo i odgovarajući rezultat za nadopunu do Parsevalovog baznog okvira.This thesis consists of three parts. The first part contains definitions and important results of the theory of normed vector spaces which will be used to describe Bessel sequences and frames. In the second, central part of the thesis, we present properties and characterizations of Bessel sequences and frames. We describe duals and dual frames and show main results concerning them. Furthermore, we make a comparison of frames and bases and state the equivalence of exact, Parsel frames and orthonormal bases. Finally, we study tight frames and highlight Parsel frames. In chapter three we state necessary and sufficient condition under which a Bessel sequence can be extended to a frame by adding a finite sequence of vectors. In the same spirit, we provide necessary and sufficient condition for the existence of a finite extension of a Bessel sequence to a Parsel frame

Agent-Based Modelling and Simulation of Product Development Teams

The success of product development highly depends on the quality of cooperation among members of a team involved in the process. Thus, a tool capable of simulating product development team may be beneficial for researchers interested in teamwork, as well as useful for managers struggling with team formation during process planning phase. This work aims at providing a detailed overview of agent-based simulators of product development teams. Specifically, the scientific databases Web of Science, Scopus, ACM DL, and IEEE were searched to extract relevant agent-based models of teamwork in mechanical engineering and aerospace context and obtained models were reviewed to identify their key advantages and limitations

Relating Problem-Solving Approach to Turn-Taking in Communication of Design Teams

This paper builds on the turn-taking model of verbal communication and proposes a framework for relating the problem-solving style to the turn-taking model. The framework aims at enabling a more comprehensive investigation of verbal communication in team design activities. An empirical study has been conducted to test the framework and identify the relationship between individuals\u27 problem-solving styles and the corresponding percentages of turn transitions. The results show a non-linear relationship between diversity in Orientation to Change and Ways of Deciding dimensions of problem-solving style and the percentage of turn transitions. The non-linear relationship has been explained by referring to team diversity-related theories on information/decision-making and social categorisation. The empirical study demonstrated that the framework is useful for providing a more comprehensive description of communication patterns within design teams

Process modularity over time : modelling process execution as an evolving activity network

Process modularity describes the extent to which processes can be decomposed into modules to be executed in parallel. So far, research has approached process modularity from a static perspective, not accounting for its temporal evolution. As a result, the understanding of process modularity has been limited to inferences drawn from aggregated analyses that disregard process execution. This article introduces and develops the notion of dynamic process modularity considering the evolving activity network structure as executed by people. Drawing on network science, the article quantifies process modularity over time using archival data from an engineering design process of a biomass power plant. This article shows how studying the temporal evolution of process modularity enables a more complete understanding of activity networks, facilitates the comparison of actual process modularity patterns against formal engineering design stages, and provides data-driven decision-support for process planning and interventions. Finally, managerial recommendations for interface management, resource allocation, and process decomposition are proposed, to help practitioners better to understand and manage dynamic processes

Višeagentski sustav za simulaciju ponašanja tima u razvoju proizvoda.

Teams play a crucial role in many product development activities. However, teams – as complex socio-technical systems – are challenging to study in a real-world setting. Computational models and simulations offer easily controllable and cost-effective tools for supporting team studies, and prove especially valuable in studies on the sufficient conditions for the emergence of various team properties and behaviours. As a consequence, computational models offer a possible explanation of the observed phenomena and provide means for theory-testing and hypothesis generation. Thus, this work develops a computational model of team behaviour in product development with the aim of enabling computational studies of team learning and adaptation. The dissertation develops a multi-agent system capable of representing various aspects of product development teams. Building on the existing theories, empirical studies and current teamwork models, the thesis derives a detail theoretical model of a designer, its cognition, its tasks, and interactions with others. The thesis implements the theoretical model in a multi-agent system directed at studies of the emergence of team properties and behaviours – in particular, team learning and adaptation. Extensive testing of the derived computational model concludes the goal of obtaining a multi-purpose research tool for studies of product development teams and confirms the appropriateness of the chosen simulation technique – agent-based modelling – for the intended research goal.Timovi imaju važnu ulogu u mnogim aktivnostima razvoja proizvoda, no istraživanja timova u stvarnom okruženju dugotrajna su te izuzetno zahtjevna. Računalni modeli i simulacije omogućavaju izvršavanje velikog broja ispitivanja u kratkom vremenu, a posebno su pogodni za istraživanja kompleksnih sustava poput timova. Računalni modeli omogućavaju ispitivanje dovoljnosti uvjeta za pojavu raznih timskih svojstava i ponašanja koja proizlaze iz interakcija članova tima, nudeći objašnjenje uočenih pojava te pružajući sredstvo za testiranje postojećih teorija i stvaranje hipoteza. U ovom radu razvijen je računalni model ponašanja tima u razvoju proizvoda s ciljem omogućavanja simulacijskih studija timskog učenja i prilagodbe. U radu je razvijen višeagentski sustav za simulaciju ponašanja tima u razvoju proizvoda. Oslanjajući se na teorije, empirijske studije i postojeće modele timskog rada, u disertaciji je opisan teorijski model člana razvojnog tima s posebnim naglaskom na prikaz njegovih kognitivnih procesa, teorijski model konstrukcijskih problema te model interakcija među članovima tima u razvoju proizvoda. Na temelju teorijskog modela izrađen je računalni prototip čija je svrha proučavanje raznih timskih svojstava, a posebice timskog učenja i adaptacije. Opsežnim testiranjem razvijenog računalnog modela omogućeno je postizanje cilja ovog rada: stvaranje višenamjenskog istraživačkog alata za proučavanje timova u razvoju proizvoda te je potvrđena prikladnost odabrane tehnike simulacije – modeliranja zasnovanog na agentima – za ostvarenje navedenog cilja

The Emergence and Impact of Synchrony in Design Teams: A Computational Study

Studies revealed that, while collaborating, humans tend to synchronise on multiple levels (e.g., neurocognitive or physiological). Inter-brain synchrony has been linked to improved problem-solving, decision-making, and creativity. Nevertheless, studies on synchrony in design teams started to emerge only recently. This study contributes to this stream of research by utilising a computational model of a design team to explore the relationships between team cohesion, synchrony, and team performance. The experiments revealed a positive link between team cohesion level and the emergence of (cognitive) synchrony. Furthermore, cohesive teams were found to be more efficient, converging quicker and producing solutions at a higher rate. In addition, the diversity of the solutions generated by highly cohesive teams tends to increase over time. Teams in medium- and low-cohesive settings initially generate highly diverse solutions, but such diversity decreases as the simulation progresses. Finally, highly-cohesive teams were found to be prone to premature convergence.Funder: Ministry of Science, Education and Sports of Republic of Croatia; US National Science Foundation (CMMI-1400466, CMMI-1762415, EEC-1929896); Croatian Science Foundation (IP-2018-01-7269)Licens fulltext: CC BY-NC-ND 4.0</p