Word Equations and Related Topics. Independence, Decidability and Characterizations

The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.

Sähkökoneiden etädiagnostiikan kenttätason tiedonsiirtotarpeen arviointi ja instrumentoinnin kehittäminen

Tässä diplomityössä tarkastellaan sähkökoneiden tyypillisiä vikoja ja joitain näiden havaitsemiseen käytettäviä mittauksia ja analyysejä; mittausten tuottamaa tietomäärää arvioidaan. Muutamia teollisuuslaitoksissa käytettyjä väyliä ja tiedonsiirtoprotokollia esitellään, ja analysoidaan kunnonvalvonnan mittauksien siirtämisen näillä väylillä vaatimaa väylän datansiirtonopeutta. Valvottavien sähkökoneiden määrän ylärajaa arvioidaan kunkin väylän/protokollan tapauksessa. Työssä esitellään ratkaisuja sähkökoneiden etädiagnostiikan tiedonsiirron toteuttamiseksi ja arvioidaan valvottavien sähkökoneiden määrän ylärajaa kussakin tapauksessa. Lisäksi työssä suunnitellaan ja toteutetaan kunnonvalvonnan mitta-antureiden kanssa käytettävä mittaustiedon keräily-yksikkö. Keräily-yksikön sisältävä kunnonvalvonnan ja etädiagnostiikan tiedonkeruu- ja tiedonsiirtojärjestelmä asennetaan kahteen pilot-kohteeseen: sellutehtaalle ja pienvesivoimalaan.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

The Process of Greening Cycle as Method of Operative Environmental

The structural change of society from product-based business to service- and further to need-based business has caused the fact that work for environmental issues has spread from conventional factories and environmentally harmful production to concern services and offices as well. Almost every company has an office, so a relatively small environmental burden caused by an individual office grows remarkable already at the state level and globally even more. Motivation to work for environmental issues in an individual office could be challenging even without the fact that wasted environmental impacts bound also wasted costs. Besides cost savings, a concretely greener image of a company has its value in the B2Cas well as in the B2B-field. Consumers and clients are more and more conscious of environmental issues and demand concrete actions instead of speeches, good thoughts and meaningless certifications. Internal work for environmental issues at a strategy level is not sufficient, so operational environmental management is needed for changing old practices. This research is about the effects of operative environmental management on the greening process of an office-based business. The research is outlined to concern the operative work in the office including field sales. Target was to concretely lower the environmental impacts of Lyreco Finland and to find cost savings directly by changing the operative practices in the office and also indirectly by affecting the level of environmental knowledge of the personnel. During the greening process, the aim was also to create concrete arguments for marketing as well. The circle of greening process, which was especially created for this diploma work, was used as a method. The circle divides a year to themes and sections separated by factors of environmental impacts. Separation is based on Brett Wills’ thoughts of seven green wastes (Wills, Brett. The Green Intensions. 2009) and follows it uneasily. The circle aimed at ensuring evolutionary growth of knowledge instead of being revolutionary in the changing process. Committing personnel to the process from its start by asking ideas from them and giving them clear directions was an important part of the research of operative management. Because of working from distance, communication with personnel was operated by frequent training days and weekly greening notes via emails and intranet. Also availability for communication was an important task because of the telecommuting. Research results of this work show that operative environmental management in an officebased business today is mostly management of change. When the strategic environmental friendliness is taken into a concrete level, the most important individual factor is motivating the operating personnel. Research shows that evolutionary change is found being an efficient way to make a change. Also understanding one´s own impact on the environmental burden and on the whole greening process clearly motivates the personnel. Results show that in the operative realization of the greening process, clear directions of new working practices, being as concrete as possible, and committing personnel to follow them make the process more effective. The operative environmental management and the cycle of the greening process decrease the environmental burden and save costs. The concrete results could be used as believable arguments in marketing and therefore exploited in communication with interest groups. Commitment of the management is also one of the key factors of success in the greening process. In this research, changes in the business field by a company trade took the focus of the management away from the greening process and made the process more inefficient by decreasing the amount of training days. The circle of greening process will be used as a tool in the future, as well, and therefore it will help observe environmental impacts of a company and increase sustainable development. Commitment of management to the evolutionary environmental work helps the operating personnel lower environmental impacts, decrease costs and build a concretely greener image.