Search results for "arithmetic"

A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups

2018

Aperiodicity in finitely generated bi-ideals and bounded bi-ideals

2014

Disertācijā pētīts aperiodiskums divu vienpusēji bezgalīgu vārdu klašu – galīgi ģenerētu biideālu un ierobežotu bi-ideālu – kontekstā. Gan galīgi ģenerētus bi-ideālus, gan ierobežotus biideālus ir ērti uzdot, izmantojot bāzes virkni. Ierobežotu bi-ideālu gadījumā tiek nofiksēta galīga vārdu kopa, no kuras tiek uzģenerēta bāzes virkne. Savukārt galīgi ģenerētu bi-ideālu gadījumā bāzes virkne ir periodiska, līdz ar to var uzskatīt, ka ir dota galīga bāze. Efektīvā ģenerēšana un zināmie aperiodiskuma nosacījumi kalpo par motivāciju apskatīt galīgi ģenerētu bi-ideālu potenciālo pielietojumu kriptogrāfijā – aperiodisku gadījuma skaitļu ģenerēšanā. Savukārt, ierobežoti bi-ideāli ir galīgi ģenerēt…

Pattern languages with and without erasing

1994

The paper deals with the problems related to finding a pattern common to all words in a given set. We restrict our attention to patterns expressible by the use of variables ranging over words. Two essentially different cases result, depending on whether or not the empty word belongs to the range. We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues. The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it.

The M/G/1/1 queue with repeated attempts and different types of feedback effects

1985

Queueing systems with repeated attempts have wide practical use in designing switching networks and computer systems. The model presented in this paper not only takes into account repetitions by congestion but also considers the feedback effects from all types of failures in establishing a connection. A semi-regenerative analysis is applied in order to determine the characteristics of the underlying queueing process. Bedienungssysteme mit wiederholten Versuchen sind von groβem praktischen Nutzen bei der Bemessung von Vermittlungseinrichtungen und Computersystemen. Das Modell, das in dieser Arbeit vorgestellt wird, berucksichtigt nicht nur Wiederholungen nach vorangegangener Blockierung, son…

Optimization of a Time-to-Digital Converter and a coincidence map algorithm for TOF-PET applications

2015

This contribution describes the optimization of a multichannel high resolution Time-to-Digital Converter (TDC) in a Field-Programmable Gate Array (FPGA) initially capable of obtaining time resolutions below 100ps for multiple channels. Due to its fast propagation capability it has taken advantage of the FPGA internal carry logic for accurate time measurements. Furthermore, the implementation of the TDC has been performed in different clock regions and tested with different frequencies as well, achieving improvements of up to 50% for a pair of channels. Moreover, since the TDC is potentially going to be used in a trigger system for Positron Emission Tomography (PET), the algorithm for coinci…

The Expressibility of Languages and Relations by Word Equations

1997

Classically, several properties and relations of words, such as being a power of a same word, can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain properties of words are not expressible as components of solutions of word equations. In particular, the primitiveness and the equal length are such properties, as well as being any word over a proper subalphabet.

Emulating Human Supervision in an Intelligent Tutoring System for Arithmetical Problem Solving

2014

This paper presents an intelligent tutoring system (ITS) for the learning of arithmetical problem solving. This is based on an analysis of a) the cognitive processes that take place during problem solving; and b) the usual tasks performed by a human when supervising a student in a one-to-one tutoring situation. The ITS is able to identify the solving strategy that the student is following and offer adaptive feedback that takes into account both the problem's constraints and the decisions previously made by the user. An observational study shows the ITS's accuracy at emulating expert human supervision, and a randomized experiment reveals that the ITS significantly improves students' learning…

Using Induced Ordered Weighted Averaging (IOWA) Operators for Aggregation in Cross-Efficiency Evaluations

2014

This paper proposes an enhancement of the cross-efficiency evaluation through the aggregation of cross-efficiencies by using a particular type of induced ordered weighted averaging IOWA operator. The use of a weighted average of cross-efficiencies for the calculation of the cross-efficiency scores, instead of the usual arithmetic mean, allows us to introduce some flexibility into the analysis. In particular, the main purpose of the approach we present is to provide aggregation weights that reflect the decision maker DM preferences regarding the relative importance that should be attached to the cross-efficiencies provided by the different decision-making units. To do it, an ordering is to b…

A Monte Carlo Study of Living Polymers in 2D: Effect of Small Chains on Static Properties

1996

A slithering snake algorithm is combined with a binding and breaking chain algorithm to simulate the static behavior of living polymers according to Cates' description. It is shown that this simple two-dimensional simulation on a square lattice gives good agreement with the mean field theory. However, the large amount of small contour length chains for small values of the mean average length 〈L 〉 appears to be one of the reasons for the discrepancies observed between the simulated results and the mean field theory. This finding could explain disagreements between experimental observation and theory. Also, the results are not in favor of a swelling of the greater chains by the smaller one.

On the Complexity of the Bernstein Combinatorial Problem

2012

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