Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Max Michel Collection. 1933-1986 Bulk dates: 1933-1937

The bulk of the collections consists of correspondence from the 1930s relating to Michels’s job applications in the U.S. in different academic institutions and activities of the Hilfsverein der Juden in Deutschland. Also included is a 36 p. typescript, ‘Geschichte der Familie Wertheimer’; pamphlets by Juda Magnes and Kurt Blumenfeld on the university in Jerusalem; as well as family trees.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Max Strauss Collection 1911-1935

Documents, medals, and photos pertaining to Max Strauss' service in the German Army before and during World War I:

Portraits of Max Pallenberg, No 9.

Pallenberg is represented in No 9 representing himself

Min-preposition kääntäminen Septuagintan Pentateukissa

Tässä tutkimuksessa tarkastellaan preposition min kääntämistä Septuagintan Pentateukissa. Työssä selvitetään, millaisia käännösvastineita Pentateukin kirjojen kääntäjät käyttävät ja millaista kreikkaa lopputulos on. Lisäksi tutkitaan, poikkeavatko Pentateukin kirjojen käännökset toisistaan. Työ on Septuagintan käännöstekniikan tutkimusta. Tämä tarkoittaa pyrkimystä ymmärtää, millaisia kriteerejä kääntäjillä on ollut ja miksi tietynlaiseen käännökseen on päädytty. Metodisesti työ liittyy Helsingin yliopistossa aiemmin tehtyyn Septuagintan käännöstekniikan tutkimukseen. Tässä työssä tutkimuskohteeksi on valittu yksi heprean syntaksin osaalue, min-prepositio. Valittu osa-alue voidaan nähdä yhtenä näkökulmana tai "mittarina" Septua-gintan käännöstekniikan tutkimukseen. Tutkimus on siten osa kokonaiskuvaa, joka saadaan, kun otetaan huomioon Septuagintan käännöstekniikkaa mahdollisimman monesta eri osa-alueesta. Tutkimuksessa on analysoitu min-preposition esiintymät Pentateukissa. Työn ulkopuolelle on rajattu min-prepositiot, jotka esiintyvät yhdistetyn preposition tai puolipreposition osana sekä min-prepositiot, jotka esiintyvät infinitiivin tai komparatiivisen ilmauksen kanssa. Analysointia varten aineisto on luokiteltu erityyppisten tapausten mukaan: 1) lokaaliset tapaukset; 2) kuvainnollisesti lokaaliset tapaukset; 3) partitiiviset tapaukset; 4) temporaaliset tapaukset; 5) kausaaliset ja instrumentaaliset tapaukset sekä agentti; 6) rektiotapaukset ja 7) erikoistapaukset. Tutkimuksessa on käynyt ilmi, että yleisimmät käännösvastineet ovat ??? (48 %) ja ?? (33 %), joita käytetään lähes aina kun se on mahdollista. Näiden kahden yleisimmän käännöksen lisäksi kääntäjät ovat monissa yksittäistapauksissa käyttäneet monia erilaisia käännöksiä. Kokonaisuutena Pentateukin kirjat näyttävät melko yhtenäiseltä. Selvimmin Pentateukista erottuu Exodus muita vapaampana käännöksenä. Kreikan kielen kannalta käännökset ovat hyvin suureksi osaksi sujuvia. Muutamat piirteet käännöksissä ovat hepraistisia. Kyse on yleensä siitä, että jokin ilmiö esiintyy Septuagintassa useammin kuin kreikkalaisessa aineistossa yleensä. Min-preposition käännöksissä Septuagintan kielessä on havaittavissa kaksi kreikan kielelle ominaista ajan ilmiötä: sijamuotojen korvautuminen prepositioilla sekä preposition ?? sulautuminen prepositioon ???.

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA)problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max-min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India.

Political transition and structural politicisation : The long shadow of Taiwan's one-party legacy

Väitöskirjatutkimuksessa tarkastellaan Taiwanin politiikkaa ensimmäisen vaalien kautta tapahtuneen vallanvaihdon jälkeen (2000) yhteiskunnan rakenteellisen politisoitumisen näkökulmasta. Koska Taiwanilla siirryttiin verettömästi autoritaarisesta yksipuoluejärjestelmästä monipuoluejärjestelmään sitä on pidetty poliittisen muodonmuutoksen mallioppilaana. Aiempi optimismi Taiwanin demokratisoitumisen suhteen on sittemmin vaihtunut pessimismiin, pitkälti yhteiskunnan voimakkaasta politisoitumisesta johtuen. Tutkimuksessa haetaan selitystä tälle politisoitumiselle. Yhteiskunnan rakenteellisella politisoitumisella tarkoitetaan tilannetta, jossa ”poliittisen” alue kasvaa varsinaisia poliittisia instituutioita laajemmaksi. Rakenteellinen politisoituminen muuttuu helposti yhteiskunnalliseksi ongelmaksi, koska siitä usein seuraa normaalin poliittisen toiminnan (esim. lainsäädännän) jähmettyminen, yhteiskunnan jyrkkä jakautuminen, alhainen kynnys poliittisille konflikteille ja yleisen yhteiskunnallisen luottamuksen alentuminen. Toisin kuin esimerkiksi Itä-Euroopassa, Taiwanissa entinen valtapuolue ei romahtanut poliittisen avautumisen myötä vaan säilytti vahvan rakenteellisen asemansa. Kun valta vaihtui ensimmäisen kerran vaalien kautta, vanha valtapuolue ei ollut valmis luovuttamaan poliittisen järjestelmän ohjaksia käsistään. Alkoi vuosia kestänyt taistelu järjestelmän hallinnasta vanhan ja uuden valtapuolueen välillä, jossa yhteiskunta politisoitui voimakkaasti. Tutkimuksessa Taiwanin yhteiskunnan politisoituminen selitetään useiden rakenteellisten piirteiden yhteisvaikutuksen tuloksena. Tällaisia politisoitumista edistäviä rakentellisia piirteitä ovat hidas poliittinen muutos, joka säilytti vanhat poliittiset jakolinjat ja niihin liittyvät vahvat edut ja intressit; sopimaton perustuslaki; Taiwanin epäselvä kansainvälinen asema ja jakautunut identiteetti; sekä sosiaalinen rakenne, joka helpottaa ihmisten nopeaa mobilisointia poliittiisiin mielenilmauksiin. Tutkimuksessa kiinnitetään huomiota toistaiseksi vähän tutkittuun poliittiseen ilmiöön, joidenkin demokratisoituvien yhteiskuntien voimakkaaseen rakenteelliseen politisoitumiseen. Tutkimuksen pääasiallinen havainto on, että yksipuoluejärjestelmän demokratisoituminen kantaa sisällään rakenteellisen politisoitumisen siemenen, jos entinen valtapuolue ei romahda demokratisoitumisen myötä.

Genetic studies of the PRP17 gene of Saccharomyces cerevisiae: a domain essential for function maps to a nonconserved region of the protein

The PRP17 gene product is required for the second step of pre-mRNA splicing reactions. The C-terminal half of this protein bears four repeat units with homology to the beta transducin repeat. Missense mutations in three temperature-sensitive prp17 mutants map to a region in the N-terminal half of the protein. We have generated, in vitro, 11 missense alleles at the beta transducin repeat units and find that only one affects function in vivo. A phenotypically silent missense allele at the fourth repeat unit enhances the slow-growing phenotype conferred by an allele at the third repeat, suggesting an interaction between these domains. Although many missense mutations in highly conserved amino acids lack phenotypic effects, deletion analysis suggests an essential role for these units. Only mutations in the N-terminal nonconserved domain of PRP17 are synthetically lethal in combination with mutations in PRP16 and PRP18, two other gene products required for the second splicing reaction. A mutually allele-specific interaction between Prp17 and snr7, with mutations in U5 snRNA, was observed. We therefore suggest that the functional region of Prp17p that interacts with Prp18p, Prp16p, and U5 snRNA is the N terminal region of the protein.

Enhancement of (BH)(max) in a hard-soft-ferrite nanocomposite using exchange spring mechanism

We have observed the exchange spring behavior in the soft (Fe3O4)-hard (BaCa2Fe16O27)-ferrite composite by tailoring the particle size of the individual phases and by suitable thermal treatment of the composite. The magnetization curve for the nanocomposite heated at 800 degrees C shows a single loop hysteresis showing the existence of the exchange spring phenomena in the composite and an enhancement of 13% in (BH)(max) compared to the parent hard ferrite (BaCa2Fe16O27). The Henkel plot provides the proof of the presence of the exchange interaction between the soft and hard grains as well as its dominance over the dipolar interaction in the nanocomposite.

Preparation of reticulated MAX-phase support with morphology-controllable nanostructured ceria coating for gas exhaust catalyst devices

Reticulated porous Ti3AlC2 ceramic, a member of the MAX-phase family (Mn+1AXn phases, where M is an early transition metal, A is an A-group element, and X is carbon and/or nitrogen), was prepared from the highly dispersed aqueous suspension by a replica template method. Through a cathodic electrogeneration method, nanocrystalline catalytic CeO2 coatings were deposited on the conductive porous Ti 3AlC2 supports. By adjusting the pH value and cathodic deposition current, coatings exhibiting nanocellar, nanosheets-like, or bubble-free morphologies can be obtained. This work expects to introduce a novel practically feasible material system and a catalytic coating preparation technique for gas exhaust catalyst devices.

Correlation, Coding, and Cooperation in Wireless Sensor Networks

We consider a single-hop data-gathering sensor network, consisting of a set of sensor nodes that transmit data periodically to a base-station. We are interested in maximizing the lifetime of this network. With our definition of network lifetime and the assumption that the radio transmission energy consumption forms the most significant portion of the total energy consumption at a sensor node, we attempt to enhance the network lifetime by reducing the transmission energy budget of sensor nodes by exploiting three system-level opportunities. We pose the problem of maximizing lifetime as a max-min optimization problem subject to the constraint of successful data collection and limited energy supply at each node. This turns out to be an extremely difficult optimization to solve. To reduce the complexity of this problem, we allow the sensor nodes and the base-station to interactively communicate with each other and employ instantaneous decoding at the base-station. The chief contribution of the paper is to show that the computational complexity of our problem is determined by the complex interplay of various system-level opportunities and challenges.

Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two endpoints of the diversity multiplexing gain tradeoff, In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multisource multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its c-error capacity.