Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

A network representation of protein structures: Implications for protein stability

This study views each protein structure as a network of noncovalent connections between amino acid side chains. Each amino acid in a protein structure is a node, and the strength of the noncovalent interactions between two amino acids is evaluated for edge determination. The protein structure graphs (PSGs) for 232 proteins have been constructed as a function of the cutoff of the amino acid interaction strength at a few carefully chosen values. Analysis of such PSGs constructed on the basis of edge weights has shown the following: 1), The PSGs exhibit a complex topological network behavior, which is dependent on the interaction cutoff chosen for PSG construction. 2), A transition is observed at a critical interaction cutoff, in all the proteins, as monitored by the size of the largest cluster (giant component) in the graph. Amazingly, this transition occurs within a narrow range of interaction cutoff for all the proteins, irrespective of the size or the fold topology. And 3), the amino acid preferences to be highly connected (hub frequency) have been evaluated as a function of the interaction cutoff. We observe that the aromatic residues along with arginine, histidine, and methionine act as strong hubs at high interaction cutoffs, whereas the hydrophobic leucine and isoleucine residues get added to these hubs at low interaction cutoffs, forming weak hubs. The hubs identified are found to play a role in bringing together different secondary structural elements in the tertiary structure of the proteins. They are also found to contribute to the additional stability of the thermophilic proteins when compared to their mesophilic counterparts and hence could be crucial for the folding and stability of the unique three-dimensional structure of proteins. Based on these results, we also predict a few residues in the thermophilic and mesophilic proteins that can be mutated to alter their thermal stability.

Immigrant Associations in the Metropolitan Area of Finland : Forms of Mobilisation, Participation and Representation

This study examines the role of immigrant associations in the societal and political integration of immigrants into Finnish society. The societal focus is on the ability of immigrant associations to mobilise their ethnic group members to participate in the socio-economic, cultural and political domains of Finnish society and in certain cases even beyond. The political integrative aims are the opportunities of immigrant associations to participate and represent the interests of their ethnic group in local and national policy making. This study focuses on associations in the Metropolitan Area of Finland, (Espoo, Helsinki and Vantaa).The qualitative research consisted of 71 interviews conducted with members of immigrant associations and civil servants. These interviews were mainly semi-structured, including some additional open-ended questions. Additional data consisted of documents, planning reports and of follow-up enquiries. -- In the analysis of the data I categorised thirty-two immigrant associations according to the activity forms and the description of the goals by the members. The four categories consisted of integrative, societal, ethno-cultural and transnational immigrant associations. Most of the immigrant associations belonged to the integrative category (15 of 32 associations). On the one hand the aims of these associations are to provide access for their ethnic group members into Finnish society, while on the other to strengthen the ethnic identity of their members by organising ethno-cultural activities. The societal associations only focused on activities with the objective of including immigrants into the Finnish labour market and educational system. The goal of ethno-cultural associations was to strengthen the ethnic identity of their ethnic group members. The transnational associations aimed at improving the living conditions of women and children in the members' country of origin. The possibilities for immigrant associations to mobilise their members depends partly on external financing. Subsidies have been allocated for societal activities in particular. There remains a risk of the crowding out of ethno-cultural activities: something which has already taken place in several European countries. Immigrant associations aim to strengthen the identity of immigrants mainly by organising social and ethno-cultural activities. Another important target was to provide peer support and therapy courses. Additionally, immigrant women's associations offer assistance to women who have encountered violence by providing counselling and in some cases access to shelter. The data showed that there is an ever growing need to pay heed to the well-being of women, children and elderly immigrants. The participation of immigrant associations in the municipalities' integrative issues takes place mainly through cooperative projects. Until the end of the 1990s there had not been much cooperation. The problem with the projects was that they had mainly been managed by civil servants, whereas members from immigrant associations had remained in a more passive position. Representation of immigrant associations in councils has been fairly weak. Immigrant associations are included in the multicultural councils of Espoo and Vantaa, but only in the planning stages. The municipality of Helsinki does not include immigrant associations due to the large number of organisations which causes problems in finding fair, democratic representation. At the national level, the ‘Advisory Board for Ethnic Relations’ – ETNO didn’t chose its members based on membership of ethnic associations, but based on belongingness to one of the larger language groups spoken by the foreign population in Finland. Since ETNO’s third period (2005-2007), the representatives of immigrant associations and ethnic minority groups have been chosen from proposed candidates. Key words: immigrant associations, integration, mobilisation, participation, representation, the Metropolitan area of Finland, immigrant (women), civil servants

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Note on the locally product and almost locally product structures

This paper is concerned with a study of some of the properties of locally product and almost locally product structures on a differentiable manifold X n of class C k . Every locally product space has certain almost locally product structures which transform the local tangent space to X n at an arbitrary point P in a set fashion: this is studied in Theorem (2.2). Theorem (2.3) considers the nature of transformations that exist between two co-ordinate systems at a point whenever an almost locally product structure has the same local representation in each of these co-ordinate systems. A necessary and sufficient condition for X n to be a locally product manifold is obtained in terms of the pseudo-group of co-ordinate transformations on X n and the subpseudo-groups [cf., Theoren (2.1)]. Section 3 is entirely devoted to the study of integrable almost locally product structures.

Dolezal's theorem revisited

This paper presents an improved version of Dolezal's theorem, in the area of linear algebra with continuously parametrized elements. An extension of the theorem is also presented, and applications of these results to system theory are indicated.

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

An improved representation of vehicle incompatibility in frontal NCAP tests using a modified rigid barrier

With the objective of better understanding the significance of New Car Assessment Program (NCAP) tests conducted by the National Highway Traffic Safety Administration (NHTSA), head-on collisions between two identical cars of different sizes and between cars and a pickup truck are studied in the present paper using LS-DYNA models. Available finite element models of a compact car (Dodge Neon), midsize car (Dodge Intrepid), and pickup truck (Chevrolet C1500) are first improved and validated by comparing theanalysis-based vehicle deceleration pulses against corresponding NCAP crash test histories reported by NHTSA. In confirmation of prevalent perception, simulation-bascd results indicate that an NCAP test against a rigid barrier is a good representation of a collision between two similar cars approaching each other at a speed of 56.3 kmph (35 mph) both in terms of peak deceleration and intrusions. However, analyses carried out for collisions between two incompatible vehicles, such as an Intrepid or Neon against a C1500, point to the inability of the NCAP tests in representing the substantially higher intrusions in the front upper regions experienced by the cars, although peak decelerations in cars arc comparable to those observed in NCAP tests. In an attempt to improve the capability of a front NCAP test to better represent real-world crashes between incompatible vehicles, i.e., ones with contrasting ride height and lower body stiffness, two modified rigid barriers are studied. One of these barriers, which is of stepped geometry with a curved front face, leads to significantly improved correlation of intrusions in the upper regions of cars with respect to those yielded in the simulation of collisions between incompatible vehicles, together with the yielding of similar vehicle peak decelerations obtained in NCAP tests.

Quest for authenticity - representation of the Sami image in Christmas tourism

Tourism is one of important livelihoods in Lapland. Christmas tourism was launched in the early 1980s and it became a success story - being labelled as the most epochal tourism product in Finland. Hence, today Christmas tourists are one of the most significant foreign groups arriving to Lapland during the winter season and contributing considerably to the economics of the northeastern periphery of the EU. Christmas tourism concentrates around Father Christmas who uses reindeer for transportation. The Sämi are the only indigenous people in the EU. They are all stereotypically perceived to be reindeer herders. Somehow these three, that is, Santa Claus, reindeer and the Sämi, have been incorporated into same fairytale dominion. In practice, this has happened by using the most visible cultural but also significant identity marker of the Sämi, the Sämi costume. This, in turn, has created controversy over authenticity due to manners in which the costume is used in tourism - often in imitational, mismatched forms by non-Sämi. In this thesis, after relevant literature review I intend to establish how the Sâmi are represented in Christmas tourism through visual data consisting of ten images from three foreign sources. Then I clarify why and to whom it matters of how the Sâmi are represented in Christmas tourism with the aid of 65 questionnaires and nineteen expert interviews collected mainly in the Finnish Sâmi Home Region in October 2009. Through the multiplicity of the voices of various interest and ethnic groups and by using critical discourse analysis I attempt to give an overview of the respondents' opinions and look at some preliminary solutions to the controversy. Based on my data, the non-Sami appear to accept the Sami costume usage in Christmas tourism most readily. Consequently, respect and attitudinal changes have become the respondents' propositions in addition to common set of rules of how the Sami image could be appropriated without violating the integrity of the Sami people, or a similar system of S¿m¡ Duodji trademark guaranteeing the authenticity of the tourism products. Additionally, though half of the interviewees explicate Sami presence in Christmas tourism by adding local flavour to otherwise commercial enterprise, the other half see no rationale to connect facts with fiction, that is, the Sami with Santa Claus.

Representation av kvinnor och män – Hur prioriterar riksdagsledamöter frågor i den finska riksdagen? En kvantitativ studie av motionerna i riksdagen 2007

Pro gradu uppsatsen diskuterar betydelsen av representation för grupper i samhället genom att diskutera kvinnors representation. Kvinnor är en grupp i samhället som länge varit underrepresenterad, men som under de senaste 100 åren fått en betydligt bättre position i den offentliga beslutfattningen. För att ge bakgrund till frågeställningen beskrivs kvinnors deltagande i den finska riksdagen. Begreppen deskriptiv, substantiell och symbolisk representation diskuteras. Undersökningar av kvinnors representation både deskriptivt och substantiellt på parlamentsnivå presenteras. Forskningsfrågan i uppsatsen består av fyra frågeställningar om hur motioner görs i riksdagen och hur kön kan identifieras i motionerna. Frågeställningarna bygger på den teoretiska diskussionen och meningen med frågeställningar är att styra analysen av motionerna. I teoriavsnittet behandlas kvinnors representation och den vetenskapliga diskussionen om sambandet mellan substantiell och deskriptiv representation. Diskussionen utgår från Hanna Pitkins olika kategorier av representation. I den teoretiska diskussionen behandlas även begreppen den kritiska massan, närvarons politik och kritiska aktörer. I stycket diskuteras även vilka frågeställningar, som är relevanta att undersöka när man diskuterar kvinnors representation i samhället. När representationen av kvinnor diskuteras är det viktigt att minnas att kvinnor inte utgör en homogen grupp och att även män kan representera kvinnor innehållsmässigt. Efter den teoretiska diskussionen presenteras metoden för undersökningen. Som metod används kvantitativa statistiska metoder för att kunna undersöka ett större material, som kan ge en bättre helhetsbild av hur kvinnor representeras i motionerna. Materialet för undersökningen är motioner som är gjorda i den finska riksdagen 2007. Resultaten i undersökningen visar att motionerna används av både opposition och regering och att det finns en möjlighet för samarbete över partigränser. Andra faktorer, som påverkade hur aktivt man gjorde motioner var bland annat riksdagsledamöternas ålder och den valregion ledamöterna var från. När man såg speciellt på motionärernas kön framkom det skillnader i kvinnors och mäns motionsbeteende. Överlag gör män mera motioner än kvinnor i den finska riksdagen. Kvinnor har än idag en större tendens att göra motioner om socialpolitik och speciellt familje- och barnpolitik än vad män har. Männen igen väljer att göra motioner, som traditionellt har setts som starkt manliga, så som trafik och allmänna utrymmen. Resultaten visade också att kvinnors intressen inte är vanligt som motivering för motioner. Man fann också att riksdagsledamöters koppling till kvinnoorganisationer hade en betydelse när det gällde sannolikheten att göra motioner som motiverades med kvinnors intressen i samhället. Uppsatsen diskuterar orsaker till resultaten och ser att det finns orsaker att fortsätta diskutera sambandet mellan deskriptiv och substantiell representation.

Representation of Thermodynamic Properties of Dilute Multi-Component Solutions--Options and Constraints

The different formalisms for the representation of thermodynamic data on dilute multicomponent solutions are critically reviewed. The thermodynamic consistency of the formalisms are examined and the interrelations between them are highlighted. The options are constraints in the use of the interaction parameter and Darken's quadratic formalisms for multicomponent solutions are discussed in the light of the available experimental data. Truncatred Maclaurin series expansion is thermodynamically inconsistent unless special relations between interaction parameters are invoked. However, the lack of strict mathematical consistency does not affect the practical use of the formalism. Expressions for excess partial properties can be integrated along defined composition paths without significant loss of accuracy. Although thermodynamically consistent, the applicability of Darken's quadratic formalism to strongly interacting systems remains to be established by experiment.

Quest for authenticity - representation of the Sami image in Christmas tourism

Tourism is one of important livelihoods in Lapland. Christmas tourism was launched in the early 1980s and it became a success story - being labelled as the most epochal tourism product in Finland. Hence, today Christmas tourists are one of the most significant foreign groups arriving to Lapland during the winter season and contributing considerably to the economics of the northeastern periphery of the EU. Christmas tourism concentrates around Father Christmas who uses reindeer for transportation. The Sämi are the only indigenous people in the EU. They are all stereotypically perceived to be reindeer herders. Somehow these three, that is, Santa Claus, reindeer and the Sämi, have been incorporated into same fairytale dominion. In practice, this has happened by using the most visible cultural but also significant identity marker of the Sämi, the Sämi costume. This, in turn, has created controversy over authenticity due to manners in which the costume is used in tourism - often in imitational, mismatched forms by non-Sämi. In this thesis, after relevant literature review I intend to establish how the Sâmi are represented in Christmas tourism through visual data consisting of ten images from three foreign sources. Then I clarify why and to whom it matters of how the Sâmi are represented in Christmas tourism with the aid of 65 questionnaires and nineteen expert interviews collected mainly in the Finnish Sâmi Home Region in October 2009. Through the multiplicity of the voices of various interest and ethnic groups and by using critical discourse analysis I attempt to give an overview of the respondents' opinions and look at some preliminary solutions to the controversy. Based on my data, the non-Sami appear to accept the Sami costume usage in Christmas tourism most readily. Consequently, respect and attitudinal changes have become the respondents' propositions in addition to common set of rules of how the Sami image could be appropriated without violating the integrity of the Sami people, or a similar system of S¿m¡ Duodji trademark guaranteeing the authenticity of the tourism products. Additionally, though half of the interviewees explicate Sami presence in Christmas tourism by adding local flavour to otherwise commercial enterprise, the other half see no rationale to connect facts with fiction, that is, the Sami with Santa Claus.