Keskeytyksiä elämässä : Naisten toimijuudet aborttikertomuksissa

The present study focuses on the question of agency in the narratives of women who have experienced an abortion. The study scrutinizes agency by analyzing narratives and their context, that is, how narratives are entwined with cultural discourses and societal practices. The study thus addresses also the wider framework within which experiences and actions can be constructed in abortion narratives in the contemporary Finnish society. The women who wrote their stories or were interviewed were of different ages and had different social and religious backgrounds. Many variations of agency were found when abortion experiences were analyzed through the women s embodied and historically specific accounts. Independent and rational choices are entwined with emotions and choices made together with other people. Intimate relationships with family and friends have an important role in the choices regarding abortion. These relationships do not, however, simply belong in the private sphere but reflect the wider socio-cultural meanings of social bonds and family ties. Women s agency with regard to abortion is also constructed in encounters with the medical profession and within the wider framework of abortion legislation. The Finnish legislation grants women an abortion within certain parameters but not solely on the basis of a woman s wish to have an abortion. The data consists primarily of written narratives and interviews. All together 39 women shared their experiences with the researcher. The analysis focuses on decision-making regarding abortion, depictions of freedom and responsibility, emotions around abortion and expressions of values and religious views. The links between the women's experiences and the wider socio-cultural norms and institutions are analyzed through materials consisting of public debate on abortion in the media, ethical statements as well as literature and legislation on abortion. The analysis sheds light on the tensions apparent in the women's narratives between the legal status of abortion and more traditional views on abortion. The study demonstrates that the freedom linked to abortion is not solely to do with the right to have an abortion but also how abortion can be experienced, understood and where one can talk about the experience afterwards. The analysis reveals that Christian values shape women's experiences but that there are also new religious ways to deal with the ethical considerations brought about by abortion. Annually over 10 000 Finnish women experience an abortion, which is a situation involving ethical considerations. The study provides a nuanced account of the ways in which one can think and act when going through an abortion.

Toiseustarinat : äitinä suomalaisessa yhteiskunnassa

The focus of this study is to analyse the power relations on how our society normalizes motherhood and what kind techniques of power can be found in the motherhood culture. This study is an educational family research, and the aim of this study was to analyse those power frames that try to limit mothers in their motherhoods. There were seven mother participants in this study. They wrote essays about their experiences of motherhood in the Finnish society. The method of the research was qualitative, and the data was analysed by discourse analysis. The theoretical part of the research consists of distinguish in parenthood, family policy in families with children and motherhood in the Finnish society. The methodological approach is Michel Foucault´s analytic of power relations, and in this viewpoint I try to find out the different discourses of motherhood. In this study, mothers process against those assumptions of motherhood, which limit their freedom as acting in their role as mothers. Mothers locate themselves in the position of the Other that differs from those motherhood discourses which mothers were talking about. From the point of the Others , mothers processed their own motherhood, and they feel that they were always distinguished from the motherhood which they were expected to belong. Six categories were found in the motherhood assumptions: the norm of education, the myths of motherhood, the role assumptions in the motherhood, the norm of motherhood and discourse of good parenting, and discourse of project parenting. These discourses of motherhood assumptions make limitations, classifications and difference among motherhood. These assumptions were told by people for example in maternity clinics, first and security houses, judiciary systems, nursery, or by some other people. Mothers in this study made a comparison between the motherhood assumptions and themselves. In this study, mothers also criticize the culture of motherhood in the society and feel incompatible with the norms of motherhood around them. This may also increase mothers exhaustion.

Nationalism Circumscribed : Transnational Governance of Minority Rights in Post-Cold War Europe

For the past two centuries, nationalism has been among the most influential legitimizing principles of political organization. According to its simple definition, nationalism is a principle or a way of thinking and acting which holds that the world is divided into nations, and that national and political units should be congruent. Nationalism can thus be divided into two aspects: internal and external. Internally, the political units, i.e., states, should be made up of only one nation. Externally each nation-state should be sovereign. Transnational national governance of rights of national minorities violates both these principles. This study explores the formation, operation, and effectiveness of the European post-Cold War minorities system. The study identifies two basic approaches to minority rights: security and justice. These approaches have been used to legitimize international minority politics and they also inform the practice of transnational governance. The security approach is based on the recognition that the norm of national self-determination cannot be fulfilled in all relevant cases, and so minority rights are offered as a compensation to the dissatisfied national groups, reducing their aspiration to challenge the status quo. From the justice perspective, minority rights are justified as a compensatory strategy against discrimination caused by majority nation-building. The research concludes that the post-Cold War minorities system was justified on the basis of a particular version of the security approach, according to which only Eastern European minority situations are threatening because of the ethnic variant of nationalism that exists in that region. This security frame was essential in internationalising minority issues and justifying the swift development of norms and institutions to deal with these issues. However, from the justice perspective this approach is problematic, since it justified double standards in European minority politics. Even though majority nation-building is often detrimental to minorities also in Western Europe, Western countries can treat their minorities more or less however they choose. One of the main contributions of this thesis is the detailed investigation of the operation of the post-Cold War minorities system. For the first decade since its creation in the early 1990s, the system operated mainly through its security track, which is based on the field activities of the OSCE that are supported by the EU. The study shows how the effectiveness of this track was based on inter-organizational cooperation in which various transnational actors compensate for each other s weaknesses. After the enlargement of the EU and dissolution of the membership conditionality this track, which was limited to Eastern Europe from the start, has become increasingly ineffective. Since the EU enlargement, the focus minorities system has shifted more and more towards its legal track, which is based on the Framework Convention for the Protection of National Minorities (Council of Europe). The study presents in detail how a network of like-minded representatives of governments, international organizations, and independent experts was able strengthen the framework convention s (originally weak) monitoring system considerably. The development of the legal track allows for a more universal and consistent, justice-based approach to minority rights in contemporary Europe, but the nationalist principle of organization still severely hinders the materialization of this possibility.

”Waxaa i bartay hooyaday waawa u muhiim naaska caruurta.” Äitini opetti, että rintamaito on tärkeää lapselle. Osallistava tutkimus auktoritatiivisen tiedon omaksumisesta somalikulttuuritaustaisten naisten imetyskäytännöissä.

Suomessa asuvat somalitaustaiset maahanmuuttajaäidit luopuvat imetyksestä ja ruokkivat vauvojaan äidinmaidonkorvikkeella, vaikka somalikulttuurissa arvostetaan imetystä. Tuen ja tiedon puutetta on arveltu syyksi pulloruokinnan yleisyyteen. Tarkoituksenani on tutkia osallistavia menetelmiä käyttäen, minkälaisia imetykseen liittyviä tietojärjestelmiä somaliäidit pitävät auktoritatiivisina eli arvovaltaisina. Tarkastelen tiedon auktoritatiivisuutta etnografisten esimerkkien valossa hyödyntäen Brigitte Jordanin auktoritatiivisen tiedon käsitettä. Tutkin Jean Pierre Olivier de Sardanin teorian avulla, kuinka paikalliset populaarit tietojärjestelmät kohtaavat tieteellis-teknisen tiedon kehityksen kontekstissa. Tutkin myös, kuinka somaliäitien imetystietojärjestelmät kohtaavat suomalaisen terveydenhoitojärjestelmän edustaman imetystiedon. Osallistavien menetelmien tarkoituksena on saada heikkojen ja sorrettujen yhteisöjen ääni kuuluviin. Tutkimukseni tiedonantajina on seitsemäntoista somalimaahanmuuttajaäitiä ja yksi suomalainen äitiys- ja lastenneuvolan terveydenhoitaja. Käytän tiedonkeruumenetelminä puolistrukturoituja teemahaastatteluja, jonka lisäksi teen osallistuvaa havainnointia ja osallistavia menetelmiä kolmessa ryhmähaastattelutilanteessa. Käytän Rapi Rurad Appraisal (RRA) –menetelmiä, kuten Venn-diagrammia ja pisteytystä. Tutkimukseni tulos on, että somaliäitien imetykseen liittyvä tieto koostuu kolmesta tietojärjestelmästä, joita ovat sukuverkostoista tuleva perinteinen tietotaito, islaminuskon terveystieto sekä suomalaisen terveydenhoitojärjestelmän tieto. Näistä eri tietolähteistä tuleva imetystieto ei ole sisällöltään ristiriidassa. Imetykseen liittyvät vaikeudet ovat käytännön ongelmiin, kuten sukuverkoston hajoamiseen ja suomalaisen terveydenhoitojärjestelmän kanssa kommunikointiin liittyviä.

Evidence in European Asylum Procedures

This thesis explores the particular framework of evidentiary assessment of three selected appellate national asylum procedures in Europe and discusses the relationship between these procedures, on the one hand, and between these procedures and other legal systems, including the EU legal order and international law, on the other. A theme running throughout the thesis is the EU strivings towards approximation of national asylum procedures and my study analyses the evidentiary assessment of national procedures with the aim of pinpointing similarities and differences, and the influences which affect these distinctions. The thesis first explores the frames construed for national evidentiary solutions by studying the object of decision-making and the impact of legal systems outside the national. Second, the study analyses the factual evidentiary assessment of three national procedures - German, Finnish and English. Thirdly, the study explores the interrelationship between these procedures and the legal systems influencing them and poses questions in relation to the strivings of EU and methods of convergence. The thesis begins by stating the framework and starting points for the research. It moves on to establish keys of comparison concerning four elements of evidentiary assessment that are of importance to any appellate asylum procedure, and that can be compared between national procedures, on the one hand, and between international, regional and national frameworks, on the other. Four keys of comparison are established: the burden of proof, demands for evidentiary robustness, the standard of proof and requirements for the methods of evidentiary assessment. These keys of comparison are then identified in three national appellate asylum procedures, and in order to come to conclusions on the evidentiary standards of the appellate asylum procedures, relevant elements of the asylum procedures in general are presented. Further, institutional, formal and procedural matters which have an impact on the evidentiary standards in the national appellate procedures are analysed. From there, the thesis moves on to establish the relationship between national evidentiary standards and the legal systems which affect them, and gives reasons for similarities and divergences. Further, the thesis studies the impact of the national frameworks on the regional and international level. Lastly, the dissertation makes a de lege ferenda survey of the relationship between EU developments, the goal of harmonization in relation to national asylum procedures and the particular feature of evidentiary standards in national appellate asylum procedures. Methodology The thesis follows legal dogmatic methods. The aim is to analyse legal norms and legal constructions and give them content and context. My study takes as its outset an understanding of the purposes for legal research also regarding evidence and asylum to determine the contents of valid law through analysis and systematization. However, as evidentiary issues traditionally are normatively vaguely defined, a strict traditional normative dogmatic approach is not applied. For the same reason a traditionalist and strict legal positivism is not applied. The dogmatics applied to the analysis of the study is supported by practical analysis. The aim is not only to reach conclusions concerning the contents of legal norms and the requirements of law, but also to study the use and practical functioning of these norms, giving them a practcial context. Further, the study relies on a comparative method. A functionalist comparative method is employed and keys of comparison are found in evidentiary standards of three selected national appellate asylum procedures. The functioning equivalences of German, Finnish and English evidentiary standards of appellate asylum procedures are compared, and they are positioned in an European and international legal setting. Research Results The thesis provides results regarding the use of evidence in national appellate asylum procedures. It is established that evidentiary solutions do indeed impact on the asylum procedure and that the results of the procedure are dependent on the evidentiary solutions made in the procedures. Variations in, amongst other things, the interpretation of the burden of proof, the applied standard of proof and the method for determining evidentiary value, are analysed. It is established that national impacts play an important role in the adaptation of national appellate procedures to external requirements. Further, it is established that the impact of national procedures on as well the international framework as on EU law varies between the studied countries, partly depending on the position of the Member State in legislative advances at the EU level. In this comparative study it is, further, established that the impact of EU requirements concerning evidentiary issues may be have positive as well as negative effects with regard to the desired harmonization. It is also concluded that harmonization using means of convergence that primaly target legal frameworks may not in all instances be optimal in relation to evidentiary standards, and that more varied and pragmatic means of convergence must be introduced in order to secure harmonization also in terms of evidence. To date, legal culture and traditions seem to prevail over direct efforts at procedural harmonization.

Doing marriage and parenthood: The division of household labour across two life course events

The current study is a longitudinal investigation into changes in the division of household labour across transitions to marriage and parenthood in the UK. Previous research has noted a more traditional division of household labour, with women performing the majority of housework, amongst spouses and couples with children. However, the bulk of this work has been cross-sectional in nature. The few longitudinal studies that have been carried out have been rather ambiguous about the effect of marriage and parenthood on the division of housework. Theoretically, this study draws on gender construction theory. The key premise of this theory is that gender is something that is performed and created in interaction, and, as a result, something fluid and flexible rather than fixed and stable. The idea that couples 'do gender' through housework has been a major theoretical breakthrough. Gender-neutral explanations of the division of household labour, positing rational acting individuals, have failed to explicate why women continue to perform an unequal share of housework, regardless of socioeconomic status. Contrastingly, gender construction theory situates gender as the key process in dividing household labour. By performing and avoiding certain housework chores, couples fulfill social norms of what it means to be a man and a woman although, given the emphasis on human agency in producing and contesting gender, couples are able to negotiate alternative gender roles which, in turn, feed back into the structure of social norms in an ever-changing societal landscape. This study adds extra depth to the doing gender approach by testing whether or not couples negotiate specific conjugal and parent roles in terms of the division of household labour. Both transitions hypothesise a more traditional division of household labour. Data comes from the British Household Panel Survey, a large, nationally representative quantitative survey that has been carried out annually since 1991. Here, data tracks the same 776 couples at two separate time points - 1996 and 2005. OLS regression is used to test whether or not transitions to marriage and parenthood have a significant impact on the division of household labour whilst controlling for host of relevant socio-economic factors. Results indicate that marriage has no significant effect on how couples partition housework. Those couples making the transition from cohabitation to marriage do not show significant changes in housework arrangements from those couples who remain cohabiting in both waves. On the other hand, becoming parents does lead to a more traditional division of household labour whilst controlling for socio-economic factors which accompany the move to parenthood. There is then some evidence that couples use the site of household labour to 'do parenthood' and generate identities which both use and inform socially prescribed notions of what it means to be a mother and a father. Support for socio-economic explanations of the division of household labour was mixed although it remains clear that they, alone, cannot explain how households divide housework.

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

New Governance and the EU Courts : The Experimentalist Architecture of Judicial Decision-Making

The dissertation examines the role of the EU courts in new governance. New governance has raised unprecedented interest in the EU in recent years. This is manifested in a plethora of instruments and actors at various levels that challenge more traditional forms of command-and-control regulation. New governance and political experimentation more generally is thought to sap the ability of the EU judiciary to monitor and review these experiments. The exclusion of the courts is then seen to add to the legitimacy problem of new governance. The starting point of this dissertation is the observation that the marginalised role of the courts is based on theoretical and empirical assumptions which invite scrutiny. The theoretical framework of the dissertation is deliberative democracy and democratic experimentalism. The analysis of deliberative democracy is sustained by an attempt to apply theoretical concepts to three distinctive examples of governance in the EU. These are the EU Sustainable Development Strategy, the European Chemicals Agency, and the Common Implementation Strategy for the Water Framework Directive. The case studies show numerous disincentives and barriers to judicial review. Among these are questions of the role of courts in shaping governance frameworks, the reviewability of science-based measures, the standing of individuals before the courts, and the justiciability of soft law. The dissertation analyses the conditions of judicial review in each governance environment and proposes improvements. From a more theoretical standpoint it could be said that each case study presents a governance regime which builds on legislation that lays out major (guide)lines but leaves details to be filled out at a later stage. Specification of detailed standards takes place through collaborative networks comprising members from national administrations, NGOs, and the Commission. Viewed this way, deliberative problem-solving is needed to bring people together to clarify, elaborate, and revise largely abstract and general norms in order to resolve concrete and specific problems and to make law applicable and enforceable. The dissertation draws attention to the potential of peer review included there and its profound consequences for judicial accountability structures. It is argued that without this kind of ongoing and dynamic peer review of accountability in governance frameworks, judicial review of new governance is difficult and in some cases impossible. This claim has implications for how we understand the concept of soft law, the role of the courts, participation rights, and the legitimacy of governance measures more generally. The experimentalist architecture of judicial decision-making relies upon a wide variety of actors to provide conditions for legitimate and efficient review.

Finlandssvenska åsikter om och attityder till modern språkpåverkan

The study describes and analyzes Finland Swedes attitudes to modern-day linguistic influence, the relationship between informants explicitly reported views and the implicit attitudes they express towards language influence. The methods are primarily sociolinguistic. For the analysis of opinions and attitudes I have further developed and tested a new tool in attitude research. With statistical correlation analysis of data collected through a quantitative survey I describe the views that Swedish-language Finns (N=500) report on the influence of English, on imports, and on domain loss. With experimental matchedguise techniques, I study Finland-Swedes (N=600) subconscious reactions to English imports in spoken text. My results show that the subconscious reactions in some respects differ markedly from the views informants explicitly report that they have: informants respond that they would like English words that come into Swedish to be replaced by Swedish replacement words, but in a matched-guise test on their subconscious attitudes, the informants consider English words in a Swedish context to have a positive effect. The topic is further dealt with in interviews where I examine 36 informants implicit attitudes through interactional sociolinguistic analyses. This study comes close to pragmatic discourse analysis in its focus on pragmatic particles and modality. The study makes a rather strict distinction between explicitly expressed opinions and implicit, subconscious attitudes. The quantitative analyses suggest that the opinions we express can be tied to the explicit in language. The outcome of the matched-guise test shows that it is furthermore possible to find subconscious, implicit attitudes that people in actual situations rely on when they make decisions. The discourse analysis finds many subconscious signals, but it also shows that the signals arise in interaction with one s interlocutor, the situation, and the norms in the society. To account for this I have introduced the concept of socioconscious attitude. Socioconscious attitudes reflect not only the traditions and values the utterer grew up with, but also the speaker s relation to the social situation (s)he takes part in.

Jouko Turkan Teatterikorkeakoulun kauden yhteiskunnallinen kontekstuaalisuus vuosina 1982 - 1985

The subject of my doctoral thesis is the social contextuality of Finnish theater director, Jouko Turkka's (b. 1942) educational tenure in the Theater Academy of Finland 1982 1985. Jouko Turkka announced in the opening speech of his rectorship in 1982 that Finnish society had undergone a social shift into a new cultural age, and that actors needed new facilities like capacity, flexibility, and ability for renewal in their work. My sociological research reveals that Turkka adapted cultural practices and norms of new capitalism and new liberalism, and built a performance environment for actors' educational work, a real life simulation of a new capitalist workplace. Actors educational praxis became a cultural performance, a media spectacle. Turkka's tenure became the most commented upon and discussed era in Finnish postwar theater history. The sociological method of my thesis is to compare information of sociological research literature about new capitalist work, and Turkka's educational theater work. In regard to the conceptions of legitimation, time, dynamics, knowledge, and social narrative consubstantial changes occurred simultaneously in both contexts of workplace. I adapt systems and chaos theory's concepts and modules when researching how a theatrical performance self-organizes in a complex social space and the space of Information. Ilya Prigogine's chaos theoretic concept, fluctuation, is the central social and aesthetic concept of my thesis. The chaos theoretic conception of the world was reflected in actors' pedagogy and organizational renewals: the state of far from equilibrium was the prerequisite of creativity and progress. I interpret the social and theater's aesthetical fluctuations as the cultural metaphor of new capitalism. I define the wide cultural feedback created by Turkka's tenure of educational praxis, and ideas adapted from the social context into theater education, as an autopoietic communicative process between theater education and society: as a black box, theater converted the virtual conception of the world into a concrete form of an actor's psychophysical praxis. Theater educational praxis performed socially contextual meanings referring to a subject's position in the social change of 1980s Finland. My other theoretic framework lies close to the American performance theory, with its close ties to the social sciences, and to the tradition of rhetoric and communication: theater's rhetorical utility materializes quotidian cultural practices in a theatrical performance, and helps the audience to research social situations and cultural praxis by mirroring them and creating an explanatory frame.

Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.

Quantitation of spermatogenesis by DNA flow cytometry: Comparative study among six species of mammals

Suspensions of testicular germ cells from six species of mammals were prepared and stained for the DNA content with a fluorochrome (ethidium bromide) adopting a common technique and subjected to DNA flow cytometry. While uniform staining of the germ cells of the mouse, hamster, rat and monkey could be obtained by treating with 0.5% pepsin for 60 min followed by staining with ethidium bromide for 30 min, that of the guinea pig and rabbit required for optimal staining pepsinization for 90 min and treatment with ethidium bromide for 60 min. The procedure adopted here provided a uniform recovery of over 80% of germ cells with each one of the species tested and the cell population distributed itself according to the DNA content (expressed as C values) into 5 major classes-spermatogonia (2C), cells in S-phase, primary spermatocytes (4C), round spermatids (1C), and elongating/elongated spermatids (HC). Comparison of the DNA distribution pattern of the germ cell populations between species revealed little variation in the relative quantities of cells with 2C (8-11%), S-phase (6-9%), and 4C (6-9%) amount of DNA. Though the spermatid cell populations exhibited variations (1C:31-46%, HCI:7-20% and and HC2:11-25%) they represented the bulk of germ cells (70-80%). The overall conversion of 2C to 1C (1C:2C ratio) and meiotic transformation of 4C cells to IC (1C:4C ratio) kinetics were relatively constant between the species studied. The present study clearly demonstrates that DNA flow cytometry can be adopted with ease and assurance to quantify germ cell transformation and as such spermatogenesis by analysing a large number of samples with consistency both within and across the species barrier. Any variation from the norms in germ cell proportions observed following treatment, for e.g. hormonal stimulation or deprivation can then be ascribed due to a specific effect of the hormone/drug on single/multiple steps in germ cell transformation

Robust Relay Precoder Design for MIMO-Relay Networks

In this paper, we consider a robust design of MIMO-relay precoder and receive filter for the destination nodes in a non-regenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a single MIMO-relay node. The source and destination nodes are single antenna nodes, whereas the MIMO-relay node has multiple transmit and multiple receive antennas. The channel state information (CSI) available at the MIMO-relay node for precoding purpose is assumed to be imperfect. We assume that the norms of errors in CSI are upper-bounded, and the MIMO-relay node knows these bounds. We consider the robust design of the MIMO-relay precoder and receive filter based on the minimization of the total MIMO-relay transmit power with constraints on the mean square error (MSE) at the destination nodes. We show that this design problem can be solved by solving an alternating sequence of minimization and worst-case analysis problems. The minimization problem is formulated as a convex optimization problem that can be solved efficiently using interior-point methods. The worst-case analysis problem can be solved analytically using an approximation for the MSEs at the destination nodes. We demonstrate the robust performance of the proposed design through simulations.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

DIMENSION FREE BOUNDEDNESS OF RIESZ TRANSFORMS FOR THE GRUSHIN OPERATOR

Let G = -Delta(xi) - vertical bar xi vertical bar(2) partial derivative(2)/partial derivative eta(2) be the Grushin operator on R-n x R. We prove that the Riesz transforms associated to this operator are bounded on L-p(Rn+1), 1 < p < infinity, and their norms are independent of dimension n.