Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Sokolosky: A Story of a Family 1860-1990

Genealogy of Sokolosky family reaching back to their Posen origins; emigration to New Orleans, Mississippi and Texas in 1860s; further family history in USA until 1990. Contains also preface by Rabbi Malcolm H. Stern, photographes of members of Sokolosky family, of gravestones and of family documents.

Solis-Cohen family papers, 1808-1990.

Correspondence, diaries, acount books, pamphlets, and other personal and professional materials pertaining to Jacob da Silva Solis and his descendents.

Julius Bisno collection, undated, 1780, 1801-1980.

Jewish organization executive. Primarily autographs, photos, writings, speeches, and biographical material, collected by Bisno, relating to ca. 120 Jews who have attained prominence in American public life; together with papers (1923-32) from Congregation Talmud Torah of Los Angeles, letters (1928-37) relating to other Jewish organizations in Los Angeles, and 3 letters of Stephen S. Wise, dealing with the general Jewish situation in Europe in 1933 and with the question of Jewish participation in the 1936 Olympic games. Persons represented include Benjamin N. Cardozo, Abe Fortas, Felix Frankfurter, Henry Horner, Herbert H. Lehman, and Lewis L. Strauss.

Eva Stroh Family Collection 1860-2005 Bulk: 1912-1950

The Eva Stroh Family Collection provides material on the lives and family history of members of the Sondheimer and Stroh families. The collection consists of numerous photos and several photo albums, family trees, official documents, correspondence, published articles and clippings and some notes, a notebook documenting cultural activities and some daily calendars.

Essays on Finnish Economic Growth and Productivity, 1860-2005

This study examines Finnish economic growth. The key driver of economic growth was productivity. And the major engine of productivity growth was technology, especially the general purpose technologies (GPTs) electricity and ICT. A new GPT builds on previous knowledge, yet often in an uncertain, punctuated, fashion. Economic history, as well as the Finnish data analyzed in this study, teaches that growth is not a smooth process but is subject to episodes of sharp acceleration and deceleration which are associated with the arrival, diffusion and exhaustion of new general purpose technologies. These are technologies that affect the whole economy by transforming both household life and the ways in which firms conduct business. The findings of previous research, that Finnish economic growth exhibited late industrialisation and significant structural changes were corroborated by this study. Yet, it was not solely a story of manufacturing and structural change was more the effect of than the cause for economic growth. We offered an empirical resolution to the Artto-Pohjola paradox as we showed that a high rate of return on capital was combined with low capital productivity growth. This result is important in understanding Finnish economic growth 1975-90. The main contribution of this thesis was the growth accounting results on the impact of ICT on growth and productivity, as well as the comparison of electricity and ICT. It was shown that ICT s contribution to GDP growth was almost twice as large as electricity s contribution over comparable periods of time. Finland has thus been far more successful as an ICT producer than a producer of electricity. Unfortunately in the use of ICT the results were still more modest than for electricity. During the end of the period considered in this thesis, Finland switched from resource-based to ICT-based growth. However, given the large dependency on the ICT-producing sector, the ongoing outsourcing of ICT production to low wage countries provides a threat to productivity performance in the future. For a developed country only change is constant and history teaches us that it is likely that Finland is obliged to reorganize its economy once again in the digital era.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Variation i kvinnors namnfraser i officiella dokument i Helsingfors 1780-1930 : Socioonomastiska synvinklar på makt och identitet

This dissertation is an onomastic study of variation in women s name phrases in official documents in Finland during the period 1780−1930. The aim is to discuss from a socio-onomastic perspective both the changeover from patronymics to inherited family names and the use of surnames after marriage (i.e. whether women adopted their husbands family names or retained their maiden names), before new laws in this area entered into force in Finland in the early 20th century. In 1920, a law on family names that required fixed names put an end to the use of the patronymic as a person s only surname. After 1929, it was no longer possible for a married woman to retain her maiden name. Methodologically, to explain this development from a socio-onomastic perspective, I have based my study on a syntactic-semantic analysis of the actual name phrases. To be able to demonstrate the extensive material, I have elaborated a scheme to divide the 115 different types of name phrases into 13 main categories. The analysis of the material for Helsinki is based on frequency calculations of the different types of name phrases every thirtieth year, as well as on describing variation in the structure and semantic content of the name phrases, e.g. social variation in the use of titles and epithets. In addition to this, by applying a biographic-genealogical method, I have conducted two case studies of the usage of women s name phrases in the two chosen families. The study is based on parish registers from the period 1780−1929, estate inventory documents from the period 1780−1928, registration forms for liberty of trade from the period 1880−1908, family announcements on newspapers from the period 1829−1888, gravestones from the period 1796−1929 and diaries from the periods 1799−1801 and 1818−1820 providing a corpus of 5 950 name phrases. The syntactic-semantic analysis has revealed the overall picture of various ways of denoting women in official documents. In Helsinki, towards the end of the 19th century, the use of inherited family names seems to be almost fully developed in official contexts. At the late 19th century, a patronymic still appears as the only surname of some working-class women whereas in the early 20th century patronymics were only entered in the parish register as a kind of middle name. In the beginning of the 19th century, most married women were still registered under their maiden names, with a few exceptions among the bourgeoisie and upper class. The comparative analysis of name phrases in diaries, however, indicates that the use of the husband s family name by married women was a much earlier phenomenon in private contexts than in official documents. Keywords: socio-onomastics, syntactic-semantic analysis, name phrase, patronymic, maiden name, husband s family name

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

Variants of Miyachi�s Theorem for Nilpotent lie Groups

We formulate and prove two versions of Miyachi�s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi�s theorem for the group Fourier transform.

Variants Of Miyachi’S Theorem For Nilpotent Lie Groups

We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Diario da viagem do Dr. Francisco Jose de Lacerda e Almeida pelas capitanias do Para, Rio Negro, Matto-Grosso, Cuyaba, e S. Paulo, nos annos de 1780 a 1790

O Diario..., como observa Borba de Moraes, "apresenta um roteiro muito resumido, mas muito exato" e, como diz Sacramento Blake, "atendendo ao que é escrito em viagem, e viagem de 648 léguas de terras invias e inexploradas. É, entretanto, trabalho de grande valor para a geografia dos lugares percorridos." O Diario... foi reeditado pelo Instituto Nacional do Livro em 1944.

Collecção das Leis do Imperio do Brasil de 1860

Parte 1 - Atos do Poder Legislativo