scholarly journals A complete classification of three-dimensional algebras over ℝ and ℂ — (visiting old, learn new)

Author(s):  
Yuji Kobayashi ◽  
Kiyoshi Shirayanagi ◽  
Makoto Tsukada ◽  
Sin-Ei Takahasi

We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a completely elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century and this century.

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.


Author(s):  
William H. Meeks ◽  
Pablo Mira ◽  
Joaquín Pérez ◽  
Antonio Ros

Abstract We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.


Author(s):  
Andy Campbell

Beyond monographic texts dedicated to single artists, it is rare to find book-length studies that solely focus African American sculpture—or, sculpture made by African Americans. The reasons for this are many and complex. Although sculpture was a mainstay of 19th-century arts education in Europe and the Americas, in the latter half of the 20th century sculpture was newly questioned as a stable category of production. Between the 18th century and today media-specific practices have been broadly replaced with multimedia ones. This begs the question: what constitutes sculpture in any history or reference text that purports to span a number of centuries? An artist like Renée Green (b. 1959), for example, creates sculpture—discrete, three-dimensional objects—but also multi-part environmental installations, sound works, videos, architecture, and websites, as well as photography and prints. In light of these historical shifts, this bibliography takes a broad view of sculpture, and includes the work of self-described sculptors, such as the 19th-century sculptor Edmonia Lewis, as well as those with pluralistic practices like Green. Similarly, the category of “African American” has come under scrutiny, as the various signifiers of such an identity (for example, phenotype and/or ancestry) shift with broader social, economic, aesthetic, and political systems. Terminology has also changed a great deal since the 18th century—with popular linguistic designations moving from “negro,” to “colored,” to “black,” to “Afro-American,” to “African American,” and back to “black” again. Each contains historical political import, tied to both in-group empowerment and extrinsic, sometimes derogatory, uses. The visual arts are uniquely positioned to approach, understand, question, and challenge these changing social and semiotic conditions, and the anxieties and pleasures of black identification are often registered in nuanced and multifaceted ways within the realm of the visual. It would be a mistake to assume that the term “African American” encompassed the full political force of all artists included here, many of whom experience(d) the reality of intersectional identities and oppressions attached to gender, race, ability, class, and sexuality. For a more complete accounting of the visual arts beyond sculpture, see the separate Oxford Bibliographies in African American Studies article Visual Arts.


Zootaxa ◽  
2020 ◽  
Vol 4802 (1) ◽  
pp. 41-60 ◽  
Author(s):  
YI-KAI TEA ◽  
ANTHONY C. GILL

The taxonomy and classification of the microcanthid fish genus Microcanthus Swainson has been a subject of contention dating back to the 19th century. Its allopatric, disjunct anti-equatorial distribution across the Indo-West Pacific has resulted in the recognition of several nominal taxa, though these have been widely regarded as synonyms of Microcanthus strigatus (Cuvier). Following the results published in a companion study elsewhere by the authors, the taxonomy of Microcanthus and the validity of these nominal synonyms are herewith revised. Microcanthus strigatus is redescribed on the basis of 66 specimens from East Asia, Hawaii and Western Australia, and M. joyceae is resurrected and redescribed on the basis of 25 specimens from eastern Australia and the southwest Pacific. Microcanthus differs from other microcanthid genera in having the following combination of characters: dorsal-fin rays XI,15–17 (usually XI,16); anal-fin rays III,13–15 (usually III,14); pectoral-fin rays 15–17 (usually 16); scales ctenoid with ctenial bases present; lateral-line scales partially or heavily obscured by adjacent scales; and body pale in preservation with five horizontal dark stripes reaching the posterior edges of dorsal and anal fins, and base of caudal fin. The review is accompanied by a key to the genera of Microcanthidae. 


1997 ◽  
Vol 24 (1-2) ◽  
pp. 95-114 ◽  
Author(s):  
Emilio Ridruejo

Summary French philosophical grammmar and grammatical rationalism developed from the 17th-century Port Royal Grammar, but they were not adopted by Spanish grammarians until early in the 19th century. Of works responsible for the introduction of French grammatical philosophy in Spain, one of the earliest and the most important one is the Principios de gramática general (Madrid 1835), by José Gómez Hermosilla (1771–1837/38?). The work was very well received; by 1841 it already was into a third edition. Even before first appearing in print, a manuscript of the Gramática General was used to adapt Gómez Hermosilla’s ideas to the 1828 Castilian grammar of Jacobo Saqueniza (anagram for Joaquín Cabezas). The most important of the Castilian grammars influenced by the work of Gómez Hermosilla were the one just mentioned and the one by Antonio Martinez de Noboa, published in 1839. The application of Hermosilla’s theories to descriptive grammars of Castilian required adapting both the theory and the description to achieve a reasonable fit between universal and language specific aspects. Other adjustments were required of the writers of descriptive grammars in order to avoid conflicts with a long and well established grammatical tradition. Nevertheless, grammars like those of Saqueniza and Noboa show innovations which resulted from their relationship with the theories of Hermosilla which will produce a deictic interpretation of articles, possesives and demonstratives, and will affect the theory of verb tenses, as well as the definitions of prepositions and conjunctions, and the classification of sentences. Additionally, Noboa’s Castilian Gramática, whose title makes a claim to be in accordance with grammatical philosophy, includes the most extensive and systematic treatment of syntax prior to the appearance of the work of Andres Bello (1781–1865) in 1847.


1970 ◽  
Vol 116 (533) ◽  
pp. 377-386 ◽  
Author(s):  
Isaac M. Marks

History of term ‘phobia’The term ‘phobia’ derives from the Greek word ‘phobos’ meaning panic-fear and terror, and from the deity of the same name who provoked fear and panic in one's enemies. Although morbid fears have been described by doctors from Hippocrates onwards, the word phobia has only been used on its own since the beginning of the 19th century, and it gradually gained acceptance during that century in the same sense as today, viz. an intense fear which is out of proportion to the apparent stimulus. Such fear cannot be explained or reasoned away and leads to avoidance of the feared situation where possible.


10.23856/4624 ◽  
2021 ◽  
Vol 46 (3) ◽  
pp. 190-194
Author(s):  
Roman Tashian

The aim of this paper is providing the analysis of the classification of invalid transactions into void and voidable, which is recognized in many countries. This classification takes roots from the times of Ancient Rome, and was further developed in the 19th century thanks to the works of pandectists, primarily F.K. von Savigny and B. Windscheid. Today many European states are reforming their civil legislation. This fact allows us to take a fresh look at many institutions of civil law. In addition to the traditional approaches that are characteristic of the countries of the pandecto system, special attention should be paid to the “theorie moderne”, which is widespread in the countries of the Romanesque legal system. In the context of the invalidity of transactions, the article analyzes the provisions of the legislation of the leading European countries – Germany, France, the Netherlands, Italy, Spain, Belgium. Based on the above, it is concluded that this classification of the invalidity of transactions has not lost its meaning and is relevant today.


The article describes the interrelationships that emerged between art, crafts, technology and design, in the period from the second half of the 19th century to the present day. Attention is paid to the classification of a work and the delineation of the category ‘Object’.


Author(s):  
Andronikos Paliathanasis

AbstractWe perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm (CH) equation and the generalized Benjamin-Bono-Mahoney (BBM) equation. From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the CH equation. We determine the one-dimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the similarity solutions for the two equations of our study. The reduced equations are studied by using the point symmetries or the singularity analysis. Finally, the singularity analysis is directly applied on the partial differential equations from where we infer that the generalized equations of our study pass the singularity test and are integrable.


2017 ◽  
Vol 28 (13) ◽  
pp. 1750092
Author(s):  
Zhenxiao Xie ◽  
Changping Wang ◽  
Xiaozhen Wang

A three-dimensional Lorentzian hypersurface [Formula: see text] is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of [Formula: see text]. In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.


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