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New partition identities for odd W odd
Get PDFIn this note we conjecture Rogers-Ramanujan type colored partition identities for an array Nwodd with odd number of rows w such that the first and the last row consist of even positive integers. In a strange way this is different from the partition identities for the array Nw with odd number of rows w such that the first and the last row consist of odd positive integers - the partition identities conjectured by S. Capparelli, A. Meurman, A. Primc and the author and related to standard representations of the affine Lie algebra of type Cl(1) for w = 2l + 1. The conjecture is based on numerical evidence
Neke varijante Pitagorinog teorema
Get PDFU ovom smo radu proučavali neke od varijanti Pitagorinog teorema. Nakon povijesti Pitagore, dokazali smo Pitagorin teorem na četiri različita načina. Prvi dokaz je bio preko sličnosti trokuta. Zatim su slijedili Euklidov dokaz, Choupeijev te Garfildov dokaz. Predstavili smo neke primjene Pitagorinog teorema u matematici, zatim i u fizici, računajući rezultantu. Naša prva varijanta Pitagorinog teorema, pokazuje da ako zamijenimo stranice trokuta vektorima u smjeru ortogonalnih osi, te hipotenuzu vektorom Pitagorin teorem vrijedi. Druga varijanta, iskazuje da projekcija vektora na osi određene jediničnim vektorima, omogućuje da vektor izrazimo kao linearnu kombinaciju jediničnih vektora. Treća varijanta, proširuje prethodnu tvrdnju na konačno dimenzionalan unitaran prostor bilo koje dimenzije. Tesarski teorem, tj. obrat Pitagorinog teorema je naša četvrta varijanta. Peta varijanta je još jedno poopćenje Pitagorinog teorema iskazanog koristeći projekciju vektora na ortogonalne osi. Šesta i sedma varijanta (propozicija 2.2.2 i propozicija 2.2.3) daje nam odgovor na pitanje, može li se nešto od prethodnog primijeniti na ortonormirane baze u višedimenzionalnim prostorima. Dok je osma varijanta (propozicija 2.2.4) malo preformulirana sedma varijanta. Obrat prethodne varijante je naša deveta varijanta. Deseta varijanta nam daje odgovor na pitanje postoji li m-dimenzionalan potprostor od na kojem projekcije elemenata baze imaju duljinu . U zadnjem poglavlju, fokusirali smo se na neke varijante Pitagorinog teorema s operatorima i matricama. Tako, naša jedanaesta varijanta pokazuje da je trag projekcije m-dimenzionalnog potprostora jednaka . Dvanaesta varijanta pokazuje da je uređena n-torka brojeva iz intervala [0, 1], čija je suma jednaka dijagonala neke Hermitske idempotentne matrice. Upravo nas, prethodna varijanta dovodi i do posljednje trinaeste varijante Pitagorinog teorema, koja je teorem 3.2.4: Ako je uređena n-torka realnih brojeva iz intervala [0, 1], čija je suma prirodan broj, onda postoji realna simetrična idempotentna matrica s dijagonalom In this work we have studied some of the variants of the Pythagorean theorem. After the history of Pythagoras, the Pythagorean theorem was proved in four different ways. The first evidence was through similarity of triangles. Followed by Euclid’s proof, Choupei’s and Garfield’s proof. Then some applications of the Pythagorean theorem in mathematics and physics were presented. Our first variant of Pythagorean theorem, shows that if we replace the two sides of the triangle by orthogonal axes and the hypotenuse by a vector of the length the Pythagorean theorem will be valid. Another variant, express as the linear combination of certain unit vectors. The third variation is to, extend the previous statement on the finite dimensional unitary space of any dimension. Carpenter’s Theorem is our fourth variant and is inverse of the Pythagorean Theorem. The fifth variant is another formulation of the Pythagorean theorem in terms of the projections of vectors of equal length along the axes onto the line determined by a vector. The sixth and seventh variant (proposition 2.2.2 and proposition 2.2.3) gives us the answer to the question: Can something of this nature be said for orthonormal bases in higher-dimensional spaces? While the eighth variant (proposition 2.2.4) is a slightly reformulated seventh variant. The inverse of the eighth variant is our ninth variant. Tenth variant gives us the answer to the question whether there is a m-dimensional subspace of on which projections of the basis elements have length of . In the last chapter, we are focused on variants of the Pythagorean theorem with operator-matrix methods. So, our eleventh variant indicates that the trace of a projection with m-dimensional range is equal to . The twelfth variant indicates that the ordered n-tuple of numbers in [0, 1], with sum is diagonal of some idempotent self-adjoint matrix. The previous variant leads to the last thirteenth variant of the Pythagorean theorem, which is a theorem 3.2.4: If is an ordered n-tuple of numbers in [0, 1] with sum a positive integer, then there is an idempotent self-adjoint matrix with diagonal entries and all entries real
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Basic Representations for Classical Affine Lie Algebras
No full textAbstractPresented here is a construction of certain bases of basic representations for classical affine Lie algebras. The starting point is a Z-grading g=g−1+g0+g1 of a classical Lie algebra g and the corresponding decomposition g̃=g̃−1+g̃0+g̃1 of the affine Lie algebra g̃. By using a generalization of the Frenkel–Kac vertex operator formula for A(1)1 one can construct a spanning set of the basic g̃-module in terms of monomials in basis elements of g̃1 and certain group element e. These monomials satisfy certain combinatorial Rogers–Ramanujan type difference conditions arising from the vertex operator formula, and the main result is that these differences coincide with the energy function of a perfect crystal corresponding to the g0-module g1. The linear independence of the constructed spanning set of the basic g̃-module is proved by using a crystal base character formula for standard modules due to S.-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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