The topic of the paper is the investigation of the homology groups of the (2n+1)-dimensional CW-complex CΩn. The spaces CΩn consist of complex-valued functions and are the analogue of the spaces Ωn, widely known in the approximation theory. The spaces CΩn have been introduced in 2015 by A.M. Pasko who has built the CW-structure of the spaces CΩn and using this CW-structure established that the spaces CΩn are simply connected. Note that the mentioned CW-structure of the spaces CΩn is the analogue of the CW-structure of the spaces Ωn constructed by V.I. Ruban. Further A.M. Pasko found the homology groups of the space CΩn in the dimensionalities 0,1,…,n,2n−1,2n,2n+1. The goal of the present paper is to find the homology group Hn+1(CΩn). It is proved that Hn+1(CΩn)=Z2n+1 if n is odd and Hn+1(CΩn)=Z2n+2 if n is even
In the present paper the spaces $\Omega_n(m)areconsidered.ThespacesΩn(m),introducedin2018byA.M.PaskoandY.O.Orekhova,arethegeneralizationofthespacesΩn(thespaceΩn(2)coincideswithΩn).TheinvestigationofhomotopypropertiesofthespacesΩnhasbeenstartedbyV.I.Rubanin1985andfollowedbyV.A.Koshcheev,A.M.Pasko.InparticularV.A.KoshcheevhasprovedthatthespacesΩnaresimplyconnected.WegeneralizedthisresultprovingthatallthespacesΩn(m)aresimplyconnected.InordertoprovethesimplyconnectednessofthespaceΩn(m)weconsiderthe1−skeletonofthisspace. Using1−cellsweformtheclosedwaysthatcreatethefundamentalgroupofthespaceΩn(m).Using2−cellsweshowthatalltheseclosedwaysareequivalenttothetrivialway.SothefundamentalgroupofthespaceΩn(m)istrivialandthespaceΩn(m)issimplyconnected.УданійстаттірозглядаютьсятопологічніпросториΩn(m).Ціпросторибуловведено2018рокувроботіА.М.ПаськатаЄ.О.ОрєховоїтаєоднимізузагальненьпросторівΩn(простірΩn(2)збігаєтьсязΩn).ДослідженнягомотопічнихінваріантівпросторуΩnбулорозпочато1985рокуВ.І.РубаномтапродовженоВ.А.Кощєєвим,А.М.Паськом.Зокрема,В.А.Кощєєвдовіводнозв′язністьпросторівΩn.ВційроботімиузагальнюєморезультатВ.А.Кощєєва,довівши,щопросториΩn(m)−однозв′язні.Щобдовестице,мирозглядаємоодновимірнийкістякпросторуΩn(m).Використовуючиодновимірніклітинивцьомукістякубудуємозамкненішляхи,якіутворюютьфундаментальнугрупупросторуΩn(m).Відтак,використовуючидвовимірніклітини,доводимо,щоцішляхигомотопнітривіальномушляху.Цеозначає,щофундаментальнагрупапросторуΩn(m)$ тривіальна, а сам простір - однозв'язний
The paper continues the investigation of the spaces of complex-valued perfect splines Ωn(m). These spaces were introduced as generalization of the spaces Ωn, the topology of which has been studied by V.I. Ruban, V.A. Koshcheev, A.M. Pasko. In our previous papers the homology groups of the spaces Ωn(m) have been found and their simply connectedness was established. The topic of the paper is finding of the homology groups of the Cartesian product Ωn1(m1)×Ωn2(m2). In order to find the homology groups of this Cartesian product the Kunneth theorem has been used. Using the Kunneth theorem and the fact that Tor(A,B)=0 if at least one of the group A,B is free we presented the homology group of the Cartesian product Ωn1(m1)×Ωn2(m2) as the sum of the tensor products of the homology groups of this spaces. Calculating the tensor products we found the homology groups of Ωn1(m1)×Ωn2(m2)
In the paper the homology groups of the (2n+1)-dimensional CW-complex CΩn are investigated. The spaces CΩn consist of complex-valued functions and generalize the widely known in the approximation theory spaces Ωn. The research of the homotopy properties of the spaces Ωn has been started by V.I. Ruban who in 1985 found the n-dimensional homology group of the space Ωn and in 1999 found all the cohomology groups of this space. The spaces CΩn have been introduced by A.M. Pasko who in 2015 has built the structure of CW-complex on these spaces. This CW-structure is analogue of the CW-structure of the space Ωn introduced by V.I. Ruban. In present paper in order to investigate the homology groups of the spaces CΩn we calculate the relative homology groups Hk(CΩn,CΩn−1), it turned out that the groups Hk(CΩn,CΩn−1) are trivial if 1≤k<n and Hk(CΩn,CΩn−1)=ZCn+1k−n if n≤k≤2n+1, in particular Hn(CΩn,CΩn−1)=Z. Further we consider the exact homology sequence of the pair (CΩn+1,CΩn) and prove that its inclusion operator i∗:Hk(CΩn)→Hk(CΩn+1) is zero. Taking into account that the relative homology groups Hk(CΩn+1,CΩn) are zero if 1≤k≤n and the inclusion operator i∗=0 we have derived from the exact homology sequence of the pair (CΩn+1,CΩn) that the homology groups Hk(CΩn),1≤k<n, are trivial. The similar considerations made it possible to calculate the group Hn(CΩn). So the homology groups Hk(CΩn),n≥2,k=1,...,n, have been found
The 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” 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
We 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
We 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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