53 research outputs found
Critical sets of PL and discrete Morse theory: a correspondence
No full textPiecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical points have been given in the literature for the discrete setting, making a clear understanding of the relationships occurring between them not obvious. This paper aims at providing equivalence results about critical points of the two discretized Morse theories. First of all, we prove the equivalence of the existing notions of PL critical points. Next, under an optimality condition called relative perfectness, we show a dimension agnostic correspondence between the set of PL critical points and that of discrete critical simplices ofthe combinatorial approach. Finally, we show how a relatively perfect discrete gradient vector field can be algorithmically built up to dimension 3. This way, we guarantee a formal and operative connection between critical sets in the PL and discrete theories
Perfect discrete morse functions on connected sums
No full textLet be a finite, regular cell complex and be a real valued function on . Then is called a textit{discrete Morse function} if for all -cell , the following conditions hold: begin{align*} displaystyle n_{1}=# {tau > sigma mid f(tau)leq f(sigma)} leq 1, \ n_{2}=# {nu < sigma mid f(nu)geq f(sigma)}leq 1. end{align*} A -cell is called a textit{critical -cell} if . A discrete Morse function is called a textit{perfect discrete Morse function} if the number of critical -cells of equals to the -th Betti number of with reference to the coefficient group. The main purpose of this thesis is to compose and decompose perfect discrete Morse functions on connected sums of closed, connected manifolds. We will first discuss the existence of perfect discrete Morse functions on finite complexes and closed, connected, triangulated -manifolds. Secondly, we will show that if the components of a connected sum of closed, connected, triangulated -manifolds admit a perfect discrete Morse function, then admits a perfect discrete Morse function that coincides with the perfect discrete Morse functions on the components. Next, we will find a separating sphere on a connected sum of closed, connected, triangulated surfaces and -manifolds if admits a perfect discrete Morse function . Finally, we will prove that can be decomposed as perfect discrete Morse functions on each component of after some local modifications of it
Variation and association in Lathyrus species based on seed biochemical constituents
No full textGülümser, Erdem (Bilecik, Author)
Mut, Hanife (Bilecik, Author)The seeds of twelve Lathyrus species were analyzed for crude protein, ODAP, ash, mineral contents and thousand seed weight. CP content varied from 20.78% in L. cicera to 30.92% in L. ochrus. ODAP content was the most variable trait (CV= 97.81%), being highest (10.31 mg g(-1)) in L. clymenum (cultivar) and lowest (0.65 mg g(-1)) in L. laxiflorus (wild). This was followed by thousand seed weight (TSW) being highest in L. sativus (114.54 g) and lowest in L. nissolia (3.45 g). These species also exhibited a reasonable variation regarding mineral contents, especially for Ca (CV= 40.29%) and Mn (CV= 40.96%). Correlation analysis, based on interspecies means indicated that ODAP was highly correlated with TSW (r = 0.762), Zinc (r= 0.732) and B (r=- 0.507), while there was no significant correlation of ODAP with CP and ash contents
Potential of community gardens for sustainable urban development in Izmir, Turkey
No full textUrban agriculture is becoming increasingly important in developed and developing countries that are experiencing serious environmental and social problems. As a developing country, Turkey has faced some environmental, social and economic issues in urban areas with typically irregular industrialization and urbanization processes since the 1950s. In this study, community gardening, as one of the urban agriculture practices, was evaluated as a tool for sustainable urban development in the Izmir Metropolitan area in Turkey. The potential of existing community gardens was investigated with two case study sites in Bornova and Buca regarding social, economic and environmental qualities of the region. A mixed method approach incorporates historical research, interviews, and diagramming. After the evaluation of findings from site observations, open discussions and interviews, the data was used to illustrate conceptual community garden network in Izmir.M.L.A.Includes bibliographical referencesby Hanife Vardi Topa
Perfect discrete Morse functions on connected sums
No full textWe study perfect discrete Morse functions on closed, connected, oriented n-dimensional manifolds. We show how to compose such functions on connected sums of manifolds of arbitrary dimensions and how to decompose them on connected sums of closed oriented surfaces
Homological properties of persistent homology
No full textIn this paper, we investigate to what extent persistent homology benefits from the properties of a homology theory. We show that persistent homology benefits from a Mayer-Vietoris sequence and a long exact sequence for a pair if one works with graded persistence modules. We also give concrete examples showing that the same is not the case for persistent homology groups
Kalıcı Homoloji
No full textKalıcı homoloji(persistent homoloji), verilerin(üzerinde bir metrik tanımlı olan ayrık noktalar kümesi) topolojik özelliklerini(bileşenleri, üzerindeki delikler, çizge yapısı vb.) anlamak için kullanılan cebirsel bir metottur. Bu projedeki amacımız, homoloji gruplarının temel özelliklerini (ikililer icin tam diziler, dualite, evrensel katsayılar vb.) kalıcı homoloji bağlamında ele alıp, bu özelliklerin hangi formlarda kalıcı homolojiye genişletilebileceğini araştırmaktır
Ebu Hanife ve el-Fıkhu’l-ekber risalesi
No full textBu çalışma, İmâm Ebû Hanîfe Nûman b. Sâbit’e atfedilen el-Fıkhu’l-ekber adlı risâlenin aidiyetine dair tartışmaları ele almaktadır. Hicrî sekizinci yüzyıldan sonraki dönemde İslâm Coğrafyası’nda yaygınlaşan bu eserin müellifine olan nispeti ile muhtevasına yönelik eleştiriler yapılmış, bunun neticesinde bu risâlenin günümüzdeki şekliyle Ebû Hanîfe’ye ait olamayacağına dair bir kanaat oluşmuştur. Risâlenin içeriğine yöneltilen eleştiriler dikkate alınarak bu eserin Ebû Hanîfe’ye olan nispeti, muhtevasının sonradan değiştirilip değiştirilmediği, risâlede geçen konuların ne ölçüde onun görüşlerini yansıttığı gibi temel konulara değinilmiştir. Bu doğrultuda yazma eserler ve ilk dönem kaynaklar incelenerek eserin müellifine olan aidiyetinin doğru olup olmadığı ortaya konulmaya çalışılmış, diğer yandan el-Fıkhu’l-ekber’in muhtevası ile Ebû Hanîfe’nin akaide dair görüşlerinin karşılaştırılması yapılarak bu risâledeki bilgilerle inanç konularındaki görüşleri arasında var olan benzerlik ve farklılıklar tespit edilmiştir. Ayrıca Ebû Hanîfe’ye el-Fıkhu’l-ekber adıyla iki farklı eser nispet edilmektedir. Bu iki ayrı risâle içerisinde hangisinin ona ait olduğunun araştırılması ise çalışmanın ana konularından birisini oluşturmuştur. Böylece erken döneme ait eserlerde el-Fıkhu’l-ekber ismi geçtiğinde hangisinin esas alınması gerektiği konusu netleştirilmeye çalışılmıştır. Ebû Hanîfe’nin diğer akaid risâlelerine yönelik eleştirilere de değinilerek bunlardan hangisinin aidiyetinin daha kuvvetli olduğuna dair oluşan kanaatler zikredilmiştir.This study debates discussions about the al-Fiqh al-Akbar attributed to Imam Abu Hanifa Nûman b. Sâbit. In the period after the eighth century of hijri. Criticisims have been made about relation with author and content of this work which has become widespread in Islamic Geography, in consequence of this there is a consensus that this risala can not belong to Abu Hanifa as it is today. Considering criticisims directed to content of risala, it is mentioned basic topics such as relative this work to Abu Hanifa and whether the content is changed or not afterwards and how reflects of his views. In this direction by viewing manuscripts and first period sources it has been tried to reveal whether the belonging of the work to author is correct or not, on the other hand by comparing content of al-Fiqh al-Akbar with the views of Abu Hanifa about akaid, it was identified similarities and differences between informations in this risala and views of belief. In addition two different works are referred Abu Hanifa in the name al-Fiqh al-Akbar. Investigation which one belongs to him in these risalas has constituted one of the main topics of study. Thus, when al-Fiqh al-Akbar’s name mentions in early works, it has been tried to clarify which should be taken as basis. By referring to Abu Hanifa’s criticisms to other risalas it has been refered to opinions which one of their belongings are strong
Embryonic development of the olive fruit fly, Bactrocera oleae Rossi (Diptera: Tephritidae), in vivo
No full textThe olive fruit fly, Bactrocera oleae (Rossi) (Diptera: Tephritidae), is a pest that infests olive fruits. The female oviposits in large green olives and larvae hatch inside the fruit, where they feed upon the fruit tissues. Larval development is completed inside the fruit. These flies cause great damage to olive production worldwide. Traditionally, insecticides have been directed against the adult stage, but the results are not efficient. This present work is a study of embryogenesis in the olive fruit fly. The external morphology of the Bactrocera oleae Rossi (Diptera: Tephritidae) egg is described from light microscopy without dechorionation. The observations were made in vivo and were photographed. The eggshell of B. oleae contains a smooth chorion with a cup-shaped anterior pole. The average length of eggs is 0.738 +/- 0.01 mm and the average diameter is 0.21 +/- 0.06 mm. The embryonic developmental progress is described as formation of the zygote, blastoderm and gastrulation, and organogenesis. The embryogenesis is completed within 65-70 h at 25 +/- 1 degrees C under laboratory conditions. External egg morphology can be useful in estimating the age of B. oleae eggs for purposes such as introducing genes into embryos by germline transformation in future studies.TUBITAK [105 O 558]; Turkish Academy of Sciences (TUBA-GEBIP); Scientific and Technological Research Council of Turkey (TUBITAK) [105 O 558]The author thanks undergraduate students Elvan Sert and Ramazan Gencer for their help in embryo observations. The author thanks Dr Alfred M Handler and Dr James L Nation who collaborated in TUBITAK Project Grant No. 105 O 558. This research was financially supported by the Turkish Academy of Sciences (TUBA-GEBIP 2009) and the Scientific and Technological Research Council of Turkey (TUBITAK, Project Grant No. 105 O 558)
Elementary Methods for Persistent Homotopy Groups
No full textIn this paper, we study the basic properties of persistent homotopy groups.
We show that the persistent fundamental group benefits from the Van Kampen
theorem, and the interleaving distance between total spaces is less than or
equal to the maximum of the interleaving distances between subspaces. We also
prove excision and Hurewicz theorems for persistent homotopy groups. As an
application, we analyze the sublevelset persistent homotopy groups of the
energy landscape of alkane molecules.Comment: 29 pages, 20 figure
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