Author

# Selahattin Beyendi

Bio: Selahattin Beyendi is an academic researcher. The author has contributed to research in topics: Mathematics & Pure mathematics. The author has an hindex of 2, co-authored 6 publications receiving 9 citations.

Topics: Mathematics, Pure mathematics, Geodesic, Pointwise, Totally geodesic

##### Papers

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11 Apr 2018

TL;DR: In this paper, the authors studied α-cosymplectic manifolds admitting a W₂-curvature tensor, and the object of their work was to study α-convex manifolds with W ₂ curvature tensors.

Abstract: The object of this paper is to study α-cosymplectic manifolds admitting a W₂-curvature tensor.

8 citations

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31 Dec 2020

TL;DR: In this paper, the authors define and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds, and study these types of submansifolds with parallel canonical structures.

Abstract: The aim of the present paper is to define and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds. We mainly concerned with quasi bi-slant submanifolds of cosymplectic manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant and quasi hemi-slant submanifolds. First, we give non-trivial examples in order to demostrate the method presented in this paper is effective and investigate the geometry of distributions. Moreover, We study these types of submanifolds with parallel canonical structures.

6 citations

29 Jun 2018

TL;DR: In this article, Bakanligi et al. presented a plan to plan a matematik program for the year 2019, which is the first year of the program.

Abstract: Matematik ogretim programlarinda farkli zamanlarda yenileme calismalari yapilmis olup en son degisiklikler 2018 yilinda yapilmistir. Calismada 2018 ve 2013 yillarinda ortaokul duzeyinde matematik dersindeki yenilikler incelenmistir. Bu baglamda calismada 2013 ve 2018 yillarinda yenilenen matematik dersi ogretim programlari icerisinde ortaokul duzeyinde yapilan degisikliklerin karsilastirmali olarak analiz edilmesi amac olarak belirlenmistir. Bu amac kapsaminda calismada nitel arastirma yaklasimi benimsenmis olup, betimsel bir durum calismasi niteliginde tasarlanmistir. Verilerin toplanmasi icin Milli Egitim Bakanligi tarafindan elektronik ortamda yayinlanan 2013 ve 2018 Matematik dersi ogretim programlari olusturdugundan, veri toplama yontemi olarak dokuman incelemesi kullanilmistir. Calismada amacli ornekleme yontemlerinden olcut ornekleme yontemi kullanilmistir. Calismada dokuman incelemesi icin olcut olarak 2013 ve 2018 Matematik dersi ogretim programlarinin ortaokul boyutunu analiz etmek belirlenmistir. Calismada elde edilen veriler analiz edilirken arastirmaci tarafindan belirlenen kategorilerin frekanslari ve yuzde hesaplamalari yapilmistir. Arastirma sonucunda 2013 ogretim programinda degerler konusunun ele alinmadigi fakat 2018 ogretim programinda kapsamli bir sekilde yer aldigi gorulmektedir. 2013 ogretim programinda toplamda 233, 2018 ogretim programinda ise toplamda 215 kazanimin yer aldigi belirlenmistir. Kazanim sayilarinda azalma oldugu tespit edilmistir. Calismada ogretim programlarinin unite sayisi acisindan degerlendirilmesi neticesinde 2013 ogretim programinda 5 olan unite sayisi 2018 ogretim programinda 6’ya yukseldigi belirlenmistir.

4 citations

15 Apr 2018

TL;DR: In this article, a Riemannian submersion from a manifold endowed with a semi-symmetric non-metric connection onto a manifold is studied, and the curvatures of the total manifold, the base manifold and the fibres are compared by computing curvatures.

Abstract: We study Riemannian submersions from a Riemannian manifold endowed with a semi-symmetric non-metric connection onto a Riemannian manifold. We give an example and investigate O'Neill's tensor fields, obtain derivatives of those tensor fields and compare curvatures of the total manifold, the base manifold and the fibres by computing curvatures.

2 citations

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TL;DR: In this paper , a new class of submanifolds which are called pointwise quasi bi-slant (PQS) submansifolds in almost Hermitian manifolds is introduced.

Abstract: In this paper, we introduce a new class of submanifolds which are called
pointwise quasi bi-slant submanifolds in almost Hermitian manifolds which
extends quasi bi-slant, bi-slant, hemi-slant, semi-slant and slant
submanifolds in a very natural way. Several basic results in this respect
are proved in this paper. Moreover, we obtain some conditions of the
distributions which is involved in the definition of the new submanifolds.
We also get some results for totally geodesic and mixed totally geodesic
conditions for pointwise quasi bi-slant submanifolds. Finally, we illustrate
some examples in order to guarantee the new kind of submanifolds.

2 citations

##### Cited by

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16 May 2017

TL;DR: This study compares Turkey and Singapore’s mathematics content standards in terms of the highligthed mathematical processes to reveal that the two countries reflected mathematical processes differently in their content standards.

Abstract: This study compares Turkey’s and Singapore’s mathematics content standards in terms of the highligthed mathematical processes. A mathematical processes framework was employed to analyze the content standards drawing on the standards for mathematical practice defined by the Common Core State Standards for Mathematics. The standards for mathematical practice include make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, look for and express regularity in repeated reasoning. The data sources are 2013 mathematics curriculum standards of Turkey and 2013 mathematics syllabus of Singapore for grades 7 and 8. Data analysis revealed that the two countries reflected mathematical processes differently in their content standards. Some mathematical processes are not identified in Turkey’s content standards while all mathematical processes are observed in Singapore’s content standards. The distribution of the observed mathematical processes are also different in the two countries. Suggestions for future content standards revisions are shared in the paper.

17 citations

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TL;DR: In this paper, the authors introduce and study the almost bi-slant submanifolds of an almost contact metric manifold and obtain integrability conditions of the distributions which are involved in their definition.

Abstract: In this paper we introduce and study the almost bi-slant submanifolds of an almost contact metric manifold. We give some characterization theorems for almost bi-slant submanifolds. Moreover, we obtain integrability conditions of the distributions which are involved in the definition of almost bi-slant submanifolds. We also get some results for totally geodesic and totally umbilical almost bi-slant submanifolds of cosymplectic manifolds and Sasakian manifolds.

7 citations

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TL;DR: In this paper , the authors studied α-cosymplectic manifold and showed that the Ricci tensor tensor is a semisymmetric manifold, which is an extension of the RICCI tensor.

Abstract: In this paper, we study α-cosymplectic manifold
$M$
admitting
$\ast $
-Ricci tensor. First, it is shown that a
$\ast $
-Ricci semisymmetric manifold
$M$
is
$\ast $
-Ricci flat and a
$\varphi $
-conformally flat manifold
$M$
is an
$\eta $
-Einstein manifold. Furthermore, the
$\ast $
-Weyl curvature tensor
${\mathcal{W}}^{\ast}$
on
$M$
has been considered. Particularly, we show that a manifold
$M$
with vanishing
$\ast $
-Weyl curvature tensor is a weak
$\varphi $
-Einstein and a manifold
$M$
fulfilling the condition
$R\left({E}_{1},{E}_{2}\right)\cdot {\mathcal{W}}^{\ast}=0$
is
$\eta $
-Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold
$M$
admitting
$\ast $
-Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting
$\ast $
-Ricci soliton and almost
$\ast $
-Ricci soliton are drawn.

4 citations

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3 citations

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TL;DR: In this article, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music, and the results showed that prospective teachers preferred verbal (92%), note and real life representations in defining the note values in general terms.

Abstract: In this study, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music. The case study, one of the qualitative research designs, was used in the study. Study group of the research consisted of 113 pre-school teachers. According to the findings of the research, prospective teachers preferred verbal (92%), note and (80%) real life representations in defining the note values in general terms. On the other hand, geometrical and algebraic representations were preferred at lower rates. The mathematical expressions of the vast majority were found to be correct when the accuracy of representations chosen by the teacher candidates were analyzed. Problems experienced in relation to mathematical expressions in teaching note values include disproportionate fragmentation, modeling error, and algebraic error . On the other hand, representations used in the teaching of note values have generally been unsuccessful in musical expressions; the problems faced in articulation were determined as not (being able to) showing note values, incorrectly showing quarter note values and incorrectly defining note values. The accuracy rates of mathematical expressions are higher than those of musical expressions, regardless of the representation used (note, real life, geometric, verbal, algebraic). In addition, research findings show that prospective teachers who use four types of representation in the teaching of note values are more successful in mathematical and musical context than those who use two and three representations.

3 citations