Yazar "Camci, Didem Karalarlioglu" seçeneğine göre listele

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    Öğe
    Equivalent curves in En
    (Amer Inst Mathematical Sciences-Aims, 2025) Mollaogullari, Ahmet; Gumus, Mehmet; Camci, Didem Karalarlioglu; Ilarslan, Kazim; Camci, Cetin
    In this paper, we first define an equivalence relation for curves in En. Based on this equivalence relation, we investigate the relationships between the Frenet frame and curvatures of equivalent curves. Next, we introduce the concept of linearly dependent curvatures in Enand examine its implications for equivalent curves. Building on this concept and the proposed equivalence relation, we present a method to construct (1,3)-Bertrand curves in E4. Additionally, we derive the relationships between the harmonic curvatures of equivalent curves and use these relationships to establish several properties of equivalent helical curves. These results enable systematic construction of curves with prescribed geometric properties.
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    Öğe
    Some results on prime rings with multiplicative derivations
    (Tubitak Scientific & Technological Research Council Turkey, 2020) Sandhu, Gurninder Singh; Camci, Didem Karalarlioglu
    Let R be a prime ring with center Z(R) and an automorphism a. A mapping delta : R -> R is called multiplicative skew derivation if delta(xy) = delta(x)y + alpha(x)delta(y) for all x, y is an element of R and a mapping F : R -> R is said to be multiplicative (generalized)-skew derivation if there exists a unique multiplicative skew derivation delta such that F(xy) = F(x)y + alpha(x)delta(y) for all x, y is an element of R. In this paper, our intent is to examine the commutativity of R involving multiplicative (generalized)-skew derivations that satisfy the following conditions: (i) F(x(2)) + x delta(x) = delta(x(2)) + xF(x), (ii) F(x circle y) = delta(x circle y) +/- x circle y, (iii) F([x, y]) = delta([x, y])+/-[x, y], (iv) F(x(2)) = delta(x(2)), (v) F([x, y]) = +/- x(k) [x, delta(y)]x(m), (vi) F(x circle y) = +/- x(k)(x circle delta(y))x(m), (vii) F([x, y]) = +/- x(k) [delta(x), y]x(m), (viii) F(x circle y) = +/- x(delta(x) circle y)x(m) for all x, y is an element of R.
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    Öğe
    THE SOURCE OF SEMIPRIMENESS OF RINGS
    (Korean Mathematical Soc, 2018) Aydin, Neset; Demir, Cagri; Camci, Didem Karalarlioglu
    Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar-domain and a vertical bar S-R vertical bar-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite vertical bar S-R vertical bar-domain is necessarily unitary, and is in fact a vertical bar S-R vertical bar-division ring. However, we provide an example showing that a finite vertical bar S-R vertical bar-division ring does not need to be commutative. All possible values for characteristics of unitary vertical bar S-R vertical bar-reduced rings and vertical bar S-R vertical bar-domains are also determined.