Two-parameter differential calculus on the h-superplane

We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space algebra.Comment: 14 page

Two-parameter nonstandard deformation of 2x2 matrices

We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup $GL_{p,q}(1|1)$ by a transformation.Comment: 10 page

Differential Geometry of the q-plane

Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.Comment: 9 page

Two-Parameter Differential Calculus on the h-Exterior Plane

We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.Comment: 7 page

Cartan calculus on the superalgebra calO(mathbbCq2vert1){cal O}({mathbb C}_q^{2vert1})

In analogy with the classical case, the noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give a Cartan calculus on the algebra of functions on quantum (2+1)-superspace ${mathbb C}_q^{2vert1}$, we first introduce two left-covariant differential calculi over ${cal O}({mathbb C}_q^{2vert1})$ and extend one of these calculi by adding inner derivations and Lie derivatives to the calculus. We also introduce tensor product realization of the wedge product of forms

Cartan calculi on the quantum superplane

Cartan calculi on the extended quantum superplane are given. To this end, the noncommutative differential calculus on the extended quantum superplane is extended by introducing inner derivations and Lie derivatives

The Effect Of Parameters Such as Development Period Of Donor Plant and Explant Source on Meristem Stamina and Growth in Grapevine Meristem Culture

Bu çalışma ile asmada meristem kültürü çalışmalarını etkileyen faktörlerden donör bitkinin gelişim dönemive eksplantın donör bitki üzerindeki pozisyonlarının meristem canlılığına ve gelişimine etkileriincelenmiştir. Bu kapsamda üç farklı çeşidin (Gamay, Trakya İlkeren ve İtalia), üç değişik fizyolojikgelişim dönemi (çiçeklenme başlangıcı, tane tutumu ve tanelerin bezelye büyüklüğü aldığı dönem) ileeksplantın bitki üzerindeki pozisyonu olarak ana sürgün uçları ve koltuk sürgünlerinin uçlarından izoleedilen meristemler kullanılmıştır. İzole edilen meristemler in vitro koşullarda MS yapay besin ortamındakültüre alınmışlar ve bunların üç hafta sonraki canlılık ve gelişim düzeyleri değerlendirilmiştir. Yapılandeğerlendirmeler sonucunda, asmada meristem canlılığı ve meristem gelişimi açısından en uygun meristemalım döneminin tanelerin bezelye büyüklüğü aldığı dönem olduğu ve bitki üzerinde koltuk sürgünlerindenalınan meristematik dokuların ana sürgün ucundan alınan meristematik dokulara oranla daha yüksekdeğerler verdiği tespit edilmiştir.In this study, two of the important factors that affect meristem culture, the effect of development period of donor plant and the position of explant on meristem stamina and growth were tried to evaluate. Three different physiological growth periods of three different varieties and meristems isolated from main shoot tips and axillary shoots of explants were used. The isolated meristems were cultured in MS in in vitro conditions for three weeks and parameters such as stamina and growth levels were evaluated. According to results of this study, it is concluded that in the point of meristem stamina and growth the most suitable period for isolation of meristems were found as period when the berries are in size like pea. Besides, meristems isolated from axillary shoots gave more values than meristems isolated from main shoot tips

On the Differential Geometry of GLq(1∣1)GL_q(1| 1)

The differential calculus on the quantum supergroup GL$_q(1| 1)$ was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL$_q(1| 1)$ in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix $\hat{R}$Comment: 14 page