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

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 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

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

Ecological properties and close relationships of some Scilla L. Taxa (asparagaceae) in Turkey

Ecological properties of some Scilla L. taxa [S. bifolia L., S. melaina Speta, S. siberica Haw. subsp. armena (Grossh.) Mordak, S. leepii Speta, S. ingridae Speta, S. mesopotamica Speta, S. autumnalis L., S. monanthos C. Koch., S. rosenii C. Koch. and S. cilicica Siehe] were compared and relationships among taxa were determined. S.leepii and S. mesopotamica are endemic to Turkey. Because of various reasons, S. melaina, S. leepii, S. ingridae, S. mesopotamica, S. monanthos, S. siberica subsp. armena, S. rosenii and S. cilicica have limited distribution in Turkey. The investigated taxa have fragrant flowers, so are used as ornamental plant in gardens, parks and balconies in Turkey. Soil samples of the taxa were taken in flowering periods and physical and chemical properties (texture class, % of total salinity, pH, % of CaCO3, % of organic matter, % of total N, P, K, Ca, Mg, Mn, Cu, Fe and Zn (in mg/kg) were determined. According to the similarities and differences in ecological characteristics, the taxa were divided into four groups. 1st group: S. melaina, S. leepii, S. ingridae and S. mesopotamica; 2nd group: S. siberica subsp. armena and S. cilicica; 3rd group: S. bifolia and S. autumnalis; 4th group: S. rosenii and S. monanthos. From the data, it has been found that organic matter, N, P, K, Ca, Fe and Zn values are more effective than the other soil factors in the distributions of the investigated taxa. © 2018 Friends Science Publishers

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

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