A singularly perturbed differential equation with piecewise constant argument of generalized type

Akhmet, Marat
Mirzakulova, Aziza
The paper considers the extension of Tikhonov Theorem for singularly perturbed differential equation with piecewise constant argument of generalized type. An approximate solution of the problem has been obtained. A new phenomenon of humping has been observed in the boundary layer area. An illustrative example with simulations is provided.


A generalisation of a theorem of Koldunov with an elementary proof
Ercan, Z (Institute of Mathematics, Czech Academy of Sciences, 1999-01-01)
We generalize a Theorem of Koldunov [2] and prove that a disjointness preserving quasi-linear operator between Resz spaces has the Hammerstein property.
On entire rational maps of real surfaces
Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01)
In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
A classification of equivariant principal bundles over nonsingular toric varieties
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2016-12-01)
We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
The Fine Moduli Space of Representations of Clifford Algebras
Coşkun, Emre (Oxford University Press (OUP), 2011-01-01)
Given a fixed binary form f(u,v) of degree d over a field k, the associated Clifford algebra is the k-algebra C(f)=k{u,v}/I, where I is the two-sided ideal generated by elements of the form (alpha u+beta v)(d)-f(alpha,beta) with alpha and beta arbitrary elements in k. All representations of C(f) have dimensions that are multiples of d, and occur in families. In this article, we construct fine moduli spaces U=U(f,r) for the irreducible rd-dimensional representations of C(f) for each r >= 2. Our construction ...
On a Fitting length conjecture without the coprimeness condition
Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01)
Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
Citation Formats
M. Akhmet and A. Mirzakulova, “A singularly perturbed differential equation with piecewise constant argument of generalized type,” TURKISH JOURNAL OF MATHEMATICS, pp. 1680–1685, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35114.