Ali Mutlu

Iterated Peiffer Pairings in the Moore Complex of a Simplicial Group

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for NGn∩Dn where Dn is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.

Free crossed resolutions from simplicial resolutions with given

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.

CW

In this paper a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥C=d(x,0), if there exist a, b, c, r and T:C→C satisfies the conditions 0⩽Φq(r)<Φq(a)+2(Φq(b)+Φq(c)) and aΦp(d(Tx,Ty))+bΦp(d(x,Tx))+cΦp(d(y,Ty))⩽rΦp(d(x,y)) for all x,y∈C, then T has at least one fixed point.MSC:47H10, 54H25.

-basis

In this article, the new Ishikawa iteration method is presented to find the approximate solution of an ordinary differential equation with an initial condition. Additionally, some numerical examples with initial conditions are given to show the properties of the iteration method. Furthermore, the results of absolute errors are compared with Euler, Runge-Kutta and Picard iteration methods. Finally, the present method, namely the new modified Ishikawa iteration method, is seen to be very effective and efficient in solving different type of the problem.MSC:65K15, 65L07, 65L06, 65L70.

Fixed point theorems for Φp operator in cone Banach spaces

Common coupled fixed point theorems are examined in this paper for comparable mappings ensuring nonlinear contraction in ordered partial metric spaces. Given theorems enlarge and universalize some conclusions of Gnana Bhaskar and Lakshmikantham (2006).

The new modified Ishikawa iteration method for the approximate solution of different types of differential equations

In this manuscript, firstly, Kannan contraction type mapping is universalised. Secondly, the unique fixed point of the universalized Kannan contraction type mappings in universalized metric space is verified. Furthermore, we clarify that it can not have a fixed point in metric space.

On Common Coupled Fixed Point Theorems for Comparable Mappings in Ordered Partially Metric Spaces

Using free simplicial algebras with given CW−basis, it is shown how to construct a free or totally free quasi 3-crossed module on suitable construction data. Quasi 3-crossed complexes are introduced and similar freeness results are given for these are discussed.

A Survey on Kannan Mappings in Universalized Metric Spaces

In this paper, we recall some definitions and properties from digital topology, and we consider the simplices and simplicial complexes in digital images due to adjacency relations. Then we define the simplicial set and conclude that the simplicial identities are satisfied in digital images. Finally, we construct the group structure in digital images and define the simplicial groups in digital images. Consequently, we calculate the digital homology group of two-dimensional digital simplicial group.MSC:55N35, 68R10, 68U10, 18G30.

Freeness conditions for quasi 3-crossed modules and complexes of using simplicial algebras with CW−bases

We consider an additive group structure in digital images and introduce the commutator in digital images. Then we calculate the hypercrossed complex pairings which generates a normal subgroup in dimension 2 and in dimension 3 by using 8-adjacency and 26-adjacency.

The construction of simplicial groups in digital images

Using a free simphicial group with given a CW-basis, we give an alternative description of the top group of the free square complex and 2-crossed complex of groups on 2-construction data in terms of tensors and coproducts of crossed module of groups. Therefore the functors are given between these categorical constructions.