In this paper, we prove common fixed point theorems for hybrid pairs of mappings satisfying an implicit relation in 2-metric spaces by using a new commutativity condition i.e. weak commutativity of type (KB). We also prove common fixed point theorem, of Gregus type for hybrid pairs of maps by using weak commutativity of type (KB) in 2-metric spaces. We extend, improve and generalize many known ...

Let S1 = {Ft}t≥0 and S2 = {Gt}t≥0 be two continuous semigroups of holomorphic self-mappings of the unit disk ∆ = {z : |z| < 1} generated by f and g, respectively. We present conditions on the behavior of f (or g) in a neighborhood of a fixed point of S1 (or S2), under which the commutativity of two elements, say, F1 and G1 of the semigroups implies that the semigroups commute, i.e., Ft◦Gs = Gs◦...

The Wilson loop in the non-commutative dipole field theory is re-examined within the framework of dual gravity description. In contrast to the previous investigations, we let the dual string be moving along the deformed S and find the exact expression of the interquark potential. The potential shows a Coulomb behavior at all distance and does not have a minimum distance between quarks, which ex...

In an invited paper, Baksalary [Algebraic characterizations and statistical implications of the commutativity of orthogonal projectors. In: T. Pukkila, S. Puntanen (Eds.), Proceedings of the Second International Tampere Conference in Statistics, University of Tampere, Tampere, Finland, [2], pp. 113–142] presented 45 necessary and sufficient conditions for the commutativity of a pair of orthogon...

We perform a perturbative O(g4) Wilson loop calculation for the U(N) YangMills theory defined on non-commutative one space one time dimensions. We choose the light-cone gauge and compare the results obtained when using the Wu-Mandelstam-Leibbrandt (WML) and the Cauchy principal value (PV ) prescription for the vector propagator. In the WML case the θ-dependent term is well-defined and regular i...

In this paper, based on recent work [13] 1 , we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this new interpretation of superPoincaré algrebra as our fundamental symmetry, we can construct Lorentz and Poincaré SUSY invariant quantum field theory on the non(anti)commutative (super)space. The key point is validity of our new twist element that guarantee...

Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with n windings a non trivial scaling intertwines n and N . In the non-commutative case the interplay becomes tighter owing to the merging of space-time and “internal” symmetries in a larger group U(∞). We perform a...

We present a least squares framework for constructing p-th degree immersed finite element (IFE) spaces for typical second-order elliptic interface problems. This least squares formulation enforces interface jump conditions including extended ones already proposed in the literature, and it guarantees the existence of p-th IFE shape functions on interface elements. The uniqueness of the proposed ...

In this paper we study the midpoint structure of the algebra of open strings from the standpoint of the operator/Moyal formalism. We construct a split string description for the continuous Moyal product of hep-th/0202087, study the breakdown of associativity in the star algebra, and identify in infinite sequence of new (anti)commutative coordinates for the star product in in the complex plane. ...