In this paper we consider convex improper affine maps of the 3-dimensional affine space and classify their singularities. The main tool developed is a generating family with properties that closely resembles the area function for non-convex improper affine maps. Mathematics Subject Classification (2010). 53A15.

We aim to introduce extended generalized Mittag-Leffler function (EGMLF) via the Beta and obtain certain integral differential representation of them. Further, we present some formulas Riemann-–Liouville fractional integration differentiation operators. Also, derive various transforms, including Euler transform, Laplace Whittakar transform K-transform. The operator images are expressed in terms...

Affine invariant functions are constructed in spatial domain. Unlike the previous affine representation functions in transform domain, these functions are constructed directly on the object contour without any transformation. To eliminate the effect of the choice of points on the contour, an affine invariant function using seven points on the contour is constructed. For objects with several sep...

The purpose of this paper is to apply Wright generalized hypergeometric (Wgh) functions in defining a linear operator and obtain some inclusion relationships between the classes of harmonic univalent functions under this linear operator whenever certain Wgh inequalities with its validity conditions hold. Results for special cases of Wgh functions are also mentioned. 2000 Mathematics Subject Cla...

Standard immune responses are the sum of many clonal responses, cross-reactive and specific. Any study of clonal expression as well as analysis of its products requires the separation of clones. There are several approaches to this goal (1-3). The one we used was to generate immune responses of restricted heterogeneity where a limited number ofclonotypes determine the response (4, 5). The prere...

Jeri Wright studies the neural basis of behaviour and the nutritional ecology of honeybees in the Institute of Neuroscience at Newcastle University. A Wyoming native, she studied botany at the University of Wyoming while working as an assistant researcher in the entomology museum. As an undergraduate, she first combined her interest in plants and insects by studying insect nutrition as a Rhodes...

Let {Si}i∈Λ be a finite contracting affine iterated function system (IFS) on Rd. (Σ,σ) denote the two-sided full shift over alphabet Λ, and let π:Σ→Rd coding map associated with IFS. We prove that projection of an ergodic σ-invariant measure Σ under π is always exact dimensional, its Hausdorff dimension satisfies Ledrappier–Young-type formula. Furthermore, result extends to average IFSs. This c...