In this talk I will outline a new semantics for dependent polymorphic type theories with Martin-Lof identity types. It is based on a class of models which interpret types as simplicial sets or topological spaces defined up to homotopy equivalence. The intuition based on the univalent semantics leads to new answers to some long standing questions of type theory providing in particular well-behav...

Let S be the standard class of univalent functions in the unit disk, and let So be the class of nonvanishing univalent functions g with g(0) = 1. It is shown that the regions of variability {g(r): g £ So} and {(1 — r2)f'(r) : f £ S} are very closely related but are not quite identical. Let 5 be the class of functions / analytic and univalent in the unit disk D, with /(0) = 0 and /'(O) = 1. Let ...

A description and comparison of various EXAFS-like phenomena are presented based on theoretical and practical considerations. Most of the phenomena are similar but not exactly the same as EXAFS. This does not limit their usefulness for structure determination but requires separate experimental calibration and theoretical calculations.

The coronavirus 2019 (COVID 19) pandemic has been a worldwide catastrophe. Four centuries after the plague pandemic, this highly contagious RNA virus ( SARS-CoV-2) become nightmare due to its relentless spread, infecting millions of people with an unpredictably higher fatality, and sequelae yet follow. This viral disease devastated world population in many ways. It affected all stages life, sta...

Abstract. In this paper we define and verify a subclass of harmonic univalent functions involving the argument of complex-value functions of the form f = h + ¯g and investigate some properties of this subclass e.g. necessary and sufficient coefficient bounds, extreme points, distortion bounds and Hadamard product.Abstract. In this paper we define and verify a subclass of harmonic univalent func...

Treatment of 6.5-S rabbit antibody with pepsin removes a large inactive fragment. The residual portion of the molecule, which is still bivalent, has a molecular weight of 106,000 and a sedimentation coefficient of 4.6 to 5.0 S (1, 2). Reduction of a single, highly labile disulfide bond cleaves this fragment approximately in half (2, 3). The resulting 3.5-S fragments are univalent and inhibit sp...