Let a function f 2 L p ?1; 1], 0 < p 1 have 1 r < 1 changes of monotonicity. For all suuciently large n, we construct algebraic polynomials p n of degree n which are comonotone with f, and such that kf ? p n k Lp?1; 1] C(r)! ' 2 (f; n ?1) p , where ! ' 2 (f; n ?1) p denotes the Ditzian-Totik second modulus of smoothness in L p metric.

1. When chick-embryo cells were treated with ultraviolet-inactivated influenza virus (Melbourne strain), interferon was produced after a lag period of about 10hr. 2. The addition of small amounts of either puromycin or p-fluorophenylalanine immediately after the virus inhibited the subsequent production of interferon. Both inhibitors primarily affected protein synthesis, and it is concluded tha...

l-2,5-Dihydrophenylalanine is extensively incorporated as a phenylalanine analogue into cell proteins. Phenylalanine-requiring Escherichia coli ATCC 9723f and sarcoma 180 grow at normal rates initially with the analogue and maximally replace 65 and 33%, respectively, of phenylalanine in the peptide residues of their cell protein without death. With the analogue alone growth of E. coli becomes n...

The effects of chloramphenicol and p-fluorophenylalanine (p-FPA) on growth, proportion of motile cells, average rate of motility, and the chemotactic response of a methionine auxotroph of Escherichia coli K-12 were studied. Kinetic studies revealed that the inhibition of chemotaxis by p-FPA can be explained by the effect on growth, proportion of motile cells, and average rate of motility rather...

In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends corresponding result of Guo and Wenger (Commun Anal Geom 28(1):89–112, 2020). The main new ingredient in our proofs is a suitable extension theory trace valued developed by Korevaar Schoen 1(3–4):561–659, 1993) . We also develop borderline case, which investigates sharp condition to charac...

Introduction/purpose: The aim of this paper is to present the concept generalized ∅-weak contractive condition involving various combinations d(x,y) in modular metric spaces. Methods: Conventional theoretical methods functional analysis. Results: This study presents result (Murthy &amp; Vara Prasad, 2013) for a single-valued mapping satisfying ∅ -weak d(x,y). It setting spaces, and then it prov...

Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

In this paper, a common fixed point theorem for $psi$-weakly commuting maps in L-fuzzy metric spaces is proved.

Let V ⊂ R be a compact real analytic surface with isolated singularities, and assume its smooth part V0 is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on R . We prove: 1. Each point of V has a neighborhood which is quasi-isometric (naturally and ’almost isometrically’) to a union of metric cones and horns, glued at their tips. 2. A full asymptotic expa...

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to