Lichnerowicz-Obata Estimate, Almost Parallel p-form and Almost Product Manifolds

We show a Lichnerowicz-Obata type estimate for the first eigenvalue of the Laplacian of n-dimensional closed Riemannian manifolds with an almost parallel p-form ($$2\le p \le n/2$$ 2 ≤ p ≤ n / 2 ) in $$L^2$$ L 2 -sense, and give a Gromov-Hausdorff approximation to a product $$S^{n-p}\times X$$ S n - p × X under some pinching conditions when $$2\le p<n/2$$ 2 ≤ p < n / 2 .

Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian

We show a Gromov-Hausdorff approximation to the product of the standard spheres for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.

On a Logistic Differential Model. Some Applications

In this article we will consider the possibility of approximating the input function s(t) (the nutrient supply for cell growth) of the form s(t)=1/(1+mt)exp(-mt)) where m>0 is parameter.We prove upper and lower estimates for the one--sided Hausdorff approximation of the shifted Heaviside function by means of the general solution of the differential equation y'(t)=ky(t)s(t) with y(t_0)=y_0.We will illustrate the evolution of the solution y(t) for approximating and modelling of three data sets: i) ''data on the development of the Drosophila melanogaster population'', published by Pearl in 1920, ii) dataStormIdentifications (Storm worm was one of the most biggest cyber threats of 2008, and ''cancer data''.Numerical examples using CAS Mathematica, illustrating our results are given.

A Study on the Unit-logistic, Unit-Weibull and Topp-Leone Cumulative Sigmoids

In this paper we study the one--sided Hausdorff approximation of the Heaviside step function by a families of Unit-Logistic (UL), Unit-Weibull (UW) and Topp-Leone (TL) cumulative sigmoids.The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ''saturation'' study.Numerical examples are presented using CAS MATHEMATICA.

Investigations on the G Family with Baseline Burr XII Cumulative Sigmoid

In this paper we study the one--sided Hausdorff approximation of the shifted Heaviside step function by a class of the Zubair-G family of cumulative lifetime distribution with baseline Burr XII c.d.f. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterion in ''saturation'' study.As an illustrative example we consider the fitting the new model against experimental oil palm data.Numerical examples, illustrating our results are presented using programming environment.

A note on the n-stage growth model. Overview

In this paper we study the one-sided Hausdorff approximation of the generalized cut function by sigmoidal general n-stage growth model. For some conditions of the reaction constants, the model has a certain right of existence insofar as the theory of sigmoidal functions is well developed. The estimates of the value of the best Hausdorff approximation obtained in this article can be used in practice as one possible additional criterions in ''saturation'' and ''lag-time'' study. We examine the small data for modeling the growth of red abalone (Haliotis Rufescens) in Northern California. Numerical examples are presented using CAS MATHEMATICA.

A family of recurrence generated sigmoidal functions based on the Log-logistic function. Some approximation aspects

In this note we construct a family of recurrence generated sigmoidal functions based on the Log--logistic function. The study of some biochemical reactions is linked to a precise Log--logistic function analysis.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given. The plots are prepared using CAS Mathematica.

Volume Comparison in the presence of a Gromov-Hausdorff ε−approximation II

Let (M, g) be any compact, connected, Riemannian manifold of dimension n. We use a transport of measures and the barycentre to construct a map from (M, g) onto a Hyperbolic manifold (ℍn/Λ, g0) (Λ is a torsionless subgroup of Isom(ℍn,g0)), in such a way that its jacobian is sharply bounded from above. We make no assumptions on the topology of (M, g) and on its curvature and geometry, but we only assume the existence of a measurable Gromov-Hausdorff ε-approximation between (ℍn/Λ, g0) and (M, g). When the Hausdorff approximation is continuous with non vanishing degree, this leads to a sharp volume comparison, if $\varepsilon < {1 \over {64\,{n^2}}}\min \left( {in{j_{\left( {{{\Bbb H}^n}/\Lambda ,{g_0}} \right)}},1} \right)$ , then $$\matrix{{Vol\left( {{M^n},g} \right) \ge }\cr {{{\left( {1 + 160n\left( {n + 1} \right)\sqrt {{\varepsilon \over {\min \left( {in{j_{\left( {{{\Bbb H}^n}/\Lambda ,{g_0}} \right)}},1} \right)}}} } \right)}^{{n \over 2}}}\left| {\deg \,h} \right| \cdot Vol\left( {{X^n},{g_0}} \right).} \cr }$$

On the Kumaraswamy-Dagum-Log-Logistic sigmoid functions with applications to population dynamics

he Kumaraswamy-Dagum distribution is a flexible and simple model with applications to income and lifetime data.We prove upper and lower estimates for the Hausdorff approximation of the shifted Heaviside function by a class of Kumaraswamy-Dagum-Log-Logistic cumulative distribution function - (KD-CDF). Numerical examples, illustrating our results are given.

The new trasmuted C.D.F. based on Gompertz function

In this paper we find application of some new cumulative distribution functions transformations to construct a family of sigmoidal functions based on the Gompertz logistic function.We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of these families.Numerical examples, illustrating our results are given.