Fractional Differential Equations

Bees are subject to numerous pressures in the modern world. The abundance and diversity of flowers has declined, bees are chronically exposed to cocktails of agrochemicals, and they are simultaneously exposed to novel parasites accidentally spread by humans. Climate change is likely to exacerbate these problems in the future. Stressors do not act in isolation; for example pesticide exposure can impair both detoxification mechanisms and immune responses, rendering bees more susceptible to parasites. It seems certain that chronic exposure to multiple, interacting stressors is driving honey bee colony losses and declines of wild pollinators, but such interactions are not addressed by current regulatory procedures and studying these interactions experimentally poses a major challenge. In the meantime, taking steps to reduce stress on bees would seem prudent; incorporating flower-rich habitat into farmland, reducing pesticide use through adopting more sustainable farming methods, and enforcing effective quarantine measures on bee movements are all practical measures that should be adopted. Effective monitoring of wild pollinator populations is urgently needed to inform management strategies into the future.

https://science.sciencemag.org/content/sci/early/2015/02/25/science.1255957.full.pdf

Bee declines driven by combined stress from parasites, pesticides, and lack of flowers

1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.

Dynamics of multibody systems

In the paper, we present a new definition of fractional deriva tive with a smooth kernel which takes on two different representations for the temporal and spatial variable. The first works on the time variables; thus it is suitable to use th e Laplace transform. The second definition is related to the spatial va riables, by a non-local fractional derivative, for which it is more convenient to work with the Fourier transform. The interest for this new approach with a regular kernel was born from the prospect that there is a class of non-local systems, which have the ability to descri be the material heterogeneities and the fluctuations of diff erent scales, which cannot be well described by classical local theories or by fractional models with singular kernel.

http://www.naturalspublishing.com/files/published/0gb83k287mo759.pdf

A new Definition of Fractional Derivative without Singular Kernel

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Biodeterioration of books and journals.

This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.© 2013 ASME

Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator

A superelement model based on Lagrangian coordinates for multibody system dynamics

Honey bees obtain their nutrition in form of pollen & nectar from flowering plants. The present study was conducted to ascertain the availability of pollen rich flora & amount of pollen collected by honey bees during pollen flow season. Natural pollen was collected by installing wooden pollen traps on the entrance of bee hives. The data of pollen collection for two different locations indicates that the amount of pollen rich bee flora was more or less similar at both locations. In Panchkula, maximum pollen (880.2 gm per colony) was collected in the month of February, while in Gwalior maximum quantity of pollen was collected in January month (1033.1 gm per colony).

http://theglobaljournals.com/paripex/file.php?val=August_2014_1408107384__61.pdf

Comparative Collection of Natural Pollen by Honey Bees in Gwalior & Panchkula (India) Zoology

A new identity, namely sum; +∞ n=1 { ∫ 0 1 yd v (λ n Y) d y J v+1 (λ n ) } 2 = 1 2 2 (v⩾0) is proposed, where Jv(z) is a Bessel function of the first kind of order v, and αn is the nth positive zero of Jv(z). It is shown that the formula can be used to find an upper bound for some integrals. Special cases of the series are discussed as well.

Om P. Agrawal

Papers

Biodeterioration of books and journals.

Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator

A superelement model based on Lagrangian coordinates for multibody system dynamics

Comparative Collection of Natural Pollen by Honey Bees in Gwalior & Panchkula (India) Zoology

A new identity involving positive roots of bessel functions of the first kind