A treatise on the differential calculus; with numerous examples

Mode of access: Internet.

Gründliche Darstellung der Differenzial- und Integral-Rechnung nach der eigenen Idee ihres Erfinders : nebst vorangehender Prüfung der sonst gewöhnlichen Erklärungsarten dieser Wissenschaft. Mit einer Kupfertafel /

Mode of access: Internet.

An elementary treatise on the differential calculus : containing the theory of plane curves, with numerous examples /

Includes index.

Concepts from tensor analysis and differential geometry.

Mode of access: Internet.

L.A. Sohncke's Sammlung von aufgaben aus der differential- und integralrechnung /

th. 1. Differentialrechnung.--th. 2. Integralrechnung.

An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of,

Mode of access: Internet.

Respiratory gene clusters of Metallosphaera sedula - differential expression and transcriptional organization

Metallosphaera sedula is a thermoacidophilic Crenarchaeon which is capable of leaching metals from sulfidic ores. The authors have investigated the presence and expression of genes encoding respiratory complexes in this organism when grown heterotrophically or chemolithotrophically on either sulfur or pyrite. The presence of three gene clusters, encoding two terminal oxidase complexes, the quinol oxidase SoxABCD and the SoxM oxidase supercomplex, and a gene cluster encoding a high-potential cytochrome b and components of a bc(1) complex analogue (cbsBA-soxL2N gene cluster) was established. Expression studies showed that the soxM gene was expressed to high levels during heterotrophic growth of M. sedula on yeast extract, while the soxABCD mRNA was most abundant in cells grown on sulfur. Reduced-minus-oxidized difference spectra of cell membranes showed cytochrome-related peaks that correspond to published spectra of Sulfolobus-type terminal oxidase complexes. In pyrite-grown cells, expression levels of the two monitored oxidase gene clusters were reduced by a factor of 10-12 relative to maximal expression levels, although spectra of membranes clearly contained oxidase-associated haems, suggesting the presence of additional gene clusters encoding terminal oxidases in M. sedula. Pyrite- and sulfur-grown cells contained high levels of the cbsA transcript, which encodes a membrane-bound cytochrome b with a possible role in iron oxidation or chemolithotrophy. The cbsA gene is not co-transcribed with the soxL2N genes, and therefore does not appear to be an integral part of this bc(1) complex analogue. The data show for the first time the differential expression of the Sulfolobus-type terminal oxidase gene clusters in a Crenarchaeon in response to changing growth modes.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

On Integral Means for Fractional Calculus Operators of Multivalent Functions

2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.