Generalized integrals with respect to base functions which are not of bounded variation

1974 ◽  
pp. 211-220
Author(s):  
R. L. Jeffery
Keyword(s):  
Bounded Variation ◽  
Base Functions

On Measures Determined by Functions with Finite Right and Left Limits Everywhere

1967 ◽  
Vol 10 (2) ◽  
pp. 207-225 ◽  
Author(s):  
H.W. Ellis ◽  
R. L. Jeffery
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Restricted Sense ◽  
Base Functions

In another paper [l] measures determined from base functions, that have finite right and left limits everywhere and are of generalized bounded variation in the restricted sense, are studied and used to define non absolutely convergent integrals of Denjoy type. In this paper base functions of bounded variation and the corresponding measures are studied as a background for that paper. The results supplement parts of [2].

Metal-organic Nanopharmaceuticals

2020 ◽  
Vol 8 (3) ◽  
pp. 163-190
Author(s):  
Benjamin Steinborn ◽  
Ulrich Lächelt
Keyword(s):  
Metal Ions ◽  
Coordination Polymers ◽  
Active Agent ◽  
Lewis Base ◽  
High Loading ◽  
Active Components ◽  
Base Functions ◽  
Metal Organic ◽  
Theranostic Applications ◽  
Pharmacologically Active

: Coordinative interactions between multivalent metal ions and drug derivatives with Lewis base functions give rise to nanoscale coordination polymers (NCPs) as delivery systems. As the pharmacologically active agent constitutes a main building block of the nanomaterial, the resulting drug loadings are typically very high. By additionally selecting metal ions with favorable pharmacological or physicochemical properties, the obtained NCPs are predominantly composed of active components which serve individual purposes, such as pharmacotherapy, photosensitization, multimodal imaging, chemodynamic therapy or radiosensitization. By this approach, the assembly of drug molecules into NCPs modulates pharmacokinetics, combines pharmacological drug action with specific characteristics of metal components and provides a strategy to generate tailorable multifunctional nanoparticles. This article reviews different applications and recent examples of such highly functional nanopharmaceuticals with a high ‘material economy’. : Lay Summary: Nanoparticles, that are small enough to circulate in the bloodstream and can carry cargo molecules, such as drugs, imaging or contrast agents, are attractive materials for pharmaceutical applications. A high loading capacity is a generally aspired parameter of nanopharmaceuticals to minimize patient exposure to unnecessary nanomaterial. Pharmaceutical agents containing Lewis base functions in their molecular structure can directly be assembled into metal-organic nanopharmaceuticals by coordinative interaction with metal ions. Such coordination polymers generally feature extraordinarily high loading capacities and the flexibility to encapsulate different agents for a simultaneous delivery in combination therapy or ‘theranostic’ applications.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

scholarly journals Some Bounds for the Complex Čebyšev Functional of Functions of Bounded Variation

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 990
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Functional Applications ◽  
Čebyšev Functional

In this paper, we provide several bounds for the modulus of the complex Čebyšev functional. Applications to the trapezoid and mid-point inequalities, that are symmetric inequalities, are also provided.

scholarly journals A Korn-type inequality in SBD for functions with small jump sets

2017 ◽  
Vol 27 (13) ◽  
pp. 2461-2484 ◽  
Author(s):  
Manuel Friedrich
Keyword(s):  
Bounded Variation ◽  
Elastic Strain ◽  
Special Functions ◽  
Type Inequality ◽  
Rigid Motion ◽  
Exceptional Set ◽  
Finite Perimeter ◽  
Functions Of Bounded Deformation ◽  
Jump Set

We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in [Formula: see text] with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in [Formula: see text] has bounded variation away from an arbitrarily small part of the domain.

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