32 research outputs found

    Metric differentiability of Lipschitz maps

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    An extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property

    On the problem of regularity in the Sobolev space Wloc1,n

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    AbstractWe prove that a variant of the Hencl's notion of ACλn-mapping (see [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189]), in which λ is not a constant, produces a new solution to the problem of regularity in the Sobolev space Wloc1,n

    Stepanoff's theorem in separable Banach spaces

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    summary:Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces

    On the Fundamental theorem of Calculus for fractal sets

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    The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock-Kurzweil type is introduced

    Solving and Applying Fractal Differential Equations: Exploring Fractal Calculus in Theory and Practice

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    In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for solving α\alpha-order differential equations. Notably, we extend our analysis to solve Fractal Bernoulli differential equations. The applications of our findings are then showcased through the solutions of problems such as fractal compound interest, the escape velocity of the earth in fractal space and time, and estimation of time of death incorporating fractal time. Visual representations of our results are also provided to enhance understanding

    Linear Dynamics Induced by Odometers

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    Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing variety dynamical properties. Recently, a systematic study of dynamical properties of composition operators on LpL^p spaces has been initiated. This class of operators includes weighted shifts and also allows flexibility in construction of other concrete examples. In this article, we study one such concrete class of operators, namely composition operators induced by measures on odometers. In particular, we study measures on odometers which induce mixing and transitive linear operators on LpL^p spaces.Comment: 15 pages, keywords: linear dynamics, composition operators, topological mixing, topological transitivity, odometer

    Edible Insects an Alternative Nutritional Source of Bioactive Compounds: A Review

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    Edible insects have the potential to become one of the major future foods. In fact, they can be considered cheap, highly nutritious, and healthy food sources. International agencies, such as the Food and Agriculture Organization (FAO), have focused their attention on the consumption of edible insects, in particular, regarding their nutritional value and possible biological, toxicological, and allergenic risks, wishing the development of analytical methods to verify the authenticity, quality, and safety of insect-based products. Edible insects are rich in proteins, fats, fiber, vitamins, and minerals but also seem to contain large amounts of polyphenols able to have a key role in specific bioactivities. Therefore, this review is an overview of the potential of edible insects as a source of bioactive compounds, such as polyphenols, that can be a function of diet but also related to insect chemical defense. Currently, insect phenolic compounds have mostly been assayed for their antioxidant bioactivity; however, they also exert other activities, such as anti-inflammatory and anticancer activity, antityrosinase, antigenotoxic, and pancreatic lipase inhibitory activitie

    The Henstock-Kurzweil-Stieltjes type integral for real functions on a fractal subset of the real line

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    The aim of this paper is to introduce an Henstock-Kurzweil type integration process for real functions on a fractal subset E of the real line

    Absolutely continuous functions in R-n

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    For each 0 < α <1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý’s and Hencl’s definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L^n, differentiable almost everywhere and satisfies the formula on change of variables
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