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Latest Published Articles

Weighting of circularity dimensions

EASL-Vol. 5 (2022), Issue 2, pp. 1 – 9 Open Access Full-Text PDF
Anders Andrae

Abstract: Methods to determine the environmental consequences of circular strategies may be a prerequisite for the circular economy. However, the weighting factors of the criteria groups in the international L.1023 circularity scoring standard need to be determined beforehand. No comprehensive analysis of the connection between carbon footprint based life cycle assessment (LCA) results – of the product to be evaluated and redesigned – and these weighting factors has been published. Here a method, based on lifetime reduction and Analytical Hierarchy Process (AHP), for establishing weighting factors in the L.1023 standard for circularity scoring of electronic goods (EEE), is presented. The scope of the present investigation is the life cycle of a generic EEE evaluated with the L.1023 standard, AHP and carbon emissions. Statistical hypothesis testing at the single circularity score level shows that for the EEE example, the chance of mistakenly favoring the redesigned alternative over the status quo when they are in reality indistinguishable can be as low as 0.6%.

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Norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity

OMA-Vol. 6 (2022), Issue 1, pp. 70 – 75 Open Access Full-Text PDF
Benard Okelo and Jeffar Oburu

Abstract:This work is an in-depth study of the class of norm-attainable operators in a general Banach space setting. We give characterizations of norm-attainable operators on involutive stereotype tubes with algebraically connected component of the identity. In particular, we prove reflexivity, boundedness and compactness properties when the set of these operators contains unit balls with involution for the tubes when they are of stereotype category.

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Stability result for a class of weakly dissipative second-order systems with infinite memory

OMA-Vol. 6 (2022), Issue 1, pp. 48 – 61 Open Access Full-Text PDF
Adel M. Al-Mahdi and Mohammad M. Al-Gharabli

Abstract:In this paper we consider the following abstract class of weakly dissipative second-order systems with infinite memory, \(u”(t)+Au(t)-\displaystyle\int_{0}^{\infty} g(s)A^\alpha u(t-s)ds=0,~t>0,\) and establish a general stability result with a very general assumption on the behavior of \(g\) at infinity; that is \(g'(t) \leq – \xi(t) G \left(g(t)\right),~~t \geq 0.\) where \(\xi\) and \(G\) are two functions satisfying some specific conditions. Our result generalizes and improves many earlier results in the literature. Moreover, we obtain our result with imposing a weaker restrictive assumption on the boundedness of initial data used in many earlier papers in the literature such as the one in [1-5]. The proof is based on the energy method together with convexity arguments.

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Global existence and decay of solutions for p-biharmonic parabolic equation with logarithmic nonlinearity

OMA-Vol. 6 (2022), Issue 1, pp. 39 – 47 Open Access Full-Text PDF
Tugrul Cömert and Erhan Piskin

Abstract:In this paper, we study the initial boundary value problem for a p-biharmonic parabolic equation with logarithmic nonlinearity. By using the potential wells method and logarithmic Sobolev inequality, we obtain the existence of the unique global weak solution. In addition, we also obtain decay polynomially of solutions.

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Multiplier properties for the \(AP\)-Henstock integral

OMA-Vol. 6 (2022), Issue 1, pp. 28 – 38 Open Access Full-Text PDF
Kwancheol Shin and JU Han Yoon

Abstract:In this paper, we investigate some properties of the \(AP\)-Henstock integral on a compact set and prove that the product of an \(AP\)-Henstock integrable function and a function of bounded variation is \(AP\)-Henstock integrable. Furthermore, we prove that the product of an \(AP\)-Henstock integrable function and a regulated function is also \(AP\)-Henstock integrable. We also define the \(AP\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.

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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory
BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC