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On the extension of interval functions [PDF]
Transactions of the American Mathematical Society, 1947 Introduction. The problem of extending the range of definition of a function defined on a class of elementary figures-intervals, rectangles-has been treated in various ways in the literature. In the theory of Lebesgue measure a particular function-length of interval (area of rectangle)-is extended in a completely additive way to an additive class of ...
L. A. Ringenberg
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Interval Functions and Non-Decreasing Functions [PDF]
Canadian Journal of Mathematics, 1963 In a previous paper the author (1) has shown the following theorem.Theorem A. If each of H and K is a real-valued bounded function of subintervals of the number interval [a, b] and m is a real-valued non-decreasing function on [a} b] such that each of the integralsexists, then the integralexists.
William D. L. Appling
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Axiomatic characterizations of Ptolemaic and chordal graphs [PDF]
Opuscula Mathematica, 2023 The interval function and the induced path function are two well studied class of set functions of a connected graph having interesting properties and applications to convexity, metric graph theory. Both these functions can be framed as special instances
Manoj Changat +2 more
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Tạp chí Khoa học và Công nghệ, 2023 The paper presents the Finite element method (FEM) that calculates the internal force and the displacement of beams on elastic foundation in the case of the uncertainty input parameters described in terms of the number intervals.
Le Cong Duy +2 more
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Advances in Applied Mathematics, 2021 Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a parking function and $b$ is a dual parking function. We say that a pair of permutations $(x,y)$ is \emph{reachable}
Emma Colaric +3 more
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Some Hadamard–Fejér Type Inequalities for LR-Convex Interval-Valued Functions
Fractal and Fractional, 2021 The purpose of this study is to introduce the new class of Hermite–Hadamard inequality for LR-convex interval-valued functions known as LR-interval Hermite–Hadamard inequality, by means of pseudo-order relation ( ≤p ).
Muhammad Bilal Khan +4 more
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JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 This research is a follow-up research of Utama (2022) on asymptotic distribution of an estimator for variance function of a compound periodic Poisson with the power function trend.
Ade Irawan +2 more
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Betweenness in graphs: A short survey on shortest and induced path betweenness
AKCE International Journal of Graphs and Combinatorics, 2019 Betweenness is a universal notion present in several disciplines of mathematics. The notion of betweenness has a profound history and many pioneers like Euclid, Pasch, Hilbert have studied betweenness axiomatically.
Manoj Changat +2 more
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2022 This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with
Rebaz B. Mustafa, Nejmaddin A Sulaiman
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On the Liouville Function in Short Intervals [PDF]
International Mathematics Research Notices, 2021 Abstract Let $\lambda $ denote the Liouville function. Assuming the Riemann Hypothesis, we prove that $\int _X^{2X}\Big |\sum _{x\leq n \leq x+h}\lambda (n) \Big |^2{\textrm{d}} x \ll Xh(\log X)^6,$ as $X\rightarrow \infty $, provided $h=h(X)\leq \exp \left (\sqrt{\left (\frac{1}{2}-o(1)\right )\log X \log \log X}\right ).$ The proof ...
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