Weili Wu, Zhao Zhang, Ding‐Zhu Du · Journal of the Operations Research Society of China · 2018
This article is an introduction to recent development of optimization theory on set functions, the nonsubmodular optimization, which contains two interesting results, DS (difference of submodular) functions decomposition and sandwich theorem, together with iterated sandwich method and data-dependent approximation. Some potential research problems will be mentioned.
Cited by 35Open access
Lantao Xu (17867355), Xuegang Chen (5265254), Xinlu Yang (17867358) · Figshare · 2024
<div><p>Tourism image classification plays an important role in the study of clarifying the real perception of tourism resources by tourists, which cannot be studied in depth by human vision alone. The development of convolutional neural networks in computer vision brings new opportunities for tourism image classification research. In this study, SqueezeNet, a lightweight convolutional neural network, was selected and improved on the basis of the original model for 3740 Slender West Lake tourism image datasets. It is found that the validation accuracy of the model is up to 85.75%, and the size is only 2.64 MB, which is a good classification effect. This reduces the parameters while ensuring high accuracy classification of tourism images, providing a more scientific reference for the study of tourism images and pointing out a new direction for the development and planning of tourism resources.</p></div>
Cited by 0Open access
Sergio Macías · Commentationes Mathematicae Universitatis Carolinae · 2025
Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, $\wp$, and present properties of it.
Cited by 0
Mihir K. Chakraborty · International Journal of Approximate Reasoning · 2013
Cited by 27
R Kodri, J Titaley, S Ishikawa et al. · International Journal of Recent Technology and Engineering (IJRTE) · 2019
Julia sets are generated by initializing a complex number z = x + yi where z is then iterated using the iteration function fc (z)= zn 2 + c, where n indicates the number of iteration and c is a constant complex number. Recently, study of cubic Julia sets was introduced in Noor Orbit (NO) with improved escape criterions for cubic polynomials. In this paper, we investigate the complex dynamics of different functions and apply the iteration function to generate an entire new class of Julia sets. Here, we introduce different types of orbits on cubic Julia sets with trigonometric functions. The two functions to investigate from Julia sets are sine and cosine functions.
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Macías, Sergio · Czech digital mathematics library · 2024
summary:Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, $\wp$, and present properties of it.
Cited by 0
Kenneth Wayne Milligan · University of North Texas Digital Library (University of North Texas) · 1971
This thesis investigates some inequalities and some relationships between function properties and integral properties.
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Denis Higgs · American Mathematical Monthly · 1983
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Allan Gut, Klaus D. Schmidt · Lecture notes in mathematics · 1983
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Josip Pečarić, Ioan Raşa · Southeast Asian Bulletin of Mathematics · 2000
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Satish Shirali · 2018
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Fahim Mohammad (406872), Jesse C. Theisen-Toupal (551668), Ramy Arnaout (263589) · Figshare · 2015
<p>A 60-40 split generated a total number of rules comparable to 70-30 and 80-20 splits but with less training data.</p>
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Dawidson Razafimahatolotra · Statistical science and interdisciplinary research · 2008
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Francesco Cellinese, Gianlorenzo D’Angelo, Gianpiero Monaco et al. · arXiv (Cornell University) · 2018
In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such that the overall cost is at most a given budget, and the profit is maximized. Each bin has its own cost and the cost of each element depends on its associated bin. The profit is measured by a monotone submodular function over the elements. We first present an algorithm that guarantees an approximation factor of $\frac{1}{2}\left(1-\frac{1}{e^α}\right)$, where $α\leq 1$ is the approximation factor of an algorithm for a sub-problem. We give two polynomial-time algorithms to solve this sub-problem. The first one gives us $α=1- ε$ if the costs satisfies a specific condition, which is fulfilled in several relevant cases, including the unitary costs case and the problem of maximizing a monotone submodular function under a knapsack constraint. The second one guarantees $α=1-\frac{1}{e}-ε$ for the general case. The gap between our approximation guarantees and the known inapproximability bounds is $\frac{1}{2}$. We extend our algorithm to a bi-criterion approximation algorithm in which we are allowed to spend an extra budget up to a factor $β\geq 1$ to guarantee a $\frac{1}{2}\left(1-\frac{1}{e^{αβ}}\right)$-approximation. If we set $β=\frac{1}α\ln \left(\frac{1}{2ε}\right)$, the algorithm achieves an approximation factor of $\frac{1}{2}-ε$, for any arbitrarily small $ε>0$.
Cited by 2Open access
Yurii Belov, A. Semenov · arXiv (Cornell University) · 2023
We prove that frame set $\mathcal{F}_g$ for imaginary shift of sinc-function $$g(t)=\frac{\sinπb(t-iw)}{t-iw}, \quad b,w\in\mathbb{R}\setminus\{0\}$$ can be described as $\mathcal{F}_g=\{(α,β): αβ\leq 1, β\leq|b|\}.$ \\ In addition, we prove that $\mathcal{F}_g=\{(α,β): αβ\leq 1 \}$ for window functions $g$ of the form $\frac{1}{t-iw}(1-\sum\limits_{k=1}^{\infty}a_ke^{2πi b_k t})$, such that $\sum_{k\geq 1}|a_k|e^{2π|w|b_k}<1$, $wb_k<0$.
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Ying Wang (11406), Peng Liu (120506) · Figshare · 2024
<div><p>To address the issue of insufficiently comprehensive representation of service composition indexes in the shared manufacturing environment, service reliability, confidence, and other indexes are decomposed in detail to establish a composition evaluation system, and a shared manufacturing service composition optimization model based on bi-level programming is proposed. The model takes Quality of Service (QoS) as the upper objective function and service reliability, service confidence and task fit as the lower objective function. The upper objective function needs to be minimized, while the lower objective function needs to be maximized. To achieve the optimal composition scheme of shared manufacturing services, the Criteria Importance Though Intercrieria Correlation (CRITIC) is used to determine the weights of the indicators, and the improved Fast Elitist Non-Dominated Sorting Genetic Algorithm (Improved NSGA-II) is employed to solve the multi-objective optimization problem. Finally, the improved NSGA-II has a 23.33% increase in convergence speed and a 69.99% gain in operational efficiency when compared to the traditional NSGA-II. The viability and effectiveness of the improved NSGA-II have been demonstrated.</p></div>
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Robert E. Mullins · Proceedings of the American Mathematical Society · 1967
Let X be a compact Hausdorff space and C(X) the Banach algebra of all complex-valued continuous functions on X under the sup-norm. By a function algebra A we mean a closed subalgebra of C(X) which separates points and contains the constant functions. Let S(A) denote the space of maxinmal ideals of A and let E(A) denote the essential set of A as defined by Bear [1], i.e. E(A) is the hull of the largest closed ideal of C(X) which is contained in A. We will obtain another characterization of the essential set in the case when S(A) =X and thereby obtain some results of a global nature from local hypotheses.
Cited by 9Open access
Francesco Cellinese, Gianlorenzo D’Angelo, Gianpiero Monaco et al. · Information and Computation · 2021
Cited by 1
Robert E. Mullins · Proceedings of the American Mathematical Society · 1967
Cited by 6
Wafa Alqurashi, Liaqat Ali Khan, Alexander V. Osipov · Applied General Topology · 2018
<p>Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.</p>
Cited by 4Open access