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182. A full characterization of multipliers for the strong $\rho$-integral in the euclidean space
- Creator:
- Tuo-Yeong, Lee
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- strong $\rho $-integral, multipliers, and dual space
- Language:
- English
- Description:
- We study a generalization of the classical Henstock-Kurzweil integral, known as the strong $\rho $-integral, introduced by Jarník and Kurzweil. Let $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ be the space of all strongly $\rho $-integrable functions on a multidimensional compact interval $E$, equipped with the Alexiewicz norm $\Vert \cdot \Vert $. We show that each element in the dual space of $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ can be represented as a strong $\rho $-integral. Consequently, we prove that $fg$ is strongly $\rho $-integrable on $E$ for each strongly $\rho $-integrable function $f$ if and only if $g$ is almost everywhere equal to a function of bounded variation (in the sense of Hardy-Krause) on $E$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
183. A function related to a Lagrange-Bürmann series
- Creator:
- Bracken, Paul
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Lagrange-Bürmann and Laplace transform
- Language:
- English
- Description:
- An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
184. A fundamental proof for the equivalence of transformations with respect to fixed and moving coordinates in reverse order
- Creator:
- Hariri, Mahdiar and Mahzoon, Mojtaba
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- transformations, rigid body motion, Euler angles, fixed coordinate, moving coordinate, and RPY
- Language:
- English
- Description:
- In elementary robotics, it is very well known that the rotation of an object by the angles respectively Ψ (x), Θ (y), Φ (z) wrt** a fixed coordinate system (RPY) results in the same angular position for the object as the position achieved by the rotation of that object by the angles respectively Φ (z), Θ (y), Ψ (x) wrt a moving (with the object) coordinate system (euler angles). The proofs given up to now for such consequences are not general and for any such problem usually involve the calculation of the transformation matrix for both cases and observing the equivalence of the two matrices [1, 2, 3]. In this paper a fundamental and at the same time general proof is given for such results. It is shown that this equivalence in reverse order can be extended to the general class of transformations which keep the local relations constant (i.e., each transformation should keep the local relations constant). For example, rotation, translation and scaling are 3 types of transformations which can be located in this general class.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
185. A fuzzy logic based system for detection of car driver's vigilance level
- Creator:
- Coufal, David
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- EEG spectrograms, implicate fuzzy system, and micro-sleeps detection
- Language:
- English
- Description:
- The paper presents an application of fuzzy logic modeling techniques for design and development of a classification system for car driver's vigilance level detection. Especially, the micro-sleeps detection is of our primary interest. Detection is based on a pattern analysis of EEG signal spectrograms, which are acquired by monitoring the driver during a driving process. The system is based on the concept of radial implicative fuzzy system, which can be treated as a logical system accommodating acquired knowledge in a structured form.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
186. A fuzzy-logic generalization of a data mining approach
- Creator:
- Holeňa, Martin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- data analysis, vague hypotheses, vague significance level, fuzzy predicate calculus, basic fuzzy logic, generalized quantifiers, and method Guha
- Language:
- English
- Description:
- Data mining nowadays belongs to the most prominent Information technologies, experiencing a boom of interest from users and software producers. Traditionally, extracting knowledge from data has been a domain of statisticians, and the largest variety of rnethods encountered in commercial data mining systems are actually methods for statistical data analysis tasks. One of the most important ones among them is testing hypotheses about the probability distribution underlying the data. Basically, it consists in checking the null hypothesis that the probability distribution, a priori cissumed to belong to a broad set of distributions, actually belongs to one of its narrow subsets, which must be precisely delimited in advance. However, in a situation in which the data mining is performed, there are seldom enough clues for such a precise delimitation. That is why the generalizations of statistical hypotheses testing to vague hypotheses háve been investigated for more than a decade, so far following the most straightforward way - to replace the set defining the null hypothesis by a fuzzy set. In this páper, a principally different generalization is proposed, based on the observational-logic approach to data mining, and in particular to hypotheses testing. Its key idea is to view statistical testing of a fuzzy hypothesis cis an application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data. The theoretical principles of the approach are elaborated for both crisp and fuzzy significance levels, and illustrated on the quantifier lower critical implication, well known from the data mining system Guha. Finally, the implementation of the approach is briefly sketched.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
187. A fuzzy-mining approach for solving rule based expert system unwieldiness in medical domain
- Creator:
- Olufunke, Oladipupo O., Charles, Uwadia O., Charles, Ayo K., Abraham , Ajith, and Snasel , Vaclav
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Expert system (ES), Fuzzy expert system (FES), Coronary Heart Disease (CHD), and rule support and confidence
- Language:
- English
- Description:
- Over the years, one of the challenges of a rule based expert system is the possibility of evolving a compact and consistent knowledge-base with a fewer numbers of rules that are relevant to the application domain, in order to enhance the comprehensibility of the expert system. In this paper, the hybrid of fuzzy rule mining interestingness measures and fuzzy expert system is exploited as a means of solving the problem of unwieldiness and maintenance complication in the rule based expert system. This negatively increases the knowledge-base space complexity and reduces rule access rate which impedes system response time. To validate this concept, the Coronary Heart Disease risk ratio determination is used as the case study. Results of fuzzy expert system with a fewer numbers of rules and fuzzy expert system with a large numbers of rules are presented for comparison. Moreover, the effect of fuzzy linguistic variable risk ratio is investigated. This makes the expert system recommendation close to human perception.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
188. A Galois connection between distance functions and inequality relations
- Creator:
- Száz, Árpád
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- distance functions and inequality relations, closure operators and Galois connections, Lipschitz and monotone functions, and fixed points
- Language:
- English
- Description:
- Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set S and inequality relations on Xs = S × R. Moreover, we also investigate a relationship between the functions of S and Xs.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
189. A general class of iterative equations on the unit circle
- Creator:
- Zdun, Marek Cezary and Zhang, Weinian
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- iterative equation, circle, lift, orientation-preserving, and continuation
- Language:
- English
- Description:
- A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb{T}}^1$. By lifting maps on ${\mathbb{T}}^1$ and maps on the torus ${\mathbb{T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
190. A general synchronization method of chaotic communication systems via Kalman filtering
- Creator:
- Lu, Suojun and Chen, Liang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- chaotic system, secure communication, synchronization, uncertain parameters, and Kalman filtering
- Language:
- English
- Description:
- A general synchronization method is proposed for a class of nonlinear chaotic systems involving uncertain parameters and nonlinear transmitted signals. Under some mild conditions, it shows that the class of nonlinear chaotic systems can be treated as linear time-varying systems driven by the additive white noise contaminated at the receiver, or the observed output. Synchronization can be achieved by using Kalman filtering technology. We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asymptotically, and good tracking performance can be obtained in the presence of the additive white noise involved in the observed output.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public