Riemann average truth-value of Łukasiewicz formulas
Riemann Integral of Functions from ℝ into Real Banach Space
In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the...
Riemann-Stieltjes Integral
In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described...
Riga -point
Right and left invertibility in -calculus
Rigid Aronszajn Trees
Rigid Aronszajn trees.
Rigid Boolean Algebras
Rigid subanalytic sets
Rigid -saturated models of superstable theories
In a countable superstable NDOP theory, the existence of a rigid -saturated model implies the existence of rigid -saturated models of power λ for every .
Rigidity, internality and analysability
We prove a version of Hrushovski's Socle Lemma for rigid groups in an arbitrary simple theory.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Rings of Real-Valued Continuous Functions. II.
Risk aversion, prudence and mixed optimal saving models
The paper studies risk aversion and prudence of an agent in the face of a risk situation with two parameters, one described by a fuzzy number, the other described by a fuzzy variable. The first contribution of the paper is the characterization of risk aversion and prudence in mixed models by conditions on the concavity and the convexity of the agent's utility function and its partial derivatives. The second contribution is the building of mixed models of optimal saving and their connection with...
Robust neural network control of robotic manipulators via switching strategy
In this paper, a robust neural network control scheme for the switching dynamical model of the robotic manipulators has been addressed. Radial basis function (RBF) neural networks are employed to approximate unknown functions of robotic manipulators and a compensation controller is designed to enhance system robustness. The weight update law of the robotic manipulator is based on switched multiple Lyapunov function method and the periodically switching law which is suitable for practical implementation...
Robust Rank Correlation Coefficients on the Basis of Fuzzy.
Rosenthal compacta and NIP formulas
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.
Rothberger gaps in fragmented ideals
The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum...
Rough membership functions: a tool for reasoning with uncertainty
A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of...
Rough relation properties
Rough Set Theory (RST) is a mathematical formalism for representing uncertainty that can be considered an extension of the classical set theory. It has been used in many different research areas, including those related to inductive machine learning and reduction of knowledge in knowledge-based systems. One important concept related to RST is that of a rough relation. This paper rewrites some properties of rough relations found in the literature, proving their validity.