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Showing 1 to 12 of 12 for “"real analysis"”.
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A Little Aspect of Real Analysis, Topology and Probability
… a Borel σ-algebra shows a special role in real-life probability because numerical data, real numbers, is gathered whenever a random experiment is performed.</p> <p>In this work a simple technique that is supported by pictorial presentation mostly is used, and for easiness most proofs are …
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The Convergence of a Sequence of Functions Defined by Radicals.
In the study of Real Analysis one problem which is often presented is to show that for x > 0, the sequence ✓x, √x + √x, ..., converges to a limit function and to determine the limit function. Since the limit function may be expressed as the positive solution of a quadratic equation, a …
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Probabilistic Methods
… combinatorial geometry, linear algebra and real analysis. More recently, it has been applied in the development of efficient algorithms and in the study of various computational problems.Broadly, the probabilistic method is somewhat opposite of the extremal graph theory. Instead of …
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Hyperreal structures arising from an infinite base logarithm
… the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of the hyperreal nU1l1ber system and the …
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Forcing in Analysis and Combinatorics
… of the forcing technique in the context of Analysis and Combinatorics by: (1) Constructing a model of Set Theory in which strong measure zero subsets of the real line are meager-additive while Borel’s conjecture fails, answering a long-standing question due to Bartoszy\'nski and Judah. (2) …
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Equivalent norms on L[superscript p] and E[superscript p] (T) speces
… In Chapter II we will restrict ourselves to the real line with the B^rel sigraa field. The class of functions we are interested in is E^(T), entire functions of exponential type T whose restrictions to R are in L^(R,dx). We mil give conditions on y and v that make (1) hold for all feEp(T). The …
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Theorem proving with the real numbers
This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of …
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Naked singularities in self-similar gravitational collapse: Stability properties of the Cauchy horizon
… parity methods, as well as some theorems from real analysis, we can demonstrate that the perturbations generically diverge pointwise on the Cauchy horizon. A general perturbation is a sum of odd and even perturbations; our results therefore indicate that a general perturbation diverges on the …
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Robust adaptive control in the presence of unmodeled dynamics
… initial conditions. The proposed method and analysis utilizes several key properties of nonlinear dynamic systems, first principles of real analysis, and properties of strictly positive real systems to derive this fundamental result. Numerical results are presented to demonstrate that the …
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Topics in shape-constrained inference
… we apply techniques from convex geometry and real analysis to elucidate the structural properties of such densities, and obtain some results of independent interest. In the third chapter, we consider the nonparametric estimation of an S-shaped regression function. The least squares estimator …
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Construction of a Non-Standard Integral on AC [0, 1]
… integral, following the path of H. L. Royden's Real Analysis. The chapter begins by showing the deficiencies of the Riemann integral. The first step in constructing the Lebesgue integral to avoid these difficulties is to define measure for sets. Next the Lebesgue integral is defined for a wider …
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Construction of a non-standard integral on AC [0, 1]
… integral, following the path of H. L. Royden's Real Analysis. The chapter begins by showing the deficiencies of the Riemann integral. The first step in constructing the Lebesgue integral to avoid these difficulties is to define measure for sets. Next the Lebesgue integral is defined for a wider …