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In this article, we introduce the notion of IK-φ convergenceof real sequences as an extension of IK-convergence. We investigatevarious properties and implication relations of this convergence method.
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The concept of convergence of sequences of points has been extended by several authors to convergence of sequences of sets. The three such extensions that we will consider in this paper are those of Kuratowski, Wijsman and Hausdor...
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The concept of convergence of sequences of points has been extended by several authors to convergence of sequences of sets. The three such extensions that we will consider in this paper are those of Kuratowski, Wijsman and Hausdorff. We shall define statistical convergence for sequences of sets and establish some basic theorems, thereby obtaining generalizations of the corresponding results for statistical convergence of sequences of points.
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In this paper, types of convergence (also referred to as Schur stability) for complex matrices are studied. In particular, it is proven that for complex matrices of order n 展开
In this paper, types of convergence (also referred to as Schur stability) for complex matrices are studied. In particular, it is proven that for complex matrices of order n 收起
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Eight measures of rate of convergence of monotone sequences of real numbers have been proposed and discussed in a paper by Beyer, Ebanks, and Qualls (Acta Appl. Math. 20 (1990), 267–284). These rates arose in discussions of dynam...
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Eight measures of rate of convergence of monotone sequences of real numbers have been proposed and discussed in a paper by Beyer, Ebanks, and Qualls (Acta Appl. Math. 20 (1990), 267–284). These rates arose in discussions of dynamical systems. In the comparisons of these rates, two problems remained. A complete answer is given to one of the problems and a partial answer is given to the other problem.
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After a brief survey of basic results about finite-dimensional approximation settings(such as mathematical frameworks of various projection methods, including the least-squares method,the dual least-squares method, and the Galerki...
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After a brief survey of basic results about finite-dimensional approximation settings(such as mathematical frameworks of various projection methods, including the least-squares method,the dual least-squares method, and the Galerkin method) for infinite-dimensional Moore-Penroseinverses, this paper proceeds to a detailed study from the following aspects: For projection methods,we investigate convergence and weak convergence of their approximation setting to develop a unifiedtheory on projection methods for infinite-dimensional Moore-Penrose inverses; this investigationyields a fundamental convergence theorem (Theorem 2.2), from which the criterion for convergence,the criterion for weak convergence, and the generalized dual least-squares method are derived. Wealso derive general results on the least-squares method, by which two flaws in Groestch's results arecorrected. For nonprojection methods (whose approximation setting is a more general framework),we investigate weak perfect convergence of their approximation setting and provide a necessaryand sufficient condition of such convergence holding (Theorem 3.2). Several examples are proposedas counterexamples to illustrate the differences between some important concepts or as concretealgorithms to show how the present work can help to analyze their behavior.
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We explore the importance of strain heating in ductile shear zones for production of leucogranites and high-temperature metamorphism in collisional orogens with temperature-dependent thermal diffusivity (D) and rock rheology. New ...
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We explore the importance of strain heating in ductile shear zones for production of leucogranites and high-temperature metamorphism in collisional orogens with temperature-dependent thermal diffusivity (D) and rock rheology. New measurements on metamorphic rocks from the Bohemian Massif show that D is -1.3 mm~2/s at 25°C and decreases exponentially to as low as 0.4 mm~2/s at >600°C. This temperature dependence causes model lithospheric geotherms to be straighter compared to geotherms calculated with a constant D. Using power law parameters for rheology, we show that deformation of quartzite at strain rate of 3 x 10~(-13) s~(-1) produces >100 μW/m~3 at 550°C and -7 μW/m~3 at 800°C. Deformation of stronger clinopyroxenite at this strain rate produces -8 μW/m~3 even at 1050°C. When strain heating is introduced by a 3 km thick ductile shear zone with quartz rheology at the depth of 35 km in a lithosphere that has 70 km thick crust and 60 km thick lithospheric mantle, the schist solidus is reached by -8 Myr in the vicinity of the shear zone deforming at the strain rate of 3 x 10~(-13) s~(-1). For clinopyroxenite rheology, ultrahigh temperature (UHT) metamorphic conditions are reached in -40 Myr after initiation of strain heating. Two-dimensional models that replicate the exhumation of the Greater Himalaya crystalline rocks above the Main Central thrust produce extensive partial melting and an inverted metamorphic field gradient. Occurrences of leucogranites within crustal shear zone systems may be evidence of the coupling between deformation and heat production in the crust.
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Purpose - This survey of the literature on the convergence of carbon dioxide (CO_2) emissions informs researchers on areas for future research by summarizing the countries examined, the types of convergence tested and the methodol...
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Purpose - This survey of the literature on the convergence of carbon dioxide (CO_2) emissions informs researchers on areas for future research by summarizing the countries examined, the types of convergence tested and the methodological approaches undertaken. Design/methodology/approach - This survey examines peer-reviewed empirical studies of CO_2 emissions convergence with respect to country coverage and alternative approaches to test for various types of convergence. Findings - For large multicountry studies, the support for convergence is quite limited. However, studies focused exclusively on a subset of countries defined by income classification, geographic region or institutional structure reveal the finding of convergence is more prevalent. Studies at the subnational level have primarily been in the cases of the US and China with the exception of two studies across industry sectors in Portugal and Sweden. Research limitations/implications - This study focuses exclusively on peer-reviewed published studies. Practical implications - This study is relevant to the design of mitigation strategies to reduce CO_2 emissions and the assumption of convergence underlying climate change models. Social implications - As a major component of greenhouse gas emissions, CO_2 emissions is of global importance in its impact on the environment and climate change. Originality/value - This study provides the most recent and comprehensive survey of the empirical literature on the convergence of CO_2 emissions.
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In this paper, we study potential convergence of modulus patterns. A modulus pattern Z is convergent if all complex matrices in Q(Z) (i.e. all matrices with modulus pattern Z) are convergent. A modulus pattern is potentially (abso...
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In this paper, we study potential convergence of modulus patterns. A modulus pattern Z is convergent if all complex matrices in Q(Z) (i.e. all matrices with modulus pattern Z) are convergent. A modulus pattern is potentially (absolutely) convergent if there exists a (nonnegative) convergent matrix in Q(Z). We also introduce types of potential convergence that correspond to diagonal and D-convergence, studied in [E. Kaszkurewicz, A. Bhaya, Matrix Diagonal Stability in Systems and Computation, Birkhauser, 2000]. Convergent modulus patterns have been completely characterized by Kaszkurewicz and Bhaya [E. Kaszkurewicz, A. Bhaya, Qualitative stability of discrete-time systems, Linear Algebra Appl. 117 (1989) 65-71]. This paper presents some techniques that can be used to establish potential convergence. Potential absolute convergence and potential diagonal convergence are shown to be equivalent, and their complete characterization for n x n modulus patterns is given. Complete characterizations of all introduced types of potential convergence for 2 x 2 modulus patterns are also presented.
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We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. ...
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We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3-4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On I and I~*-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177] and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.
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In [10, 11, 12] a new graph topology #tau# was introduced which is useful in applications to differential equations. In this paper we study topological properties of #tau# and relations between #tau# and other known topologies. Fo...
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In [10, 11, 12] a new graph topology #tau# was introduced which is useful in applications to differential equations. In this paper we study topological properties of #tau# and relations between #tau# and other known topologies. For example, we find conditions under which #tau# coincides with Back's generalized compact-open topology successfully used for convergence of utility functions [2] and for convergence of dynamic programming models [19].
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