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An asymmetric MarcinkiewiczZygmund LLN for random fields
, 2008
"... The classical MarcinkiewiczZygmund law for iid random variables has been generalized by Gut (1978) to random fields. Therein all indices have the same power in the normalization. Looking into some weighted means of random fields, such as Cesàro summation, it is of interest to generalize these laws ..."
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The classical MarcinkiewiczZygmund law for iid random variables has been generalized by Gut (1978) to random fields. Therein all indices have the same power in the normalization. Looking into some weighted means of random fields, such as Cesàro summation, it is of interest to generalize these laws to the case where different indices have different powers in the normalization. In this paper we give precise moment conditions for such laws.
SIGN CHANGES IN SHORT INTERVALS OF COEFFICIENTS OF SPINOR ZETA FUNCTION OF A SIEGEL CUSP FORM OF GENUS 2
"... Abstract. In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results on the number of its positive (resp. negative) coefficients in some short intervals. ..."
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Abstract. In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results on the number of its positive (resp. negative) coefficients in some short intervals.
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
THE ACADEMY CORNER No. 42
"... In this issue, we present problems of the Undergraduate Mathematics Competition ..."
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In this issue, we present problems of the Undergraduate Mathematics Competition
Allan Gut
"... Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of i.i.d. random variables. The natural extension of results corresponding to Cesàro summation amounts to proving almost sure convergence of the Cesàro means. In the present paper we ..."
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Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of i.i.d. random variables. The natural extension of results corresponding to Cesàro summation amounts to proving almost sure convergence of the Cesàro means. In the present paper we extend such results as well as weak laws and results on complete convergence to random fields, more specifically to random variables indexed by Z 2 +, the positive twodimensional integer lattice points. 1
Ecole Polytechnique Fédérale de Lausanne
"... This paper studies questions of changes of variables in a class of hyperbolic stochastic partial differential equations in two variables driven by white noise. Two types of changes of variables are considered: naive changes of variables which do not involve a change of filtration, which affect the e ..."
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This paper studies questions of changes of variables in a class of hyperbolic stochastic partial differential equations in two variables driven by white noise. Two types of changes of variables are considered: naive changes of variables which do not involve a change of filtration, which affect the equation much as though it were deterministic, and changes of variables that do involve a change of filtration, such as timereversals. In particular, if the process in reversed coordinates does satisfy an s.p.d.e., then we show how this s.p.d.e. is related to the original one. Timereversals for the Brownian sheet and for equations with constant coefficients are considered in detail. A necessary and sufficient condition is provided under which the reversal of the solution to the simplest hyperbolic s.p.d.e. with certain random initial conditions again satisfies such an s.p.d.e. This yields a negative conclusion concerning the reversal in time of the solution to the stochastic wave equation (in one spatial dimension) driven by white noise.
doi:10.1155/2007/28205 Research Article λRearrangements Characterization of Pringsheim Limit Points
, 2007
"... Sufficient conditions are given to assure that a fourdimensional matrix A will have the property that any double sequence x with finite Plimit point has a λrearrangement z such that each finite Plimit point of x is a Plimit point of Az. Copyright © 2007 Richard F. Patterson. This is an open ac ..."
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Sufficient conditions are given to assure that a fourdimensional matrix A will have the property that any double sequence x with finite Plimit point has a λrearrangement z such that each finite Plimit point of x is a Plimit point of Az. Copyright © 2007 Richard F. Patterson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Uniform Convergence of Reversed
"... A necessary and sufficient condition for the uniform convergence of a family of reversed martingales converging to a degenerated limiting process is given. The condition is expressed by means of regular convergence (in Hardy’s sense) of corresponding means. It is shown that the given regular converg ..."
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A necessary and sufficient condition for the uniform convergence of a family of reversed martingales converging to a degenerated limiting process is given. The condition is expressed by means of regular convergence (in Hardy’s sense) of corresponding means. It is shown that the given regular convergence is equivalent to HoffmannJørgensen’s eventually total boundedness in the mean which is necessary and sufficient for the uniform law of large numbers. Analogous results are carried out for families of reversed submartingales. By applying derived results several convergence statements are obtained which extend those from the uniform law of large numbers to the general reversed martingale case. 1.