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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.
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.
Allan Gut
"... Motivated by our earlier work on changepoint analysis we prove a number of limit theorems for increments of renewal counting processes, or the corresponding first passage times. The starting point of the increments are deterministic as well as random, the typical example being the first stopping ti ..."
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Motivated by our earlier work on changepoint analysis we prove a number of limit theorems for increments of renewal counting processes, or the corresponding first passage times. The starting point of the increments are deterministic as well as random, the typical example being the first stopping time to detect a changepoint of some (continuously) observed process. 1
The Mayhem Problems editors are:
"... Mathematical Mayhem began in 1988 as a Mathematical Journal for and by ..."
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
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.