Characterization of the microstructure of disordered media: A unified approach

1987 ◽  
Vol 35 (10) ◽  
pp. 5385-5387 ◽  
Author(s):  
S. Torquato
Keyword(s):  
Disordered Media ◽  
Unified Approach

Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem

1986 ◽  
Vol 18 (03) ◽  
pp. 660-678 ◽  
Author(s):  
C. Radhakrishna Rao ◽  
D. N. Shanbhag
Keyword(s):  
Negative Binomial ◽  
Short Proof ◽  
Probability Distributions ◽  
Direct Link ◽  
Unified Approach ◽  
Binomial Distributions ◽  
Characterization Of Probability Distributions ◽  
Special Cases ◽  
Convolution Equations

The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

scholarly journals Homotopy of compact symmetric spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 221-228 ◽  
Author(s):  
John M. Burns
Keyword(s):  
Symmetric Spaces ◽  
Unified Approach ◽  
Topological Characterization ◽  
New Approach ◽  
Totally Geodesic ◽  
Compact Symmetric Space ◽  
Geodesic Submanifolds ◽  
Totally Geodesic Submanifolds ◽  
Compact Symmetric Spaces

In recent years a new approach to the study of compact symmetric spaces has been taken by Nagano and Chen [10]. This approach assigned to each pair of antipodal points on a closed geodesic a pair of totally geodesic submanifolds. In this paper we will show how these totally geodesic submanifolds can be used in conjunction with a theorem of Bott to compute homotopy in compact symmetric spaces. Some of the results are already known (see [1], [5], [11] for example) but we include them here for completeness and to illustrate this unified approach. We also exhibit a connection between the second homotopy group of a compact symmetric space and the multiplicity of the highest root. Using this in conjunction with a theorem of J. H. Cheng [6] we obtain a topological characterization of quaternionic symmetric spaces with antiquaternionic involutive isometry. The author would like to thank Prof T. Nagano for all his help and his detailed descriptions of the totally geodesic submanifolds mentioned above.

A NEW UNIFIED SOLIDS FLUX-BASED APPROACH FOR THE DESIGN OF FINAL CLARIFIERS: DESCRIPTION AND COMPARISON WITH TRADITIONAL CRITERIA

1994 ◽  
Vol 30 (4) ◽  
pp. 57-66 ◽  
Author(s):  
M. von Sperling
Keyword(s):  
Activated Sludge ◽  
Unified Approach ◽  
Traditional Design

The paper presents a methodology for the derivation of the overflow rate and the solids flux for the design of final sedimentation tanks in activated sludge plants. The method is based on a simplified characterization of the sludge into three ranges, according to its settleability (good, fair or poor). The coefficients were derived from the integration of well known results obtained by different authors, which have to-date been used only individually. This unified approach widens the breadth of the previous studies, allowing a more reliable detennination of the design rates. The rates obtained with the proposed method were compared with the values suggested by traditional design manuals, with both approaches leading to similar results.

Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem

1986 ◽  
Vol 18 (3) ◽  
pp. 660-678 ◽  
Author(s):  
C. Radhakrishna Rao ◽  
D. N. Shanbhag
Keyword(s):  
Negative Binomial ◽  
Short Proof ◽  
Probability Distributions ◽  
Direct Link ◽  
Unified Approach ◽  
Binomial Distributions ◽  
Characterization Of Probability Distributions ◽  
Special Cases ◽  
Convolution Equations

The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

The characterization of distributions by order statistics and record values — a unified approach

1984 ◽  
Vol 21 (2) ◽  
pp. 326-334 ◽  
Author(s):  
Paul Deheuvels
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Simple Proof ◽  
Order Statistic ◽  
Continuous Distribution ◽  
Record Values ◽  
Discrete Distributions ◽  
Unified Approach ◽  
Characterization Of Distributions

It is shown that, in some particular cases, it is equivalent to characterize a continuous distribution by properties of records and by properties of order statistics. As an application, we give a simple proof that if two successive jth record values and associated to an i.i.d. sequence are such that and are independent, then the sequence has to derive from an exponential distribution (in the continuous case). The equivalence breaks up for discrete distributions, for which we give a proof that the only distributions such that Xk, n and Xk+1, n – Xk, n are independent for some k ≧ 2 (where Xk, n is the kth order statistic of X1, ···, Xn) are degenerate.

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