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## Analogues of some Tauberian theorems for bounded variation

Acta Mathematica Hungarica
Author:
R. Patterson

## Abstract

In this paper definitions for “bounded variation”, “subsequences”, “Pringsheim limit points”, and “stretchings” of a double sequence are presented. Using these definitions and the notion of regularity for four dimensional matrices, the following two questions will be answered. First, if there exists a four dimensional regular matrix A such that Ay = Σ k,l=1,1 ∞∞ a m,n,k,l y k,l is of bounded variation (BV) for every subsequence y of x, does it necessarily follow that x ∈ BV? Second, if there exists a four dimensional regular matrix A such that Ay ∈ BV for all stretchings y of x, does it necessarily follow that x ∈ BV? Also some natural implications and variations of the two Tauberian questions above will be presented.

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## Core theorems for double subsequences and rearrangements

Acta Mathematica Hungarica
Authors:
H. Miller
and
R. Patterson

## Abstract

The concepts of subsequence and rearrangement of double sequence are used to present multidimensional analogues of the following core questions. If x is a bounded real sequence and A is a matrix summability method, under what conditions does there exist y, a subsequence (rearrangement) of x such that each number t in the core of x is a limit point of Ay?

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## Four dimensional matrix that induces the double Gibbs phenomenon

Acta Mathematica Hungarica
Authors:
R. Patterson
and

## Abstract

In 1930 Knopp presented the following matrix characterization for the core of ordinary sequences. If A is a nonnegative regular matrix then the core of [Ax] is contained in the core of [x], provided that [Ax] exists. Patterson in 1999 extended Knopp’s results to double sequences via four dimensional matrices. In a manner similar to the Knopp’s and Patterson’s results we present multidimensional extensions of Bustoz’s singular dimensional Gibbs phenomenon results. These results include a notion of what it means for a four dimensional matrix transformation to induce the double Gibbs phenomenon in s. In addition, necessary and sufficient conditions for a four dimensional matrix to induce the double Gibbs phenomenon is also presented.

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## Enhanced phenylpyruvic acid production with Proteus vulgaris by optimizing of the fermentation medium

Acta Alimentaria
Authors:
H.B. Coban
,
A. Demirci
,
P.H. Patterson
, and
R.J. Elias

Alpha keto acids are important food additives, which commonly produced by microbial deamination of amino acids. In this study, production of phenylpyruvic acid (PPA), which is the alpha keto acid of phenylalanine was enhanced in 2-l bench scale bioreactors by optimizing of fermentation medium composition using the Box-Behnken Response Surface Methodology (RSM). Optimum glucose, yeast extract, and phenylalanine concentrations were determined to be 119.4 g 1−1, 3.7 g 1−1, and 14.8 g 1−1, respectively, for PPA production, and 163.8 g 1−1, 10.8 g 1−1, and 9.8 g 1−1, respectively, for biomass production. Under these optimum conditions, PPA concentration was enhanced to 1349 mg 1−1, which was 28% and 276% higher than the unoptimized bioreactor and shake-flask fermentations, respectively. Moreover, P. vulgaris biomass concentration was optimized at 4.36 g 1−1, which was 34% higher than under the unoptimized bioreactor condition. Overall, this study demonstrated that optimization of the fermentation media improved PPA concentration and biomass production in bench scale bioreactors compared to previous studies in the literature and sets the stage for scale up to industrial production.

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## Nuclear, chemical, and physical characterization of nuclear materials

Journal of Radioanalytical and Nuclear Chemistry
Authors:
L. Tandon
,
E. Hastings
,
J. Banar
,
J. Barnes
,
D. Beddingfield
,
D. Decker
,
J. Dyke
,
D. Farr
,
J. FitzPatrick
,
D. Gallimore
,
S. Garner
,
R. Gritzo
,
T. Hahn
,
G. Havrilla
,
B. Johnson
,
K. Kuhn
,
S. LaMont
,
D. Langner
,
C. Lewis
,
V. Majidi
,
P. Martinez
,
R. McCabe
,
S. Mecklenburg
,
D. Mercer
,
S. Meyers
,
V. Montoya
,
B. Patterson
,
R. Pereyra
,
D. Porterfield
,
J. Poths
,
,
C. Ruggiero
,
D. Schwartz
,
M. Scott
,
K. Spencer
,
R. Steiner
,
R. Villarreal
,
H. Volz
,
L. Walker
,
A. Wong
, and
C. Worley

## Abstract

The goal of nuclear forensics is to establish an unambiguous link between illicitly trafficked nuclear material and its origin. The Los Alamos National Laboratory (LANL) Nuclear Materials Signatures Program has implemented a graded “conduct of operations” type analysis flow path approach for determining the key nuclear, chemical, and physical signatures needed to identify the manufacturing process, intended use, and origin of interdicted nuclear material. This analysis flow path includes both destructive and non-destructive characterization techniques and has been exercized against different nuclear materials from LANL’s special nuclear materials archive. Results obtained from the case study will be presented to highlight analytical techniques that offer the critical attribution information.

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