scholarly journals Some remarks concerning finitely Subadditive outer measures with applications

1998 ◽  
Vol 21 (4) ◽  
pp. 653-669 ◽  
Author(s):  
John E. Knight
Keyword(s):  
General Theory ◽  
Outer Measure ◽  
Additive Measure ◽  
Finitely Additive Measure ◽  
Set Functions ◽  
Relationship Of ◽  
The Relationship ◽  
General Method

The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the relationship of their properties to those of an associated finitely subadditive outer measure. In particular, the interconnections between the measurable sets determined by both the outer measure and its associated inner measure are examined. Finally, several applications of the general theory are given, with special attention being paid to various lattice related set functions.

THE SYNTHESIS OF POSSIBLE DEGRADATION PRODUCTS OF METATHEBAINONE. I.

1944 ◽  
Vol 22b (3) ◽  
pp. 56-65 ◽  
Author(s):  
H. L. Holmes ◽  
L. W. Trevoy
Keyword(s):  
Carboxylic Acid ◽  
Ethyl Ester ◽  
Degradation Products ◽  
Aldehyde Group ◽  
Carboxyl Group ◽  
Unsuccessful Attempt ◽  
Naphthoic Acid ◽  
Relationship Of ◽  
The Relationship ◽  
General Method

The method of Crowley and Robinson (5) for the synthesis of 6-methoxy-3,4-dihydro-2-naphthoic acid has been modified to provide an improved and general method for the synthesis of 3,4-dihydro-2-naphthoic acids. The 7-methoxy-3,4-dihydro-2-naphthoic acid and its ethyl ester have been shown to react with butadiene and 2,3-dimethylbutadiene to give 3-methoxy-5,8,9,10,13,14-hexahydrophenanthrene-14-carboxylic acid and its 6,7-dimethyl derivative. The relationship of these hydrophenanthrenes to possible degradation products of morphine and metathebainone has been discussed. An unsuccessful attempt was made to lengthen the C14-chain by converting the carboxyl group to an aldehyde group by the Rosenmund method followed by condensation with malonic acid. The projected conversion failed in the first stage.

Toward a General Theory of Vegetability and Mechanism

2018 ◽  
pp. 150-180
Author(s):  
William R. Newman
Keyword(s):  
General Theory ◽  
The Body ◽  
Sea Salt ◽  
Detailed Consideration ◽  
Original Theory ◽  
The Earth ◽  
Similarities And Differences ◽  
Relationship Of ◽  
The Relationship ◽  
Living Creature

This chapter focuses on Newton's treatise, Of Natures obvious laws & processes in vegetation. The treatise begins with a detailed consideration of the similarities and differences between mineral generation and that of animals and vegetables, then passes to a quite original theory of the different methods by which nature produces two common products, sea salt and niter, incidentally invoking the aerial niter theory of Sendivogius. After this, Newton presents his view that the earth is itself a living creature and uses its respiration to account for gravity, leading him into an intricate discussion of different “airs” as well as the relationship of even more subtle materials, namely, ether and the “body” of light. From here he launches into a discussion of God and attempts to improve on the proofs that René Descartes had supplied for the existence of the divinity. In the final paragraphs of the text, Newton returns to the theme of generation and employs the principle of vegetability to distinguish between the growth and activity imparted by nature from the more superficial processes of mechanism.

Measures Below Outer Measures

1994 ◽  
Vol 37 (2) ◽  
pp. 270-271
Author(s):  
Stephen Watson
Keyword(s):  
Simple Proof ◽  
Cantor Set ◽  
Outer Measure ◽  
Additive Measure ◽  
Finitely Additive Measure ◽  
Finite Set

AbstractWe give a simple proof that, for any ॉ > 0, there is an outer measure μ* on a finite set X such that, for any measure Thus there is a non-zero outer (finitely subadditive) measure v* on the clopen subsets of the Cantor set such that, if v ≤ v* is a finitely additive measure on the clopen subsets of the Cantor set, then v ≡ 0.

Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research

1980 ◽  
Vol 17 (1) ◽  
pp. 1-13 ◽  
Author(s):  
William D. Perreault ◽  
Forrest W. Young
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Continuous Distribution ◽  
Marketing Research ◽  
Optimal Scaling ◽  
Alternating Least Squares ◽  
Scaling Analysis ◽  
Relationship Of ◽  
The Relationship ◽  
General Method

The authors discuss and illustrate the advantages and limitations of a family of new approaches to the analysis of metric and nonmetric data in marketing research. The general method, which is based on alternating least squares optimal scaling procedures, extends the analytical flexibility of the general linear model procedures (ANOVA, regression, canonical correlation, discriminant analysis, etc.) to situations in which the data (1) are measured at any mixture of the nominal, ordinal, or interval levels and (2) are derived from either a discrete or continuous distribution. The relationship of these procedures to traditional linear models and to other nonmetric approaches (such as multidimensional scaling and conjoint analysis) is reviewed.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Studies on Leukemogenic and Sarcomagenic Viruses

1970 ◽  
Vol 28 ◽  
pp. 156-157
Author(s):  
Leon Dmochowski
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Morphological Properties ◽  
Mode Of Development ◽  
Relationship Of ◽  
The Relationship

Electron microscopy has proved to be an invaluable discipline in studies on the relationship of viruses to the origin of leukemia, sarcoma, and other types of tumors in animals and man. The successful cell-free transmission of leukemia and sarcoma in mice, rats, hamsters, and cats, interpreted as due to a virus or viruses, was proved to be due to a virus on the basis of electron microscope studies. These studies demonstrated that all the types of neoplasia in animals of the species examined are produced by a virus of certain characteristic morphological properties similar, if not identical, in the mode of development in all types of neoplasia in animals, as shown in Fig. 1.

The relationship of IGE receptor topography to signaling activity in RBL-2H3 mast cells

1991 ◽  
Vol 49 ◽  
pp. 236-237
Author(s):  
J.R. Pfeiffer ◽  
J.C. Seagrave ◽  
C. Wofsy ◽  
J.M. Oliver
Keyword(s):  
Mast Cells ◽  
Protein A ◽  
Scattered Electron ◽  
Ige Receptor ◽  
Receptor Complexes ◽  
Ige Binding ◽  
Electron Imaging ◽  
Small Clusters ◽  
Relationship Of ◽  
The Relationship

In RBL-2H3 rat leukemic mast cells, crosslinking IgE-receptor complexes with anti-IgE antibody leads to degranulation. Receptor crosslinking also stimulates the redistribution of receptors on the cell surface, a process that can be observed by labeling the anti-IgE with 15 nm protein A-gold particles as described in Stump et al. (1989), followed by back-scattered electron imaging (BEI) in the scanning electron microscope. We report that anti-IgE binding stimulates the redistribution of IgE-receptor complexes at 37“C from a dispersed topography (singlets and doublets; S/D) to distributions dominated sequentially by short chains, small clusters and large aggregates of crosslinked receptors. These patterns can be observed (Figure 1), quantified (Figure 2) and analyzed statistically. Cells incubated with 1 μg/ml anti-IgE, a concentration that stimulates maximum net secretion, redistribute receptors as far as chains and small clusters during a 15 min incubation period. At 3 and 10 μg/ml anti-IgE, net secretion is reduced and the majority of receptors redistribute rapidly into clusters and large aggregates.

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