The Relationship Between The Canonical Elements In The Formal Acts Of Defection From The Faith And Schism With Regard To The Canonical Form Of Marriage

2003 ◽  
Author(s):  
James S. KEE
Keyword(s):  
Canonical Form ◽  
The Relationship

EP Operators and Generalized Inverses

1975 ◽  
Vol 18 (3) ◽  
pp. 327-333 ◽  
Author(s):  
Stephen L. Campbell ◽  
Carl D. Meyer
Keyword(s):  
Hilbert Space ◽  
Canonical Form ◽  
Generalized Inverse ◽  
Generalized Inverses ◽  
Space Setting ◽  
The Relationship

AbstractThe relationship between properties of the generalized inverse of A, A†, and of the adjoint of A, A*, are studied. The property that A†A and AA† commute, called (E4), is investigated. (E4) generalizes the property of A being EPr. A canonical form and a formula for A† are given if a matrix A is (E4). Results are in a Hilbert space setting whenever possible. Examples are given.

scholarly journals INTER-LEVEL SUBSTITUTION – THE CANONICAL FORM OF THE INTER-LEVEL BALANCE

2018 ◽  
pp. 9-17
Author(s):  
Alexander Dubyagin ◽  
Keyword(s):  
Canonical Form ◽  
Balance Model ◽  
Mathematical Form ◽  
Control Effect ◽  
Aggregate Form ◽  
Target Setting ◽  
Object Based ◽  
External Impact ◽  
The Impact ◽  
The Relationship

Urgency of the research. Inter-level substitution is the basis for the formation in the aggregate form of a model and sys-tem of indices of the inter-level balance, and the latter comprehensively assess the consequences of the control effect on the structured object and the effectiveness of the impact itself. Target setting. Existing evaluation methods do not take into account the factor of movement of object units from one level of the characteristic to another, which is why the structural analysis of the results of the impact is incomplete.Actual scientific researches and issues analysis. Inter-level substitution is a new concept. Earlier, the author proposed a model and a system of indices of inter-level balance, constructed only in the values of the number of object units at the level. Uninvestigated parts of general matters defining. The model of inter-level balance and a system of balance indicators, presented in aggregate form. The research objective. Formalization of the concept of “inter-level substitution” as a canonical form of the inter-level balance in the form of paired indicators of aggregated absolute balance of inter-level movement and inter-level turnover ofunits of a structured object. The statement of basic materials. The inter-level substitution of object units leads to level (extra-level) losses or to a level (extra-level) replenishment of the object based on the characteristic measured in these units in the relationship scale at a certain level (outside the level) in the “after” and “before” conditions of external impact. The overall result of the latter can be analytically represented as a generalized balance ratio. In the aggregate form, it is determined through the elemen-tary components of the balance, which are the number of displacements and the level values of the characteristic. Conclusions. The mathematical form of the inter-level substitution is the key in the formation of the inter-level balance model and the system of balance indicators of movement.

scholarly journals Parameterized Structure-Preserving Transformations of Matrix Polynomials

2020 ◽  
Vol 36 (36) ◽  
pp. 723-743
Author(s):  
Daniel T. Kawano
Keyword(s):  
Canonical Form ◽  
Equivalence Transformation ◽  
Regular Matrix ◽  
Quadratic Polynomials ◽  
Structure Preserving ◽  
Matrix Polynomials ◽  
The Relationship

This paper examines the relationship between the companion forms of regular matrix polynomials with singular leading coefficients. When two such polynomials have the same underlying finite and infinite Jordan structures, it is shown that their companion forms are connected by a strict equivalence transformation that can be parameterized using the commutant of the companion forms' common Weierstrass canonical form. The process developed herein for generating such parameterized transformations is applied to the useful class of diagonalizable quadratic polynomials.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

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.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

Tinkering with cognitive gadgets: Cultural evolutionary psychology meets active inference

2019 ◽  
Vol 42 ◽  
Author(s):  
Paul Benjamin Badcock ◽  
Axel Constant ◽  
Maxwell James Désormeau Ramstead
Keyword(s):  
Evolutionary Psychology ◽  
Research Program ◽  
Active Inference ◽  
Innovative Research ◽  
Cognitive Faculties ◽  
Cultural Evolutionary ◽  
The Relationship

Abstract Cognitive Gadgets offers a new, convincing perspective on the origins of our distinctive cognitive faculties, coupled with a clear, innovative research program. Although we broadly endorse Heyes’ ideas, we raise some concerns about her characterisation of evolutionary psychology and the relationship between biology and culture, before discussing the potential fruits of examining cognitive gadgets through the lens of active inference.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

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.

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