scholarly journals Polyhedrons the Faces of which are Special Quadric Patches

KoG ◽  
2021 ◽  
pp. 45-52
Author(s):  
Milena Stavrić ◽  
Albert Wiltsche ◽  
Gunter Weiss
Keyword(s):  
Symmetry Axis ◽  
The Other ◽  
Platonic Solids ◽  
Simple Criterion ◽  
Hyperbolic Paraboloids

We seize an idea of Oswald Giering (see [1] and [2]), who replaced pairs of faces of a polyhedron by patches of hyperbolic paraboloids and link up edge-quadrilaterals of a polyhedron with the pencil of quadrics determined by that quadrilateral. Obviously only ruled quadrics can occur. There is a simple criterion for the existence of a ruled hyperboloid of revolution through an arbitrarily given quadrilateral. Especially, if a (not planar) quadrilateral allows one symmetry, there exist two such hyperboloids of revolution through it, and if the quadrilateral happens to be equilateral, the pencil of quadrics through it contains even three hyperboloids of revolution with pairwise orthogonal axes. To mention an example, for right double pyramids, as for example the octahedron, the axes of the hyperboloids of revolution are, on one hand, located in the plane of the regular guiding polygon, and on the other, they are parallel to the symmetry axis of the double pyramid. Not only for platonic solids, but for all polyhedrons, where one can define edge-quadrilaterals, their pairs of face-triangles can be replaced by quadric patches, and by this one could generate roofing of architectural relevance. Especially patches of hyperbolic paraboloids or, as we present here, patches of hyperboloids of revolution deliver versions of such roofing, which are also practically simple to realize.

THE ISOPIESTIC METHOD APPLIED TO SORPTION ISOTHERMS

1949 ◽  
Vol 27b (2) ◽  
pp. 87-100 ◽  
Author(s):  
S. Barnartt ◽  
J. B. Ferguson
Keyword(s):  
Carbon Tetrachloride ◽  
Linear Relation ◽  
Sorption Isotherms ◽  
Sorption Process ◽  
The Other ◽  
Isopiestic Method ◽  
Simple Criterion ◽  
Water Vapors ◽  
Linear Sections ◽  
Wide Pressure

The isopiestic method has been applied to the sorption of carbon tetrachloride and water vapors by activated coconut shell charcoals. The isopiestic charges were found to be linearly related over wide pressure ranges. Isotherms formed by plotting the isopiestic charges of two charcoals one against the other consisted of three linear sections for both carbon tetrachloride and water. If the pressure isotherm of one charcoal be known, those of other charcoals may be computed from it by weighing relatively few isopiestic charges. Errors inherent in the measurement of equilibrium pressures, as well as those caused by the drift of the pressure isotherms towards higher sorption capacities at a given pressure, are eliminated in the isopiestic method of comparing charcoals. The linear relation between the isopiestic charges affords a simple criterion of rejection for equations proposed to fit the pressure isotherms. It also throws into relief the structural regularities in activated charcoals. The existence of discontinuities m the sorption process, reported by previous experimenters, is supported by the isopiestic data.

scholarly journals Deprojection of Galaxies: How Much Can Be Learned?

1987 ◽  
Vol 127 ◽  
pp. 397-398 ◽  
Author(s):  
George B. Rybicki
Keyword(s):  
Symmetry Axis ◽  
Three Dimensional ◽  
Light Distribution ◽  
Axially Symmetric ◽  
Simple Criterion ◽  
Slice Theorem ◽  
Intrinsic Shape ◽  
Model Independent ◽  
Fourier Slice Theorem

A general discussion, based on the ht “Fourier Slice Theorem,” is given for the problem of deprojecting the observed light distribution of galaxies to obtain their intrinsic three dimensional light distribution or “shape.” Several results are obtained: 1) A model-independent deprojection of an axially symmetric galaxy is shown to be possible only if the symmetry axis lies in the plane of the sky. 2) A simple criterion is given to test whether two different galaxies can have the same intrinsic shape, based solely on their observed projections. 3) It is shown that a homogeneous class of galaxies can be deprojected using a sufficiently large number of projections of random perspective.

The estimation of the critical load of a braced framework

1955 ◽  
Vol 231 (1184) ◽  
pp. 25-36 ◽  
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
The Other ◽  
Simple Criterion ◽  
Relaxation Methods ◽  
The Stability

With present methods of estimating the critical loads of triangulated frameworks by relaxation methods it is difficult to decide near the critical load whether the process is converging and the structure is stable, or whether the process is diverging and the structure unstable. This difficulty does not arise in the method presented here. Each triangle of the framework in turn is replaced by a hypothetical member until finally only one member of the truss remains, and this member has been modified in such a way as to take into account the stiffnesses of all the other members of the truss. A simple criterion for the stability of this final equivalent member is established and an example of the application of the method given.

scholarly journals THE FRONTIER OF DECIDABILITY IN PARTIALLY OBSERVABLE RECURSIVE GAMES

2012 ◽  
Vol 23 (07) ◽  
pp. 1439-1450 ◽  
Author(s):  
DAVID AUGER ◽  
OLIVIER TEYTAUD
Keyword(s):  
Decision Problem ◽  
Winning Strategy ◽  
The Other ◽  
Simple Criterion ◽  
Stochastic Case ◽  
Recursive Games ◽  
Partially Observable ◽  
Random Part ◽  
Classical Decision

The classical decision problem associated with a game is whether a given player has a winning strategy, i.e. some strategy that leads almost surely to a victory, regardless of the other players' strategies. While this problem is relevant for deterministic fully observable games, for a partially observable game the requirement of winning with probability 1 is too strong. In fact, as shown in this paper, a game might be decidable for the simple criterion of almost sure victory, whereas optimal play (even in an approximate sense) is not computable. We therefore propose another criterion, the decidability of which is equivalent to the computability of approximately optimal play. Then, we show that (i) this criterion is undecidable in the general case, even with deterministic games (no random part in the game), (ii) that it is in the jump 0', and that, even in the stochastic case, (iii) it becomes decidable if we add the requirement that the game halts almost surely whatever maybe the strategies of the players.

Convex Polyhedra with Regular Faces

1966 ◽  
Vol 18 ◽  
pp. 169-200 ◽  
Author(s):  
Norman W. Johnson
Keyword(s):  
The Other ◽  
Convex Polyhedra ◽  
Regular Polygons ◽  
Platonic Solids ◽  
Geometric Figures ◽  
Regular Polyhedra ◽  
The Subject ◽  
Symmetry Operations

An interesting set of geometric figures is composed of the convex polyhedra in Euclidean 3-space whose faces are regular polygons (not necessarily all of the same kind). A polyhedron with regular faces is uniform if it has symmetry operations taking a given vertex into each of the other vertices in turn (5, p. 402). If in addition all the faces are alike, the polyhedron is regular.That there are just five convex regular polyhedra—the so-called Platonic solids—was proved by Euclid in the thirteenth book of the Elements (10, pp. 467-509). Archimedes is supposed to have described thirteen other uniform, “semi-regular” polyhedra, but his work on the subject has been lost.

scholarly journals Inheritance of extrachromosomal rDNA in Physarum polycephalum.

1983 ◽  
Vol 3 (4) ◽  
pp. 635-642 ◽  
Author(s):  
P J Ferris ◽  
V M Vogt ◽  
C L Truitt
Keyword(s):  
Inverted Repeat ◽  
Physarum Polycephalum ◽  
Symmetry Axis ◽  
Single Copy ◽  
The Other ◽  
Cleavage Pattern ◽  
Extrachromosomal Dna ◽  
Repeat Sequences ◽  
Rdna Sequences ◽  
Restriction Endonuclease Cleavage

In the acellular slime mold Physarum polycephalum, the several hundred genes coding for rRNA are located on linear extrachromosomal DNA molecules of a discrete size, 60 kilobases. Each molecule contains two genes that are arranged in a palindromic fashion and separated by a central spacer region. We investigated how rDNA is inherited after meiosis. Two Physarum amoebal strains, each with an rDNA recognizable by its restriction endonuclease cleavage pattern, were mated, the resulting diploid plasmodium was induced to sporulate, and haploid progeny clones were isolated from the germinated spores. The type of rDNA in each was analyzed by blotting hybridization, with cloned rDNA sequences used as probes. This analysis showed that rDNA was inherited in an all-or-nothing fashion; that is, progeny clones contained one or the other parental rDNA type, but not both. However, the rDNA did not segregate in a simple Mendelian way; one rDNA type was inherited more frequently than the other. The same rDNA type was also in excess in the diploid plasmodium before meiosis, and the relative proportions of the two rDNAs changed after continued plasmodial growth. The proportion of the two rDNA types in the population of progeny clones reflected the proportion in the parent plasmodium before meoisis. The rDNAs in many of the progeny clones contained specific deletions of some of the inverted repeat sequences at the central palindromic symmetry axis. To explain the pattern of inheritance of Physarum rDNA, we postulate that a single copy of rDNA is inserted into each spore or is selectively replicated after meiosis.

STEREOCHEMSTRY OF ARSENIC: PART III. o-PHENYLENEDIARSINE OXYCHLORIDE

1962 ◽  
Vol 40 (6) ◽  
pp. 1113-1117 ◽  
Author(s):  
W. R. Cullen ◽  
J. Trotter
Keyword(s):  
Symmetry Axis ◽  
Van Der Waals ◽  
Membered Ring ◽  
Unit Cell ◽  
The Other ◽  
Van Der Waals Interactions ◽  
Chlorine Atoms ◽  
Space Group ◽  
Bond Lengths ◽  
Aromatic Character

Crystals of o-phenylenediarsine oxychloride, C6H4As2Cl2O, are monoclinic with four molecules in a unit cell of dimensions a = 14.50, b = 8.38, c = 7.66 Å, β = 105.8°, space group C2/c. The structure has been determined from projections along the b and c axes. Each molecule is situated on a 2-fold symmetry axis and is planar except for the chlorine atoms, which lie one on either side of the plane of the other atoms. The values of the bond lengths and valency angles have been obtained. Abnormal valency angles at the arsenic and oxygen atoms are the result of their presence in the five-membered ring, and the unusual stability of the molecule in spite of these angles can be interpreted in terms of aromatic character, involving dπ–pπ bonding. The intermolecular separations correspond to normal van der Waals interactions.

scholarly journals Mutual Contradiction of Two Self-Consistent Abstractions

1966 ◽  
Vol 28 ◽  
pp. 59-61 ◽  
Author(s):  
Katuzi Ono
Keyword(s):  
The Other ◽  
Sufficient Condition ◽  
Restricted Class ◽  
Simple Criterion ◽  
Other Hand ◽  
Self Consistent

A vast class of abstractions are proved self-contradictory by Russell-type paradoxes in the sense that the negation of any one of them can be proved tautologically. On the other hand, there are a vast class of abstractions, each being self-consistent. A simple criterion for abstractions to be self-consistent (a sufficient condition) can be given. However, even a fairly restricted class of abstractions, each satisfying the criterion to be self-consistent, may contradict to each other.

Comparative Analytical Solutions to the Problem of Profiling the End Mill Cutter to Generate Helical Surfaces

2015 ◽  
Vol 809-810 ◽  
pp. 39-44
Author(s):  
Gabriel Frumuşanu ◽  
Virgil Teodor ◽  
Nicolae Oancea
Keyword(s):  
Minimum Distance ◽  
Symmetry Axis ◽  
The Other ◽  
Numerical Representation ◽  
Classical Theorem ◽  
End Mill ◽  
Helical Surface ◽  
Constant Pitch ◽  
Revolution Surfaces ◽  
Mill Cutter

In this paper, we present, comparatively, two analytical methods for profiling the tools delimited by revolution surfaces, used to generate helical surfaces with constant pitch. The first method lays on a complementary theorem used for tools profiling, namely the Minimum distance theorem. A specific algorithm for applying it has been developed, in order to profile the tools delimited by revolution surfaces, which generates helical surfaces with constant pitch by enwrapping. The methodic is referring, here, to a tool whose symmetry axis is incident and, at the same time, normal to the helical surface axis – the end mill cutter. The other analytical method here applied grounds on Nikolaev classical theorem. We also present an example of application for both methods, in the case of profiling the end mill cutter used to generate a helicoid with circular frontal generatrix. The tool axial sections are determined and compared in a numerical representation.

A Utilitarian Approach for the Governance of Humanitarian Migration

2018 ◽  
Vol 40 (2) ◽  
pp. 293-320
Author(s):  
Herbert Brücker
Keyword(s):  
Social Costs ◽  
The Other ◽  
Simple Criterion ◽  
Host Countries ◽  
Marginal Costs ◽  
The Core ◽  
Political Problem ◽  
Utilitarian Approach ◽  
The One ◽  
Forms Of Violence

Abstract Humanitarian migration creates, on the one hand, huge benefits for those who are protected from war, persecution and other forms of violence, but, on the other hand, involves also net monetary and social costs for the population in host countries providing protection at the same time. This is the core of the ethical and political problem associated with the governance of humanitarian migration. Against this background, this paper discusses whether the provision of protection can be founded on rational ethical principles. By drawing on a utilitarian approach a simple criterion is derived: Humanitarian migration is welfare improving, as long as the benefits of the marginal humanitarian migrant exceed the marginal costs of providing shelter per refugee. Based on this principle, practical solutions for the admission of humanitarian migrants and the international and European coordination of asylum policies are discussed.

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