On the Family of Curves z=(t-tn)/2

1962 ◽  
Vol 35 (4) ◽  
pp. 211
Author(s):  
M. Stephanie Sloyan
Keyword(s):  
Family Of Curves ◽  
The Family

scholarly journals Duality of Moduli and Quasiconformal Mappings in Metric Spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 166-181
Author(s):  
Rebekah Jones ◽  
Panu Lahti
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Poincaré Inequality ◽  
Quasiconformal Mappings ◽  
Duality Relation ◽  
Doubling Measure ◽  
Poincare Inequality ◽  
Family Of Curves ◽  
The Family

AbstractWe prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.

scholarly journals The Tritangent Circles of a Circular Quartic Curve

1932 ◽  
Vol 3 (1) ◽  
pp. 46-52
Author(s):  
H. W. Richmond
Keyword(s):  
Fixed Points ◽  
Space Curve ◽  
Cubic Surface ◽  
Quartic Curve ◽  
Family Of Curves ◽  
The Family ◽  
The Subject ◽  
Simple Notation ◽  
Pass Through

§1. In a recent paper with this title Prof. W. P. Milne has discussed the properties of the conics which pass through two fixed points of a plane quartic curve and touch the curve at three other points. In dealing with a numerous family of curves such as this it is very desirable to have a scheme of marks or labels to distinguish the different members of the family; Hesse's notation for the double tangents of a C4 illustrates this. By using another line of approach to the subject, by projecting the curve of intersection of a quadric and a cubic surface from a point at which (under exceptional circumstances) the surfaces touch, I find that a fairly simple notation for the 64 conics, in harmony with that for the bitangents, can be obtained. This paper, let it be said, from start to finish is no more than an adaptation of results known for the sextic space-curve referred to; it will be sufficient therefore to state results with short explanations.

The development of resistance to Terramycin by Bact. lactis aerogenes ( Aerobacter aerogenes )

1965 ◽  
Vol 161 (985) ◽  
pp. 571-582 ◽  
Keyword(s):  
Mathematical Expression ◽  
Secondary Effects ◽  
Aerobacter Aerogenes ◽  
Original Population ◽  
Development Of Resistance ◽  
Solid Media ◽  
Family Of Curves ◽  
The Family ◽  
Adaptive Processes ◽  
Drug Free

The relation between the concentration of Terramycin and the lag preceding growth has been determined for the unadapted strain and for strains of Bact . latics aerogenes (Aerobacter aerogenes) fully adapted to a range of concentrations of drug. The family of curves so obtained, whose horizontal spacing can be predicted by a simple mathematical expression, shows that the resistance is continuously graded to the ‘training’ concentration. After one subculture in a low concentration of drug the resistance declines gradually, on growth in drug-free medium, to a state intermediate between full resistance and sensitivity and remains in this state for at least 500 generations in the absence of drug. Longer ‘training’ in which secondary effects of the drug occur results in a more stable resistance. Time-number relations for colony formation on solid media containing Terramycin show that no fully resistant forms exist in the original population. These responses are interpreted in terms of a competition between lethal and adaptive processes, and the changes in the macromolecular composition of the cells during the first subculture in liquid medium containing Terramycin are in accord with this.

scholarly journals An interesting family of curves of genus1

2000 ◽  
Vol 23 (6) ◽  
pp. 431-434 ◽  
Author(s):  
Andrew Bremner
Keyword(s):  
Elliptic Curves ◽  
Small Range ◽  
Minimal Rank ◽  
Family Of Curves ◽  
The Family ◽  
Interesting Family ◽  
Integral Solutions

We study the family of elliptic curvesy2=x3−t2x+1, both overℚ(t)and overℚ. In the former case, all integral solutions are determined; in the latter case, computation in the range1≤t≤999shows large ranks are common, giving a particularly simple example of curves which (admittedly over a small range) apparently contradict the once held belief that the rank under specialization will tend to have minimal rank consistent with the parity predicted by the Selmer conjecture.

scholarly journals NEW SYMPLECTIC V-MANIFOLDS OF DIMENSION FOUR VIA THE RELATIVE COMPACTIFIED PRYMIAN

2007 ◽  
Vol 18 (10) ◽  
pp. 1187-1224 ◽  
Author(s):  
D. MARKUSHEVICH ◽  
A. S. TIKHOMIROV
Keyword(s):  
Linear System ◽  
Euler Number ◽  
Singular Points ◽  
K3 Surface ◽  
Abelian Surfaces ◽  
The Third ◽  
Lagrangian Fibration ◽  
Family Of Curves ◽  
The Family ◽  
Symplectic Varieties

Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop. They have the same singularities as two of Fujiki's examples, namely, 28 isolated singular points analytically equivalent to the Veronese cone of degree 8, but a different Euler number. The family of curves used in this construction forms a linear system on a K3 surface with involution. The structure morphism of both Prymians to the base of the family is a Lagrangian fibration in abelian surfaces with polarization of type (1,2). No example of such fibration is known on nonsingular irreducible symplectic varieties.

scholarly journals Patterns of apparent co-operativity in a simple random non-equilibrium enzyme–substrate–modifier mechanism. Comparison with equilibrium allosteric models

1979 ◽  
Vol 177 (2) ◽  
pp. 631-639 ◽  
Author(s):  
Edward P. Whitehead ◽  
Maarten R. Egmond
Keyword(s):  
Steady State ◽  
Substrate Affinity ◽  
State Equations ◽  
Allosteric Interactions ◽  
Enzyme Substrate ◽  
Steady State Kinetics ◽  
Family Of Curves ◽  
The Family ◽  
Kinetics Of ◽  
Non Equilibrium

It has often been claimed that random non-equilibrium mechanisms can result in apparent homotropic and heterotropic effects in steady-state kinetics of the kind more usually attributed to intersubunit allosteric interactions. However, it has never been shown whether any simple random mechanism could in fact give patterns of apparent interaction similar to those predicted by the well-known allosteric models. The patterns of apparent substrate co-operativity and affinity given by the steady-state of a standard simple random substrate–modifier mechanism in which catalytic velocity is proportional to substrate binding have been analysed mathematically and numerically. All patterns possible with this model are described. Some of them rather resemble those possible with standard allosteric models, in that there is a high-affinity and a low-affinity form at zero and infinite modifier concentrations (or vice versa) which show Michaelian behaviour, apparent co-operativity passing through a maximum or minimum at intermediate affinities. Unlike the allosteric models the family of curves is in principle not symmetrical. The random model can also give behaviour not possible with the standard allosteric models, such as higher substrate affinity at intermediate modifier concentrations than at either zero or infinite modifier, with concomitant negative apparent substrate co-operativity, or a single change of sign of apparent substrate co-operativity. The analysis uses recently discovered simplified forms of steady-state equations for random models.

scholarly journals Some Properties of a Family of Curves on a Surface

1928 ◽  
Vol 1 (3) ◽  
pp. 160-165 ◽  
Author(s):  
C. E. Weatherburn
Keyword(s):  
Infinite Family ◽  
Differential Invariants ◽  
Fundamental Properties ◽  
Family Of Curves ◽  
The Family ◽  
The Given

This paper shows briefly how, for a singly infinite family of curves on a given surface, the fundamental properties of the family at any point are associated with three central conies determined by the curves, in a manner resembling that in which the curvature properties of a surface at any point are associated with Dupin's indicatrix. The differential invariants employed are the two-parametric invariants for the given surface.

MODELING OF THE CURING PROCESS OF A POLYMER RESIN AND CHANGES IN MICROHARDNESS IN ITS VOLUME

2021 ◽  
pp. 92-99
Author(s):  
V.I. Postnov ◽  
◽  
S.M. Kachura ◽  
E.A. Veshkin ◽  
◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Physical And Mechanical Properties ◽  
Degree Of Conversion ◽  
Curing Temperature ◽  
Curing Process ◽  
The Finite Element Method ◽  
Polymer Resin ◽  
Family Of Curves ◽  
The Family ◽  
Thermophysical Modeling

Curing parameters have the greatest impact on the physical and mechanical properties of FRP, therefore their optimum value is of particular importance for obtaining quality products. During curing temperature of the inner layers of the FRP can increase unevenly, which can lead to the formation of a gradient in the degree of conversion and heterogeneity of physical and mechanical properties. The article is devoted to the development of a mathematical model of the curing process of the EDT-69N resin, taking into account the kinetic parameters of curing and implementation thermophysical modeling using the finite element method. The correspondence of the family of curves for the degree of conversion along the sample cross-section and the family of microhardness curves is also shown.

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