scholarly journals Topological type of discriminants of some special families

2021 ◽  
Author(s):  
Evelia R. García Barroso ◽  
M. Fernando Hernández Iglesias
Keyword(s):  
Topological Type ◽  
Smooth Curve ◽  
Milnor Number ◽  
Irreducible Curve ◽  
Tjurina Number ◽  
Discriminant Curve ◽  
The Difference

AbstractWe will describe the topological type of the discriminant curve of the morphism $$(\ell , f)$$ ( ℓ , f ) , where $$\ell $$ ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

Milnor number and Tjurina number of complete intersections

1985 ◽  
Vol 271 (1) ◽  
pp. 121-124 ◽  
Author(s):  
Eduard Looijenga ◽  
Joseph Steenbrink
Keyword(s):  
Milnor Number ◽  
Complete Intersections ◽  
Tjurina Number

scholarly journals EXPRESSION OF THE CONCEPT “THICK” IN BURYAT AND CHINESE: PERCEPTIVE ASPECT

2021 ◽  
pp. 152-159
Author(s):  
BABASAN D. TSYRENOV ◽  
◽  
MARINA B.-O. KHAIDAPOVA ◽  
Keyword(s):  
Topological Type ◽  
Continuous Sampling ◽  
Time Translation ◽  
Topological Parameter ◽  
General Scientific ◽  
The Common ◽  
The Difference ◽  
Definition Of ◽  
The Comparative Study ◽  
First Time

The article discusses the patterns of expressing the concept "thick" in two typologically and genetically unrelated languages - Buryat and Chinese. The research of different concepts manifestation in unrelated languages has recently become widespread, and the comparative study of Buryat and Chinese in this regard is conducted for the first time. Translation dictionaries and electronic corpora of the languages were taken as sources for the material from which the necessary tokens were selected using continuous sampling method. To interpret the obtained examples in various contexts, we applied a general scientific method and comparative analysis techniques. As a result, it was discovered that despite the difference in the genesis and typology of Buryat and Chinese, common patterns in the concept expression were found. The common pattern is the differentiation by "topological type", which dictates the use of synonymous words to denote the thickness of objects with different geometric parameters. According to the topological parameter, the objects can be classified as relatively flat (zuzaan, Chinese 厚 hou) or relatively cylindrical (buduun and粗 si), and this can also be applied to the parameters of the human body. Another common feature is the expression of human fatness (fat) in correlation with domestic animals’ fatness degree: targan and 肥 fei. In this context, the definition of fatness has negative connotation.

Tactile Discrimination of Surface Curvature and Shape by the Octopus

1964 ◽  
Vol 41 (2) ◽  
pp. 433-445
Author(s):  
M. J. WELLS
Keyword(s):  
Sensory Input ◽  
Muscle Tension ◽  
Smooth Curve ◽  
Surface Curvature ◽  
Sense Organs ◽  
Tactile Discrimination ◽  
The Difference ◽  
Smooth Objects ◽  
Composite Cylinders ◽  
Made In

1. Experiments are described in which octopuses were trained to discriminate by touch between pairs of Perspex cylinders of different diameter. 2. The proportion of errors made in experiments with thirteen different pairs of cylinders shows that octopuses distinguish cylinders on a basis of the difference in their surface curvature. 3. Curvature is detected from the degree of distortion of individual suckers. The bend of the arm or arms grasping an object can be shown to be irrelevant by using composite cylinders built up from narrower rods. These are treated as being of the diameter of their components. 4. Having been trained to take the larger and reject the smaller of two cylinders, octopuses tested with rough and smooth objects of the same size reject the rough and accept the smooth. Apparently the sensory input produced by contact with an object having a rough surface is similar to that produced by bending the suckers round a smooth curve of narrow radius. 5. The discrimination of cubes and spheres, which appears to be based on sucker distortion at the corners of the cube, is upset by cutting grooves into the surfaces of the two objects. 6. These findings are discussed in relation to the anatomy of the sense organs in the suckers. The development of two parallel mechanosensory systems, one related exclusively to the local adjustment of muscle tension, the other more concerned with the animal's relations to its external environment and hence involved in learned responses, is common to the organization of cephalopods and vertebrates.

scholarly journals Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities

2015 ◽  
Vol 218 ◽  
pp. 29-50
Author(s):  
Christophe Eyral ◽  
Maria Aparecida Soares Ruas
Keyword(s):  
Deformation Parameter ◽  
Topological Type ◽  
Type A ◽  
Milnor Number ◽  
Hypersurface Singularities ◽  
Special Case ◽  
Parameter Deformation

AbstractWe show that the possible jump of the order in an 1-parameter deformation family of (possibly nonisolated) hypersurface singularities, with constant Lê numbers, is controlled by the powers of the deformation parameter. In particular, this applies to families of aligned singularities with constant topological type—a class for which the Lê numbers are “almost” constant. In the special case of families withisolatedsingularities—a case for which the constancy of the Lê numbers is equivalent to the constancy of the Milnor number—the result was proved by Greuel, Plénat, and Trotman.As an application, we prove equimultiplicity for new families of nonisolated hypersurface singularities with constant topological type, answering partially the Zariski multiplicity conjecture.

scholarly journals The relative Bruce–Roberts number of a function on a hypersurface

2021 ◽  
pp. 1-13
Author(s):  
B. K. Lima-Pereira ◽  
J. J. Nuño-Ballesteros ◽  
B. Oréfice-Okamoto ◽  
J. N. Tomazella
Keyword(s):  
Ambient Space ◽  
Milnor Number ◽  
Hypersurface Singularity ◽  
Characteristic Variety ◽  
The Difference

Abstract We consider the relative Bruce–Roberts number $\mu _{\textrm {BR}}^{-}(f,\,X)$ of a function on an isolated hypersurface singularity $(X,\,0)$ . We show that $\mu _{\textrm {BR}}^{-}(f,\,X)$ is equal to the sum of the Milnor number of the fibre $\mu (f^{-1}(0)\cap X,\,0)$ plus the difference $\mu (X,\,0)-\tau (X,\,0)$ between the Milnor and the Tjurina numbers of $(X,\,0)$ . As an application, we show that the usual Bruce–Roberts number $\mu _{\textrm {BR}}(f,\,X)$ is equal to $\mu (f)+\mu _{\textrm {BR}}^{-}(f,\,X)$ . We also deduce that the relative logarithmic characteristic variety $LC(X)^{-}$ , obtained from the logarithmic characteristic variety $LC(X)$ by eliminating the component corresponding to the complement of $X$ in the ambient space, is Cohen–Macaulay.

scholarly journals Intercomparison of Lunar Laser and Traditional Determinations of Earth Rotation

1981 ◽  
Vol 63 ◽  
pp. 53-88 ◽  
Author(s):  
H. F. Fliegel ◽  
J. O. Dickey ◽  
J. G. Williams
Keyword(s):  
Earth Rotation ◽  
Smooth Curve ◽  
Systematic Errors ◽  
Polar Coordinates ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Rotational Orientation ◽  
The Difference

AbstractThe rotational orientation of the earth (UTO at McDonald Observatory) has been determined from lunar laser ranging (LLR) measurements for the interval 1971 to 1980. The results have been differenced from those obtained by conventional means as published by the Bureau International de l’Heure (BIH), on its 1979 system. The difference displays a quasi-seasonal signature, which we ascribe to systematic errors in the conventional measurements. The lunar data are well represented by a smooth curve, which gives UTO at McDonald with a precision of about 3/4 milliseconds or better, and UT1 to within 1 millisecond using BIH polar coordinates.

scholarly journals Deformations with constant Lê numbers and multiplicity of nonisolated hypersurface singularities

2015 ◽  
Vol 218 ◽  
pp. 29-50 ◽  
Author(s):  
Christophe Eyral ◽  
Maria Aparecida Soares Ruas
Keyword(s):  
Deformation Parameter ◽  
Topological Type ◽  
Type A ◽  
Milnor Number ◽  
Hypersurface Singularities ◽  
Special Case ◽  
Parameter Deformation

AbstractWe show that the possible jump of the order in an 1-parameter deformation family of (possibly nonisolated) hypersurface singularities, with constant Lê numbers, is controlled by the powers of the deformation parameter. In particular, this applies to families of aligned singularities with constant topological type—a class for which the Lê numbers are “almost” constant. In the special case of families with isolated singularities—a case for which the constancy of the Lê numbers is equivalent to the constancy of the Milnor number—the result was proved by Greuel, Plénat, and Trotman.As an application, we prove equimultiplicity for new families of nonisolated hypersurface singularities with constant topological type, answering partially the Zariski multiplicity conjecture.

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