A theorem on algebraic correspondences

1936 ◽  
Vol 32 (3) ◽  
pp. 337-341
Author(s):  
W. V. D. Hodge
Keyword(s):  
Algebraic Curves ◽  
Present Note ◽  
Exact Formulation ◽  
Finite Integrals

In his chapter on correspondences between algebraic curves Prof. Baker has raised a problem concerning the possibility, when we are given the equations of Hurwitz for a correspondence between two algebraic curves, of obtaining therefrom a reduction of the everywhere finite integrals on either curve into complementary regular defective systems of integrals. The problem is stated as an unproved theorem, an exact formulation of which is given below. The object of the present note is to give a proof of this theorem on the lines of Prof. Baker's chapter.

Subrings of the first neighbourhood ring: II

1982 ◽  
Vol 92 (1) ◽  
pp. 35-39
Author(s):  
D. Kirby
Keyword(s):  
Commutative Ring ◽  
Local Ring ◽  
Algebraic Curves ◽  
Present Note ◽  
Quotient Ring ◽  
Singular Points ◽  
Local Rings ◽  
Embedding Dimension ◽  
One Dimensional ◽  
Finite Lattices

In (1) and (2) we studied a lattice of extension rings associated with a commutative ring R with identity. When R, M is a one-dimensional Cohen-Macaulay local ring the elements of are just those integral extensions of R contained in the total quotient ring T(R) and such that lengthR(S/R) is finite. Experiments with local rings of singular points on algebraic curves indicate that only the simplest singularities give rise to finite lattices. So the problem arises as to which local rings R give rise to which finite lattices. In later papers this problem will be investigated in detail, at least when R is of low embedding dimension. The purpose of the present note is to establish some general results which indicate the size of the problem.

Algebraic Curves over Finite Fields

1991 ◽  
Author(s):  
Carlos Moreno
Keyword(s):  
Finite Fields ◽  
Algebraic Curves ◽  
Curves Over Finite Fields

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Invariant Algebraic Curves and Hyperelliptic Limit Cycles of Liénard Systems

2021 ◽  
Vol 20 (2) ◽  
Author(s):  
Xinjie Qian ◽  
Yang Shen ◽  
Jiazhong Yang
Keyword(s):  
Limit Cycles ◽  
Algebraic Curves ◽  
Liénard Systems ◽  
Invariant Algebraic Curves

Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure

2021 ◽  
pp. 001316442110086
Author(s):  
Tenko Raykov ◽  
Natalja Menold ◽  
Jane Leer
Keyword(s):  
Latent Variable ◽  
Large Scale ◽  
Present Note ◽  
Interval Estimation ◽  
Psychological Research ◽  
Latent Variable Modeling ◽  
Model Choice ◽  
Modeling Methodology ◽  
Level 3 ◽  
Level 2

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

scholarly journals Real plane algebraic curves with prescribed singularities

Topology ◽  
1993 ◽  
Vol 32 (4) ◽  
pp. 845-856 ◽  
Author(s):  
Eugenii Shustin
Keyword(s):  
Algebraic Curves ◽  
Real Plane

scholarly journals A Note on Units of Algebraic Number Fields

1955 ◽  
Vol 9 ◽  
pp. 115-118 ◽  
Author(s):  
Tomio Kubota
Keyword(s):  
Existence Theorem ◽  
Algebraic Number ◽  
Present Note ◽  
Number Fields ◽  
Algebraic Number Fields

We shall prove in the present note a theorem on units of algebraic number fields, applying one of the strongest formulations, be Hasse [3], of Grunwald’s existence theorem.

Archilochus and Lycambes

1986 ◽  
Vol 36 (1) ◽  
pp. 60-67 ◽  
Author(s):  
C. Carey
Keyword(s):  
Present Note ◽  
Old Comedy ◽  
English Speaking ◽  
The Voice

A persistent ancient tradition has it that a man named Lycambes promised his daughter Neoboule in marriage to the poet Archilochus of Paros, that he subsequently refused Archilochus, and that the poet attacked Lycambes and his daughters with such ferocity that they all committed suicide. When we reflect that the iambographer Hipponax drove his enemies Bupalus and Athenis and Old Comedy a man named Poliager to suicide, that the ancestress of iambos, Iambe, killed herself, and that all these suicides, like those of Lycambes and his daughters, took the form of hanging, we will not take too seriously the ending of the story of Archilochus' relations with Lycambes and his family.However, it seems now to be generally accepted, at least among English-speaking scholars, that the whole Lycambes tradition is to be rejected. The present note seeks to demonstrate that this extreme scepticism is misguided. I shall begin with a survey of Archilochus' references to Lycambes and his family to ascertain how far the indirect tradition is consistent with the surviving fragments.Lycambes appears to have played a consistent role in Archilochus, as far as the fragments allow us to see. In fr. 38 he appears as the father of two daughters (οἴην Λυκάμβεω παῖδα τ⋯ν ύπερτέρην), in fr. 33 (where the voice of ‘the daughter of Lycambes’ is mentioned) as the father of at least one daughter. In fr. 71 his role cannot be determined. But in fr. 54, if his name is correctly restored in v. 8, he may again figure as the father of a daughter, for a female is mentioned in the fragment, whether for good or ill. If his patronymic is correctly supplied in fr. 57.7, it may be significant that the letters πατρ occur in the same verse.

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