scholarly journals Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristic

2020 ◽  
Author(s):  
Michelle Bucher ◽  
Caterina Campagnolo
Keyword(s):  
Euler Characteristic ◽  
Simplicial Volume ◽  
The Third ◽  
Surface Bundles ◽  
Surface Bundle ◽  
Ramified Coverings ◽  
New Inequalities

AbstractWe present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely the ones that arise through ramified coverings. These are among the main known examples of bundles with non-zero signature.

scholarly journals Moment inequalities of the Liapunov type

1981 ◽  
Vol 31 (2) ◽  
pp. 236-251
Author(s):  
H. L. MacGillivray
Keyword(s):  
Particle Size ◽  
Random Variable ◽  
Moment Inequality ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Central Moments ◽  
Log Transformation ◽  
The Third ◽  
Family Of Distributions ◽  
New Inequalities

AbstractCharacterisations of the distribution of a non-negative random variable are sought for which the Liapunov moment inequality is extended to give inequalities between inverse powers of moment ratios, which are known as mean sizes in considerations of particle size distributions. A solution is found for continuous distributions, and the conditions applied to a number of well-known distributions. A further class of distributions is considered for which the new inequalities hold but the inequality direction is reversed for some orders of the moments. The study involves examination of the signs of the third central moments of a family of distributions, obtained by a log transformation, from the weighted, or moment, distributions induced by the non-negative random variable.

ON FRAMED LINK PRESENTATIONS OF SURFACE BUNDLES

1998 ◽  
Vol 07 (08) ◽  
pp. 1087-1092
Author(s):  
KAZUHIRO ICHIHARA
Keyword(s):  
Orientable Surface ◽  
Closed Orientable Surface ◽  
Surface Bundles ◽  
Fibered Link ◽  
Surface Bundle ◽  
Framed Link

In this paper, we show that every closed orientable surface bundle over the circle is represented by a fibered link in the 3-sphere with framings induced by the fibration of the complement.

scholarly journals BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS

2021 ◽  
pp. 1-15
Author(s):  
Stefan Friedl ◽  
Stefano Vidussi
Keyword(s):  
Fundamental Group ◽  
Broad Class ◽  
Interesting Case ◽  
Finitely Generated ◽  
Group Extensions ◽  
Finitely Generated Group ◽  
Surface Bundles ◽  
Surface Bundle

Abstract Let G be a finitely generated group that can be written as an extension $$ \begin{align*} 1 \longrightarrow K \stackrel{i}{\longrightarrow} G \stackrel{f}{\longrightarrow} \Gamma \longrightarrow 1 \end{align*} $$ where K is a finitely generated group. By a study of the Bieri–Neumann–Strebel (BNS) invariants we prove that if $b_1(G)> b_1(\Gamma ) > 0$ , then G algebraically fibres; that is, admits an epimorphism to $\Bbb {Z}$ with finitely generated kernel. An interesting case of this occurrence is when G is the fundamental group of a surface bundle over a surface $F \hookrightarrow X \rightarrow B$ with Albanese dimension $a(X) = 2$ . As an application, we show that if X has virtual Albanese dimension $va(X) = 2$ and base and fibre have genus greater that $1$ , G is noncoherent. This answers for a broad class of bundles a question of J. Hillman ([9, Question 11(4)]). Finally, we show that there exist surface bundles over a surface whose BNS invariants have a structure that differs from that of Kodaira fibrations, determined by T. Delzant.

scholarly journals Characteristic-dependent linear rank inequalities in 21 variables

2019 ◽  
Vol 43 (169) ◽  
pp. 764-770
Author(s):  
Victor Peña-Macias ◽  
Humberto Sarria - Zapata
Keyword(s):  
Finite Field ◽  
Linear Inequality ◽  
Binary Matrix ◽  
The Third ◽  
Linear Rank ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Characteristic 2 ◽  
Characteristic 3 ◽  
New Inequalities

In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of spans of vector subspaces of a finite dimensional vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. This paper shows a preliminary result in the production of these inequalities. We produce three new inequalities in 21 variables using as guide a particular binary matrix, with entries in a finite field, whose rank is 8, with characteristic 2; 9 with characteristic 3; or 10 with characteristic neither 2 nor 3. The first inequality is true over fields whose characteristic is 2; the second inequality is true over fields whose characteristic is 2 or 3; the third inequality is true over fields whose characteristic is neither 2 nor 3.

scholarly journals IX.—On the Deflection of the Plummet due to Solar and Lunar Attraction.

1862 ◽  
Vol 23 (1) ◽  
pp. 89-93
Author(s):  
Edward Sang
Keyword(s):  
Plumb Line ◽  
The Third ◽  
Decimal Fraction ◽  
New Inequalities

As the means for making observations on the heavenly bodies become more and more exact, astronomers are compelled to introduce new refinements into their calculations; new inequalities are discovered, and the computation of those whose sources are already known has to be carried to a greater number of approximative steps.Discussions on the amount of solar parallax, of aberration and of nutation, are now carried on to the third and fourth decimal fraction of a second; with such a refinement of computation, it seems almost impossible to proceed too far in the refinement of theoretical deductions, and on that account, it may not be inopportune to discuss the influence which the sun's and moon's attraction exert upon the direction of the plumb-line.

A REDUCIBILITY PROBLEM FOR MONODROMY OF SOME SURFACE BUNDLES

2004 ◽  
Vol 13 (05) ◽  
pp. 597-616
Author(s):  
YOICHI IMAYOSHI ◽  
MANABU ITO ◽  
HIROSHI YAMAMOTO
Keyword(s):  
Interesting Case ◽  
Base Space ◽  
Closed Path ◽  
Monodromy Representation ◽  
Surface Bundles ◽  
Reducibility Problem ◽  
Surface Bundle

A surface bundle determines a monodromy representation recording the twisting of the fiber under transport around a closed path in the base space. The fascinating relation between these monodromy representations and the Thurston classification of surface automorphisms will be studied. In this note we deal with a simple and interesting case: the fibrations of Fadell and Neuwirth.

Progress report on 21-cm observations at low latitude between longitudes (l 11) 0° and 66°

1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane
Keyword(s):  
Preliminary Report ◽  
Progress Report ◽  
Galactic Centre ◽  
Low Latitude ◽  
The Third ◽  
Introductory Lecture ◽  
Centre Region

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

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