THE MINIMAL GENUS PROBLEM IN RULED MANIFOLDS

2008 ◽  
Vol 17 (04) ◽  
pp. 471-482
Author(s):  
XU-AN ZHAO ◽  
HONGZHU GAO
Keyword(s):  
Cohomology Class ◽  
Standard Form ◽  
Geometric Construction ◽  
Diffeomorphism Group ◽  
Minimal Genus ◽  
Adjunction Formula ◽  
Embedded Surfaces

In this paper, we consider the minimal genus problem in a ruled 4-manifold M. There are three key ingredients in the studying, the action of diffeomorphism group of M on H2(M,Z), the geometric construction of surfaces representing a cohomology class and the generalized adjunction formula. At first, we discuss the standard form (see Definition 1.1) of a class under the action of diffeomorphism group on H2(M,Z), we prove the uniqueness of the standard form. Then we construct some embedded surfaces representing the standard forms of some positive classes, the generalized adjunction formula is used to show that these surfaces realize the minimal genera.

scholarly journals Embedded surfaces in four-manifolds, branched covers, and SO(3)-invariants

1995 ◽  
Vol 117 (2) ◽  
pp. 275-286 ◽  
Author(s):  
D. Kotschick ◽  
G. Matić
Keyword(s):  
Algebraic Curves ◽  
Homology Class ◽  
Algebraic Surfaces ◽  
Branched Covers ◽  
Minimal Genus ◽  
Adjunction Formula ◽  
Embedded Surfaces ◽  
Four Manifolds ◽  
Image Position ◽  
Simply Connected

One of the outstanding problems in four-dimensional topology is to find the minimal genus of an oriented smoothly embedded surface representing a given homology class in a smooth four-manifold. For an arbitrary homology class in an arbitrary smooth manifold not even a conjectural lower bound is known. However, for the classes represented by smooth algebraic curves in (simply connected) algebraic surfaces, it is possible that the genus of the algebraic curve, given by the adjunction formulais the minimal genus. This is usually called the (generalized) Thom conjecture. It is mentioned in Kirby's problem list [11] as Problem 4·36.

Torsion Elements and the Classification of Vector Bundles

1977 ◽  
Vol 29 (2) ◽  
pp. 327-332
Author(s):  
Robert D. Little
Keyword(s):  
Algebraic Topology ◽  
Cohomology Class ◽  
Cohomology Group ◽  
Vector Bundles ◽  
Geometric Construction ◽  
Integral Cohomology

There are many situations in algebraic topology when a geometric construction is possible if, and only if, a certain integral cohomology class, an obstruction is zero. When attempts are made to compute the obstruction, it often happens that it is relatively easy to show that m times the obstruction is zero, where m is an integer, and consequently the geometric construction is possible if the cohomology group in question has no elements of order m.

Production of New and Revised A.A.V.S.O. Charts

1979 ◽  
Vol 46 ◽  
pp. 368
Author(s):  
Clinton B. Ford
Keyword(s):  
Variable Star ◽  
Standard Form ◽  
Original Data ◽  
University Of Pennsylvania ◽  
Standard Format ◽  
Additional Information ◽  
The Gift ◽  
The University

A “new charts program” for the Americal Association of Variable Star Observers was instigated in 1966 via the gift to the Association of the complete variable star observing records, charts, photographs, etc. of the late Prof. Charles P. Olivier of the University of Pennsylvania (USA). Adequate material covering about 60 variables, not previously charted by the AAVSO, was included in this original data, and was suitably charted in reproducible standard format.Since 1966, much additional information has been assembled from other sources, three Catalogs have been issued which list the new or revised charts produced, and which specify how copies of same may be obtained. The latest such Catalog is dated June 1978, and lists 670 different charts covering a total of 611 variables none of which was charted in reproducible standard form previous to 1966.

Stuttering mHealth Applications: A Qualitative Rubric Assessment (Preprint)

2020 ◽  
Author(s):  
Fazwa M. Fadzilah ◽  
Noreen Izza Arshad ◽  
Izuddin Zainal-Abidin ◽  
Hui Min Low ◽  
Ahmad Kamil Mahmood ◽  
...  
Keyword(s):  
Research Evidence ◽  
Mobile Apps ◽  
Group Discussion ◽  
Standard Form ◽  
Mobile App ◽  
Evidence Based ◽  
Evaluation Instrument ◽  
Collective Effort ◽  
Speech Therapists

BACKGROUND Mobile applications (apps) that offer a variety of techniques to improve stuttering have been flourishing in the digital marketplace. In evidence-based clinical practice, speech therapists will recommend audio-enriched mobile apps to individuals with stuttering problems based on empirical research evidence. Unfortunately, many stuttering mobile apps available in the market are developed without a substantial research base. Hence, speech therapists necessitate a guideline which they could use to assess the quality of a stuttering mobile app before recommending the app to stutterers. OBJECTIVE The objective of this study is to develop a rubric for assessing the quality of the stuttering mobile app in assisting speech therapists to make informed recommendations METHODS The rubric was initially developed based on a set of criteria reviewed from the literature. Online surveys and focused group discussion were then conducted for results verification. RESULTS The outcome of this study is a rubric designed with four categories and 18-evaluative dimensions tailored to analyze the quality of stuttering mobile apps. The stuttering mobile app assessment rubric presented in the serve multiple purposes, including an evaluation instrument, providing guidelines for developing stuttering mobile apps and for creating a standard form that can be shared with professionals to facilitate a collective effort. CONCLUSIONS This rubric also offers a guidance to steer drive the future development of stuttering mobile apps that are evidence-based, and theoretically grounded

Protest from the Top Down

2018 ◽  
Author(s):  
Mason W. Moseley
Keyword(s):  
Standard Form ◽  
State Theory ◽  
Political Elites ◽  
Political Organizations ◽  
Top Down ◽  
Political Expression ◽  
National Surveys ◽  
Political Voice ◽  
The Masses

This chapter tests another observable implication of the protest state theory; namely that where protest has normalized as an everyday form of political voice, political elites actively mobilize demonstrators in pursuit of their goals. In other words, rather than serving only as a spontaneous political expression of the masses, protest is often orchestrated and managed by formal political organizations. I first investigate how linkages to political organizations fuel contentious behavior in protest states like Argentina and Bolivia, but are more strongly associated with conventional participation in strongly institutionalized contexts like Chile and Uruguay. Then, utilizing a unique battery of questions from the AmericasBarometer national surveys of Argentina and Bolivia, I also test the hypothesis that clientelism can motivate protest participation in a context where protest has normalized as a standard form of political voice.

The Centralizer

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Group ◽  
Group Structure ◽  
Diffeomorphism Group ◽  
Group Diff ◽  
Local Solutions

The pseudogroup of local solutions in Chapter 3 defines another pseudogroup by taking its centralizer inside the diffeomorphism group Diff(M) of a manifold M. These two pseudogroups define a Lie group structure on M.

scholarly journals Molecular mechanisms of Zika virus teratogenesis from animal studies: a systematic review protocol

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Gabriela Elis Wachholz ◽  
Julia do Amaral Gomes ◽  
Juliano André Boquett ◽  
Fernanda Sales Luiz Vianna ◽  
Lavínia Schuler-Faccini ◽  
...  
Keyword(s):  
Systematic Review ◽  
Animal Models ◽  
Zika Virus ◽  
Methodological Quality ◽  
Molecular Mechanisms ◽  
Grey Literature ◽  
Standard Form ◽  
Teratogenic Effect ◽  
Control Group

Abstract Background Due to the diversity of studies in animal models reporting that molecular mechanisms are involved in the teratogenic effect of the Zika virus (ZIKV), the objective of the present study is to evaluate the methodological quality of these studies, as well as to demonstrate which genes and which molecular pathways are affected by ZIKV in different animal models. Methods This search will be performed in four databases: PubMed/MEDLINE, EMBASE, Web of Science, and Scopus, as well as in the grey literature. The studies selection process will be reported through the PRISMA Statement diagram model. All studies describing the molecular mechanisms possibly involved in the development of malformations caused by embryonic/fetal ZIKV exposure in animal models with an appropriate control group and methodology will be included (including, for instance, randomized and non-randomized studies). All animals used as experimental models for ZIKV teratogenesis may be included as long as exposure to the virus occurred during the embryonic/fetal period. From the selected studies, data will be extracted using a previously prepared standard form. Bias risk evaluation will be conducted following the SYRCLE’s Risk of Bias tool. All data obtained will be tabulated and organized by outcomes (morphological and molecular). Discussion With the proposed systematic review, we expect to present results about the methodological quality of the published studies with animal models that investigated the molecular mechanisms involved in the teratogenic effect of ZIKV, as well as to show the studies with greater reliability. Systematic review registration PROSPERO CRD42019157316

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