scholarly journals Connecting Homomorphism and Separating Cycles

2021 ◽  
Vol 14 (5) ◽  
pp. 647-658
Author(s):  
Roman V. Ulvert ◽  
Keyword(s):  
Complex Manifold ◽  
Finite Union ◽  
Sufficient Condition ◽  
Separation Condition ◽  
N Form

We discuss the construction of a long semi-exact Mayer–Vietoris sequence for the homology of any finite union of open subspaces. This sequence is used to obtain topological conditions of representation of the integral of a meromorphic n-form on an n-dimensional complex manifold in terms of Grothendieck residues. For such a representation of the integral to exist, it is necessary that the cycle of integration separates the set of polar hypersurfaces of the form. The separation condition in a number of cases turns out to be a sufficient condition for representing the integral as a sum of residues. Earlier, when describing such cases (in the works of Tsikh, Yuzhakov, Ulvert, etc.), the key was the condition that the manifold be Stein. The main result of this article is the relaxation of this condition

scholarly journals Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds

2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Lorenzo Sillari ◽  
Adriano Tomassini
Keyword(s):  
Complex Manifold ◽  
Sufficient Condition ◽  
Complex Manifolds ◽  
Necessary And Sufficient Condition ◽  
Dolbeault Cohomology ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Necessary And Sufficient

AbstractIn this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.

scholarly journals JUCYS–MURPHY ELEMENTS AND CENTRES OF CELLULAR ALGEBRAS

2011 ◽  
Vol 85 (2) ◽  
pp. 261-270 ◽  
Author(s):  
YANBO LI
Keyword(s):  
Integral Domain ◽  
Sufficient Condition ◽  
Separation Condition ◽  
Symmetric Polynomials ◽  
Necessary And Sufficient Condition ◽  
Cellular Algebra ◽  
Cellular Basis ◽  
Cellular Algebras ◽  
Necessary And Sufficient

AbstractLet R be an integral domain and A a cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ and S,T∈M(λ)}. Suppose that A is equipped with a family of Jucys–Murphy elements which satisfy the separation condition in the sense of Mathas [‘Seminormal forms and Gram determinants for cellular algebras’, J. reine angew. Math.619 (2008), 141–173, with an appendix by M. Soriano]. Let K be the field of fractions of R and AK=A⨂ RK. We give a necessary and sufficient condition under which the centre of AK consists of the symmetric polynomials in Jucys–Murphy elements. We also give an application of our result to Ariki–Koike algebras.

scholarly journals The union problem on complex manifolds

2002 ◽  
Vol 30 (10) ◽  
pp. 621-625
Author(s):  
Patrick W. Darko
Keyword(s):  
Complex Manifold ◽  
Sufficient Condition ◽  
Complex Manifolds ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

LetΩbe a relatively compact subdomain of a complex manifold, exhaustable by Stein open sets. We give a necessary and sufficient condition forΩto be Stein, in terms ofL2-estimates for the∂¯-operator, equivalent to the condition of Markoe (1977) and Silva (1978).

scholarly journals On the Equationally Artinian Groups

2020 ◽  
pp. 583-595
Author(s):  
Mohammad Shahryari ◽  
Javad Tayyebi
Keyword(s):  
Abelian Group ◽  
Normal Subgroup ◽  
Large Class ◽  
Finite Extension ◽  
Finite Union ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Sets ◽  
Necessary And Sufficient

In this article, we study the property of being equationally Artinian in groups. We define the radical topology corresponding to such groups and investigate the structure of irreducible closed sets of these topologies. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian group of the form G[t] by a normal subgroup which is a finite union of radicals, is again equationally Artnian. A necessary and sufficient condition for an Abelian group to be equationally Artinian will be given as the last result. This will provide a large class of examples of equationally Artinian groups

The Caratheodory Metric and its Majorant Metrics

1977 ◽  
Vol 29 (4) ◽  
pp. 771-780 ◽  
Author(s):  
Jacob Burbea
Keyword(s):  
Fixed Point ◽  
Complex Manifold ◽  
Carathéodory Metric ◽  
Complex Dimension ◽  
N Form

One of the main purposes of the present paper is to provide a proof for the following statement:Theorem A. Let M be a complex manifold of a complex dimension n. Let be a fixed point in M such that there exists a square integrable holomorphic n-form a(z) on M with .

DOUBLING PROPERTIES OF SELF-AFFINE MEASURES SUPPORTED ON GATZOURAS–LALLEY FRACTALS

Fractals ◽  
2019 ◽  
Vol 27 (08) ◽  
pp. 1950127
Author(s):  
CHUANYAN HOU ◽  
JUN JIE MIAO
Keyword(s):  
Sufficient Conditions ◽  
Horizontal Direction ◽  
Sufficient Condition ◽  
Separation Condition ◽  
Vertical Separation ◽  
Strong Separation

In this paper, we study the doubling properties of self-affine measures supported on a class of self-affine sets named Gatzouras–Lalley sets. First, we show that every self-affine measure is doubling if the Gatzouras–Lalley sets satisfy “strong separation” in both horizontal and vertical directions. Then we provide a sufficient condition for self-affine measures supported on Gatzouras–Lalley sets to be doubling if the sets do not satisfy the “separation condition” in the horizontal direction. Finally, we investigate measures without “vertical separation”, and give sufficient conditions for them to be doubling.

scholarly journals HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY FLAT NORMAL BUNDLE

2018 ◽  
Vol 238 ◽  
pp. 104-136
Author(s):  
TAKAYUKI KOIKE
Keyword(s):  
Line Bundle ◽  
Complex Manifold ◽  
Normal Bundle ◽  
Holomorphic Foliation ◽  
Compact Complex Manifold ◽  
Sufficient Condition ◽  
Existence Problem ◽  
Hermitian Metric ◽  
Flat Normal Bundle ◽  
Compact Submanifold

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher codimensional generalization of Ueda’s result, we give a sufficient condition for the existence of a nonsingular holomorphic foliation on a neighborhood of $Y$ which includes $Y$ as a leaf with unitary-linear holonomy. We apply this result to the existence problem of a smooth Hermitian metric with semipositive curvature on a nef line bundle.

scholarly journals Normal Families of Möbius Maps

2020 ◽  
Vol 20 (3-4) ◽  
pp. 523-538
Author(s):  
A. F. Beardon ◽  
D. Minda ◽  
I. Short
Keyword(s):  
Normal Family ◽  
Sufficient Conditions ◽  
Normal Families ◽  
Sufficient Condition ◽  
Separation Condition ◽  
Möbius Maps ◽  
Average Value ◽  
The Family ◽  
Extended Complex ◽  
Necessary And Sufficient

AbstractSeveral necessary and sufficient conditions for a family of Möbius maps to be a normal family in the extended complex plane $$\mathbb {C}_\infty $$ C ∞ are established. Each of these conditions involves collections of two or three points which may vary with the Möbius maps in the family, provided the points satisfy a uniform separation condition. In addition, we derive a sufficient condition for the normality of a family of Möbius maps in terms of the average value of the reciprocal of the chordal derivative.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

Größe im Schatten

2008 ◽  
Vol 27 (03) ◽  
pp. 188-191
Author(s):  
H. P. Schmitt
Keyword(s):  
N Form

ZusammenfassungIm Jahr 2007 jährte sich das Geburtsjahr des Nervenarztes Johann Hoffmann zum 150. Mal.Der am 28. März 1857 als Sohn des Landwirtes Paul Hoffmann in Hahnheim/Rheinhessen geborene Johann Hoffmann studierte Medizin in Heidelberg, Straßburg und Berlin. 1882 trat Hoffmann als Assistent von Friedreich in die Medizinische Klinik, Heidelberg, ein und wurde dort 1883 von dem Nachfolger des früh verstorbenen Friedreich, Wilhelm Erb, übernommen.1888 habilitierte sich Hoffmann, wurde 1891 zum außerordentlichen Professor ernannt, sowie 1910 zum ordentlichen Honorar-Professor, 1914 zum etatmäßigen außerordentlichen Professor und stellvertretenden Leiter der Medizinischen Klinik und schließlich 1919, kurz vor seinem Tode, zum ordentlichen Professor für Nervenpathologie mit der Leitung einer Abteilung für Nervenkrankheiten bestellt. Wissenschaftlich wandte sich Hoffmann hauptsächlich dem Gebiete der progressiven Muskelatrophien zu und beschrieb in drei Publikationen die myelogene(n), infantile(n) Form(en) der hereditären, spinalen Muskelatrophie. Damit hatte er, zusammen mit dem Grazer Neurologen Werdnig, die ,,Werdnig-Hoffmannsche Krankheit“ aus der Taufe gehoben. Weiter wurde Hoffmann durch den Knipsreflex (Hoffmann‘sches Zeichen) bekannt und definierte die Merkmale des ,,Hoffmann-Syndroms“ (hypothyreote Myotonie) in einer Arbeit von 1896. Darüber hinaus demonstrierte Hoffmann in einem Gesamtwerk von etwa 57 Originalarbeiten und Autorenreferaten in medizinischen Fachzeitschriften seine umfassenden Kenntnisse als Nervenarzt. Auch hielt er in Vertretung von Ludolf Krehl, Leiter der Medizinischen Klinik, Vorlesungen auf dem gesamten Gebiet der Inneren Medizin.Die vorliegende Würdigung anlässlich seines 150. Geburtsjahres soll dem Zweck dienen, das Andenken des großen Nervenarztes und Hochschullehrers Johann Hoffmann zu bewahren.

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