scholarly journals Variation formulas for principal functions, II: Applications to variation for harmonic spans

2011 ◽  
Vol 204 ◽  
pp. 19-56 ◽  
Author(s):  
Sachiko Hamano ◽  
Fumio Maitani ◽  
Hiroshi Yamaguchi
Keyword(s):  
Direct Application ◽  
Total Space ◽  
Geometric Meaning ◽  
Principal Function ◽  
Variation Formula ◽  
Circular Slit ◽  
Moving Domain

AbstractA domainD⊂ Czadmits the circular slit mappingP(z) fora, b∈Dsuch thatP(z) – 1/(z–a) is regular ataandP(b) = 0. We callp(z) =log|P(z)|theLi-principal functionandα= log |P′(b)| theL1-constant, and similarly, the radial slit mappingQ(z) implies theL0-principal functionq(z) and theL0-constantβ. We calls=α–βtheharmonic spanfor (D, a, b). We show the geometric meaning ofs. Hamano showed the variation formula for theL1-constantα(t) for the moving domainD(t) in Czwitht∈B:= {t∈ C: |t| <ρ}. We show the corresponding formula for theL0-constantβ(t) forD(t) and combine these to prove that, if the total spaceD =∪t∈B(t, D(t)) is pseudoconvex inB× Cz, thens(t) is subharmonic onB. As a direct application, we have the subharmonicity of log coshd(t) onB, whered(t) is the Poincaré distance betweenaandbonD(t).

scholarly journals Variation formulas for principal functions, II: Applications to variation for harmonic spans

2011 ◽  
Vol 204 ◽  
pp. 19-56
Author(s):  
Sachiko Hamano ◽  
Fumio Maitani ◽  
Hiroshi Yamaguchi
Keyword(s):  
Direct Application ◽  
Total Space ◽  
Geometric Meaning ◽  
Principal Function ◽  
Variation Formula ◽  
Circular Slit ◽  
Moving Domain

AbstractA domain D ⊂ Cz admits the circular slit mapping P(z) for a, b ∈ D such that P(z) – 1/(z – a) is regular at a and P(b) = 0. We call p(z) = log|P(z)| the Li-principal function and α = log |P′(b)| the L1-constant, and similarly, the radial slit mapping Q(z) implies the L0-principal function q(z) and the L0-constant β. We call s = α – β the harmonic span for (D, a, b). We show the geometric meaning of s. Hamano showed the variation formula for the L1-constant α(t) for the moving domain D(t) in Cz with t ∈ B:= {t ∈ C: |t| < ρ}. We show the corresponding formula for the L0-constant β (t) for D(t) and combine these to prove that, if the total space D = ∪t∈B(t, D (t)) is pseudoconvex in B × Cz, then s(t) is subharmonic on B. As a direct application, we have the subharmonicity of log cosh d(t) on B, where d(t) is the Poincaré distance between a and b on D(t).

scholarly journals Willmore-Like Tori in Killing Submersions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Manuel Barros ◽  
Óscar J. Garay ◽  
Álvaro Pámpano
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Total Space ◽  
Lagrange Equations ◽  
Base Surface ◽  
Variation Formula ◽  
First Variation ◽  
Invariant Potential ◽  
The First Variation

The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.

Contributions to the mechanisms of mitosis and roles of cytoplasmic microtubules from ultrastructural analyses of fungi

1978 ◽  
Vol 36 (2) ◽  
pp. 266-267
Author(s):  
I. Brent Heath
Keyword(s):  
Nuclear Envelope ◽  
Direct Application ◽  
Ultrastructural Analysis ◽  
General Interest ◽  
Research Results ◽  
Organelle Motility ◽  
Cytoplasmic Microtubules

Detailed ultrastructural analysis of fungal mitotic systems and cytoplasmic microtubules might be expected to contribute to a number of areas of general interest in addition to the direct application to the organisms of study. These areas include possibly fundamental general mechanisms of mitosis; evolution of mitosis; phylogeny of organisms; mechanisms of organelle motility and positioning; characterization of cellular aspects of microtubule properties and polymerization control features. This communication is intended to outline our current research results relating to selected parts of the above questions.Mitosis in the oomycetes Saprolegnia and Thraustotheca has been described previously. These papers described simple kinetochores and showed that the kineto- chores could probably be used as markers for the poorly defined chromosomes. Kineto- chore counts from serially sectioned prophase mitotic nuclei show that kinetochore replication precedes centriole replication to yield a single hemispherical array containing approximately the 4 n number of kinetochore microtubules diverging from the centriole associated "pocket" region of the nuclear envelope (Fig. 1).

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

Digital polarograph-impedancemeters for frequency range of 10-3-10-5 Hz

1983 ◽  
Vol 48 (4) ◽  
pp. 1123-1128
Author(s):  
S. P. Novitskii ◽  
I. I. Burenkov ◽  
V. I. Kenzin ◽  
R. Yu. Beck
Keyword(s):  
Kinetics And Mechanism ◽  
Frequency Range ◽  
Principal Function ◽  
Technical Parameters ◽  
Electrode Processes ◽  
Analytical Applications

Design, principal function and technical parameters of two polarograph-impendancemeters are given. The instruments are suitable both for analytical applications and for investigation of the kinetics and mechanism of electrode processes.

The Developmental Trading State

2017 ◽  
Author(s):  
Alex J. Bellamy
Keyword(s):  
Economic Growth ◽  
East Asia ◽  
National Economy ◽  
East Asian ◽  
The State ◽  
State Model ◽  
Principal Function ◽  
Mass Violence ◽  
The Way

This chapter demonstrates that the downwards pressure that state consolidation placed on mass violence was amplified by the type of state that emerged. Across East Asia, governments came to define themselves as “developmental” or “trading” states whose principal purpose was to grow the national economy and thereby improve the economic wellbeing of their citizens. Governments with different ideologies came to embrace economic growth and growing the prosperity of their populations as the principal function of the state and its core source of legitimacy. Despite some significant glitches along the way the adoption of the developmental trading state model has proven successful. Not only have East Asian governments succeeded in lifting hundreds of millions of people out of poverty, the practices and policy orientations dictated by this model helped shift governments and societies away from belligerent practices towards postures that prioritized peace and stability. This reinforced the trend towards greater peacefulness.

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

Non-collinear magnetism & multiferroicity: the perovskite case

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Eric Bousquet ◽  
Andrés Cano
Keyword(s):  
Reference Materials ◽  
Perovskite Oxides ◽  
Direct Application ◽  
Spin Hamiltonian ◽  
Multiferroic Properties ◽  
Magnetic Orders

AbstractThe most important types of non-collinear magnetic orders that are realized in simple perovskite oxides are outlined in relation to multiferroicity. These orders are classified and rationalized in terms of a mimimal spin Hamiltonian, based on which the notion of spin-driven ferroelectricity is illustrated. These concepts find direct application in reference materials such as BiFeO3, GdFeO3and TbMnO3whose multiferroic properties are briefly reviewed.

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