scholarly journals Lagrangian submanifolds from tropical hypersurfaces

2021 ◽  
pp. 2150046
Author(s):  
Diego Matessi

We prove that a smooth tropical hypersurface in [Formula: see text] can be lifted to a smooth embedded Lagrangian submanifold in [Formula: see text]. The idea of the proof is to use Lagrangian pairs of pants, which are the lifts of tropical hyperplanes introduced by the author in an earlier paper, as the main building blocks.

2020 ◽  
pp. 104225871989941 ◽  
Author(s):  
Dean A. Shepherd ◽  
Marc Gruber

The lean startup framework is one of the most popular contributions in the practitioner-oriented entrepreneurship literature. This study seeks to generate new insights into how new ventures are started by describing the five main building blocks of the lean startup framework (business model, validated learning/customer development, minimum viable product, perseverance vs. pivoting, market-opportunity navigation), enriching the framework with existing research findings, and proposing promising research opportunities in a way that reduces the academic−practitioner divide. In so doing, we hope to enhance researchers’ understanding of the startup process; provide knowledge for educators; and, ultimately, improve the startup process for practitioners.


2019 ◽  
Vol 6 (1) ◽  
pp. 303-319
Author(s):  
Yoshihiro Ohnita

AbstractAn R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is one of invariants under Hamiltonian isotopies and very fundamental to study the Floer homology for intersections of Lagrangian submanifolds. In this paper we show a Lie theoretic formula for the minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces, and provide some examples of the calculation by the formula.


2006 ◽  
Vol 03 (05n06) ◽  
pp. 1273-1292
Author(s):  
PAOLO DE BARTOLOMEIS ◽  
ADRIANO TOMASSINI

We consider generalized Calabi–Yau manifolds and we give a formula for the Maslov class of a Lagrangian submanifold of a generalized Calabi–Yau manifold. In particular, we characterize the Lagrangian submanifolds with vanishing Maslov class. In the 6-dimensional case, we refine our definition. Finally, we construct some examples.


2004 ◽  
Vol 04 (03) ◽  
pp. 277-296 ◽  
Author(s):  
HANS CRAUEL ◽  
LUU HOANG DUC ◽  
STEFAN SIEGMUND

A generalization of the concepts of deterministic Morse theory to random dynamical systems is presented. Using the notions of attraction and repulsion in probability, the main building blocks of Morse theory such as attractor–repeller pairs, Morse sets, and the Morse decomposition are obtained for random dynamical systems.


Nanoscale ◽  
2016 ◽  
Vol 8 (33) ◽  
pp. 15101-15114 ◽  
Author(s):  
Theo G. M. van de Ven ◽  
Amir Sheikhi

Cellulose nanofibrils (left), the main building blocks of wood fibers, are chemically treated to fall apart from the amorphous regions and yield hairy nanocrystalline celluloses and modified cellulose biopolymers (right).


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Marika Arena ◽  
Giovanni Azzone ◽  
Giulia Piantoni

PurposeAlthough innovation ecosystems (IEs) are generally considered capable of creating shared value (SV), this potentiality has often been taken for granted and not deeply analysed, yet. As a result, in the literature, there is not a framework that defines the process of SV creation in IEs or which aspects should be considered for understanding it. Moving from these considerations, this paper aims to propose a conceptual model of how IEs can create SV, identifying the main building blocks of the process and the aspects that characterize these building blocks.Design/methodology/approachThe authors reviewed the literature on IEs and value creation over the last 15 years, by structurally analysing 120 articles. On the basis of such review, the authors identified main dimensions of analysis focusing on the conceptualization of SV in IEs.FindingsFirst, the authors developed a conceptual model relying on a process-based logic and framing the SV creation in terms of inputs, here intended as four key characteristics (actors, structure, governance and relations), internal processes (strategies and internal mechanisms) and outputs (the value created). Second, each element of value creation is explored, highlighting the main evidence emerging from prior studies in connection to each block.Originality/valueThis paper drives the identification of some relevant relationships that connect the characteristics of the IEs, the strategies and the internal mechanisms to the output of the process, i.e. the SV created.


2013 ◽  
Vol 8 (0) ◽  
pp. 3404052-3404052 ◽  
Author(s):  
Irina V. ALEKSANDROVA ◽  
Elena R. KORESHEVA ◽  
Eugeniy L. KOSHELEV ◽  
Igor E. OSIPOV

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