scholarly journals Volume Growth, Curvature, and Buser-Type Inequalities in Graphs

2019 ◽  
Author(s):  
Brian Benson ◽  
Peter Ralli ◽  
Prasad Tetali
Keyword(s):  
Lower Bound ◽  
Riemannian Manifolds ◽  
Volume Growth ◽  
Discrete Curvature ◽  
Eigenvalues Of The Laplacian ◽  
Discrete Spaces ◽  
The Relationship ◽  
Metric Balls ◽  
Continuous Setting ◽  
Discrete Hardy Inequality

Abstract We study the volume growth of metric balls as a function of the radius in discrete spaces and focus on the relationship between volume growth and discrete curvature. We improve volume growth bounds under a lower bound on the so-called Ollivier curvature and discuss similar results under other types of discrete Ricci curvature. Following recent work in the continuous setting of Riemannian manifolds (by the 1st author), we then bound the eigenvalues of the Laplacian of a graph under bounds on the volume growth. In particular, $\lambda _2$ of the graph can be bounded using a weighted discrete Hardy inequality and the higher eigenvalues of the graph can be bounded by the eigenvalues of a tridiagonal matrix times a multiplicative factor, both of which only depend on the volume growth of the graph. As a direct application, we relate the eigenvalues to the Cheeger isoperimetric constant. Using these methods, we describe classes of graphs for which the Cheeger inequality is tight on the 2nd eigenvalue (i.e. the 1st nonzero eigenvalue). We also describe a method for proving Buser’s Inequality in graphs, particularly under a lower bound assumption on curvature.

Relationship between Cross-Border Mergers and Acquisitions and International Trade: The Case of Russian Pharmaceutical Industry

2020 ◽  
pp. 81-94
Author(s):  
Alexandra V. Chugunova ◽  
Olga A. Klochko
Keyword(s):  
International Trade ◽  
Mergers And Acquisitions ◽  
Volume Growth ◽  
Pharmaceutical Products ◽  
Pharmaceutical Companies ◽  
Cross Border ◽  
Export Volume ◽  
Relationship Of ◽  
Geographical Diversification ◽  
The Relationship

This research studies the relationship of cross-border mergers and acquisitions to international trade through the lens of Russian pharmaceutical market. To this aim, the study analyses the woks of foreign economists dedicated to evaluating the link between foreign direct investment and international trade, and the influence of mergers and acquisitions on countries’ export and import flows. The research also presents a correlation analysis between the volume of Russian pharmaceutical exports and imports and cross-border deals performed by foreign pharmaceutical companies in Russia. We characterize these deals and conduct a comparative analysis of the regional structure of Russian pharmaceutical exports and imports as well as of the countries of origin of buyers in cross-border mergers and acquisitions. The results of the analysis indicate a positive relationship between cross-border mergers and acquisitions and Russian pharmaceutical exports, which is reflected in the export volume growth and its geographical diversification. However, it is outlined that particular problems of the industry hinder the amelioration of Russian positions in international exports. Similarly, the relationship between cross-border deals and Russian imports is positive: the major pharmaceutical products supply flow occurs from the countries of origin of buyers in cross-border mergers and acquisitions conducted in the Russian pharmaceutical sector.

scholarly journals A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds

1998 ◽  
Vol 151 ◽  
pp. 25-36 ◽  
Author(s):  
Kensho Takegoshi
Keyword(s):  
Riemannian Manifold ◽  
Maximum Principle ◽  
Growth Condition ◽  
Riemannian Manifolds ◽  
Volume Growth ◽  
Complete Riemannian Manifold ◽  
Volume Estimate ◽  
Complete Riemannian Manifolds ◽  
Generalized Maximum Principle

Abstract.A generalized maximum principle on a complete Riemannian manifold (M, g) is shown under a certain volume growth condition of (M, g) and its geometric applications are given.

scholarly journals On low-dimensional Ricci limit spaces

2013 ◽  
Vol 209 ◽  
pp. 1-22 ◽  
Author(s):  
Shouhei Honda
Keyword(s):  
Lower Bound ◽  
Hausdorff Dimension ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Limit Space ◽  
Low Dimensional ◽  
Complete Riemannian Manifolds

AbstractWe call a Gromov–Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. Furthermore, we prove that any Ricci limit space has integral Hausdorff dimension, provided that its Hausdorff dimension is not greater than 2. We also classify 1-dimensional Ricci limit spaces.

scholarly journals A note on bounded variation and heat semigroup on Riemannian manifolds

2007 ◽  
Vol 76 (1) ◽  
pp. 155-160 ◽  
Author(s):  
A. Carbonaro ◽  
G. Mauceri
Keyword(s):  
Lower Bound ◽  
Euclidean Space ◽  
Heat Kernel ◽  
Ricci Curvature ◽  
Bounded Variation ◽  
Riemannian Manifolds ◽  
Heat Semigroup ◽  
Functions Of Bounded Variation ◽  
Fixed Radius ◽  
Lower Bound Estimate

In a recent paper Miranda Jr., Pallara, Paronetto and Preunkert have shown that the classical De Giorgi's heat kernel characterisation of functions of bounded variation on Euclidean space extends to Riemannian manifolds with Ricci curvature bounded from below and which satisfy a uniform lower bound estimate on the volume of geodesic balls of fixed radius. We give a shorter proof of the same result assuming only the lower bound on the Ricci curvature.

scholarly journals Slow volume growth for Reeb flows on spherizations and contact Bott–Samelson theorems

2015 ◽  
Vol 07 (03) ◽  
pp. 407-451 ◽  
Author(s):  
Urs Frauenfelder ◽  
Clémence Labrousse ◽  
Felix Schlenk
Keyword(s):  
Lower Bound ◽  
Polynomial Growth ◽  
Polynomial Complexity ◽  
Cohomology Ring ◽  
Volume Growth ◽  
Universal Cover ◽  
Geodesic Flows ◽  
Dynamical Complexity ◽  
Reeb Flows ◽  
Rank One

We give a uniform lower bound for the polynomial complexity of Reeb flows on the spherization (S*M, ξ) over a closed manifold. Our measure for the dynamical complexity of Reeb flows is slow volume growth, a polynomial version of topological entropy, and our lower bound is in terms of the polynomial growth of the homology of the based loop space of M. As an application, we extend the Bott–Samelson theorem from geodesic flows to Reeb flows: If (S*M, ξ) admits a periodic Reeb flow, or, more generally, if there exists a positive Legendrian loop of a fiber [Formula: see text], then M is a circle or the fundamental group of M is finite and the integral cohomology ring of the universal cover of M agrees with that of a compact rank one symmetric space.

Resistance, tolerance, and yield of western black cottonwood infected by Melampsora rust

1992 ◽  
Vol 22 (2) ◽  
pp. 183-192 ◽  
Author(s):  
J. Wang ◽  
B.J. van der Kamp
Keyword(s):  
Disease Severity ◽  
Volume Growth ◽  
Severe Infection ◽  
Dry Weight ◽  
Stem Volume ◽  
Yield Losses ◽  
Black Cottonwood ◽  
Total Dry Weight ◽  
Significant Discovery ◽  
The Relationship

Potted ramets of 14 western black cottonwood (Populustrichocarpa Torr. & Gray) clones from southern British Columbia were inoculated with Melampsoraoccidentalis H. Jacks to produce a range of disease severities, and their size and dry weight were determined after 1 or 2 years. Response to inoculation varied significantly between clones. Clones from drier interior locations were less resistant than those from coastal or moister interior locations. Local- (within leaf) or systemic-induced resistance was not detected. Yield (total dry weight) decreased linearly with disease severity. Percent reduction in yield was greater than the cumulative percent leaf area infected for all clones. Yield losses were substantial: dry weights of ramets with disease severity levels similar to those experienced by natural cottonwood populations were about 75% of controls; heavily infected ramets were <50% of controls. Stem:root ratios increased rapidly with increasing disease severity in all clones, and at significantly different rates. Severe infection resulted in substantial mortality in the following winter and reduced initial stem volume growth in the following growing season. Tolerance, defined as the relationship between disease severity and yield, varied significantly between clones. The most significant discovery of this study was that tolerance and resistance were correlated, greater tolerance being associated with reduced resistance. The concepts of resistance, tolerance, and disease hazard, as quantified in this study, can be used to predict yield and to select the most appropriate clones for different disease hazard conditions.

On a generalization of Jensen's □κ, and strategic closure of partial orders

1983 ◽  
Vol 48 (4) ◽  
pp. 1046-1052 ◽  
Author(s):  
Dan Velleman
Keyword(s):  
Lower Bound ◽  
Partial Order ◽  
Recent Work ◽  
Partial Orders ◽  
Closure Condition ◽  
Forcing Axioms ◽  
Combinatorial Principles ◽  
The Relationship ◽  
Mahlo Cardinals ◽  
Forcing Axiom

It is well known that many statements provable from combinatorial principles true in the constructible universe L can also be shown to be consistent with ZFC by forcing. Recent work by Shelah and Stanley [4] and the author [5] has clarified the relationship between the axiom of constructibility and forcing by providing Martin's Axiom-type forcing axioms equivalent to ◊ and the existence of morasses. In this paper we continue this line of research by providing a forcing axiom equivalent to □κ. The forcing axiom generalizes easily to inaccessible, non-Mahlo cardinals, and provides the motivation for a corresponding generalization of □κ.In order to state our forcing axiom, we will need to define a strategic closure condition for partial orders. Suppose P = 〈P, ≤〉 is a partial order. For each ordinal α we will consider a game played by two players, Good and Bad. The players choose, in order, the terms in a descending sequence of conditions 〈pβ∣β < α〉 Good chooses all terms pβ for limit β, and Bad chooses all the others. Bad wins if for some limit β<α, Good is unable to move at stage β because 〈pγ∣γ < β〉 has no lower bound. Otherwise, Good wins. Of course, we will be rooting for Good.

scholarly journals Inflation Expectations and Readiness to Spend: Cross-Sectional Evidence

2015 ◽  
Vol 7 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Rüdiger Bachmann ◽  
Tim O. Berg ◽  
Eric R. Sims
Keyword(s):  
Lower Bound ◽  
Inflation Expectations ◽  
Zero Lower Bound ◽  
Cross Sectional ◽  
Percentage Point Increase ◽  
Expected Inflation ◽  
Percentage Points ◽  
Point Increase ◽  
The Impact ◽  
The Relationship

There have been suggestions for monetary policy to engineer higher inflation expectations to stimulate spending. We examine the relationship between expected inflation and spending attitudes using the microdata from the Michigan Survey of Consumers. The impact of higher inflation expectations on the reported readiness to spend on durables is generally small, outside the zero lower bound, often statistically insignificant, and inside of it typically significantly negative. In our baseline specification, a one percentage point increase in expected inflation during the recent zero lower bound period reduces households' probability of having a positive attitude towards spending by about 0.5 percentage points. (JEL D12, D84, E21, E31, E52)

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