scholarly journals A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs

Author(s):  
Álvaro Martínez-Pérez ◽  
José M. Rodríguez

AbstractWe study in this paper the relationship of isoperimetric inequality and hyperbolicity for graphs and Riemannian manifolds. We obtain a characterization of graphs and Riemannian manifolds (with bounded local geometry) satisfying the (Cheeger) isoperimetric inequality, in terms of their Gromov boundary, improving similar results from a previous work. In particular, we prove that having a pole is a necessary condition to have isoperimetric inequality and, therefore, it can be removed as hypothesis.

2018 ◽  
Vol 20 (05) ◽  
pp. 1750050 ◽  
Author(s):  
Alvaro Martínez-Pérez ◽  
José M. Rodríguez

In this paper, we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis). As an application of our results, we obtain the solvability of the Dirichlet problem at infinity for these Riemannian manifolds and graphs, and that the Martin boundary is homeomorphic to the Gromov boundary.


Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.


2004 ◽  
Vol 28 (1) ◽  
pp. 15-49
Author(s):  
Simon Perry

Mussorgsky's Sunless cycle is aesthetically and stylistically an anomalous member of his oeuvre. Its notably effaced, pared-down, and withdrawn qualities present challenges to critical interpretation. Its uniqueness, however, renders it a crucial work for furnishing the fullest possible picture of Mussorgsky as a creative artist. The author of its texts, Golenishchev-Kutuzov (whose relationship with Mussorgsky at the time of its writing possibly extended beyond the platonic) has been identified by recent scholarship as an essential "eye-witness" for those to whom Stasov's populist characterization of the composer does not ring entirely true. Golenishchev-Kutuzov believed that in Sunless Mussorgsky first revealed his authentic artistic self. According to Golenishchev-Kutuvoz, Mussorgsky regarded his signal achievement in Sunless to have been the eradication of all elements other than "feeling." In other words, he had thrown off the stylistic shackles imposed by the aesthetics of realism and relied entirely on intuitive harmonic invention as the sole conveyor of a purely subjective, "affective" meaning in the cycle. This hypothesis forms the point of departure for an investigation of select numbers of the cycle. Analysis reveals that the affective aspect is not the only significant element operative. Alongside remnants of the realist style, there is evidence, of varying degrees of subtlety, for a knowing use of symmetrical pitch organization. Mussorgsky not only adapted the usual referential attachments of symmetrically based chromaticism--typically found in Russian operas of the second half of the nineteenth century--he also, through extremely simple but effective means, synthesized the "intuitive" harmonic and "rational" symmetrical elements of the cycle's pitch organization so that the latter emerges seamlessly out of the former. This remarkable synthesis ensures the cycle's uniformity of tone while also allowing for a reading that extends beyond the generally affective to the symbolically more specific. This symbolic level of reading offers several interpretative possibilities, one of which may refer even to the relationship of the poet and the composer. Irrespective of such potentials for interpretation, the most significant achievement in the cycle remains the synthesis of the intuitive/affective and rational/symbolic elements of its organization. Songs 1, 2, 3, and 6 of the cycle are considered in detail.


Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 141 ◽  
Author(s):  
Gregg Jaeger

The question of whether virtual quantum particles exist is considered here in light of previous critical analysis and under the assumption that there are particles in the world as described by quantum field theory. The relationship of the classification of particles to quantum-field-theoretic calculations and the diagrammatic aids that are often used in them is clarified. It is pointed out that the distinction between virtual particles and others and, therefore, judgments regarding their reality have been made on basis of these methods rather than on their physical characteristics. As such, it has obscured the question of their existence. It is here argued that the most influential arguments against the existence of virtual particles but not other particles fail because they either are arguments against the existence of particles in general rather than virtual particles per se, or are dependent on the imposition of classical intuitions on quantum systems, or are simply beside the point. Several reasons are then provided for considering virtual particles real, such as their descriptive, explanatory, and predictive value, and a clearer characterization of virtuality—one in terms of intermediate states—that also applies beyond perturbation theory is provided. It is also pointed out that in the role of force mediators, they serve to preclude action-at-a-distance between interacting particles. For these reasons, it is concluded that virtual particles are as real as other quantum particles.


1987 ◽  
Vol 80 (3) ◽  
pp. 287-306 ◽  
Author(s):  
John S. Kloppenborg

The relationship of the preaching and teaching of Jesus to apocalyptic has been a vexed one ever since Albert Schweitzer's assault on the liberal “Lives of Jesus” and his advocacy of consistent eschatology along with his characterization of Jesus’ teachings as interim ethics. While many of the details of Schweitzer's hypothesis failed to be persuasive, his insistence that Jesus’ activity be seen in the context of apocalypticism has made a profound impact on subsequent historical Jesus scholarship and, in spite of his own noncommital stance with regard to the Two Document Hypothesis, on the theological characterization of Q.


1971 ◽  
Vol 123 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. W. Dale

1. The amino acid composition of the β-lactamase from E. coli (R-1818) was determined. 2. The R-1818 β-lactamase is inhibited by formaldehyde, hydroxylamine, sodium azide, iodoacetamide, iodine and sodium chloride. 3. The Km values for benzylpenicillin, ampicillin and oxacillin have been determined by using the R-factor enzyme from different host species. The same values were obtained, irrespective of the host bacterium. 4. The molecular weight of the enzyme was found to be 44600, and was the same for all host species. 5. The relationship of R-1818 and R-GN238 β-lactamases is discussed.


2002 ◽  
Vol 718 ◽  
Author(s):  
Job Rijssenbeek ◽  
Sylvie Malo ◽  
Takashi Saito ◽  
Vincent Caignaert ◽  
Masaki Azuma ◽  
...  

AbstractPerovskite-like mixed metal ruthenates are of interest owing to their varied electronic and magnetic properties, which are heavily dependent on the ordering of the transition metals. We report the synthesis and structural characterization of the first 1:2 ordered perovskite ruthenate, Sr3CaRu2O9. The structure was determined from a combination of powder X-ray, electron and neutron diffraction data and is characterized by a 1:2 ordering of Ca2+ and Ru5+ over the sixcoordinate B-sites of the perovskite lattice. Sr3CaRu2O9 is the first example of this structure-type to include a majority metal with d electrons (Ru(V), d3). The relationship of this material to the K2NiF4-type Sr1.5Ca0.5RuO4 (i.e., Sr3CaRu2O8) highlights the dramatic effects of the ruthenium valence on the resultant structure. Remarkably, these two structures can be quantitatively interconverted by the appropriate choice of reaction temperature and atmosphere.


Author(s):  
Justin E. H. Smith

This Introduction takes a broadly focused, global, and comparative view of the concept of embodiment, focusing particularly on some of the ways it has been interpreted outside of the history of European thought. It also provides a general overview of the central concerns and questions of the volume as a whole, such as: What is the historical and conceptual relationship between the idea of embodiment and the idea of subjecthood? Am I who I am principally in virtue of the fact that I have the body I have? Relatedly, what is the relationship of embodiment to being and to individuality? Is embodiment a necessary condition of being? Of being an individual? What are the theological dimensions of embodiment? To what extent has the concept of embodiment been deployed in the history of philosophy to contrast the created world with the state of existence enjoyed by God? What are the normative dimensions of theories of embodiment? To what extent is the problem of embodiment a distinctly western preoccupation?


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