1,874 research outputs found
Reaction studied of steam with niobium and tantalum
Study reveals the kinetics of niobium and tantalum with steam at elevated temperatures to determine the suitability of high melting metals for fabrication of equipment for temperature steam environments. Niobium obeyed linear kinetics from 1050 degrees to 1500 degrees C but tantalum followed a paralinear rate law
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the
refinement of calculus tools on metric measure spaces (X,d,m). Our main results
are:
- A general study of the relations between the Hopf-Lax semigroup and
Hamilton-Jacobi equation in metric spaces (X,d).
- The equivalence of the heat flow in L^2(X,m) generated by a suitable
Dirichlet energy and the Wasserstein gradient flow of the relative entropy
functional in the space of probability measures P(X).
- The proof of density in energy of Lipschitz functions in the Sobolev space
W^{1,2}(X,d,m).
- A fine and very general analysis of the differentiability properties of a
large class of Kantorovich potentials, in connection with the optimal transport
problem.
Our results apply in particular to spaces satisfying Ricci curvature bounds
in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the
doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4,
Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop.
4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6
simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients,
still equivalent to all other ones, has been propose
Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II
Let be a symmetric diffusion operator
with an invariant measure on a complete Riemannian
manifold. In this paper we prove Li-Yau gradient estimates for weighted
elliptic equations on the complete manifold with
and -dimensional Bakry-\'{E}mery Ricci curvature bounded below by some
negative constant. Based on this, we give an upper bound on the first
eigenvalue of the diffusion operator on this kind manifold, and thereby
generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975)
289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau
gradient estimate method has been moved to the appendix. The new proof is
simple and direc
Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds
Measure contraction property is one of the possible generalizations of Ricci
curvature bound to more general metric measure spaces. In this paper, we
discover sufficient conditions for a three dimensional contact subriemannian
manifold to satisfy this property.Comment: 49 page
Folding and unfolding phylogenetic trees and networks
Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network can be "unfolded" to obtain a MUL-tree and, conversely, a MUL-tree can in certain circumstances be "folded" to obtain a phylogenetic network that exhibits . In this paper, we study properties of the operations and in more detail. In particular, we introduce the class of stable networks, phylogenetic networks for which is isomorphic to , characterise such networks, and show that they are related to the well-known class of tree-sibling networks.We also explore how the concept of displaying a tree in a network can be related to displaying the tree in the MUL-tree . To do this, we develop a phylogenetic analogue of graph fibrations. This allows us to view as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in and reconcilingphylogenetic trees with networks
The Dirac operator on generalized Taub-NUT spaces
We find sufficient conditions for the absence of harmonic spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler base. These
conditions are fulfilled for certain perturbations of the Euclidean metric, and
also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a
conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
Neo-Aristotelian Naturalism and the Evolutionary Objection: Rethinking the Relevance of Empirical Science
Neo-Aristotelian metaethical naturalism is a modern attempt at naturalizing ethics using ideas from Aristotleâs teleological metaphysics. Proponents of this view argue that moral virtue in human beings is an instance of natural goodness, a kind of goodness supposedly also found in the realm of non-human living things. Many critics question whether neo-Aristotelian naturalism is tenable in light of modern evolutionary biology. Two influential lines of objection have appealed to an evolutionary understanding of human nature and natural teleology to argue against this view. In this paper, I offer a reconstruction of these two seemingly different lines of objection as raising instances of the same dilemma, giving neo-Aristotelians a choice between contradicting our considered moral judgment and abandoning metaethical naturalism. I argue that resolving the dilemma requires showing a particular kind of continuity between the norms of moral virtue and norms that are necessary for understanding non-human living things. I also argue that in order to show such a continuity, neo-Aristotelians need to revise the relationship they adopt with empirical science and acknowledge that the latter is relevant to assessing their central commitments regarding living things. Finally, I argue that to move this debate forward, both neo-Aristotelians and their critics should pay attention to recent work on the concept of organism in evolutionary and developmental biology
A Renormalization Group Approach to Relativistic Cosmology
We discuss the averaging hypothesis tacitly assumed in standard cosmology.
Our approach is implemented in a "3+1" formalism and invokes the coarse
graining arguments, provided and supported by the real-space Renormalization
Group (RG) methods. Block variables are introduced and the recursion relations
written down explicitly enabling us to characterize the corresponding RG flow.
To leading order, the RG flow is provided by the Ricci-Hamilton equations
studied in connection with the geometry of three-manifolds. The properties of
the Ricci-Hamilton flow make it possible to study a critical behaviour of
cosmological models. This criticality is discussed and it is argued that it may
be related to the formation of sheet-like structures in the universe. We
provide an explicit expression for the renormalized Hubble constant and for the
scale dependence of the matter distribution. It is shown that the Hubble
constant is affected by non-trivial scale dependent shear terms, while the
spatial anisotropy of the metric influences significantly the scale-dependence
of the matter distribution.Comment: 57 pages, LaTeX, 15 pictures available on request from the Author
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