554 research outputs found
Subdivisions with Distance Constraints in Large Graphs
In this dissertation we are concerned with sharp degree conditions that guarantee the existence of certain types of subdivisions in large graphs. Of particular interest are subdivisions with a certain number of arbitrarily specified vertices and with prescribed path lengths. Our non-standard approach makes heavy use of the Regularity Lemma (Szemerédi, 1978), the Blow-Up Lemma (Komlós, Sárkózy, and Szemerédi, 1994), and the minimum degree panconnectivity criterion (Williamson, 1977).Sharp minimum degree criteria for a graph G to be H-linked have recently been discovered. We define (H,w,d)-linkage, a condition stronger than H-linkage, by including a weighting function w consisting of required lengths for each edge-path of a desired H-subdivision. We establish sharp minimum degree criteria for a large graph G to be (H,w,d)-linked for all nonnegative d. We similarly define the weaker condition (H,S,w,d)-semi-linkage, where S denotes the set of vertices of H whose corresponding vertices in an H-subdivision are arbitrarily specified. We prove similar sharp minimum degree criteria for a large graph G to be (H,S,w,d)-semi-linked for all nonnegativeWe also examine path coverings in large graphs, which could be seen as a special case of (H,S,w)-semi-linkage. In 2000, Enomoto and Ota conjectured that a graph G of order n with degree sum σ2(G) satisfying σ2(G) \u3e n + k - 2 may be partitioned into k paths, each of prescribed order and with a specified starting vertex. We prove the Enomoto-Ota Conjecture for graphs of sufficiently large order
Long Path Lemma Concerning Connectivity and Independence Number
We show that, in a k-connected graph G of order n with α(G)=α, between any pair of vertices, there exists a path P joining them with
|P|≥min{n,(k−1)(n−k)/α +k}.
This implies that, for any edge e∈E(G), there is a cycle containing e of length at least
min{n,(k−1)(n−k)/α +k}.
Moreover, we generalize our result as follows: for any choice S of s≤k vertices in G, there exists a tree T whose set of leaves is S with
|T|≥min{n,(k−s+1)(n−k)/α +k}
A Decomposition of Gallai Multigraphs
An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed trees
FEATURES IMPACT NANOSILVER COLLOIDAL SOLUTION ON THE MORPHOLOGICAL AND BIOCHEMICAL PARAMETERS IN RATS
Modern nanotechnology development and use of nanomaterials is one of the most perspective directions of science and technology of the XXI century. Objective - study the morphological and biochemical parameters influence of colloidal nanosilver solution in the experiment. The experiment was performed on mature white nonlinear rats with weight 180- 200 g. During 7 days nanostructured silver solution was administered at a dose of 3.5 mg / kg (concentration of metal at 800 micrograms / ml) intraperitoneally. At the end of the introduction of colloidal nanosilver solution to test animals was carried out blood sampling and conducted morphological study of the effect of nanosilver at the tissue level in parenchymal organs (liver, kidneys, adrenals, brain, heart)
Gaffnian holonomy through the coherent state method
We analyze the effect of exchanging quasiholes described by Gaffnian quantum
Hall trial state wave functions. This exchange is carried out via adiabatic
transport using the recently developed coherent state Ansatz. We argue that our
Ansatz is justified if the Gaffnian parent Hamiltonian has a charge gap, even
though it is gapless to neutral excitations, and may therefore properly
describe the adiabatic transport of Gaffnian quasiholes. For nonunitary states
such as the Gaffnian, the result of adiabatic transport cannot agree with the
monodromies of the conformal block wave functions, and may or may not lead to
well-defined anyon statistics. Using the coherent state Ansatz, we find two
unitary solutions for the statistics, one of which agrees with the statistics
of the non-Abelian spin-singlet state by Ardonne and Schoutens.Comment: 11 pages, 4 figure
Effects of counterion fluctuations in a polyelectrolyte brush
We investigate the effect of counterion fluctuations in a single
polyelectrolyte brush in the absence of added salt by systematically expanding
the counterion free energy about Poisson-Boltzmann mean field theory. We find
that for strongly charged brushes, there is a collapse regime in which the
brush height decreases with increasing charge on the polyelectrolyte chains.
The transition to this collapsed regime is similar to the liquid-gas
transition, which has a first-order line terminating at a critical point. We
find that for monovalent counterions the transition is discontinuous in theta
solvent, while for multivalent counterions the transition is generally
continuous. For collapsed brushes, the brush height is not independent of
grafting density as it is for osmotic brushes, but scales linear with it.Comment: 9 pages, 9 figure
Magnon Localization in Mattis Glass
We study the spectral and transport properties of magnons in a model of a
disordered magnet called Mattis glass, at vanishing average magnetization. We
find that in two dimensional space, the magnons are localized with the
localization length which diverges as a power of frequency at small
frequencies. In three dimensional space, the long wavelength magnons are
delocalized. In the delocalized regime in 3d (and also in 2d in a box whose
size is smaller than the relevant localization length scale) the magnons move
diffusively. The diffusion constant diverges at small frequencies. However, the
divergence is slow enough so that the thermal conductivity of a Mattis glass is
finite, and we evaluate it in this paper. This situation can be contrasted with
that of phonons in structural glasses whose contribution to thermal
conductivity is known to diverge (when inelastic scattering is neglected).Comment: 11 page
Field Theory of the Random Flux Model
The long-range properties of the random flux model (lattice fermions hopping
under the influence of maximally random link disorder) are shown to be
described by a supersymmetric field theory of non-linear sigma model type,
where the group GL(n|n) is the global invariant manifold. An extension to
non-abelian generalizations of this model identifies connections to lattice
QCD, Dirac fermions in a random gauge potential, and stochastic non-Hermitian
operators.Comment: 4 pages, 1 eps figur
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