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1.
A. Georgakopoulos 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):235-245
We construct infinite planar graphs of arbitrarily large connectivity and girth, and study their separation properties. These
graphs have no thick end but continuum many thin ones. Every finite cycle separates them, but they corroborate Diestel’s conjecture
that everyk-connected locally finite graph contains a possibly infinite cycle — see [3] — whose deletion leaves it (k — 3)-connected. 相似文献
2.
We consider rational functions with n prescribed poles for which there exists a divided difference operator transforming them to rational functions with n−1 poles. The poles of such functions are shown to lie on the elliptic grids. There is a one-to-one correspondence between
this problem of admissible grids and the Poncelet problem on two quadrics. Additionally, we outline an explicit scheme of
the Padé interpolation with prescribed poles and zeros on the elliptic grids.
Dedicated to Richard Askey on the occasion of his seventieth birthday.
2000 Mathematics Subject Classification Primary—42C05; Secondary—39A13, 41A05, 41A21. 相似文献
3.
Stefan Felsner 《Order》2003,20(2):135-150
Schnyder labelings are known to have close links to order dimension and drawings of planar graphs. It was observed by Ezra
Miller that geodesic embeddings of planar graphs are another class of combinatorial or geometric objects closely linked to
Schnyder labelings. We aim to contribute to a better understanding of the connections between these objects. In this article
we prove
• a characterization of 3-connected planar graphs as those graphs admitting rigid geodesic embeddings,
• a bijection between Schnyder labelings and rigid geodesic embeddings,
• a strong version of the Brightwell–Trotter theorem.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
This paper introduces a subgradient descent algorithm to compute a Riemannian metric that minimizes an energy involving geodesic
distances. The heart of the method is the Subgradient Marching Algorithm to compute the derivative of the geodesic distance
with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element
of the subgradient in O(N
2 log(N)) operations on a discrete grid of N points. It performs a front propagation that computes a subgradient of a discrete geodesic distance. We show applications
to landscape modeling and to traffic congestion. Both applications require the maximization of geodesic distances under convex
constraints, and are solved by subgradient descent computed with our Subgradient Marching. We also show application to the
inversion of travel time tomography, where the recovered metric is the local minimum of a non-convex variational problem involving
geodesic distances. 相似文献
5.
In a seminal paper from 1983, Burr and Erdős started the systematic study of Ramsey numbers of cliques vs. large sparse graphs,
raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemerédi
regularity lemma, embedding of sparse graphs, Turán type stability, and other structural results. We give exact Ramsey numbers
for various classes of graphs, solving five — all but one — of the Burr-Erdős problems. 相似文献
6.
Jeremy Rouse 《The Ramanujan Journal》2006,12(2):197-205
We provide uniform formulas for the real period and the trace of Frobenius associated to an elliptic curve in Legendre normal
form. These are expressed in terms of classical and Gaussian hypergeometric functions, respectively.
2000 Mathematics Subject Classification Primary—11G05, 33C05
This research was supported by K. Ono’s NSF grant 相似文献
7.
Kevin W. J. Kadell 《The Ramanujan Journal》2007,13(1-3):449-469
We use telescoping partial fractions decompositions to give new proofs of the orthogonality property and the normalization
relation for the little q-Jacobi polynomials, and the q-Saalschütz sum. In [20], we followed the development [19] of Schur functions for partitions with complex parts, and we showed
that there exist natural little q-Jacobi functions of complex order which satisfy extensions of the orthogonality property and normalization relation of the
little q-Jacobi polynomials, and that these two results follow from and together imply the nonterminating form of the q-Saalschütz sum. Writing the q-Pochhammer symbol of complex order as a ratio of infinite products in the usual way, we obtain new telescoping partial fractions
decomposition proofs of our results [20] for the little q-Jacobi functions of complex order. We give several new proofs of the q-Saalschütz sum and its nonterminating form.
For our friends Dick and Liz
2000 Mathematics Subject Classification Primary—42C05; Secondary—33C45, 33C47 相似文献
8.
Stamatis Koumandos 《The Ramanujan Journal》2007,14(1):1-38
We establish a best possible extension of a famous Theorem of Vietoris about the positivity of a general class of cosine sums.
Our result refines and sharpens several earlier generalizations of this Theorem, and settles some open questions regarding
the possibility of further improvement of it. Some new inequalities for trigonometric sums are given. We show that our results
have applications within the context of positive sums of Gegenbauer polynomials and quadrature methods. We also obtain some
existing estimates for the location of zeros of certain trigonometric polynomials under a weakened condition on their coefficients.
2000 Mathematics Subject ClassificationPrimary—42A05; Secondary—42A32,26D05, 26D15, 33B15, 33C45
Dedicated to Richard Askey on the occasion of his 70th birthday 相似文献
9.
We consider a graph, where the nodes have a pre-described degree distribution F, and where nodes are randomly connected in accordance to their degree. Based on a recent result (R. van der Hofstad, G. Hooghiemstra
and P. Van Mieghem, “Random graphs with finite variance degrees,” Random Structures and Algorithms, vol. 17(5) pp. 76–105, 2005), we improve the approximation of the mean distance between two randomly chosen nodes given
by M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distribution and their application,”
Physical Review. E vol. 64, 026118, pp. 1–17, 2001. Our new expression for the mean distance involves the expectation of the logarithm of the
limit of a super-critical branching process. We compare simulations of the mean distance with the results of Newman et al.
and with our new approach.
AMS 2000 Subject Classification: 05C80, 60F05 相似文献
10.
We show that the Edmonds—Gallai decomposition theorem for matchings in finite graphs generalizes to all locally finite graphs.
C.N.R.S.
Dedicated to Tibor Gallai on his seventieth birthday 相似文献
11.
In this article, we apply the concept of m-polar fuzzy sets in labeling graphs and introduce the concept of m-polar fuzzy labeling graphs. We present properties of m-polar fuzzy labeling cycle and m-polar fuzzy labeling with bridge and cut nodes. We introduce several different types of distances, including w-distance, strongest strong distance, strong geodesic distance, \(\delta \)-distance in m-polar fuzzy labeling graph and investigate some of their properties. We also present an application of m-polar fuzzy labeling graphs in image processing. 相似文献
12.
We present a new family of locally geodesic transitive graphs with arbitrarily large diameter and valencies, containing a particular case to be geodesic transitive. We also prove that it is a unique family in some generalised family of graphs. 相似文献
13.
Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map
from the Culler–Vogtmann outer space CV (F
k
) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and
thus obtain a new compactification of the outer space. We also prove that for every k ≥ 2 the minimum of the volume entropy of the universal covers of finite connected volume-one metric graphs with fundamental
group of rank k and without degree-one vertices is equal to (3k − 3) log 2 and that this minimum is realized by trivalent graphs with all edges of equal lengths, and only by such graphs.
Received: December 2005, Accepted: March 2006 相似文献
14.
Warren P. Johnson 《The Ramanujan Journal》2007,13(1-3):167-201
More than 200 years ago, Pfaff found two generalizations of Leibniz’s rule for the nth derivative of a product of two functions. Thirty years later Cauchy found two similar identities, one equivalent to one
of Pfaff’s and the other new. We give simple proofs of these little-known identities and some further history. We also give
applications to Abel-Rothe type binomial identities, Lagrange’s series, and Laguerre and Jacobi polynomials. Most importantly,
we give extensions that are related to the Pfaff/Cauchy theorems as Hurwitz’s generalized binomial theorems are to the Abel-Rothe
identities. We apply these extensions to Laguerre and Jacobi polynomials as well.
Dedicated to Dick Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—05A19; Secondary—33C45 相似文献
15.
We show how functions F(z) which satisfy an identity of the form F(α z) = g(F(z)) for some complex number α and some function g(z) give rise to infinite product formulas that generalize Viète's product formula for π. Specifically, using elliptic and trigonometric
functions we derive closed form expressions for some of these infinite products. By evaluating the expressions at certain
points we obtain formulas expressing infinite products involving nested radicals in terms of well-known constants. In particular,
simple infinite products for π and the lemniscate constant are obtained.
2000 Mathematics Subject Classification: Primary—40A20; Secondary—33E05 相似文献
16.
Lénaïc Chizat Gabriel Peyré Bernhard Schmitzer François-Xavier Vialard 《Journal of Functional Analysis》2018,274(11):3090-3123
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation. 相似文献
17.
We obtain (two equivalent) presentations — in terms of generators and relations — of the planar algebra associated with the
subfactor corresponding to (an outer action on a factor by) a finite-dimensional Kac algebra. One of the relations shows that
the antipode of the Kac algebra agrees with the ‘rotation on 2-boxes’. 相似文献
18.
Abstract. We consider the Riemannian geometry defined on a convex set by the Hessian of a self-concordant barrier function, and its
associated geodesic curves. These provide guidance for the construction of efficient interior-point methods for optimizing
a linear function over the intersection of the set with an affine manifold. We show that algorithms that follow the primal—dual
central path are in some sense close to optimal. The same is true for methods that follow the shifted primal—dual central
path among certain infeasible-interior-point methods. We also compute the geodesics in several simple sets. 相似文献
19.
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifold. Motivated by
the “complexifier” approach of T. Thiemann as well as certain formulas of V. Guillemin and M. Stenzel, we obtain the polarization
associated to the adapted complex structure by applying the “imaginary-time geodesic flow” to the vertical polarization. Meanwhile,
at the level of functions, we show that every holomorphic function is obtained from a function that is constant along the
fibers by “composition with the imaginary-time geodesic flow.” We give several equivalent interpretations of this composition,
including a convergent power series in the vector field generating the geodesic flow. 相似文献
20.
Lynn Margaret Batten 《Journal of Graph Theory》1983,7(2):159-163
Define a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We do this also for triangle-free graphs. 相似文献