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1.
Jean Mawhin 《Journal of Fixed Point Theory and Applications》2007,1(2):159-187
Some applications given in Jean Leray’s thesis of 1933 seem to have been forgotten, before being rediscovered and then widely
developed. The reason may be found in the fact that the Arzelà–Schmidt’s method introduced in the thesis was superseded one
year later by the more general and fruitful Leray-Schauder’s method. We also show that, despite its fame and a steadily increasing
number of applications, some aspects of Leray–Schauder’s paper were somewhat forgotten too.
Dedicated, with admiration, to the living memory of Jean Leray 相似文献
2.
S. I. Kalmykov 《Journal of Mathematical Sciences》2009,157(4):623-631
The paper considers the equality cases in the rnajoration principle for meromorphic functions established earlier by V. N.
Dubinin and S. I. Kalmykov [Mat. Sb., 198, No. 12, 37–46 (2007)]. As corollaries of this principle, new inequalities for the coefficients and derivatives of polynomials
satisfying certain conditions on two intervals are obtained. Simple proofs of some Lukashov’s theorems on the derivatives
of rational functions on several intervals are provided. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 143–157. 相似文献
3.
Tom Meyerovitch 《Inventiones Mathematicae》2011,184(3):567-589
We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth
rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson (A strange two-dimensional
symbolic system, 1992), we show that growth complexities of the form exp (n
α+o(1)) are possible for non-integer α’s. In terminology of de Carvalho (Port. Math. 54(1):19–40, 1997), such subshifts have entropy dimension α. The class of possible α’s are identified in terms of arithmetical classes of real numbers of Weihrauch and Zheng (Math. Log. Q. 47(1):51–65, 2001). 相似文献
4.
Saul I. Gass 《Journal of Global Optimization》2008,42(3):347-355
For a set of measured points, we describe a linear-programming model that enables us to find concentric circumscribed and
inscribed circles whose annulus encompasses all the points and whose width tends to be minimum in a Chebychev minmax sense.
We illustrate the process using the data of Rorres and Romano (SIAM Rev. 39: 745–754, 1997) that is taken from an ancient Greek stadium in Corinth. The stadium’s racecourse had an unusual circular
arc starting line, and measurements along this arc form the basic data sets of Rorres and Romano (SIAM Rev. 39: 745–754, 1997). Here we are interested in finding the center and radius of the circle that defined the starting line arc.
We contrast our results with those found in Rorres and Romano (SIAM Rev. 39: 745–754, 1997). 相似文献
5.
Ring semigroups whose subsemigroups form a chain 总被引:1,自引:1,他引:0
Greg Oman 《Semigroup Forum》2009,78(2):374-377
A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics,
pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups
containing 0 form a chain with respect to set inclusion. 相似文献
6.
Howard’s conjecture, which states that in the linear instability problem of inviscid heterogeneous parallel shear flow growth
rate of an arbitrary unstable wave must approach zero as the wave length decreases to zero, is established in a mathematically
rigorous fashion for plane parallel heterogeneous shear flows with negligible buoyancy forcegΒ ≪ 1 (Miles J W,J. Fluid Mech.
10 (1961) 496–508), where Β is the basic heterogeneity distribution function).
An erratum to this article is available at . 相似文献
7.
J. Bourgain 《Israel Journal of Mathematics》1987,59(2):150-166
The main purpose of this paper is to prove the existence of Poincaré sequences of integers which are not van der Corput sets.
This problem was considered in I. Ruzsa’s expository article [R1] (1982–83) on correlative and intersective sets. Thus the existence is shown of a positive non-continuous measureμ on the circle which Fourier transform vanishes on a set of recurrence, i.e.S={n ∈Z;
(n)=0} is a set of recurrence but not a van der Corput set. The method is constructive and involves some combinatorial considerations.
In fact, we prove that the generic density condition for both properties are the same. 相似文献
8.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
9.
The spiral is one of nature’s more ubiquitous shapes: It can be seen in various media, from galactic geometry to cardiac tissue.
Mathematically, spiral waves arise as solutions to reaction–diffusion partial differential equations (RDS). In the literature,
various experimentally observed dynamical states and bifurcations of spiral waves have been explained using the underlying
Euclidean symmetry of the RDS—see for example (Barkley in Phys. Rev. Lett. 68:2090–2093, 1992; Phys. Rev. Lett. 76:164–167, 1994; Sandstede et al. in C. R. Acad. Sci. 324:153–158, 1997; J. Differ. Equ. 141:122–149, 1997; J. Nonlinear Sci. 9:439–478, 1999), or additionally using the concept of forced Euclidean symmetry-breaking for situations where an inhomogeneity or anisotropy
is present—see (LeBlanc in Nonlinearity 15:1179–1203, 2002; LeBlanc and Wulff in J. Nonlinear Sci. 10:569–601, 2000).
In this paper, we further investigate the role of medium inhomogeneities on spiral wave dynamics by considering the effects
of several localized sites of inhomogeneity. Using a model-independent approach based on n>1 simultaneous translational symmetry-breaking perturbations of the dynamics near rotating waves, we fully characterize the
local anchoring behavior of the spiral wave in the n-dimensional parameter space of relative “amplitudes” of the individual perturbations. For the case n=2, we supplement the local anchoring results with a classification of the generic one-parameter bifurcation diagrams of anchored
states which can be obtained by circling the origin of the two-dimensional amplitude parameter space. Numerical examples are
given to illustrate our various results. 相似文献
10.
Rade T. Živaljević 《Combinatorica》2010,30(4):471-484
L. Lovász (Matroids and Sperner’s Lemma, Europ. J. Comb.
1 (1980), 65–66) has shown that Sperner’s combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. We prove that Ky Fan’s theorem admits an oriented matroid generalization of similar nature. Classical Ky Fan’s theorem is obtained as a corollary if the underlying oriented matroid
is chosen to be the alternating matroid C
m,r
. 相似文献
11.
Andrew V. Sills 《The Ramanujan Journal》2006,11(3):403-429
A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50, 421–435 (1949)), is derived and used to find a number of new Rogers-Ramanujan type identities. Consideration of associated
q-difference equations points to a connection with a mild extension of Gordon’s combinatorial generalization of the Rogers-Ramanujan
identities (Amer. J. Math., 83, 393–399 (1961)). This, in turn, allows the formulation of natural combinatorial interpretations of many of the identities
in Slater’s list (Proc. London Math. Soc. (2) 54, 147–167 (1952)), as well as the new identities presented here. A list of 26 new double sum–product Rogers-Ramanujan type
identities are included as an Appendix.
2000 Mathematics Subject Classification Primary—11B65; Secondary—11P81, 05A19, 39A13 相似文献
12.
A. N. Degtev 《Russian Mathematics (Iz VUZ)》2011,55(7):17-22
In this paper we specify classes of weakly implicative selector sets and describe their interconnections for the case when
the number of variables n does exceed 3 (see A. N. Degtev and D. I. Ivanov, “Weakly Implicative Selector Sets of Dimension 3” Diskretn. Matem. 11 (3), 126–132 (1999)). 相似文献
13.
Guy David 《Journal of Geometric Analysis》2010,20(4):837-954
We give a new proof and a partial generalization of Jean Taylor’s result (Ann. Math. (2) 103(3), 489–539, 1976) that says that Almgren almost-minimal sets of dimension 2 in ℝ3 are locally C
1+α
-equivalent to minimal cones. The proof is rather elementary, but uses a local separation result proved in Ann. Fac. Sci.
Toulouse 18(1), 65–246, 2009 and an extension of Reifenberg’s parameterization theorem (David et al. in Geom. Funct. Anal. 18, 1168–1235, 2008). The key idea is still that if X is the cone over an arc of small Lipschitz graph in the unit sphere, but X is not contained in a disk, we can use the graph of a harmonic function to deform X and substantially diminish its area. The local separation result is used to reduce to unions of cones over arcs of Lipschitz
graphs. A good part of the proof extends to minimal sets of dimension 2 in ℝ
n
, but in this setting our final regularity result on E may depend on the list of minimal cones obtained as blow-up limits of E at a point. 相似文献
14.
Klaus Barner 《Mathematische Semesterberichte》2011,7(5):13-45
In his papers on the determination of maxima and minima and on the calculation of tangents Pierre Fermat uses two different
Latin verbs, ?quare and ad?quare, which do not differ semantically but are used by him obviously in different meanings. While ?quabitur is used unambiguously in the sense of “is equal” the meaning of ad?quabitur is disputed by the experts since Tannery’s French translation (Œuvres complètes de Fermat, Vol. III, 1896). Herbert Breger (Arch. Hist. Exact Sci. 46, 193–219, (1994), p. 197 f), for instance, holds the view that Fermat used the word ad?quare in the sense of “to put equal” and adds: In a mathematical context, the only difference between “?quare” and “ad?quare” (if there is any) seems to be that the latter
gives more stress on the fact that the equality is achieved. In contrast to this Michael Mahoney holds the thesis that ad?quare describes a counterfactual equality (Mahoney, M.S.: Fermat, Pierre de. In: Dictionary of Scientific Biography, vol. IV (1971), p. 569) or a pseudo-equality (Mahoney, M.S.: The Mathematical Career of Pierre de Fermat (1601–1665), (1973), p. 164), whatever that may mean. This viewpoint has been taken up again recently by Enrico Giusti (Ann. Fac. Sci. Toulouse,
Math. (6), 18 fascicule spécial, 59–85 (2009)) in order to bring arguments to bear against Breger. In contrast to these (and other) authors, I show that Fermat makes
a subtle logical distinction between the words ?quare and ad?quare. The same distinction is made by Nicolas Bourbaki introducing his ?théorie égalitaire?. Notwithstanding: both verbs stand for a ?relation d’égalité?. On this premiss, I describe—using six selected examples—that Fermat’s “method” may be justified right down to the last
detail, even from the view of today’s mathematical knowledge. 相似文献
15.
We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator
to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (Maximum principles and eigenvalue
problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow,
175, pp. 34–48, 1988) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary
value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate
ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006). 相似文献
16.
We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service
requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where
the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results
of Morrison (SIAM J. Appl. Math. 45:152–167, [1985]) and Flatto (Ann. Appl. Probab. 7:382–409, [1997]).
This work was partly supported by NSF grant DMS 05-03745. 相似文献
17.
Peter Vadovič 《Mathematica Slovaca》2008,58(4):509-520
We consider a special space of set-valued functions (multifunctions), the space of densely continuous forms D(X, Y) between Hausdorff spaces X and Y, defined in [HAMMER, S. T.—McCOY, R. A.: Spaces of densely continuous forms, Set-Valued Anal. 5 (1997), 247–266] and investigated also in [HOLá, L’.: Spaces of densely continuous forms, USCO and minimal USCO maps, Set-Valued Anal. 11 (2003), 133–151]. We show some of its properties, completing the results from the papers [HOLY, D.—VADOVIČ, P.: Densely continuous forms, pointwise topology and cardinal functions, Czechoslovak Math. J. 58(133) (2008), 79–92] and [HOLY, D.—VADOVIČ, P.: Hausdorff graph topology, proximal graph topology and the uniform topology for densely continuous forms and minimal USCO maps, Acta Math. Hungar. 116 (2007), 133–144], in particular concerning the structure of the space of real-valued locally bounded densely continuous forms
D
p
*(X) equipped with the topology of pointwise convergence in the product space of all nonempty-compact-valued multifunctions.
The paper also contains a comparison of cardinal functions on D
p
*(X) and on real-valued continuous functions C
p
(X) and a generalization of a sufficient condition for the countable cellularity of D
p
*(X).
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904 and by the Eco-Net
(EGIDE) programme of the Laboratoire de Mathématiques de l’Université de Saint-Etienne (LaMUSE), France. 相似文献
18.
We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide
sharp upper bounds for the sum of modified Bessel functions I0(x) + I1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent
random variables due to Čekanavičius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).
相似文献
19.
Mihai Cristea 《Complex Analysis and Operator Theory》2011,5(3):863-880
The paper continues the work of Royster (Duke Math J 19:447–457, 1952), Mocanu [Mathematica (Cluj) 22(1):77–83, 1980; Mathematica
(Cluj) 29:49–55, 1987], Cristea [Mathematica (Cluj) 36(2):137–144, 1994; Complex Var 42:333–345, 2000; Mathematica (Cluj)
43(1):23–34, 2001; Mathematica (Cluj), 2010, to appear; Teoria Topologica a Functiilor Analitice, Editura Universitatii Bucuresti,
Romania, 1999] of extending univalence criteria for complex mappings to C
1 mappings. We improve now the method of Loewner chains which is usually used in complex univalence theory for proving univalence
criteria or for proving quasiconformal extensions of holomorphic mappings f : B → C
n
to C
n
. The results are surprisingly strong. We show that the usual results from the theory, like Becker’s univalence criteria remain
true for C
1 mappings and since we use a stronger form of Loewner’s theory, we obtain results which are stronger even for holomorphic
mappings f : B → C
n
. In our main result (Theorem 4.1) we end the researches dedicated to quasiconformal extensions of K-quasiregular and holomorphic mappings f : B → C
n
to C
n
. We show that a C
1 quasiconformal map f : B → C
n
can be extended to a quasiconformal map F : C
n
→ C
n
, without any metric condition imposed to the map f. 相似文献
20.
We use Klee’s Dehn–Sommerville relations and other results on face numbers of homology manifolds without boundary to (i) prove
Kalai’s conjecture providing lower bounds on the f-vectors of an even-dimensional manifold with all but the middle Betti number vanishing, (ii) verify Kühnel’s conjecture that
gives an upper bound on the middle Betti number of a 2k-dimensional manifold in terms of k and the number of vertices, and (iii) partially prove Kühnel’s conjecture providing upper bounds on other Betti numbers of
odd- and even-dimensional manifolds. For manifolds with boundary, we derive an extension of Klee’s Dehn–Sommerville relations
and strengthen Kalai’s result on the number of their edges.
I. Novik research partially supported by Alfred P. Sloan Research Fellowship and NSF grant DMS-0500748.
E. Swartz research partially supported by NSF grant DMS-0600502. 相似文献