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1.
An account of the error and the convergence theory is given for Gauss–Laguerre and Gauss–Radau–Laguerre quadrature formulae.
We develop also truncated models of the original Gauss rules to compute integrals extended over the positive real axis. Numerical
examples confirming the theoretical results are given comparing these rules among themselves and with different quadrature
formulae proposed by other authors (Evans, Int. J. Comput. Math. 82:721–730, 2005; Gautschi, BIT 31:438–446, 1991).
相似文献
2.
The purpose of this paper is to prove some new common fixed point theorems in (GV)-fuzzy metric spaces. While proving our results, we utilize the idea of compatibility due to Jungck (Int J Math Math Sci
9:771–779, 1986) together with subsequentially continuity due to Bouhadjera and Godet-Thobie (arXiv: 0906.3159v1 [math.FA] 17 Jun 2009) respectively (also alternately reciprocal continuity due to Pant (Bull Calcutta Math Soc 90:281–286, 1998) together with subcompatibility due to Bouhadjera and Godet-Thobie (arXiv:0906.3159v1 [math.FA] 17 Jun 2009) as patterned in Imdad et al. (doi:) wherein conditions on completeness (or closedness) of the underlying space (or subspaces) together with conditions on continuity
in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant
common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant
results due to Imdad et al. (J Appl Math Inform 26:591–603, 2008), Mihet (doi:), Mishra (Tamkang J Math 39(4):309–316, 2008), Singh (Fuzzy Sets Syst 115:471–475, 2000) and several others. 相似文献
3.
John A. Ford Yasushi Narushima Hiroshi Yabe 《Computational Optimization and Applications》2008,40(2):191-216
Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of
matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87–101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput.
Optim. Appl. 28:203–225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step
secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357–370, 1993; J. Comput. Appl. Math. 50:305–323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent
under certain assumptions. Numerical results are reported. 相似文献
4.
Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently
by Fedorčuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Colloq Math 17:35–39, 1967). In this note we give a simple characterization of the topology of a totally ordered space, as well as give a new simplified
proof of the main results of Blatter (J Approx Theory 13:56–65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional
totally ordered space X, we determine which order-compactifications of X are Priestley order-compactifications. 相似文献
5.
Wenchang Chu 《The Ramanujan Journal》2011,26(2):251-255
The general summation theorem for well-poised 5
F
4-series discovered by Dougall (Proc. Edinb. Math. Soc. 25:114–132, 1907) is shown to imply several infinite series of Ramanujan-type for 1/π and 1/π
2, including those due to Bauer (J. Reine Angew. Math. 56:101–121, 1859) and Glaisher (Q. J. Math. 37:173–198, 1905) as well as some recent ones by Levrie (Ramanujan J. 22:221–230, 2010). 相似文献
6.
We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods,
under mild differentiability conditions. It turns out that our sufficient convergence conditions are weaker, and the error
bounds are tighter than in earlier studies in some interesting cases (Chen, Ann Inst Stat Math 42:387–401, 1990; Chen, Numer Funct Anal Optim 10:37–48, 1989; Cianciaruso, Numer Funct Anal Optim 24:713–723, 2003; Cianciaruso, Nonlinear Funct Anal Appl 2009; Dennis 1971; Deuflhard 2004; Deuflhard, SIAM J Numer Anal 16:1–10, 1979; Gutiérrez, J Comput Appl Math 79:131–145, 1997; Hernández, J Optim Theory Appl 109:631–648, 2001; Hernández, J Comput Appl Math 115:245–254, 2000; Huang, J Comput Appl Math 47:211–217, 1993; Kantorovich 1982; Miel, Numer Math 33:391–396, 1979; Miel, Math Comput 34:185–202, 1980; Moret, Computing 33:65–73, 1984; Potra, Libertas Mathematica 5:71–84, 1985; Rheinboldt, SIAM J Numer Anal 5:42–63, 1968; Yamamoto, Numer Math 51: 545–557, 1987; Zabrejko, Numer Funct Anal Optim 9:671–684, 1987; Zinc̆ko 1963). Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential
equation are also provided in this study. 相似文献
7.
We address two fundamental questions in the representation theory of affine Hecke algebras of classical types. One is an inductive
algorithm to compute characters of tempered modules, and the other is the determination of the constants in the formal degrees
of discrete series (in the form conjectured by Reeder (J. Reine Angew. Math. 520:37–93, 2000)). The former is completely different from the Lusztig-Shoji algorithm (Shoji in Invent. Math. 74:239–267, 1983; Lusztig in Ann. Math. 131:355–408, 1990), and it is more effective in a number of cases. The main idea in our proof is to introduce a new family of representations
which behave like tempered modules, but for which it is easier to analyze the effect of parameter specializations. Our proof
also requires a comparison of the C
∗-theoretic results of Opdam, Delorme, Slooten, Solleveld (J. Inst. Math. Jussieu 3:531–648, 2004; ; Int. Math. Res. Not., 2008; Adv. Math. 220:1549–1601, 2009; Acta Math. 205:105–187, 2010), and the geometric construction from Kato (Duke Math. J. 148:305–371, 2009; Am. J. Math. 133:518–553, 2011), Ciubotaru and Kato (Adv. Math. 226:1538–1590, 2011). 相似文献
8.
The existence of solution for the 2D-Keller-Segel system in the subcritical case, i.e. when the initial mass is less than
8π, is reproved. Instead of using the entropy in the free energy and free energy dissipation, which was used in the proofs (Blanchet
et al. in SIAM J. Numer. Anal. 46:691–721, 2008; Electron. J. Differ. Equ. Conf. 44:32, 2006 (electronic)), the potential energy term is fully utilized by adapting Delort’s theory on 2D incompressible Euler equation
(Delort in J. Am. Math. Soc. 4:553–386, 1991). 相似文献
9.
Gaku Sadasue 《Journal of Theoretical Probability》2008,21(3):571-585
Quasi-invariance of infinite product measures is studied when a locally compact second countable group acts on a standard
Borel space. A characterization of l
2-quasi-invariant infinite product measures is given. The group that leaves the measure class invariant is also studied. In
the case where the group acts on itself by translations, our result extends previous ones obtained by Shepp (Ann. Math. Stat.
36:1107–1112, 1965) and by Hora (Math. Z. 206:169–192, 1991; J. Theor. Probab. 5:71–100, 1992) to all connected Lie groups.
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10.
Lance Nielsen 《Acta Appl Math》2010,110(1):409-429
In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are
not necessarily analytic at the origin in ℂ
n
. The method of disentangling follows Feynman’s heuristic rules from in (Feynman in Phys. Rev. 84:18–128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and
Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ
n
while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that
the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established. 相似文献
11.
We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average
Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton
method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295,
2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study. 相似文献
12.
Yunyan Yang 《Annals of Global Analysis and Geometry》2011,40(4):411-425
Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci
curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound. This
partly extends previous a priori estimates of Li (J Geom Anal 17:495–511, 2007; Adv Math 223:1924–1957, 2010). 相似文献
13.
We prove induced Ramsey theorems in which the monochromatic induced subgraph satisfies that all members of a prescribed set
of its partial isomorphisms extend to automorphisms of the colored graph (without requirement of preservation of colors).
We consider vertex and edge colorings, and extensions of partial isomorphisms in the set of all partial isomorphisms between
singletons as considered by Babai and Sós (European J Combin 6(2):101–114, 1985), the set of all finite partial isomorphisms as considered by Hrushovski (Combinatorica 12(4):411–416, 1992), Herwig (Combinatorica 15:365–371, 1995) and Herwig-Lascar (Trans Amer Math Soc 5:1985–2021, 2000), and the set of all total isomorphisms. We observe that every finite graph embeds into a finite vertex transitive graph
by a so called bi-embedding, an embedding that is compatible with a monomorphism between the corresponding automorphism groups. We also show that every
countable graph bi-embeds into Rado’s universal countable graph Γ. 相似文献
14.
Ioannis K. Argyros 《Numerical Algorithms》2010,54(4):485-501
We provide a semilocal convergence analysis for a certain class of secant-like methods considered also in Argyros (J Math
Anal Appl 298:374–397, 2004, 2007), Potra (Libertas Mathematica 5:71–84, 1985), in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and
center-Lipschitz conditions for the computation of the upper bounds on the inverses of the linear operators involved, instead
of only Lipschitz conditions (Potra, Libertas Mathematica 5:71–84, 1985), we provide an analysis with the following advantages over the work in Potra (Libertas Mathematica 5:71–84, 1985) which improved the works in Bosarge and Falb (J Optim Theory Appl 4:156–166, 1969, Numer Math 14:264–286, 1970), Dennis (SIAM J Numer Anal 6(3):493–507, 1969, 1971), Kornstaedt (1975), Larsonen (Ann Acad Sci Fenn, A 450:1–10, 1969), Potra (L’Analyse Numérique et la Théorie de l’Approximation 8(2):203–214, 1979, Aplikace Mathematiky 26:111–120, 1981, 1982, Libertas Mathematica 5:71–84, 1985), Potra and Pták (Math Scand 46:236–250, 1980, Numer Func Anal Optim 2(1):107–120, 1980), Schmidt (Period Math Hung 9(3):241–247, 1978), Schmidt and Schwetlick (Computing 3:215–226, 1968), Traub (1964), Wolfe (Numer Math 31:153–174, 1978): larger convergence domain; weaker sufficient convergence conditions, finer error bounds on the distances involved, and
a more precise information on the location of the solution. Numerical examples further validating the results are also provided. 相似文献
15.
Recently, Roos (SIAM J Optim 16(4):1110–1136, 2006) presented a primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides
with the best known bound for infeasible interior-point algorithms. In the current paper we use a different feasibility step
such that the definition of the feasibility step in Mansouri and Roos (Optim Methods Softw 22(3):519–530, 2007) is a special case of our definition, and show that the same result on the order of iteration complexity can be obtained.
相似文献
16.
Sung-Geun Lim 《The Ramanujan Journal》2009,19(2):121-136
B.C. Berndt (J. Reine Angew. Math. 272:182–193, 1975; 304:332–365, 1978) has derived a number of new transformation formulas, in particular, the transformation formulae of the logarithms of the
classical theta functions, by using a transformation formula for a more general class of Eisenstein series. In this paper,
we continue his study. By using a transformation formula for a class of twisted generalized Eisenstein series, we generalize
a transformation formula given by J. Lehner (Duke Math. J. 8:631–655, 1941) and give a new proof for transformation formulas proved by Y. Yang (Bull. Lond. Math. Soc. 36:671–682, 2004).
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-214-C00003).
This work also partially supported by BK21-Postech CoDiMaRo. 相似文献
17.
We establish sharp L
2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [Guillemin and Uhlmann (Duke Math J 48:251–267,
1981), Melrose and Uhlmann (Commun Pure Appl Math 32:483–519, 1979)] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered
include both singular integral operators along curves in
\mathbb R2{\mathbb R^2} with simple inflection points and normal operators arising in linearized seismic imaging in the presence of fold caustics
[Felea (Comm PDE 30:1717–1740, 2005), Felea and Greenleaf (Comm PDE 33:45–77, 2008), Nolan (SIAM J Appl Math 61:659–672, 2000)]. 相似文献
18.
In this note we adopt the approach in Bonnit et al. (Czechoslov. Math. J. 60(2):527–539, 2010) to give a direct proof of some recent results in Haak and Le Merdy (Houst. J. Math., 2005) and Haak and Kunstmann (SIAM J. Control Optim. 45:2094–2118, 2007) which characterizes the L
p
-admissibility of type α depending on p of unbounded observation operators for bounded analytic semigroups. 相似文献
19.
Themba Dube 《Applied Categorical Structures》2009,17(1):63-73
Coz-unique frames were defined and characterized by Banaschewski and Gilmour (J Pure Appl Algebra 157:1–22, 2001). In this note we give further characterizations of these frames along the lines of characterizations of absolutely z-embedded spaces obtained by Blair and Hager (Math Z 136:41–52, 1974) on the one hand, and by Hager and Johnson (Canad J Math 20:389–393, 1968) on the other. We also extend to frames certain characterizations of z-embedded spaces; namely, we give a characterization of coz-onto frame homomorphisms in terms of normal covers.
相似文献
20.
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined
on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles,
rather than ordinary scalar-valued functions, are considered. In particular, we propose needlet-type spin wavelets as an extension of the needlet approach recently introduced by Narcowich et al. in SIAM J. Math. Anal. 38, 574–594 (2006) and J. Funct. Anal. 238, 530–564 (2006) and then considered for more general manifolds by Geller and Mayeli in Math. Z. 262, 895–927 (2009), Math. Z. 263, 235–264 (2009), and Indiana Univ. Math. J. (2009). We discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis
of spin random fields. Our results are strongly motivated by cosmological applications, in particular in connection to the
analysis of Cosmic Microwave Background polarization data. 相似文献