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1.
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
2.
We consider a two-phase problem in thermal conductivity: inclusions filled with a material of conductivity σ
1 are layered in a body of conductivity σ
2. We address the shape sensitivity of the first eigenvalue associated with Dirichlet boundary conditions when both the boundaries
of the inclusions and the body can be modified. We prove a differentiability result and provide the expressions of the first
and second order derivatives. We apply the results to the optimal design of an insulated body. We prove the stability of the
optimal design thanks to a second order analysis. We also continue the study of an extremal eigenvalue problem for a two-phase
conductor in a ball initiated by Conca et al. (Appl. Math. Optim. 60(2):173–184, 2009) and pursued in Conca et al. (CANUM 2008, ESAIM Proc., vol. 27, pp. 311–321, EDP Sci., Les Ulis, 2009). 相似文献
3.
Frédéric Bernicot 《Journal of Geometric Analysis》2010,20(1):39-62
In this paper we construct a new class of bilinear pseudodifferential operators which contains both the Coifman-Meyer class
as well as the non-translation invariant class closely related both to the bilinear Hilbert transform and previously studied
in Bényi et al. (J. Geom. Anal. 16(3):431–453, 2006), Bényi et al. (J. Anal. Math., 2009), Bernicot (Anal. PDE 1:1–27, 2008) as well as the bilinear Marcinkiewicz class studied in Grafakos and Kalton (Stud. Math. 146(2):115–156, 2001). We prove boundedness on Sobolev spaces for these operators as well as establish a symbolic calculus that exhibits the nice
behavior of our new class under transposition and composition with linear operators. 相似文献
4.
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
5.
Hurwitz numbers count genus g, degree d covers of ℙ1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piece-wise linear objects called tropical curves. This paper develops a tropical
counterpart of the branch map and shows that its degree recovers classical Hurwitz numbers. Further, the combinatorial techniques
developed are applied to recover results of Goulden et al. (in Adv. Math. 198:43–92, 2005) and Shadrin et al. (in Adv. Math. 217(1):79–96, 2008) on the piecewise polynomial structure of double Hurwitz numbers in genus 0. 相似文献
6.
Song Heng Chan 《The Ramanujan Journal》2009,20(1):69-79
We present a new proof of a general transformation formula for basic hypergeometric series that was discovered by D.B. Sears
(Proc. Lond. Math. Soc. 53(2): 181–191, 1951) and discuss some special cases. Next we apply Sears’s general transformation to give an extension of a result of Andrews
et al. (Duke Math. J. 108: 395–419, 2001). 相似文献
7.
Deckelnick and Dziuk (Math. Comput. 78(266):645–671, 2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of the elastic flow
of closed curves in
\mathbbRd, d 3 2{\mathbb{R}^d, d\geq2} . We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of
the features of the formulations in Barrett et al. (J Comput Phys 222(1): 441–462, 2007; SIAM J Sci Comput 31(1):225–253, 2008; IMA J Numer Anal 30(1):4–60, 2010), in particular an equidistribution mesh property. For this new approximation, we obtain also a stability bound for a continuous-in-time
semidiscrete scheme. Apart from the isotropic situation, we also consider the case of an anisotropic elastic energy. In addition
to the evolution of closed curves, we also consider the isotropic and anisotropic elastic flow of a single open curve in the
plane and in higher codimension that satisfies various boundary conditions. 相似文献
8.
9.
In this paper, we establish the local well-posedness for the quasi-geostrophic equations and obtain a blow-up criterion of
smooth solutions in the framework of Triebel-Lizorkin-Lorentz spaces by adapting a method in Chen-Miao-Zhang (Arch. Rational
Mech. Anal. 195: 2010, 561–578). Our new function spaces contain the classical Triebel-Lizorkin spaces and Sobolev spaces, and thus the corresponding
results generalize several known ones, for instance, Chae (Nonlinearity 16: 2003, 479–495) and Castro et al. (Nonlinearity 22: 2009, 1791–1815). The main ingredients of our proofs are Littlewood–Paley decomposition and the paradifferential calculus. 相似文献
10.
In this paper, optimal derivative design when multiple firms compete for heterogenous customers is studied. Ties in the agents’
best responses generate discontinuous payoffs. Efficient tie-breaking rules are considered: In a first step, the model presented
by Carlier et al. (Math Financ Econ 1:57–80, 2007) is extended, and results of Page and Monteiro (J Math Econ 39:63–109, 2003, J Econ Theory 134:566–575, 2007, Econ Theory 34:503–524, 2008) are used to prove the existence of (mixed-strategies) Nash equilibria. In a second step, the case of risk minimizing firms
is studied. Socially efficient allocations are introduced, and their existence is proved. In particular, the entropic risk
measure is considered. 相似文献
11.
R. Abreu-Blaya J. Bory-Reyes F. Brackx H. De Schepper F. Sommen 《Complex Analysis and Operator Theory》2012,6(2):359-372
We consider H?lder continuous circulant (2 × 2) matrix functions G12{{\bf G}^1_2} defined on the fractal boundary Γ of a Jordan domain Ω in
\mathbbR2n{\mathbb{R}^{2n}}. The main goal is to establish a Hilbert transform for such functions, within the framework of Hermitian Clifford analysis.
This is a higher dimensional function theory centered around the simultaneous null solutions of two first order vector valued
differential operators, called Hermitian Dirac operators. In Brackx et al. (Bull Braz Math Soc 40(3): 395–416, 2009) a Hermitian Cauchy integral was constructed by means of a matrix approach using circulant (2 × 2) matrix functions, from
which a Hilbert transform was derived in Brackx et al. (J Math Anal Appl 344: 1068–1078, 2008) for the case of domains with smooth boundary. However, crucial parts of the method are not extendable to the case where
the boundary of the considered domain is fractal. At present we propose an alternative approach which will enable us to define
a new Hermitian Hilbert transform in that case. As a consequence, we give necessary and sufficient conditions for the Hermitian
monogenicity of a circulant matrix function G12{{\bf G}^1_2} in the interior and exterior of Ω, in terms of its boundary value g12=G12|G{{\bf g}^1_2={\bf G}^1_2|_\Gamma}, extending in this way also results of Abreu Blaya et al. (Bound. Value Probl. 2008: 2008) (article ID 425256), (article ID 385874), where Γ is required to be Ahlfors–David regular. 相似文献
12.
In this paper we analyze the hydrodynamic equations for Ginzburg–Landau vortices as derived by E (Phys. Rev. B. 50(3):1126–1135,
1994). In particular, we are interested in the mean field model describing the evolution of two patches of vortices with equal
and opposite degrees. Many results are already available for the case of a single density of vortices with uniform degree.
This model does not take into account the vortex annihilation, hence it can also be seen as a particular instance of the signed
measures system obtained in Ambrosio et al. (Ann. Inst. H. Poincaré Anal. Non Linéaire 28(2):217–246, 2011) and related to the Chapman et al. (Eur. J. Appl. Math. 7(2):97–111, 1996) formulation. We establish global existence of L
p
solutions, exploiting some optimal transport techniques introduced in this context in Ambrosio and Serfaty (Commun. Pure
Appl. Math. LXI(11):1495–1539, 2008). We prove uniqueness for L
∞ solutions, as expected by analogy with the incompressible Euler equations in fluidodynamics. We also consider the corresponding
Dirichlet problem in a bounded domain. Moreover, we show some simple examples of 1-dimensional dynamic. 相似文献
13.
In this paper, we introduce two iterative schemes (one implicit and one explicit) for finding a common element of the set
of solutions of the generalized equilibrium problems and the set of all common fixed points of a nonexpansive semigroup in
the framework of a real Hilbert space. We prove that both approaches converge strongly to a common element of such two sets.
Such common element is the unique solution of a variational inequality, which is the optimality condition for a minimization
problem. Furthermore, we utilize the main results to obtain two mean ergodic theorems for nonexpansive mappings in a Hilbert
space. The results of this paper extend and improve the results of Li et al. (J Nonlinear Anal 70:3065–3071, 2009), Cianciaruso et al. (J Optim Theory Appl 146:491–509, 2010) and many others. 相似文献
14.
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
15.
Pao-sheng Shen 《Computational Statistics》2011,26(3):521-537
We analyze left-truncated and right-censored (LTRC) data using semiparametric transformation models. It is demonstrated that
the approach of Chen et al. (Biometrika 89: 659–668, 2002) can be extended to LTRC data. Furthermore, when covariates are discrete, similar to the approach of Cai and Cheng (Biometrika
91: 277–290, 2004), we propose an alternative estimator. A simulation study is conducted to investigate the performance of the proposed estimators. 相似文献
16.
In this paper we describe how techniques of asymptotic analysis can be used in a systematic way to perform ‘aggregation’ of
variables, based on a separation of different time scales, in a population model with age and space structure. The main result
of the paper is proving the convergence of the formal asymptotic expansion to the solution of the original equation. This
result improves and clarifies earlier results of Arino et al. (SIAM J Appl Math 60(2):408–436, 1999), Auger et al. (Structured population models in biology and epidemiology. Springer Verlag, Berlin, 2008), Lisi and Totaro (Math Biosci 196(2):153–186, 2005). 相似文献
17.
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
18.
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated
multiresolution transforms. As soon as a nonlinear scheme can be written as a specific perturbation of a linear and convergent
subdivision scheme, we show that if some contractivity properties are satisfied, then stability and convergence can be achieved.
This approach is applied to various schemes, which give different new results. More precisely, we study uncentered Lagrange
interpolatory linear schemes, WENO scheme (Liu et al., J Comput Phys 115:200–212, 1994), PPH and Power-P schemes (Amat and Liandrat, Appl Comput Harmon Anal 18(2):198–206, 2005; Serna and Marquina, J Comput Phys 194:632–658, 2004) and a nonlinear scheme using local spherical coordinates (Aspert et al., Comput Aided Geom Des 20:165–187, 2003). Finally, a stability proof is given for the multiresolution transform associated to a nonlinear scheme of Marinov et al.
(2005). 相似文献
19.
This paper systematically studies numerical solution of fourth order problems in any dimensions by use of the Morley–Wang–Xu
(MWX) element discretization combined with two-grid methods (Xu and Zhou (Math Comp 69:881–909, 1999)). Since the coarse and fine finite element spaces are nonnested, two intergrid transfer operators are first constructed
in any dimensions technically, based on which two classes of local and parallel algorithms are then devised for solving such
problems. Following some ideas in (Xu and Zhou (Math Comp 69:881–909, 1999)), the intrinsic derivation of error analysis for nonconforming finite element methods of fourth order problems (Huang et al.
(Appl Numer Math 37:519–533, 2001); Huang et al. (Sci China Ser A 49:109–120, 2006)), and the error estimates for the intergrid transfer operators, we prove that the discrete energy errors of the two classes
of methods are of the sizes O(h + H
2) and O(h + H
2(H/h)(d−1)/2), respectively. Here, H and h denote respectively the mesh sizes of the coarse and fine finite element triangulations, and d indicates the space dimension of the solution region. Numerical results are performed to support the theory obtained and
to compare the numerical performance of several local and parallel algorithms using different intergrid transfer operators. 相似文献
20.
In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145–210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms
arising in the analytic torsion due to the boundary, using generalizations of the Cheeger–Müller theorem. We use a formula
proved by Brüning and Ma (GAFA 16:767–873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary
(Lück, J Diff Geom 37:263–322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion
for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also
consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695–714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529–533, 2009). 相似文献