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1.
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
2.
Michel Hébert 《Applied Categorical Structures》2011,19(1):9-38
We describe a one-to-one correspondence between saturated weak factorization systems and weak reflections in categories C\mathcal{C} with finite products. This actually extends to an adjunction between the category of natural weak factorization systems on
C\mathcal{C} (in the sense of Grandis and Tholen, Arch Math 42:397–408, 2006, and Garner, arXiv preprint, 2007) and the category of monads on C\mathcal{C}. Explicit comparisons are made with the parallel result of Cassidy et al. (J Aust Math Soc 38:287–329, 1985), linking factorization systems and reflective subcategories. 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.
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
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.
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
7.
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
8.
In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601–628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453–1459, 1998) to get approximation of a compact space of homogeneous type by a uniform sequence of finite spaces of homogeneous type.
The convergence holds in the sense of a metric built on the Hausdorff distance between compact sets and on the Kantorovich-Rubinshtein
metric between measures.
The authors were supported by CONICET, CAI+D (UNL) and ANPCyT. 相似文献
9.
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
10.
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
11.
We introduce a new iterative method in order to approximate a locally unique solution of variational inclusions in Banach
spaces. The method uses only divided differences operators of order one. An existence–convergence theorem and a radius of
convergence are given under some conditions on divided difference operator and Lipschitz-like continuity property of set-valued
mappings. Our method extends the recent work related to the resolution of nonlinear equation in Argyros (J Math Anal Appl
332:97–108, 2007) and has the following advantages: faster convergence to the solution than all the previous known ones in Argyros and Hilout
(Appl Math Comput, 2008 in press), Hilout (J Math Anal Appl 339:53–761, 2008, Positivity 10:673–700, 2006), and we do not need to evaluate any Fréchet derivative. We provide also an improvement of the ratio of our algorithm under
some center-conditions and less computational cost. Numerical examples are also provided.
相似文献
12.
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
13.
Takemitsu Hasegawa Susumu Hibino Yohsuke Hosoda Ichizo Ninomiya 《Numerical Algorithms》2007,45(1-4):101-112
An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980) of adaptive type based on the Newton–Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani
(ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation
of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971).
相似文献
14.
Arnold, Falk, and Winther recently showed (Bull. Am. Math. Soc. 47:281–354, 2010) that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied
using the powerful, abstract language of Hilbert complexes. In another recent article (arXiv:), we extended the Arnold–Falk–Winther framework by analyzing variational crimes (à la Strang) on Hilbert complexes. In particular,
this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element
methods and recovering earlier a priori estimates for the Laplace–Beltrami operator on 2- and 3-surfaces, due to Dziuk (Lecture Notes in Math., vol. 1357:142–155,
1988) and later Demlow (SIAM J. Numer. Anal. 47:805–827, 2009), as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the
study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed
problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for
semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold–Falk–Winther results in the linear case. We also consider
the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate
application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces. 相似文献
15.
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
16.
A note on sensitivity of semigroup actions 总被引:1,自引:0,他引:1
It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several
authors: Banks, Brooks, Cairns, Davis and Stacey (Am. Math. Mon. 99, 332–334, 1992), Silverman (Rocky Mt. J. Math. 22, 353–375, 1992) and Glasner and Weiss (Nonlinearity 6, 1067–1075, 1993). In the latter article Glasner and Weiss established a stronger result (for compact metric systems) which implies that a
transitive non-minimal compact metric system (X,f) with dense set of almost periodic points is sensitive. This is true also for group actions as was proved in the book of
Glasner (Ergodic Theory via Joinings, 2003).
Our aim is to generalize these results in the frame of a unified approach for a wide class of topological semigroup actions
including one-parameter semigroup actions on Polish spaces. 相似文献
17.
Bayram Ṣahin 《Acta Appl Math》2010,109(3):829-847
Riemannian maps were introduced by Fischer (Contemp. Math. 132:331–366, 1992) as a generalization isometric immersions and Riemannian submersions. He showed that such maps could be used to solve the
generalized eikonal equation and to build a quantum model. On the other hand, horizontally conformal maps were defined by
Fuglede (Ann. Inst. Fourier (Grenoble) 28:107–144, 1978) and Ishihara (J. Math. Kyoto Univ. 19:215–229, 1979) and these maps are useful for characterization of harmonic morphisms. Horizontally conformal maps (conformal maps) have
their applications in medical imaging (brain imaging)and computer graphics. In this paper, as a generalization of Riemannian
maps and horizontally conformal submersions, we introduce conformal Riemannian maps, present examples and characterizations.
We show that an application of conformal Riemannian maps can be made in weakening the horizontal conformal version of Hermann’s
theorem obtained by Okrut (Math. Notes 66(1):94–104, 1999). We also give a geometric characterization of harmonic conformal Riemannian maps and obtain decomposition theorems by using
the existence of conformal Riemannian maps. 相似文献
18.
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
19.
Jorge Aragona Roseli Fernandez Stanley O. Juriaans Michael Oberguggenberger 《Monatshefte für Mathematik》2012,88(1):1-18
In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144:13–29,
2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on
generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al.
(Monatsh. Math. 144:13–29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat
Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like
the inverse and implicit function theorems and Green’s theorem, are transferred to the generalized setting. Further, we indicate
that solution formulas for transport and wave equations with generalized initial data can be obtained as well. 相似文献
20.
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