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2. Construction of weak solutions to compressible Navier–Stokes equations with general inflow/outflow boundary conditions via a numerical approximation.
- Author
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Kwon, Young-Sam and Novotný, Antonin
- Subjects
NAVIER-Stokes equations ,HARMONIC analysis (Mathematics) ,DIFFERENTIAL geometry ,NUMERICAL analysis ,MATHEMATICS ,FUNCTIONAL analysis - Abstract
The construction of weak solutions to compressible Navier–Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in Karper (Numer Math, 125(3):441–510, 2013) for the no slip boundary conditions and the isentropic pressure with adiabatic coefficient γ > 3 . Here we consider the same problem for the general non zero inflow–outflow boundary conditions, which is definitely more appropriate setting from the point of view of applications, but which is essentially more involved as far as the existence of weak solutions is concerned. There is a few recent proofs of existence of weak solutions in this setting, but none of them is performed via a numerical method. The goal of this paper is to fill this gap. The existence of weak solutions on the continuous level requires several tools of functional and harmonic analysis and differential geometry whose numerical counterparts are not known. Our main strategy therefore consists in rewriting of the numerical scheme in its variational form modulo remainders and to apply and/or to adapt to the new variational formulation the tools developed in the theoretical analysis. In addition to the result, which is new, the synergy between numerical and theoretical analysis is the main originality of the present paper. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. On Weak Generalized Stability of Random Variables via Functional Equations.
- Author
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Jarczyk, Witold, Járai, Antal, Matkowski, Janusz, and Misiewicz, Jolanta
- Subjects
FUNCTIONAL equations ,CHARACTERISTIC functions ,FUNCTIONAL analysis ,MATHEMATICS ,EQUATIONS - Abstract
In this paper we characterize random variables which are stable but not strictly stable in the sense of generalized convolution. We generalize the results obtained in Jarczyk and Misiewicz (J Theoret Probab 22:482-505, 2009), Misiewicz and Mazurkiewicz (J Theoret Probab 18:837-852, 2005), Oleszkiewicz (in Milman VD and Schechtman Lecture Notes in Math. 1807, Geometric Aspects of Functional Analysis (2003), Israel Seminar 2001–2002, Springer-Verlag, Berlin). The main problem was to find the solution of the following functional equation for symmetric generalized characteristic functions φ , ψ : ∀ a , b ≥ 0 ∃ c (a , b) ≥ 0 ∃ d (a , b) ≥ 0 ∀ t ≥ 0 φ (a t) φ (b t) = φ (c (a , b) t) ψ (d (a , b) t) , (A) where both functions c and d are continuous, symmetric, homogeneous but unknown. We give the solution of equation (A) assuming that for fixed ψ , c , d there exist at least two different solutions of (A). To solve (A) we also determine the functions that satisfy the equation (f (t (x + y)) - f (t x)) (f (x + y) - f (y)) = (f (t (x + y)) - f (t y)) (f (x + y) - f (x)) , (B) x , y , t > 0 , for a function f : (0 , ∞) → R . As an additional result we infer that each Lebesgue measurable or Baire measurable function f satisfying equation (B) is infinitely differentiable. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. Fruitful and helpful ordinal functions.
- Author
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Simmons, Harold
- Subjects
ORDINAL numbers ,FUNCTION spaces ,FUNCTIONAL analysis ,MATHEMATICAL logic ,MATHEMATICS - Abstract
In Simmons (Arch Math Logic 43:65–83, 2004), I described a method of producing ordinal notations ‘from below’ (for countable ordinals up to the Howard ordinal) and compared that method with the current popular ‘from above’ method which uses a collapsing function from uncountable ordinals. This ‘from below’ method employs a slight generalization of the normal function—the fruitful functions—and what seems to be a new class of functions—the helpful functions—which exist at all levels of the function space hierarchy over ordinals. Unfortunately, I was rather sparing in my description of these classes of functions. In this paper I am much more generous. I describe the properties of the helpful functions on all finite levels and, in the final section, indicate how they can be used to simplify the generation of ordinal notations. The main aim of this paper is to fill in the details missing from [7]. The secondary aim is to indicate what can be done with helpful functions. Fuller details of this development will appear elsewhere. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
5. Approximation of Periodic Solutions of a System of Periodic Linear Nonhomogeneous Differential Equations.
- Author
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Alexandr Fischer
- Subjects
APPROXIMATION theory ,FUNCTIONAL analysis ,DIFFERENTIAL equations ,LINEAR systems ,MATHEMATICS - Abstract
Abstract The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid. [ABSTRACT FROM AUTHOR]
- Published
- 2004
6. A Sup-Function Approach to Linear Semi-Infinite Optimization.
- Author
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Goberna, M. A., López, M. A., and Todorov, M. I.
- Subjects
LINEAR programming ,MATHEMATICAL programming ,CONVEX domains ,FUNCTIONAL analysis ,MATHEMATICS - Abstract
In this paper, we consider linear semi-infinite programming problems and the possibility of having no active constraint at a boundary point of the corresponding feasible set. This phenomenon causes serious troubles when one intends to construct the cone of feasible directions at this point. The main feature of our approach consists of exploiting the (sub)differential properties of the sup-function that allows replacing infinitely many constraints with a unique convex constraint. In the case where the set of active constraints is empty, this sup-function can present a quite abnormal behavior. To face this situation, two families of relaxed active constraint sets are introduced in the paper, and the relationship between them is studied in detail. Under the so-called strong Slater condition, we obtain two different formulas for the polar of the cone of feasible directions. They are derived through an extension of Valadier's formula for the subdifferential of a sup-function. Finally, a stability result is given for the most relevant mapping in our context. [ABSTRACT FROM AUTHOR]
- Published
- 2003
- Full Text
- View/download PDF
7. Functional inequalities, regularity and computation of the deficit and surplus variables in the financial equilibrium problem.
- Author
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Daniele, Patrizia, Giuffrè, Sofia, and Lorino, Mariagrazia
- Subjects
MATHEMATICAL inequalities ,MATHEMATICS ,EQUILIBRIUM ,LIABILITIES (Accounting) ,FUNCTIONAL analysis - Abstract
This paper is concerned with a general model of financial flows and prices related to individual entities, called sectors, which invest in financial instruments as assets and as liabilities. In particular, using delicate tools of Functional Analysis, besides existence results of financial equilibrium, in the dual formulation, the Lagrange functions $$\rho _j^{*1}(t)$$ and $$\rho _j^{*2}(t)$$ , called 'deficit' and 'surplus' variables, appear and reveal to be very relevant in order to analyze the financial model and the possible insolvencies, which can lead to a financial contagion. In the paper the continuity of these Lagrange functions is proved. Finally, a procedure for the calculus of these variables is suggested. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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8. Further Reading.
- Author
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Axler, S., Ribet, K. A., Martínez-Avendaño, Rubén A., and Rosenthal, Peter
- Abstract
This book is merely an introduction to a vast subject. There is a great deal of additional knowledge concerning these topics, and there are a number of excellent books and expository papers treating much of that material. We briefly describe some of these expositions in order to make it easier for the reader to pursue further study. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
9. Modified Hochschild and Periodic Cyclic Homology.
- Author
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Burghelea, Dan, Melrose, Richard, Mishchenko, Alexander S., Troitsky, Evgenij V., and Teleman, Nicolae
- Abstract
The Hochschild and (periodic) cyclic homology of Banach algebras are either trivial or not interesting, see Connes [2], [4], [6]. To correct this deficiency, Connes [3] had produced the entire cyclic cohomology (see also [4], [6], [5]). The entire cyclic cochains are elements of the infinite product (b,B) cohomology bi-complex which satisfy a certain bidegree asymptotic growth condition. The entire cyclic cohomology is a natural target for the asymptotic Chern character of θ-summable Fredholm modules. More recently, Puschnigg [15] introduced the local cyclic cohomology based on precompact subsets of the algebra in an inductive limits system setting. The main purpose of this paper is to create an analogue of the Hochschild and periodic cyclic homology which gives the right result (i.e., the ordinary ℤ2-graded Alexander-Spanier co-homology of the manifold) when applied, at least, onto the algebra of continuous functions on topological manifolds and CW-complexes. This is realized by replacing the Connes periodic bi-complex (b,B), see Connes [2], [4] and Loday [12], by the bi-complex ($$ \tilde b $$, d), where the operator $$ \tilde b $$ is obtained by blending the Hochschild boundary b with the Alexander-Spanier boundary d; the operator $$ \tilde b $$ anti-commutes with the operator d. The homologies of these complexes will be called modified Hochschild, resp. modified periodic cyclic homology. Our construction uses in addition to the algebraic structure solely the locality relationship extracted from the topological structure of the algebra. The modified periodic cyclic homology is invariant under continuous homotopies, while the others are invariant at smooth homotopies (diffeotopies) only. The modified Hochschild and periodic cyclic homology are directly connected to the Alexander-Spanier cohomology. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
10. Higher Algebraic K-Theory of Schemes and of Derived Categories.
- Author
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Cartier, Pierre, Katz, Nicholas M., Manin, Yuri I., Illusie, Luc, Laumon, Gérard, Ribet, Kenneth A., Thomason, R. W., and Trobaugh, Thomas
- Abstract
In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of those perfect complexes on the scheme which are acyclic on the open subscheme. The localization theorem of Quillen [Q1] for K′- or G-theory is the main support of his many results on the G-theory of noetherian schemes. The previous lack of an adequate localization theorem for K-theory has obstructed development of this theory for the fifteen years since 1973. Hence our theorem unleashes a pack of new basic results hitherto known only under very restrictive hypotheses like regularity. These new results include the "Bass fundamental theorem" 6.6, the Zariski (Nisnevich) cohomological descent spectral sequence that reduces problems to the case of local (hensel local) rings 10.3 and 19.8, the Mayer-Vietoris theorem for open covers 8.1, invariance mod ℓ under polynomial extensions 9.5, Vorst-van der Kallen theory for NK 9.12, Goodwillie and Ogle-Weibel theorems relating K-theory to cyclic cohomology 9.10, mod ℓ Mayer-Vietoris for closed covers 9.8, and mod ℓ comparison between algebraic and topological K-theory 11.5 and 11.9. Indeed most known results in K-theory can be improved by the methods of this paper, by removing now unnecessary regularity, affineness, and other hypotheses. [ABSTRACT FROM AUTHOR]
- Published
- 1990
- Full Text
- View/download PDF
11. On adaptive estimation of probability density functions.
- Author
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Ibragimov, I. A
- Subjects
DENSITY functionals ,PROBABILITY theory ,MATHEMATICAL inequalities ,FUNCTIONAL analysis ,MATHEMATICS - Abstract
The paper presents a method of adaptive estimation for a class of probability density functions. This method is a continual analog of some known methods. Bibiligraphy: 10 titles. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
12. Best m-term one-sided trigonometric approximation of some function classes defined by a kind of multipliers.
- Author
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Ren Suo Li and Yong Ping Liu
- Subjects
FUNCTIONAL analysis ,APPROXIMATION theory ,TRIGONOMETRIC functions ,MULTIPLIERS (Mathematical analysis) ,MATHEMATICS - Abstract
In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
13. An error bound of the Ritz method for a singular second-order differential equation.
- Author
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Yakovlev, M.
- Subjects
DIFFERENTIAL equations ,FUNCTIONAL analysis ,BESSEL functions ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
The paper presents an error bound of the Ritz method for the problem of minimizing the functional in the space $$ {\mathop W\limits^{\text{o}} }^{1}_{2} {\left( {0,1} \right)} $$ in the case where the standard assumption on the continuity of q(t) is replaced by the condition q
2 (t)t(1-t) ∈ L(0,1). In the case where q(t) is continuous, the new bound is sharper than the known one. Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
14. Optimal recovery on the classes of functions with bounded mixed derivative.
- Author
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Gen Fang and Li Duan
- Subjects
MATHEMATICAL functions ,SOBOLEV spaces ,FUNCTION spaces ,FUNCTIONAL analysis ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L
p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
15. Robust Observer Design for a Class of Nonlinear Systems Using the System Internal Dynamics Structure.
- Author
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Diao, Z. F. and Yan, X. G.
- Subjects
NONLINEAR systems ,SYSTEMS theory ,LYAPUNOV functions ,DIFFERENTIAL equations ,FUNCTIONAL analysis ,DYNAMICS ,MATHEMATICS - Abstract
In this paper, an observer design strategy is presented for a class of nonlinear systems with structural uncertainty. The modern geometric approach is exploited to simplify the system structure. Then, based on the Lyapunov direct method, a robust observer is proposed using the system internal dynamics structure and the distribution of the uncertainty structure. The bound on the uncertainty, which is employed in the observer design, is allowed to be nonlinear and have a more general form. Simulation shows that the proposed approach is effective. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
16. Connectedness of the Set of Efficient Solutions for Generalized Systems.
- Author
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Gong, X. H. and Yao, J. C.
- Subjects
VECTOR spaces ,FUNCTIONAL analysis ,VECTOR analysis ,MONOTONE operators ,COMPLEX numbers ,LINEAR algebra ,OPERATOR theory ,GENERALIZED spaces ,MATHEMATICS - Abstract
We introduce the concept of positive proper efficient solutions to the generalized system in this paper. We show that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of efficient solutions to the generalized system. We discuss also the connectedness of the set of efficient solutions for the generalized system with monotone bifunctions in real locally convex Hausdorff topological vector spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
17. Sequences of 0’s and 1’s: Special sequence spaces with the separable Hahn property.
- Author
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Boos, J. and Leiger, T.
- Subjects
INTEGRAL theorems ,VECTOR topology ,SEQUENCE spaces ,FUNCTIONAL analysis ,MATRICES (Mathematics) ,MATHEMATICS - Abstract
As pointed out in [4] the paper [2], authored by G. Bennett, J. Boos and T. Leiger, contains a nontrivial gap in the argumentation of the proof of Theorem 5.2 which is one of main results of that paper and has been applied three times. Till now neither the gap is closed nor a counterexample has been stated. That is why the authors have examined in [4] the situation around the ‘gap’ aiming to a better understanding for the gap. The aim of this paper is to prove the mentioned applications of the theorem in doubt by using gliding hump arguments (quite similar to the classical proofs of the Theorems of Schur and Hahn in the first case (cf. [3]) and a very technical and artful construction, being of independent mathematical interest, in the second case). [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
18. LefschetzâVerdier Trace Formula and a Generalization of a Theorem of Fujiwara.
- Author
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Yakov Varshavsky
- Subjects
FUNCTIONAL analysis ,GEOMETRY ,MATHEMATICS ,SCIENCE - Abstract
Abstract.  The goal of this paper is to generalize a theorem of Fujiwara (Deligneâs conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the LefschetzâVerdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
19. Quasiperiodic Solutions for Dissipative Boussinesq Systems.
- Author
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Valls, Claudia
- Subjects
PERTURBATION theory ,FUNCTIONAL analysis ,APPROXIMATION theory ,WATER waves ,MATHEMATICS ,WAVE resistance (Hydrodynamics) ,HYDRODYNAMICS - Abstract
In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems where α, β, c > 0 are parameters. Those systems model two-dimensional small amplitude long wavelength water waves. For α ≤ 1, this equation is ill-posed and most initial conditions do not lead to solutions. Nevertheless, we show that, for almost every β, c and almost every α ≤ 1, it admits solutions that are quasiperiodic in time. The proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the Boussinesq system to the center manifold, uses arguments of classical perturbation theory by considering the Hamiltonian formulation of the problem and studying the Birkhoff normal form. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
20. Some categorical properties of the functors O τ and O R of weakly additive functionals.
- Author
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Zaitov, A.
- Subjects
FUNCTIONALS ,FUNCTIONAL analysis ,MATHEMATICAL functions ,MATHEMATICAL mappings ,MATHEMATICS - Abstract
In the paper, the spaces of weakly additive τ-smooth and Radon functionals are investigated. It is proved that the functors of weakly additive τ-smooth and Radon functionals weakly preserve the density of Tychonoff spaces, and the functor of weakly additive τ-smooth functionals forms a monad in the category of Tychonoff spaces and their continuous mappings. Examples and remarks are given showing that these functors fail to satisfy certain Shchepin normality conditions. Problems having positive solutions for normal functors are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
21. On Almost Isometric Embedding from C(Ω) into C0(Ω0).
- Author
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Guang Gui Ding
- Subjects
FUNCTIONAL analysis ,OPERATOR theory ,FUNCTIONAL equations ,INTEGRAL equations ,MATHEMATICS - Abstract
In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C
0 (Ω0 ). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0 (Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]- Published
- 2005
- Full Text
- View/download PDF
22. Strong Approximation by Cesàro Means with Critical Index in the Hardy SpacesHp(0<pࣘ 1).
- Author
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Feng Dai and Kun Wang
- Subjects
APPROXIMATION theory ,FUNCTIONAL analysis ,HARDY spaces ,COMPLEX variables ,EUCLIDEAN algorithm ,MATHEMATICS - Abstract
Letbe a unit sphere of thed-dimensional Euclidean space R
d and let(0 < p= 1) denote the real Hardy space onFor 0 < p= 1 andletEj (f,Hp ) (j= 0, 1, ...) be the best approximation offby spherical polynomials of degree less than or equal toj, in the spaceGiven a distributionfonits Cesàro mean of order d>-1 is denoted byFor 0p. In this paper, the following result is proved:TheoremLet0
N(f)˜B
N (f)means that there’s a positive constant C, independent of N and f, such thatIn the cased= 2,this result was proved by Belinskii in 1996. [ABSTRACT FROM AUTHOR]- Published
- 2005
- Full Text
- View/download PDF
23. Undecidability without Arithmetization.
- Author
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Andrzej Grzegorczyk
- Subjects
MATHEMATICS ,FUNCTIONAL analysis ,MATHEMATICAL analysis ,MATHEMATICAL functions - Abstract
Abstract In the present paper the well-known Gdels Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
24. Inverse Analysis of Magnetic Charge Densities using Discrete Fourier Transform with Tikhonov Regularization.
- Author
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Kojima, Fumio and Ito, Kazufumi
- Subjects
MAGNETIC fields ,FUNCTIONAL analysis ,GEOMAGNETISM ,MAGNETICS ,ELECTROMAGNETIC induction ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
This paper is concerned with a computational method for recovering induced magnetic fields due to the existence of surface or subsurface cracks. The inversion formula can be simply represented by an integral equation of the first kind. The problem is transformed into a well-posed difference equation using output least squares approach with a Tikhonov regularization. A fast computational algorithm is also proposed using discrete Fourier convolution techniques. [ABSTRACT FROM AUTHOR]
- Published
- 2004
25. Scattering of SH wave by a crack terminating at the interface of a bimaterial.
- Author
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Lu, J.-F. and Hanyga, A.
- Subjects
FUNCTIONAL analysis ,FOURIER transforms ,RECIPROCITY theorems ,MATHEMATICS ,FUNCTIONAL equations ,FOURIER analysis - Abstract
A general method for solving the scattering of plane SH wave by a crack terminating at the interface of a bimaterial is presented. The crack can terminate at the interface in an arbitrary angle. In order to solve the proposed problem, the Green’s function for a point harmonic force applied at an arbitrary point of the bimaterial is established by the Fourier transformation method. Using the obtained Green’s function and the Betti-Rayleigh reciprocal theorem, the total scattered field of the crack is constructed. The total scattered field of the crack is divided into a regular part and a singular part. The hypersingular integral equation of the crack is obtained in terms of the regular and singular scattered field as well as the free wave field. The stress singularity order and singular stress at the terminating point are analyzed by the hypersingular integral equation and the singular scattered field of the crack. The dynamic stress intensity factor (DSIF) at the terminating point is defined in terms of the singular stresses at the terminating point. Numerical solution of the hypersingular integral equation gives the DSIFs at the crack tips. Comparison of our results with known results confirms the proposed method. Some numerical results and corresponding analysis are given in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
26. The structure of the minimum size supertail of a subspace partition.
- Author
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Năstase, Esmeralda and Sissokho, Papa
- Subjects
VECTOR spaces ,INTEGERS ,LINEAR algebra ,FUNCTIONAL analysis ,MATHEMATICS - Abstract
Let $$V=V(n,q)$$ denote the vector space of dimension n over the finite field with q elements. A subspace partition $$\mathcal {P}$$ of V is a collection of nontrivial subspaces of V such that each nonzero vector of V is in exactly one subspace of $$\mathcal {P}$$ . For any integer d, the d -supertail of $$\mathcal {P}$$ is the set of subspaces in $$\mathcal {P}$$ of dimension less than d, and it is denoted by ST. Let $$\sigma _q(n,t)$$ denote the minimum number of subspaces in any subspace partition of V in which the largest subspace has dimension t. It was shown by Heden et al. that $$|ST|\ge \sigma _q(d,t)$$ , where t is the largest dimension of a subspace in ST. In this paper, we show that if $$|ST|=\sigma _q(d,t)$$ , then the union of all the subspaces in ST constitutes a subspace under certain conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
27. On cyclic and $$n$$ -cyclic monotonicity of bifunctions.
- Author
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Alizadeh, M., Bianchi, M., Hadjisavvas, N., and Pini, R.
- Subjects
MONOTONE operators ,OPERATOR theory ,FUNCTIONAL analysis ,DIFFERENTIAL equations ,MATHEMATICS - Abstract
In the recent literature, the connection between maximal monotone operators and the Fitzpatrick function is investigated. Subsequently, this relation has been extended to maximal monotone bifunctions and their Fitzpatrick transform. In this paper we generalize some of these results to maximal $$n$$ -cyclically monotone and maximal cyclically monotone bifunctions, by introducing and studying the Fitzpatrick transforms of order $$n$$ or infinite order for bifunctions. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
28. Elliptic Theory on Manifolds with Corners: I. Dual Manifolds and Pseudodifferential Operators.
- Author
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Burghelea, Dan, Melrose, Richard, Mishchenko, Alexander S., Troitsky, Evgenij V., Nazaikinskii, Vladimir, Savin, Anton, and Sternin, Boris
- Abstract
In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in C*-algebras. In the second part, these results will be applied to the solution of Gelfand's problem on the homotopy classification of elliptic operators for the case of manifolds with corners. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
29. Torsion, as a Function on the Space of Representations.
- Author
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Burghelea, Dan, Melrose, Richard, Mishchenko, Alexander S., Troitsky, Evgenij V., and Haller, Stefan
- Abstract
Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex-valued Ray-Singer torsion, the Milnor-Turaev torsion, and the dynamical torsion. They are associated essentially to a closed smooth manifold equipped with a (co)Euler structure and a Riemannian metric in the first case, a smooth triangulation in the second case, and a smooth flow of type described in Section 2 in the third case. In this paper we define these functions, describe some of their properties and calculate them in some case. We conjecture that they are essentially equal and have analytic continuation to rational functions on the variety of representations. We discuss what we know to be true. As particular cases of our torsion, we recognize familiar rational functions in topology such as the Lefschetz zeta function of a diffeomorphism, the dynamical zeta function of closed trajectories, and the Alexander polynomial of a knot. A numerical invariant derived from Ray-Singer torsion and associated to two homotopic acyclic representations is discussed in the last section. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
30. Positive Operators on Lp-spaces.
- Author
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Boulabiar, Karim, Buskes, Gerard, Triki, Abdelmajid, and Schep, Anton R.
- Abstract
Throughout this paper we denote by Lp the Banach lattice of p-integrable functions on a σ-finite measure space (X, B, μ), where 1 ≤ p ≤ ∞. We will consider those aspects of the theory of positive linear operators, which are in some way special due to the fact the operators are acting on Lp-spaces. For general information about positive operators on Banach lattices we refer to the texts [1]. [20], and [36]. Our focus on Lp-spaces does not mean that in special cases some of the results can not be extended to a larger class of Banach lattices of measurable function such as Orlicz spaces or re-arrangement invariant Banach function spaces. However in many cases the results in these extensions are not as precise or as complete as in the case of Lp-spaces. We will discuss results related to the boundedness of positive linear operators on Lp-spaces. The most important result is the so-called Schur criterion for boundedness. This criterion is the most frequently used tool to show that a concrete positive linear operator is bounded from Lp to Lq. Then we will show how this result relates to the change of density result of Weis [33]. Next the equality case of Schur's criterion is shown to be closely related to the question whether a given positive linear operator attains its norm. We discuss in detail the properties of norm attaining operators on Lp-spaces and discuss as an example the weighted composition operators on Lp-spaces. Then we return to the Schur criterion and show how it can be applied to the factorization theorems of Maurey and Nikišin. Most results mentioned in this paper have appeared before in print, but sometimes only implicitly and scattered over several papers. Also a number of the proofs presented here are new. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
31. Results in f-algebras.
- Author
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Boulabiar, Karim, Buskes, Gerard, Triki, Abdelmajid, Boulabiar, K., Buskes, G., and Triki, A.
- Abstract
We wrote a survey [18] on lattice ordered algebras five years ago. Why do we return to f-algebras once more? We hasten to say that there is only little overlap between the current paper and that previous survey.We have three purposes for the present paper. In our previous survey we remarked that one aspect that we did not discuss, while of some historical importance to the topic, is the theory of averaging operators. That theory has its roots in the nineteenth century and predates the rise of vector lattices. Positivity is a crucial tool in averaging, and positivity has been a fertile ground for the study of averaging-like operators. The fruits of positivity in averaging have recently (see [24]) started to appear in probability theory (to which averaging operators are close kin) and statistics. In the first section of our paper, we survey the literature for our selection of old theorems on averaging operators, at the same time providing some new perspectives and results as well. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
32. F-Isocrystals on Open Varieties Results and Conjectures.
- Author
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Cartier, Pierre, Katz, Nicholas M., Manin, Yuri I., Illusie, Luc, Laumon, Gérard, Ribet, Kenneth A., and Faltings, Gerd
- Abstract
(a) In this paper we want to present some results and conjectures about crystalline cohomology. In particular, we shall show that many results from ℓ-adic étale cohomology have analogues, like the Lefschetz trace-formula, unipotence of monodromy, and the theory of weights. Our results are a sequel to the paper [Fa2]. However, there are some differences between the approaches taken. First of all, in [Fa2] we are mainly concerned with ℤp-valued cohomology, and show at the end how results carry over to the ℚp-adic theory (which works under much more general circumstances, but gives weaker results as we neglect p-torsion). Also, in [Fa2] the results are fairly complete, that is we show pretty much the results one can hope for. Finally, we were mostly interested in the relation between crystalline cohomology and p-adic étale cohomology. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
33. From Toeplitz Eigenvalues through Green's Kernels to Higher-order Wirtinger-Sobolev Inequalities.
- Author
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Gohberg, I., Alpay, D., Arazy, J., Atzmon, A., Ball, J. A., Ben-Artzi, A., Bercovici, H., Böttcher, A., Clancey, K., Coburn, L. A., Curto, R. E., Davidson, K. R., Douglas, R. G., Dijksma, A., Dym, H., Fuhrmann, P. A., Gramsch, B., Helton, J. A., Kaashoek, M. A., and Kaper, H. G.
- Abstract
The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary differential operators, the norm of the Green kernels of these operators, the best constant in a Wirtinger-Sobolev inequality, and the conditioning of a special least squares problem. The main result of the paper gives the asymptotics of this sequence. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
34. Numerical Approximation of PDEs and Clément's Interpolation.
- Author
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Gohberg, I., Alpay, D., Arazy, J., Atzmon, A., Ball, J. A., Ben-Artzi, A., Bercovici, H., Böttcher, A., Clancey, K., Coburn, L. A., Curto, R. E., Davidson, K. R., Douglas, R. G., Dijksma, A., Dym, H., Fuhrmann, P. A., Gramsch, B., Helton, J. A., Kaashoek, M. A., and Kaper, H. G.
- Abstract
In this short paper, we present a formalism which specifies the notions of consistency and stability of finite element methods for the numerical approximation of nonlinear partial differential equations of elliptic and parabolic type. This formalism can be found in [4], [7], [10], and allows to establish a priori and a posteriori error estimates which can be used for the refinement of the mesh in adaptive finite element methods. In concrete cases, the Cléement's interpolation technique [6] is very useful in order to establish local a posteriori error estimates. This paper uses some ideas of [10] and its main goal is to show in a very simple setting, the mathematical arguments which lead to the stability and convergence of Galerkin methods. The bibliography concerning this subject is very large and the references of this paper are no exhaustive character. In order to obtain a large bibliography on the a posteriori error estimates, we report the lecturer to Verfürth's book and its bibliography [12]. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
35. Positive lyapounov exponents for most energies.
- Author
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Dold, A., Takens, F., Teissier, B., Milman, Vitali D., Schechtman, Gideon, and Bourgain, J.
- Abstract
Consider the ID lattice Schrödinger operator (1) $$H = \lambda \cos (2\pi n^\rho \omega + \theta )\delta _{nn'} + \Delta$$ with 1 < ρ < 2 and define $$\gamma (E,\lambda )\mathop {\underline {\lim } }\limits_{N \to \infty } \frac{1}{N}\int_\mathbb{T} {\log } \left\
{\prod\limits_N^0 {\left( {\begin{array}{*{20}c}{E - \lambda cos(2\pi n^\rho \omega + \theta ) - 1} \\{10} \\\end{array} } \right)} } \right\ d\theta$$ . If λ > 2, M. Herman's [H] argument implies that γ(E,λ)≥log λ/2 >0, for all E. We are interested here in small λ and show that for all E∈Eλ⊂[−2,2] (2) $$mes([ - 2,2]\backslash \mathcal{E}_\lambda )\xrightarrow{{\lambda \to 0}}0$$ we have that γ(E, λ) > 0. See Proposition 4. Considering the skew shift on $$\mathbb{T}^2$$ (3) $$T(x,y) = (x + y,y + \omega )$$ and the Hamiltonian (4) $$H = \lambda \cos (\pi _1 T^m (x,y))\delta _{nn'} + \Delta$$ where $$\pi _1 T^m (x,y) = x + ny + \frac{{n(n - 1)}}{2}\omega$$ we show that the Lyapounov exponent $$\gamma (E,\lambda )^{\underline{\underline {a.e.}} } \mathop {\underline {\lim } }\limits_{N \to \infty } \frac{1}{N}\log \left\ {\prod\limits_N^0 {\left( {\begin{array}{*{20}c}{E - \lambda \cos \pi _1 T^n (x,y) - 1} \\{10} \\\end{array} } \right)} } \right\ $$ is strictly positive for E∈Eλ⊂[−2,2] satisfying (2), provided we assume in (3) that $$\left \omega \right < \varepsilon (\lambda )$$ . See Proposition 5. The method is based on a local approximation of (1), (4) by the almost Mathieu model (5) $$H_{\alpha ,\lambda ,\theta } = \lambda \cos (2\pi \alpha + \theta )\delta _{nn'} + \Delta$$ and uses the fact (see Corollary 3) that for λ small and E∈Eλ⊂[−2,2] satisfying (2), (6) $$\int_\mathbb{T} {\gamma (\alpha ,\lambda ,E)d\alpha > 0}$$ where γ(α, λ, E) refers to the Lyapounov exponents of (5). The proof of (6) does rely on the Aubry duality, [A-A], [La]). Added in Proof. Concerning lattice Schrödinger operators of the form (1), related references were pointed out to the author by Y. Last. First, it is shown in the paper [L-S] that H=λcos(mρ)+Δ on ℤ has no absolutely continuous spectrum for λ > 2, ρ > 1. In fact, Theorem 1.4 from [L-S] provides an alternative proof of Proposition 4 in this paper. Other numerical and heuristic studies appear in [G-F],[B-F]. The particular case 1 < ρ < 2 was studied in [Th]. See [L-S] for further details. [ABSTRACT FROM AUTHOR] - Published
- 2000
- Full Text
- View/download PDF
36. On the lipschitz property of a class of mappings.
- Author
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Salimov, R.
- Subjects
MATHEMATICS ,LIPSCHITZ spaces ,FUNCTION spaces ,FUNCTIONAL analysis ,BERGMAN spaces - Abstract
Open discrete annular Q-mappings with respect to the p-modulus in ℝ, n ≥ 2, are considered in this paper. It is established that such mappings are finite Lipschitz for n − 1 < p < n if the integral mean value of the function Q( x) over all infinitesimal balls B( x, ɛ) is finite everywhere. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
37. Hilbert algebras with supremum.
- Author
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Celani, Sergio and Montangie, Daniela
- Subjects
HILBERT algebras ,FUNCTIONAL analysis ,VON Neumann algebras ,MATHEMATICS ,TOPOLOGY - Abstract
In this paper, we will study the class of Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join-semilattice. First, we will give a simplified topological duality for Hilbert algebras using sober topological spaces with a basis of open-compact sets satisfying an additional condition. Next, we will extend this duality to Hilbert algebras with supremum. We shall prove that the ordered set of all ideals of a Hilbert algebra with supremum has a lattice structure. We will also see that in this lattice, it is possible to define an implication, but the resulting structure is neither a Heyting algebra nor an implicative semilattice. Finally, we will give a dual description of the lattice of ideals of a Hilbert algebra with supremum. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
38. Stability of sets for impulsive functional differential equations via Razumikhin method.
- Author
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Xie, Shenglan and Shen, Jianhua
- Subjects
ASYMPTOTIC theory in functional differential equations ,IMPULSIVE differential equations ,NUMERICAL analysis ,PERTURBATION theory ,FUNCTIONAL analysis ,LYAPUNOV functions ,MATHEMATICS - Abstract
In this paper, we consider the functional differential equation with impulsive perturbationsCriteria on uniform asymptotic stability of sets are established for the above system using Lyapunov functions and the Razumikhin technique. Some examples are also discussed to illustrate the theorems. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
39. A classification of cubic symmetric graphs of order 16 p.
- Author
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ALAEIYAN, MEHDI, ONAGH, B, and HOSSEINIPOOR, M
- Subjects
GRAPH theory ,MATHEMATICAL symmetry ,INVARIANT subspaces ,HILBERT space ,FUNCTIONAL analysis ,MATHEMATICS ,GRAPH connectivity - Abstract
A graph is called symmetric if its automorphism group acts transitively on its arc set. In this paper, we classify all connected cubic symmetric graphs of order 16 p for each prime p. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
40. An almost sure central limit theorem for the weight function sequences of NA random variables.
- Author
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Wu, Qunying
- Subjects
CENTRAL limit theorem ,LIMIT theorems ,PROBABILITY theory ,RANDOM variables ,MATHEMATICAL sequences ,FUNCTIONAL analysis ,MATHEMATICS - Abstract
Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure central limit theorem previously obtained from the i.i.d. case to NA sequences. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
41. Drawing Curves Over Number Fields.
- Author
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Cartier, Pierre, Katz, Nicholas M., Manin, Yuri I., Illusie, Luc, Laumon, Gérard, Ribet, Kenneth A., Shabat, G. B., and Voevodsky, V. A.
- Abstract
0.0. This paper develops some of the ideas outlined by Alexander Grothendieck in his unpublished Esquisse d'un programme [0] in 1984. [ABSTRACT FROM AUTHOR]
- Published
- 1990
- Full Text
- View/download PDF
42. Prisms and Pyramids of Shelling Components.
- Author
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Ehrenborg, Richard
- Subjects
RECURSION theory ,OPERATOR theory ,FUNCTIONAL analysis ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
We study how the shelling components behave under the pyramid and prism operations. As a consequence we obtain a concise recursion for the cubical shelling contributions. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
43. On an equation involving weighted quasi-arithmetic means.
- Author
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Jarczyk, J.
- Subjects
ARITHMETIC ,FUNCTIONAL analysis ,MATHEMATICS ,FUNCTIONAL equations ,MONOTONIC functions - Abstract
Let I ⊂ ℝ be an interval and κ, λ ∈ ℝ / {0, 1}, µ, ν ∈ (0, 1). We find all pairs ( φ, ψ) of continuous and strictly monotonic functions mapping I into ℝ and satisfying the functional equation which generalizes the Matkowski-Sutô equation. The paper completes a research stemming in the theory of invariant means. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
44. New characterizations of inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type.
- Author
-
Yan Han
- Subjects
BESOV spaces ,FUNCTION spaces ,FUNCTIONAL analysis ,MATHEMATICS ,RIEMANNIAN manifolds ,DIFFERENTIAL geometry - Abstract
In this paper we use the T
1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for ℝn . [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
45. A weak type inequality for the maximal operator of ( C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system.
- Author
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GÁT, GY. and GOGINAVA, U.
- Subjects
FOURIER series ,HARDY spaces ,FUNCTIONAL analysis ,HARMONIC functions ,MATHEMATICS - Abstract
Simon [12] proved that the maximal operator of ( C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system is bounded from the martingale Hardy space H
p to the space Lp for p > 1/(1 + α). In this paper we prove that this boundedness result does not hold if p ≦ 1/(1 + α). However, in the endpoint case p = 1/(1 + α) the maximal operator σ is bounded from the martingale Hardy space H1/(1+ α) to the space weak- L1/(1+ α) . [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
46. The limit as p → ∞ in a nonlocal p-Laplacian evolution equation: a nonlocal approximation of a model for sandpiles.
- Author
-
ANDREU, F., MAZóN, J. M., ROSSI, J. D., and TOLEDO, J.
- Subjects
EQUATIONS ,FUNCTIONAL analysis ,MASS transfer ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
In this paper, we study the nonlocal ∞-Laplacian type diffusion equation obtained as the limit as p → ∞ to the nonlocal analogous to the p-Laplacian evolution, We prove exist ence and uniqueness of a limit solution that verifies an equation governed by the subdifferential of a convex energy functional associated to the indicator function of the set $${K = \{ u \in L^2(\mathbb{R}^N) \, : \, | u(x) - u(y)| \le 1, \mbox{ when } x-y \in {\rm supp} (J)\}}$$ . We also find some explicit examples of solutions to the limit equation. If the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L
∞ (0, T; L2 ( Ω)) to the limit solution of the local evolutions of the p-Laplacian, vt = Δp v. This last limit problem has been proposed as a model to describe the formation of a sandpile. Moreover, we also analyze the collapse of the initial condition when it does not belong to K by means of a suitable rescale of the solution that describes the initial layer that appears for p large. Finally, we give an interpretation of the limit problem in terms of Monge–Kantorovich mass transport theory. [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
47. Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space.
- Author
-
Tao Yu and Shi Wu
- Subjects
TOEPLITZ operators ,LINEAR operators ,SOBOLEV spaces ,FUNCTION spaces ,FUNCTIONAL analysis ,PERTURBATION theory ,MATHEMATICS - Abstract
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
48. Weighted composition operators of H∞ into α-Bloch spaces on the unit ball.
- Author
-
Min Zhang and Huai Chen
- Subjects
FUNCTION spaces ,LINEAR operators ,OPERATOR theory ,FUNCTIONAL analysis ,MATHEMATICAL analysis ,MATHEMATICS - Abstract
In this paper we characterize the boundedness and compactness of weighted composition operators of H
∞ into α-Bloch spaces on the unit ball in ℂn . [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
49. On Polyhedral Projection and Parametric Programming.
- Author
-
Jones, C. N., Kerrigan, E. C., and Maciejowski, J. M.
- Subjects
POLYHEDRAL functions ,LINEAR programming ,ALGEBRAIC functions ,POLYNOMIALS ,ALGORITHMS ,DYNAMIC programming ,FUNCTIONAL analysis ,MATHEMATICS ,APPROXIMATION theory - Abstract
This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time-this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
50. New Robust Model Predictive Control for Uncertain Systems with Input Constraints Using Relaxation Matrices.
- Author
-
Lee, S. M., Won, S. C., and Park, J. H.
- Subjects
MATRICES (Mathematics) ,MATRIX inequalities ,MATHEMATICAL inequalities ,PREDICTIVE control systems ,UNIVERSAL algebra ,VECTOR spaces ,LINEAR algebra ,FUNCTIONAL analysis ,MATHEMATICS - Abstract
In this paper, we propose a new robust model predictive control (MPC) method for time-varying uncertain systems with input constraints. We formulate the problem as a minimization of the worst-case finite-horizon cost function subject to a new sufficient condition for cost monotonicity. The proposed MPC technique uses relaxation matrices to derive a less conservative terminal inequality condition. The relaxation matrices improve feasibility and system performance. The optimization problem is solved by semidefinite programming involving linear matrix inequalities (LMIs). A numerical example shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
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