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171.
We investigate the optimal solution of systems of initial-value problems with smooth right-hand side functions f from a Hölder class \(F^{r,\varrho }_{\text {reg}}\), where r ≥ 0 is the number of continuous derivatives of f, and ? ∈ (0, 1] is the Hölder exponent of rth partial derivatives. We consider algorithms that use n evaluations of f, the ith evaluation being corrupted by a noise δi of deterministic or random nature. For δ ≥ 0, in the deterministic case the noise δi is a bounded vector, ∥δi∥≤δ. In the random case, it is a vector-valued random variable bounded in average, (E(∥δi∥q))1/q ≤ δ, q ∈ [1, + ∞). We point out an algorithm whose Lp error (p ∈ [0, + ∞]) is O(n ? (r + ?) + δ), independently of the noise distribution. We observe that the level n ? (r + ?) + δ cannot be improved in a class of information evaluations and algorithms. For ε > 0, and a certain model of δ-dependent cost, we establish optimal values of n(ε) and δ(ε) that should be used in order to get the error at most ε with minimal cost. 相似文献
172.
Paweł Przybyłowicz 《Numerical Algorithms》2016,73(2):323-348
We consider strong global approximation of SDEs driven by a homogeneous Poisson process with intensity λ > 0. We establish the exact convergence rate of minimal errors that can be achieved by arbitrary algorithms based on a finite number of observations of the Poisson process. We consider two classes of methods using equidistant or nonequidistant sampling of the Poisson process, respectively. We provide a construction of optimal schemes, based on the classical Euler scheme, which asymptotically attain the established minimal errors. It turns out that methods based on nonequidistant mesh are more efficient than those based on the equidistant mesh. 相似文献
173.
Rafał Pierzchała 《Journal d'Analyse Mathématique》2016,129(1):285-307
The paper contains a full geometric characterization of compact semialgebraic sets in C satisfying the ?ojasiewicz-Siciak condition. The ?ojasiewicz-Siciak condition is a certain estimate for the Siciak extremal function. In a previous paper, we gave a sufficient criterion for a compact, connected, and semialgebraic set in C to satisfy this condition. In the present paper, we remove completely the connectedness assumption and prove that the aforementioned sufficient condition is also necessary. Moreover, we obtain some new results concerning the ?ojasiewicz-Siciak condition in CN. For example, we prove that if K1,...,Kp are compact, nonpluripolar, and pairwise disjoint subsets of CN, each satisfying the ?ojasiewicz-Siciak condition, and K:= K1?· · ·?Kp is polynomially convex, then K satisfies this condition as well. 相似文献
174.
W. P. Węglarz A. Jasiński A. T. Krzyżak P. Kozłowski D. Adamek P. Sagnowski J. Pindel 《Applied magnetic resonance》1998,15(3-4):333-341
Diffusion tensor imaging (DTI) of the control and mechanically injured spinal cord of a ratin vitro andin vivo are reported.In vitro experiments were done on a home-built 6.4 T magnetic resonance microscope. Results for formaline-fixed samples show significant differences in diffusion tensor components between gray matter and white matter of the control spinal cord. Moreover, it is shown that already 6–10 min after the injury DTI can detect changes in water diffusion in areas extending far beyond the region of primary tissue damage.In vivo experiments were performed using a 9.4 T Magnex magnet and Bruker Medspec imaging system. Good-quality DTI images, free from motion artifacts were obtained. Results from control samples confirm differences in water diffusion between white matter and gray matter, observedin vitro. In vivo experiments show that characteristic changes in water diffusion observedin vitro 6–10 min after injury are preserved 60–360 min after injury, without significant alteration during this time. 相似文献
175.
Zdzisław Naniewicz 《Set-Valued and Variational Analysis》2011,19(3):417-456
The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow–Debreu model of economic equilibrium introduced in Naniewicz (Math Oper Res 32:436–466, 2007) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used. 相似文献
176.
L. Chełmicki J. Leciejewicz A. Zygmunt 《Journal of Physics and Chemistry of Solids》1985,46(5):529-538
Neutron diffraction and magnetization measurements indicate that, at low temperatures, long-range magnetic order is present in UCO2Si2, UNi2Si2, UCu2Si2, UNi2Ge2, and UCo2Ge2. UCo2Si2 and UNi2Ge2 are simple collinear antiferromagnets of +-+- type, UCu2Si2 a simple collinear ferromagnet. In UNi2Si2, a magnetic phase transition from a LSW type structure to collinear antiferromagnetism of +-+- type was found, while in UCu2Ge2, the antiferromagnetic structure of ++-- transforms into collinear ferromagnetism. Crystal structure and magnetic parameters are given. No magnetic moment on transition metal ions was found within the accuracy of a powder neutron diffraction experiment. The stability of particular magnetic ordering schemes is discussed in terms of an isotropic RKKY mechanism. 相似文献
177.
Jan J. Skławianowski 《Reports on Mathematical Physics》1985,22(3):323-371
We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL+ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL+ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL+ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL+ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL+ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories. 相似文献
178.
In the paper we consider the Bessel differential operator in half‐line , , and its Dirichlet heat kernel . For , by combining analytical and probabilistic methods, we provide sharp two‐sided estimates of the heat kernel for the whole range of the space parameters and every , which complements the recent results given in 1 , where the case was considered. 相似文献
179.
Marcin Pilipczuk Michał Pilipczuk Riste Škrekovski 《Discrete Applied Mathematics》2012,160(16-17):2484-2490
The well-known conjecture of Vizing on the domination number of Cartesian product graphs claims that for any two graphs and , . We disprove its variations on independent domination number and Barcalkin–German number, i.e. Conjectures 9.6 and 9.2 from the recent survey Bre?ar et al. (2012) [4]. We also give some extensions of the double-projection argument of Clark and Suen (2000) [8], showing that their result can be improved in the case of bounded-degree graphs. Similarly, for rainbow domination number we show for every that , which is closely related to Question 9.9 from the same survey. We also prove that the minimum possible counterexample to Vizing’s conjecture cannot have two neighboring vertices of degree two. 相似文献
180.
The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020. 相似文献