Academic literature on the topic 'L^infinity Data'

It is known that the condition ‘either ∂L (F) ≠ Ø or there exist υ1,…,υq ∈ Rnsuch thatF ∈ int co {υ1,…,υq} characterizes solvability of the problem with f(·) = 〈F,·〉.We extend this result to the case of lower semicontinuous integrands L : Rn → R.We also show that validity of this condition for all F ∈ Rn is both a necessary and sufficient requirement for solvability of all minimization problems with sufficiently regular Ω and f. Moreover, the assumptions on Ω and f can be completely dropped if L has sufficiently fast growth at infinity.

Limiting activity coefficients for 64 solutes in [BzMIM][NTf₂] and [BzMIM][DCA], the gas–liquid partition coefficients, K_L, thermodynamic functions and selectivity for hexane/hex-1-ene, cyclohexane/cyclohexene and ethylbenzene/styrene separation were presented.

AbstractWe present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that $$L^2$$ L 2 -based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce $$L^2$$ L 2 -based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

We investigate the properties of data collection in wireless sensor networks, in terms of both capacity and power allocation strategy. We consider a scenario in which a number of sensors observe a target being estimated at fusion center (FC) using minimum mean-square error (MMSE) estimator. Based on the relationship between mutual information and MMSE (I-MMSE), the capacity of data collection in coherent and orthogonal multiple access channel (MAC) models is derived. Considering power constraint, the capacity is derived under two scenarios: equal power allocation and optimal power allocation of both models. We provide the upper bound of capacity as a benchmark. In particular, we show that the capacity of data collection scales as Θ((1/2)log(1+L)) when the number of sensors L grows to infinity. We show through simulation results that for both coherent and orthogonal MAC models, the capacity of the optimal power is larger than that of the equal power. We also show that the capacity of coherent MAC is larger than that of orthogonal MAC, particularly when the number of sensors L is large and the total power P is fixed.

<p><strong>Abstract.</strong> In Geographic Information Science, polynomial methods such as linear estimation and non-polynomial methods including Inverse Distance Weighting and Kriging have been used for elevation data interpolation. In this paper, 3D data interpolation using linear and non-linear homotopy continuation as well as advanced polynomial interpolation methods are researched. Continuous deformations that reconstruct straight lines or algebraic curves between any pair of 3D data are presented. The implemented topological mathematical algorithm for 3D elevation data interpolation is compared to Inverse Distance Weighting and Triangulated Irregular Network (TIN) methods. The presented linear and non-linear mathematical algorithms show better results compared to Inverse Distance Weighting and TIN in terms of Root Mean Square Error and L-infinity.</p>

We investigate local/global existence, blowup criterion and long-time behavior of classical solutions for a hyperbolic–parabolic system derived from the Keller–Segel model describing chemotaxis. It is shown that local smooth solution blows up if and only if the accumulation of the L∞ norm of the solution reaches infinity within the lifespan. Our blowup criteria are consistent with the chemotaxis phenomenon that the movement of cells (bacteria) is driven by the gradient of the chemical concentration. Furthermore, we study the long-time dynamics when the initial data is sufficiently close to a constant positive steady state. By using a new Fourier method adapted to the linear flow, it is shown that the smooth solution exists for all time and converges exponentially to the constant steady state with a frequency-dependent decay rate as time goes to infinity.

We prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide L∞ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the entropy condition through the doubling of variable technique. The limit model as the kernel support tends to infinity is also studied.

AbstractThe generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time, the interior {L^{\infty}}-estimates for the pressure, its gradient and time derivative, and the interior {L^{2}}-estimates for its Hessian. The De Giorgi and Ladyzhenskaya–Uraltseva iteration techniques are used taking into account the special structures of the equations for both pressure and its gradient. These are combined with the uniform Gronwall-type bounds in establishing the asymptotic estimates when time tends to infinity.

 In recent years, the iterative decoding techniques have played a role in improving the performance (e.g., bit error rate) and reducing the complexity of various digital communication systems. Techniques of Multiple-Input Multiple-Output (MIMO) are the main technology to enhance and achieve high-speed, high data rates, improved reliability and coverage in wireless communications. The modern wireless communications require a low complexity system for detection, since a high CPU processing involves more energy consumption and thus less flexibility in mobility terms. The sphere decoding (SD) technique proposed to solve this problem, such as an efficient algorithm. The norm-2 or l^2-norm (Euclidean metric) considered as a traditional norm that is used to achieve the tree traversal stage in SD algorithm. This work is divided into two parts; Firstly, we propose to using Infinity-Norm or l^∞-norm instead l^2-norm to decreases the hardware complexity of SD with a loss of performance is negligible, the simulation results show that the proposed l^∞-norm SD needs 14.5% to 5.9% fewer complexities than l^2-norm SD. Secondly, we are investigating the impact of choosing initial radius on the performance and complexity of SD algorithm, we can conclude from the simulation results, that gain a better performance requires increasing in the initial radius of an SD algorithm from d1 (γ =2) to d3 (γ =8), and this mean addition more complexity due to the tradeoff  between performance and complexity.    In recent years, the iterative decoding techniques have played a role in improving the performance (e.g., bit error rate) and reducing the complexity of various digital communication systems. Techniques of Multiple-Input Multiple-Output (MIMO) are the main technology to enhance and achieve high-speed, high data rates, improved reliability and coverage in wireless communications. The modern wireless communications require a low complexity system for detection, since a high CPU processing involves more energy consumption and thus less flexibility in mobility terms. The sphere decoding (SD) technique proposed to solve this problem, such as an efficient algorithm. The norm-2 or -norm (Euclidean metric) considered as a traditional norm that is used to achieve the tree traversal stage in SD algorithm. This work is divided into two parts; Firstly, we propose to using Infinity-Norm or -norm instead -norm to decreases the hardware complexity of SD with a loss of performance is negligible, the simulation results show that the proposed -norm SD needs 14.5% to 5.9% fewer complexities than -norm SD. Secondly, we are investigating the impact of choosing initial radius on the performance and complexity of SD algorithm, we can conclude from the simulation results, that gain a better performance require increasing in the initial radius of an SD algorithm from d1 ( =2) to d3 ( =8), and this mean addition more complexity due to the tradeoff between performance and complexity.