Search results for "Applied Mathematic"
showing 10 items of 4398 documents
THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE
2014
We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…
Rotationally symmetric p -harmonic maps fromD2toS2
2013
We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.
Non-periodic Discrete Splines
2015
Discrete Splines with different spans were introduced in Sect. 3.3.1. This chapter focuses on a special case of discrete splines whose spans are powers of 2. These splines are discussed in more detail. The Zak transform provides an integral representation of such splines. Discrete exponential splines are introduced. Generators of the discrete-spline spaces are described whose properties are similar to properties of polynomial-spline spaces generators. Interpolating discrete splines provide efficient tools for upsampling 1D and 2D signals. An algorithm for explicit computation of discrete splines is described.
An Exact Solution for the Level-Crossing Rate of Shadow Fading Processes Modelled by Using the Sum-of-Sinusoids Principle
2008
Published version of an article in the journal: Wireless Personal Communications. The original publication is available at Springerlink. http://dx.doi.org/10.1007/s11277-008-9512-3 The focus of this paper is on the higher order statistics of spatial simulation models for shadowing processes. Such processes are generally assumed to follow the lognormal distribution. The proposed spatial simulation model is derived from a non-realizable lognormal reference model with given correlation properties by using Rice's sum-of-sinusoids. Both exact and approximate expressions are presented for the level-crossing rate (LCR) and the average duration of fades (ADF) of the simulation model. It is pointed …
On the Correlation and Ergodic Properties of the Squared Envelope of SOC Rayleigh Fading Channel Simulators
2012
Published version of an article in the journal: Wireless Personal Communications. Also available from the publisher at: http://dx.doi.org/10.1007/s11277-011-0493-2 In this paper, we investigate the correlation and ergodic properties of the squared envelope of a class of autocorrelation-ergodic (AE) sum-of-cisoids (SOC) simulation models for mobile Rayleigh fading channels. Novel closed-form expressions are presented for both the ensemble and the time autocorrelation functions (ACFs) of the SOC simulation model’s squared envelope. These expressions have been derived by assuming that the SOC model’s inphase and quadrature (IQ) components have arbitrary autocorrelation and cross-correlation pr…
Fuzzy Investment Portfolio Selection Models Based on Interval Analysis Approach
2012
Published version of an article from the journal: Mathematical Problems in Engineering. Also available from the publisher:http://dx.doi.org/10.1155/2012/628295 This paper employs fuzzy set theory to solve the unintuitive problem of the Markowitz mean-variance (MV) portfolio model and extend it to a fuzzy investment portfolio selection model. Our model establishes intervals for expected returns and risk preference, which can take into account investors' different investment appetite and thus can find the optimal resolution for each interval. In the empirical part, we test this model in Chinese stocks investment and find that this model can fulfill different kinds of investors' objectives. Fi…
BIBO Stability Analysis for Delay Switched Systems with Nonlinear Perturbation
2013
Published version of a paper from the journal:Abstract and Applied Analysis. Also available from Hindawi:http://dx.doi.org/10.1155/2013/738653 The problem of bounded-input bounded-output ( BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.
The Unbalanced Linguistic Aggregation Operator in Group Decision Making
2012
Published version of an article in the journal: Mathematical problems in engineering. Also available from Hindawi: http://dx.doi.org/10.1155/2012/619162 Many linguistic aggregation methods have been proposed and applied in the linguistic decision- making problems. In practice, experts need to assess a number of values in a side of reference domain higher than in the other one; that is, experts use unbalanced linguistic values to express their evaluation for problems. In this paper, we propose a new linguistic aggregation operator to deal with unbalanced linguistic values in group decision making, we adopt 2-tuple representation model of linguistic values and linguistic hierarchies to expres…
Consistency of Probability Decision Rules and Its Inference in Probability Decision Table
2012
In most synthesis evaluation systems and decision-making systems, data are represented by objects and attributes of objects with a degree of belief. Formally, these data can be abstracted by the form (objects; attributes; P), wherePrepresents a kind degree of belief between objects and attributes, such that,Pis a basic probability assignment. In the paper, we provide a kind of probability information system to describe these data and then employ rough sets theory to extract probability decision rules. By extension of Dempster-Shafer evidence theory, we can get probabilities of antecedents and conclusion of probability decision rules. Furthermore, we analyze the consistency of probability de…
Exploring the best classification from average feature combination
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/602763 Open Access Feature combination is a powerful approach to improve object classification performance. While various combination algorithms have been proposed, average combination is almost always selected as the baseline algorithm to be compared with. In previous work we have found that it is better to use only a sample of the most powerful features in average combination than using all. In this paper, we continue this work and further show that the behaviors of features in average combination can be integrated into the k-Nearest-Neighbor …