Aleksandar S. Cvetković

Common Fixed Point Theorems for Four Mappings on Cone Metric Type Space

In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.

A generalized Birkhoff–Young–Chebyshev quadrature formula for analytic functions

Abstract A generalized N -point Birkhoff–Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived.

Common fixed point under contractive condition of Ćirić's type on cone metric type spaces

The purpose of this article is to generalize common fixed point theorems under contractive condition of Ćirić’s type on a cone metric type space. We give basic facts about cone metric type spaces, and we prove common fixed point theorems under contractive condition of Ćirić’s type on a cone metric type space without assumption of normality for cone. As special cases we get the corresponding fixed point theorems on a cone metric space with respect to a solid cone. Obtained results in this article extend, generalize, and improve, well-known comparable results in the literature.2000 Mathematics Subject Classification: 47H10; 54H25; 55M20.

Outage Performance of Dual-Hop AF Relay Channels with Co-Channel Interferences over Rayleigh Fading

This paper studies the outage performance of a dual-hop amplify-and-forward (AF) relay fading channel in an interference-limited environment. The relay and destination nodes are corrupted by multiple co-channel Rayleigh interferences. New exact closed-form expressions for the outage probability for channel-state-information (CSI)—assisted relay, in which gain is dependent on previous hop CSI and interference, are derived. Monte Carlo simulations are performed to verify the obtained theoretical results. For the cases where the number of interferers at the relay and the destination node is equal, we derive novel expressions for outage probability upper and lower bounds.

On the First and the Second Order Statistics of the Capacity of κ-μ Fading Channels

Abstract Consideration of the channel capacity temporal behavior, in order to design a system that could adapt the transmission rate according to the capacity evolving process, and could transmit close to the ergodic capacity, is provided in this paper. Channel conditions have been modeled by the recently introduced general κ-μ fading model. We have studied statistical properties of the capacity of κ-μ fading channels. Analytical expressions for the first order statistical properties: probability density function (PDF), cumulative distribution function (CDF) and the outage capacity (OC), as well as the second-order statistical properties, such as the level-crossing rate (LCR), and average fade duration (AFD) of the instantaneous channel capacity, have been derived. Obtained results are numerically presented and visualized by the corresponding graphs.

Local trilateral upsampling for thermal image

This paper presents an image upsampling method. Joint-bilateral filtering has been successfully applied to this problem that upsample “target” images using high-resolutional “control” images. In this filtering, the kernel is a product of weights representing spatial proximity and color (or intensity) proximity of the “control” image. However, when the “target” image involves textures that are invisible in the “control” image, these textures are damaged by this upsampling. In the case of thermal target image and visible-light control image, we can often find such textures. For solving this problem, we first propose trilateral upsampling, which is a simple extension of joint-bilateral upsampling incorporating color (or intensity) proximity weight in the “target” image. For improving this method so as to increase the spatial resolution, we introduce weight control based on local mutual information between target and control images. We confirmed that resulted images have higher spatial resolution and lower noise.

Trading defect tolerance for chip area in nanotecnology implementations of systolic arrays

New self-assembling techniques used to build nano-scale architecture prototypes have a drawback of being prone to defects and transient faults. Fault and defect tolerance techniques will be crucial to the use of nano-electronics in the future. However, these techniques usually introduce a significant hardware overhead. In these paper we are proposing a method for trading an architecture tolerance on fabrication defects for chip area. The method will be presented using an architecture with generic topology and illustrated on the example of partially defect tolerant bit-plane semi-systolic array. In order to illustrate the method the results of FPGA implementation of completely fault tolerant bit-plane array, and partially fault tolerant bit-plane array will be given.

Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree

Abstract Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w ( x ) on [ 0 , 2 π ) have been considered firstly by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337–359 (translation in English from Uchenye Zapiski, Vypusk 1(149), Seria Math. Theory of Functions, Collection of papers, Izdatel’stvo Belgosuniversiteta imeni V.I. Lenina, Minsk, (1959) pp. 31–54)]. Such orthogonal systems are connected with quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes), which have application in numerical integration of 2 π -periodic functions. In this paper we study asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree with respect to a strictly positive weight function satisfying the Lipschitz-Dini condition.

Gaussian interval quadrature rule for exponential weights

Abstract Interval quadrature formulae of Gaussian type on R and R + for exponential weight functions of the form w(x)xa0=xa0exp(−Q(x)), where Q is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to w, are considered. For a given set of nonoverlapping intervals and an arbitrary n, the uniqueness of the n-point interval Gaussian rule is proved. The results can be applied also to corresponding quadratures over (−1,xa01). An algorithm for the numerical construction of interval quadratures is presented. Finally, in order to illustrate the presented method, two numerical examples are done.