The paper deals with inclusion relations between s(p) and H-s(p). Here s(p) is the set of all a is an element ofJ such that the Weyl operator a(w) (x, D) is a Schatten-von Neumann operator on L-2 to the order p is an element of [1, infinity], and H-s(p) is the Sobolev space of distributions with s derivatives in L-p. At the same time we compute the trace norm for a(w) (x, D), when a is an arbitrary Gauss function.
Let M-p,M- q denote the modulation space with parameters p, q is an element of [1, infinity]. If 1/p(1) + 1/p(2) = 1 + 1/p(0) and 1/q(1) + 1/q(2) = 1/q(0), then it is proved that M-p1,M- q1 * M-p2,M- q2 subset of M-p0,M- q0. The result is used to get inclusions between modulation spaces, Besov spaces and Schatten classes in calculus of psido (pseudo-differential operators), and to extend the definition of Toeplitz operators. We also discuss continuity of ambiguity functions and psido in the framework of modulation spaces.
Den första delen av uppsatsen berör faltningsegenskaper mellan moduleringsrum och Lebesguerum. Detta tillämpas sedan för att få fram inbäddningsrelationer mellan moduleringsrum och Besovrum.
We discuss certain continuity properties for modulation spaces, and prove certain convolution relations. The results are then applied to get inclusions between modulation spaces, Besov spaces and Schatten classes in calculus of pseudo-differential operators, and to extend the definition of Toeplitz operators. We also discuss continuity of ambiguity functions and pseudo-differential operators in the framework of modulation spaces.
We prove that the most usual modulation spaces of non-standard type may be obtained in a canonical way from the corresponding modulation spaces of standard type. We use the results to get inclusions between certain modulation spaces and Besov spaces, and for proving continuity properties in pseudo-differential calculus.
We study Y'(+), of all a is an element of D' such that (a *sigma, phi, phi) greater than or equal to 0 for every phi is an element of C-0(infinity), where *phi denotes the twisted convolution. We prove that certain boundedness for a E Y' are completely determined of the behaviour for a at origin, for example that a is an element of Y'(+), and that if a(0) < &INFIN;, then a &ISIN; L-2 &AND; L-&INFIN;. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.
In this paper we shall deal with some positivity questions arises in the Weyl calculus.
We study general continuous properties for an increasing family of Banach spaces of classes for pseudo-differential symbols, where the largest symbol space was introduced by J. Sjöstrand 1993. We prove that corresponding pseudo-differential operators are contained in the some certain sets of Schatten-von Neumann operators. We prove also that one obtains Hölder relations from the operator product and the usual multiplication, and that the convolution multiplication give rise to some Young type relations. Some further extensions are also discussed
We study general continuity properties for an increasing family of Banach spaces S-W(P) of classes for pseudo-differential symbols, where S-W(infinity) = S-w was introduced by J. Sjostrand in 1993. We prove that the operators in Op(S-W(P)) are Schattenvon Neumann operators of order p on L-2. We prove also that Op(S-w(p))Op(S-w(r)) subset of Op(S-w(r)) and S-w(p) . S-w(q) subset of S-w(r) provided 1/p+1q = 1/r. If instead 1/p + 1/q = 1+1/r, then S-w(p) w* S-w(q) subset of S-w(r). By modifying the definition of the S-w(p) -spaces, one also obtains symbol classes related to the S(m, g) spaces.
The most usual weighted modulation spaces is considered. It is proved that a lot of such spaces can be obtained in a canonical way from the corresponding standard modulation spaces. The results are used to get inclusions between certain modulation spaces and Besov spaces, and for proving continuity properties in pseudo-differential calculus.
With the increasing traffic volumes in many railway networks and reports on capacity deficiencies that result in insufficient punctuality and reliability, the need for efficient disturbance management solutions becomes evident. This thesis focuses on solutions that aim to minimise the consequences of disturbances for the various stakeholders and specifically on methods for re-scheduling the traffic. Railway traffic re-scheduling is a complex task with many influencing factors to consider and multiple stakeholders with sometimes conflicting interests. This problem is typically handled manually by traffic dispatchers that have a very limited access to support systems to facilitate their decision-making. This limitation hampers the possibilities to achieve sustainable and system-optimal decision-making and to provide the stakeholders with reliable traffic prognoses. We first study how railway traffic system users experience and are affected by the way the disturbances are communicated and handled by the traffic dispatchers. The results indicate that the disturbance-related information provided by the dispatchers is currently insufficient. The stakeholders need to acquire improved prognoses of their traffic and immediate part of the network to internally be able to minimise the negative effects of the disturbances. Furthermore, an analysis of the disturbance management problem structure and how the problem can be modelled is provided. The analysis shows that there exist fundamental restrictions in the traffic system that bounds the traffic flow but also a large number of context-dependent considerations such as sustaining certain connections or prioritising specific trains. The prevalence and feasibility of such considerations are difficult to identify and model. Moreover, the objectives of the disturbance management are vague and partly unclear, and therefore it is also difficult to measure and evaluate the outcome of the corresponding decision-making. Finally, a number of optimisation-based solution approaches with the purpose to facilitate for the dispatchers and their decision-making has been developed. The performance and applicability of the approaches have been evaluated for various disturbance settings using data for parts of the Swedish railway network that currently experience capacity deficiencies. The evaluation has identified certain disturbances characteristics that have a significant influence on the disturbance propagation, and which in some cases complicate the re-scheduling procedure. Furthermore, the significance of applying certain re-scheduling objectives and their correlation with performance measures has been analysed. The analysis shows e.g. that a minimisation of accumulated delays has a tendency to delay more trains than a minimisation of total final delay or total delay costs. An experimental study of the long-term effects when applying a limited planning perspective has also been conducted. The results indicate that solutions which are good on longer-term can be achieved despite the use of a limited planning horizon. In parallel to the optimisation-based approaches, an agent-based conceptual model with emphasis on the interplay between the different components in the railway traffic system has been proposed.
The demand of wireless spectrum is increasing very fast as the field of telecommunication is advancing rapidly. The spectrum was underutilized because of fixed spectrum assignment policy and this valuable spectrum can be utilized efficiently by cognitive radio technology. In this thesis we have studied spectrum selection problems in cognitive radio network. Channel sharing and channel contention problems arise when multiple secondary users tend to select same channel. The thesis work is focused on spectrum selection issue with the aim to minimize the overall system time and to solve the problem of channel contention and channel sharing. The overall system time of secondary connection is an important performance measure to provide quality of service for secondary users in cognitive radio network. We studied two spectrum selection schemes that considerably reduce the overall system time and resolve the problems of channel sharing and channel contention. An analytical model associated with Preemptive Resume Priority (PRP) M/G/1 queuing model has been provided to evaluate the studied spectrum selection scheme. This model also analyzes the effect of multiple handoffs due to arrival of primary users. According to this scheme, the traffic load is distributed among multiple channels to balance the traffic load. Secondary users select the operating channels based on the spectrum selection algorithm. They can intelligently adopt better channel selection scheme by considering traffic statistics and overall transmission time. All simulation scenarios are developed in MATLAB. Based on our result we can conclude that both channel selection schemes considerably reduce the overall transmission time of secondary users in cognitive radio network. The overall transmission time increase with the rise of arrival rate of secondary user. The probability based channel selection scheme perform better with lower arrival rate and sensing based channel selection scheme perform better with higher arrival rate of secondary users. These channel selection schemes help distribute the traffic load of secondary users evenly among multiple channels. Hence, increase the channel utilization and resolve the channel contention problem.
In this paper, Impulse Response Function in Circular Synthetic Aperture Radar Imaging (IRF-CSAR), which is a special version of Impulse Response Function in Ultrawideband-Ultrawidebeam Synthetic Aperture Radar Imaging (IRF-USAR), is presented and shown to be valid for representing the CSAR image of a point-like scatterer. IRF-CSAR can therefore be used in studying different CSAR systems such as predicting the pattern of a point-like scatterer illuminated by a CSAR system, estimating resolution achieved by that system. Applying IRF-CSAR to define the image quality assessments for CSAR is also presented in the paper.
This paper discusses spatial resolutions for narrowband narrowbeam (NB) synthetic aperture radar (SAR) as well as for ultrawideband ultrawidebeam (UWB) SAR. The similarity and difference between the impulse response function in NB SAR imaging (IRF-NSAR) - sinc function - and the impulse response function in UWB SAR imaging (IRF-USAR) is investigated and the result of this investigation shows that in the intensity interval from −6 dB to 0 dB, the behavior of IRF-NSAR and IRF-USAR in azimuth and range are similar. This is the basis for a derivation of new spatial resolution equations for UWB SAR based on −3 dB width or half power beamwidth (HPBW). The investigated result also shows that there exists the so-called HPBW narrowing/broadening factor in an IRF-USAR.
In synthetic aperture radar (SAR) processing, there is a trade-off between accuracy and speed. The approximations in an algorithm help to increase the algorithm’s speed but cause deterministic phase errors which directly affect the SAR image quality. This paper discusses the phase error calculations for bistatic fast backprojection (BiFBP) and bistatic fast factorized backprojection (BiFFBP) which are essential for setting their parameters. The phase error calculation principle for bistatic SAR in comparison to monostatic SAR is presented. This principle is used to derive the maximum phase error equation.
Genetic Algorithm (GA) as a class of Evolutionary Algorithm (EA) is a search algorithm based on the mechanics of natural selection and natural genetics. This dissertation presents the description, solving procedures and application of GA. The definitions of selection, crossover and mutation operators are given in details and an application based on GA in Time Table Problem (TTP) is performed in a new way. Due to its high capability of overall search, GA is particularly appropriate for solving timetabling and scheduling problems. TTP (Time Table Problem) which belongs to NP-hard problem is a special problem concerning resource management. In this dissertation, a new chromosome coding is designed in order to solve TTP more effectively. And the result presented by MATLAB will converge to a steady condition.
A biological reaction diusion model has gained much attention recently. This model is formulated as a system of nonlinear partial dierential equations that contains an unknown function of one dependent variable. How to determine this unknown function is complicated but also useful. This model is considered in this master thesis. The generators of the equivalence groups and invariant solutions are calculated.
This thesis provides an analytical and two numerical methods for solving a parabolic equation of two-dimensional mean curvature flow with some applications. In analytical method, this equation is solved by Lie group analysis method, and in numerical method, two algorithms are implemented in MATLAB for solving this equation. A geometric algorithm and a step-wise algorithm; both are based on a deterministic game theoretic representation for parabolic partial differential equations, originally proposed in the genial work of Kohn-Serfaty [1].