dealing with uncertainties on phase weighting of linear antenna arrays by means of interval based tolerance analysis the analysis of the tolerances on the power patterns radiated by linear antenna arrays whose excitations are affected by phase errors is carried out by means of an approach based on the interval analysis ia the rules and the features of the arithmetic of intervals already effectively applied to analyze the effects of errors on the amplification levels are exploited here to derive a suitable set of analytical relationships predicting the maximum deviations i e upper and lower bounds with respect to the nominal power pattern once the phase errors are defined as belonging to intervals of values representative numerical examples are reported and discussed to assess potentialities and limitations of the ia based approach toward this end different configurations of the beamforming weights affording low sidelobes and steered beam patterns are analyzed

probabilistic interval analysis for the analytic prediction of the pattern tolerance distribution in linear phased arrays with random excitation errors a statistical approach based on the interval analysis ia is proposed for the analysis of the effects on the radiation patterns radiated by phased arrays of random errors and tolerances in the amplitudes and phases of the array elements excitations starting from the efficient reliable and inclusive computation of the bounds of the complex valued interval array pattern function by means of ia an analytic method is presented to yield closed form expressions for the probability of occurrence of a user chosen value of the power pattern or of its features within the corresponding ia derived bounds a set of numerical examples is reported and discussed to assess the reliability of the proposed probabilistic interval analysis pia method with the results from monte carlo simulations as well as to point out its effectiveness and potentialities advantages efficiency in real applications of great industrial interest

on an integration rule for products of barycentric coordinates over simplexes in rn in finite element computations one often needs to calculate integrals of products of powers of monomials over simplexes in this manuscript we prove a generalisation of the exact integration formula that was reported and proved for two dimensional simplexes by holand bell in 1969 we extend the proof to n dimensional simplexes and to simplexes on d dimensional manifolds in n dimensional space the results are used to develop finite element and boundary element simulation tools the proofs of the theorems are based on mathematical induction and coordinate mappings

fast calderon preconditioning for helmholtz boundary integral equations abstract calderon multiplicative preconditioners are an effective way to improve the condition number of first kind boundary integral equations yielding provable mesh independent bounds however when discretizing by local low order basis functions as in standard galerkin boundary element methods their computational performance worsens as meshes are refined this stems from the barycentric mesh refinement used to construct dual basis functions that guarantee the discrete stability of l 2 pairings based on coarser quadrature rules over dual cells and h matrix compression we propose a family of fast preconditioners that significantly reduce assembly and computation times when compared to standard versions of calderon preconditioning for the three dimensional helmholtz weakly and hyper singular boundary integral operators several numerical experiments validate our claims and point towards further enhancements

on the efficiency of nested gmres preconditioners for 3d acoustic and elastodynamic h matrix accelerated boundary element methods abstract this article is concerned with the derivation of fast boundary element methods for 3d acoustic and elastodynamic problems in particular we are interested in the acceleration of hierarchical matrix h matrix based iterative solvers while h matrix representations allow to reduce the storage requirements and the cost of a matrix vector product the number of iterations for an iterative solver as the frequency or the problem size increases remains an issue we consider an inner outer preconditioning strategy i e the preconditioner is applied through an iterative solver at the inner level the preconditioner is defined as a h matrix representation of the system matrix with a given accuracy we investigate the influence of various parameters of the preconditioner i e the h matrix accuracy the gmres threshold and the maximum number of iterations of the inner solver different numerical results are presented to compare the efficiency of the preconditioner with respect to the unpreconditioned reference system finally we propose a way to define the optimal setting for this preconditioner

tolerance analysis of antenna arrays through interval arithmetic an analytical method based on interval analysis ia is proposed to predict the impact of the manufacturing tolerances of the excitation amplitudes on the radiated array pattern by expressing the array factor according to the rules of the interval arithmetic the radiation features of the linear array are described in terms of intervals whose bounds are analytically determined as functions of the nominal value and the tolerances of the array amplitudes a set of representative numerical experiments dealing with different radiated beams and linear array sizes is reported and discussed to point out the features and potentials of the proposed approach

on a generalized l_2 projection and some related stability estimates in sobolev spaces in this paper we investigate a stability estimate needed in hybrid finite and boundary element methods especially in hybrid coupled domain decomposition methods including mortar finite elements this stability estimate is equivalent to the stability of a generalized l 2 projection in certain sobolev spaces using piecewise linear trial spaces and appropriate piecewise constant test spaces the stability of the generalized l 2 projection is proved assuming some mesh conditions locally

minkowski sum method for planar arrays sensitivity analysis with uncertain but bounded excitation tolerances the sensitivity of the power pattern generated by a planar array to both amplitude and phase excitation errors is addressed under the hypothesis of uncertain but bounded tolerances on the element excitations an innovative approach based on the integration of the interval analysis and the minkowski sum is proposed to predict tight reliable and inclusive pattern bounds representative numerical results are reported and discussed to point out the potentialities and the effectiveness of the proposed approach also in comparison with the state of the art interval based methods

a new interval pattern analysis method of array antennas based on taylor expansion in this communication a new taylor expansion based interval pattern analysis method is developed to predict the impact of the small excitation amplitude uncertainty on the radiated array pattern the dependence problem of the classical interval arithmetic which may lead to overestimation of performance intervals is addressed in this communication the proposed method approximates by approximating the antenna power values to the first order with respect to the uncertain amplitude the new method is simpler and can produce more accurate bounds of the antenna pattern and the pattern features than the existing techniques several representative numerical examples are investigated to demonstrate the validity and efficiency of the proposed method

far field pattern tolerance analysis of the antenna radome system with the material thickness error an interval arithmetic approach as the geometry thickness error of composite radome impacts the electromagnetic em performance of the antenna radome system a novel interval arithmetic analytic approach to the analysis of the effect on average power pattern of antenna radome system with the thickness error in the composite radome based is proposed the thickness error of radome s composite material is modeled as interval valued errors the link between the interval of thickness error and the interval power pattern along with some main em characteristics sidelobe level peak power and half power beamwidth expressed as intervals are efficiently constructed some comparisons with measured and simulated results reported in the state of the art literature experiment data and monte carlo mc method result serve as a way to validate the interval analysis ia based method some numerical examples are reported to reveal the effect of the main geometric properties i e location size width and midpoint of the error interval of the thickness error interval on power pattern the obtained results show that the proposed ia based approach offers tangible advantages and exhibits effectiveness versus some traditional statistical techniques e g mc method

optimal synthesis of robust beamformer weights exploiting interval analysis and convex optimization an approach for the optimal design of linear arrays in the presence of tolerances on the amplitude weights is presented starting from the knowledge of the maximum deviations from the nominal values of the amplitude coefficients of the beam forming network bfn an analytical tool based on interval analysis ia and integrating a convex programming cp method is exploited to maximize the minimum peak value of the main beam of the radiated power pattern along the boresight direction while fitting an arbitrary user defined bound on the secondary lobes in a globally optimal fashion in order to analyze the behavior of the proposed approach also assessing its effectiveness a set of representative numerical examples regarding arrays of ideal and realistic radiating elements is reported where different sidelobe constraints array configurations and tolerance errors are considered

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

matrix based interval arithmetic for linear array tolerance analysis with excitation amplitude errors this communication proposes a novel matrix based interval arithmetic mia method for linear antenna array pattern tolerance analysis with excitation amplitude errors it derives the closed form array power pattern bounds in an analytical fashion which can predict the maximum deviations with respect to the referenced value efficiently the array power pattern upper bound is its midpoint value summing two error items the first order derivative and the array error pattern while the lower bound is its midpoint value subtracting the first order derivative the new expression derived by the mia method only involves matrix manipulation and requires no condition judgment which inherits simple coding and easy implementation representative numerical examples are presented to validate and demonstrate the effectiveness of the proposed mia method

rough approximation of a preference relation by dominance relations an original methodology for using rough sets to preference modeling in multi criteria decision problems is presented this methodology operates on a pairwise comparison table pct including pairs of actions described by graded preference relations on particular criteria and by a comprehensive preference relation it builds up a rough approximation of a preference relation by graded dominance relations decision rules derived from the rough approximation of a preference relation can be used to obtain a recommendation in multi criteria choice and ranking problems the methodology is illustrated by an example of multi criteria programming of water supply systems

inverse inequalities on non quasi uniform meshes and application to the mortar element method we present a range of mesh dependent inequalities for piecewise constant and continuous piecewise linear finite element functions u defined on locally refined shape regular but possibly non quasi uniform meshes these inequalities involve norms of the form h u w s p for positive and negative s and where h is a function which reflects the local mesh diameter in an appropriate way the only global parameter involved is n the total number of degrees of freedom in the finite element space and we avoid estimates involving either the global maximum or minimum mesh diameter our inequalities include new variants of inverse inequalities as well as trace and extension theorems they can be used in several areas of finite element analysis to extend results previously known only for quasi uniform meshes to the locally refined case here we describe applications to i the theory of nonlinear approximation and ii the stability of the mortar element method for locally refined meshes

computational scales of sobolev norms with application to preconditioning this paper provides a framework for developing computationally efficient multilevel preconditioners and representations for sobolev norms specifically given a hilbert space v and a nested sequence of subspaces v 1 c v 2 c c v we construct operators which are spectrally equivalent to those of the form a k k q k q k 1 here k k 1 2 are positive numbers and q k is the orthogonal projector onto v k with q 0 0 we first present abstract results which show when a is spectrally equivalent to a similarly constructed operator a defined in terms of an approximation q k of q k for k 1 2 we show that these results lead to efficient preconditioners for discretizations of differential and pscudo differential operators of positive and negative order these results extend to sums of operators for example singularly perturbed problems such as i e can be preconditioned uniformly independently of the parameter e we also show how to precondition an operator which results from tikhonov regularization of a problem with noisy data finally we describe how the technique provides computationally efficient bounded discrete extensions which have applications to domain decomposition

frequency diverse array antenna using time modulated optimized frequency offset to obtain time invariant spatial fine focusing beampattern for a frequency diverse array fda antenna the combination of time modulated and nonlinear distributed frequency offset is proposed to realize time invariant spatial fine focusing beampatterns the distribution of the nonlinear function is optimized by using artificial bee colony algorithm and the resultant frequency offset is termed as time modulated optimized frequency offset tmofo in addition to design a tmofo fda in realistic situations the interval based tolerance analysis is introduced to predict the impact of frequency offset uncertainties or errors on the time invariant spatial focusing beampattern the spatial focusing performance of the tmofo fda is compared with an analytical fda scheme based on a time modulated logarithmically increasing frequency offset tmlfo numerical examples of a ten element linear fda with lambda 0 2 element spacing in the presence of mutual coupling effects based on the tmofo and the tmlfo are reported and compared the comparative results between the ideal tmlfo and tmofo show that in range angle plane the size of the focal spot for tmofo fda is reduced by about 70 compared to that for tmlfo fda the side lobe level is reduced about 49 the comparative results from ia based beampattern tolerance analysis also reveal the superiority of the tmofo fda scheme

multi criteria classification a new scheme for application of dominance based decision rules abstract we are considering the problem of multi criteria classification in this problem a set of if then decision rules is used as a preference model to classify objects evaluated by a set of criteria and regular attributes given a sample of classification examples called learning data set the rules are induced from dominance based rough approximations of preference ordered decision classes according to the variable consistency dominance based rough set approach vc drsa the main question to be answered in this paper is how to classify an object using decision rules in situation where it is covered by i no rule ii exactly one rule iii several rules the proposed classification scheme can be applied to both learning data set to restore the classification known from examples and testing data set to predict classification of new objects a hypothetical example from the area of telecommunications is used for illustration of the proposed classification method and for a comparison with some previous proposals

some observations on babu vs ka and brezzi theories summary some observations are made on abstract error estimates for galerkin approximations based on babuska brezzi conditions a basic error estimate due to babuska is sharpened by means of an identity that p i p for any nontrivial idempotent operator p some remarks are also made on the brezzi s theory for mixed variational problems and their galerkin approximations

uniform preconditioners for problems of positive order uniform preconditioners for operators of negative order discretized by dis continuous piecewise polynomials of any order are constructed from a boundedly invertible operator of opposite order discretized by continuous piecewise linears besides the cost of the application of the latter discretized operator the other cost of the preconditioner scales linearly with the number of mesh cells compared to earlier proposals the preconditioner has the following advantages it does not require the inverse of a non diagonal matrix it applies without any mildly grading assumption on the mesh and it does not require a barycentric refinement of the mesh underlying the trial space

rule learning for classification based on neighborhood covering reduction rough set theory has been extensively discussed in the domain of machine learning and data mining pawlak s rough set theory offers a formal theoretical framework for attribute reduction and rule learning from nominal data however this model is not applicable to numerical data which widely exist in real world applications in this work we extend this framework to numerical feature spaces by replacing partition of universe with neighborhood covering and derive a neighborhood covering reduction based approach to extracting rules from numerical data we first analyze the definition of covering reduction and point out its advantages and disadvantages then we introduce the definition of relative covering reduction and develop an algorithm to compute it given a feature space we compute the neighborhood of each sample and form a neighborhood covering of the universe and then employ the algorithm of relative covering reduction to the neighborhood covering thus derive a minimal covering rule set some numerical experiments are presented to show the effectiveness of the proposed technique