complete metrizability of topologies of strong uniform convergence on bornologies abstract we continue the study of topologies of strong uniform convergence on bornologies initiated by beer and levi 2009 4 in beer and levi 2009 4 the metrizability of such topologies restricted to continuous functions was characterized and a compatible metric was displayed we find necessary and sufficient conditions for completeness of the metric for complete metrizability and for polishness of topologies of strong uniform convergence on bornologies on continuous functions polishness of such topologies forces their coincidence with the compact open topology

a note on isometries of lipschitz spaces abstract the main purpose of this article is to generalize a recent result about isometries of lipschitz spaces botelho fleming and jamison 2 described surjective linear isometries between vector valued lipschitz spaces under certain conditions in this article we extend the main result of 2 by removing the quasi sub reflexivity condition from banach spaces

a predictive classified vector quantizer and its subjective quality evaluation for x ray ct images the authors have developed a new classified vector quantizer cvq using decomposition and prediction which does not need to store or transmit any side information to obtain better quality in the compressed images human visual perception characteristics are applied to the classification and bit allocation this cvq has been subjectively evaluated for a sequence of x ray ct images and compared to a dct coding method nine x ray ct head images from three patients are compressed at 10 1 and 15 1 compression ratios and are evaluated by 13 radiologists the evaluation data are analyzed statistically with analysis of variance and tukey s multiple comparison even though there are large variations in judging image quality among readers the proposed algorithm has shown significantly better quality than the dct at a statistical significance level of 0 05 only an interframe cvq can reproduce the quality of the originals at 10 1 compression at the same significance level while the cvq can reproduce compressed images that are not statistically different from the originals in quality the effect on diagnostic accuracy remains to be investigated

lipschitz extensions and approximations abstract the classical hahn banach theorem is based on a successive point by point procedure of extending bounded linear functionals in the setting of a general metric domain the conditions are less restrictive and the extension is only required to be lipschitz with the same lipschitz constant in this case the successive procedure can be replaced by a much simpler one which was done by mcshane and whitney in the 1930s using virtually the same construction czipszer and geher showed a similar extension property for pointwise lipschitz functions in the present paper we relate this construction to another classical result obtained previously by hausdorff and dealing with pointwise lipschitz approximations of semi continuous functions moreover we furnish complementary extension approximation results for locally lipschitz functions which fit naturally in this framework

medical image compression by using three dimensional wavelet transformation this paper proposes a three dimensional 3 d medical image compression method for computed tomography ct and magnetic resonance mr that uses a separable nonuniform 3 d wavelet transform the separable wavelet transform employs one filter bank within two dimensional 2 d slices and then a second filter bank on the slice direction ct and mr image sets normally have different resolutions within a slice and between slices the pixel distances within a slice are normally less than 1 mm and the distance between slices can vary from 1 mm to 10 mm to find the best filter bank in the slice direction the authors use the various filter banks in the slice direction and compare the compression results the results from the 12 selected mr and ct image sets at various slice thickness show that the haar transform in the slice direction gives the optimum performance for most image sets except for a ct image set which has 1 mm slice distance compared with 2 d wavelet compression compression ratios of the 3 d method are about 70 higher for ct and 35 higher for mr image sets at a peak signal to noise ratio psnr of 50 db in general the smaller the slice distance the better the 3 d compression performance

existence and uniqueness of fixed points for some mixed monotone operators abstract in this paper we introduce the e concave convex operator without any compact or continuous assumptions we prove the existence and uniqueness of fixed points giving monotone iterative sequences for the unique fixed point for the operator finally we apply the results to an integral equation of polynomial type which possesses items of measurable functions

dft spectrum filtering a e kahveci and e l hall see ieee trans comput vol c 23 no 9 p 976 81 sept 1974 introduced the concept of filtering discrete fourier transform dft spectra in the walsh sequency domain this is accomplished by finding a real and block diagonal walsh filter matrix g sub w in the walsh domain that performs the sample filtering operation as the prototype complex diagonal fourier filter matrix g sub f in the fourier domain the present authors provide additional information on the structure of g sub w and generalize some results by c j zarowski and m yunik see ibid vol assp 33 p 1246 52 oct 1985 they consider a more general class of transforms the t transforms and the structure of the resulting t transform filter matrices g sub t examples of t besides t w are considered such as the harr transform and fourth order chrestenson transform the implementation of the presented dft spectrum filtering techniques using linear systolic arrays is briefly considered

a boundary value technique for singular perturbation problems abstract a new way to solve singular perturbation problems is introduced it is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems easy to use modest problem preparation and ready computer implementation as with other methods the original problem is partitioned into inner and outer solution differential equation systems however asymptotic solution techniques are not employed the method is distinguished by the following facts the inner solution problem is solved as a two point boundary problem where the terminal boundary conditions are supplied by the solution of the outer solution problem in turn the outer solution differential equations are solved as an initial value system where the initial conditions are supplied by the inner solution at its terminal point the method is iterative on the terminal point of the inner solution problem three numerical examples are included

when is the space of minimal usco cusco maps a topological vector space abstract we will define a vector structure on the space of minimal usco resp cusco maps from a locally compact space to a stegall locally convex space we will prove that these spaces equipped with the topology of uniform convergence on compacta are locally convex spaces

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

variable rate vector quantization for medical image compression three techniques for variable rate vector quantizer design are applied to medical images the first two are extensions of an algorithm for optimal pruning in tree structured classification and regression due to breiman et al the code design algorithms find subtrees of a given tree structured vector quantizer tsvq each one optimal in that it has the lowest average distortion of all subtrees of the tsvq with the same or lesser average rate since the resulting subtrees have variable depth natural variable rate coders result the third technique is a joint optimization of a vector quantizer and a noiseless variable rate code this technique is relatively complex but it has the potential to yield the highest performance of all three techniques

a greedy tree growing algorithm for the design of variable rate vector quantizers image compression a technique for directly designing a variable rate tree structured vector quantizer by growing the tree one node at a time rather than one layer at time is presented the technique is a natural extension of a tree growing method for decision trees when the tree is pruned with a generalized algorithm for optimally pruning trees improvement is measured in the signal to noise ratio at high rates over pruning a fixed rate tree structured vector quantizer of the same initial rate the growing algorithm can be interpreted as a constrained inverse of the pruning algorithm

spectral filtering using the fast walsh transform this paper describes a method of doing spectral filtering using the fast walsh transform fwt rather than the fast fourier transform fft rather than using the walsh transform to find fourier coefficients which can then be filtered by ordinary means as was done in 2 we find a new filter function expressed as a matrix that does the same filtering operation in the walsh domain as the filter function matrix in the fourier domain this new filter matrix called the walsh gain matrix g w is block diagonal and real while the fourier gain matrix g f is complex diagonal the block diagonal structure of g w and a condition that causes g w to be real are proven an off line method for finding g w given g f is presented using the block diagonal structure of g w it is proven that spectral filtering via fwt requires fewer multiplications than spectral filtering via fft for n leq 64 where n is the length of the sequence of samples of the input signal n is a power of 2 a special condition on g f gives a g w such that spectral filtering via fwt becomes better in terms of multiplications than spectral filtering via fft for n leq 128

solvability of some fourth and higher order singular boundary value problems abstract existence results for a variety of singular fourth order boundary value problems of the form yiv f t y y y are given here our nonlinear term f may be singular at t 0 t 1 y 0 and or y 0 for example some singularities of the type y a and y b are included also we discuss and treat the extension of these results to nth order boundary value problems

on the lower and upper solutions method for the problem of elastic beam with hinged ends abstract we establish the existence theorem for solutions of fourth order nonlinear equations with the lidstone boundary conditions which model deflections of an elastic beam curve with the hinged ends the new lower and upper solutions method is formulated and then applied to a class of singularly perturbed problems and here is shown that the solutions uniformly converge to the solution of a reduced problem in the interior points of elastic curve and formula for an approximate solution without the use of numerical or iterative methods is derived

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

pointwise lipschitz functions on metric spaces abstract for a metric space x we study the space d x of bounded functions on x whose pointwise lipschitz constant is uniformly bounded d x is compared with the space lip x of bounded lipschitz functions on x in terms of different properties regarding the geometry of x we also obtain a banach stone theorem in this context in the case of a metric measure space we also compare d x with the newtonian sobolev space n 1 x in particular if x supports a doubling measure and satisfies a local poincare inequality we obtain that d x n 1 x

positive solutions of the nonlinear fourth order beam equation with three parameters abstract this paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth order beam equation u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f t u 0 1 0 0 is continuous and and are parameters we show that there exists a 0 such that the above boundary value problem bvp has at least two one and no positive solutions for 0 and respectively furthermore by using the semiorder method on cones of banach space we establish a uniqueness criterion for positive solution of the bvp in particular such a positive solution u t of the bvp depends continuously on the parameter i e u t is nondecreasing in lim 0 u t 0 and lim u t for any t 0 1

noncompactness and noncompleteness in isometries of lipschitz spaces abstract we solve the following three questions concerning surjective linear isometries between spaces of lipschitz functions lip x e and lip y f for strictly convex normed spaces e and f and metric spaces x and y i characterize those base spaces x and y for which all isometries are weighted composition maps ii give a condition independent of base spaces under which all isometries are weighted composition maps iii provide the general form of an isometry both when it is a weighted composition map and when it is not in particular we prove that requirements of completeness on x and y are not necessary when e and f are not complete which is in sharp contrast with results known in the scalar context

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

the samuel realcompactification of a metric space abstract in this paper we introduce a realcompactification for any metric space x d defined by means of the family of all its real valued uniformly continuous functions we call it the samuel realcompactification according to the well known samuel compactification associated to the family of all the bounded real valued uniformly continuous functions among many other things we study the corresponding problem of the samuel realcompactness for metric spaces at this respect we prove that a result of kat tov shirota type occurs in this context where the completeness property is replaced by bourbaki completeness a notion recently introduced by the authors and the closed discrete subspaces are replaced by the uniformly discrete ones more precisely we see that a metric space x d is samuel realcompact iff it is bourbaki complete and every uniformly discrete subspace of x has non measurable cardinal as a consequence we derive that a normed space is samuel realcompact iff it has finite dimension and this means in particular that realcompactness and samuel realcompactness can be very far apart the paper also contains results relating this realcompactification with the so called lipschitz realcompactification also studied here with the classical hewitt nachbin realcompactification and with the completion of the initial metric space

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

alternatives to the discrete cosine transform for irreversible tomographic image compression full frame irreversible compression of medical images is currently being performed using the discrete cosine transform dct although the dct is the optimum fast transform for video compression applications the authors show here that it is outperformed by the discrete fourier transform dft and discrete hartley transform dht for images obtained using positron emission tomography pet and magnetic resonance imaging mri and possibly for certain types of digitized radiographs this difference occurs because pet and mri images are characterized by a roughly circular region d of non zero intensity bounded by a region r in which the image intensity is essentially zero clipping r to its minimum extent can reduce the number of low intensity pixels but the practical requirement that images be stored on a rectangular grid means that a significant region of zero intensity must remain an integral part of the image to be compressed with this constraint imposed the dct loses its advantage over the dft because neither transform introduces significant artificial discontinuities the dft and dht have the further important advantage of requiring less computation time than the dct

a combined transform coding ctc scheme for medical images a combined transform coding ctc scheme is proposed to reduce the blocking artifact of conventional block transform coding and hence to improve the subjective performance the proposed ctc scheme is described and its information theoretic properties are investigated computer simulation results for a class of chest x ray images are presented a comparison between the ctc scheme and the conventional discrete cosine transform dct and discrete walsh hadamard transform dwht demonstrates the performance improvement of the proposed scheme in addition combined coding can also be used in noiseless coding yielding a slight improvement in the compression performance if it is used properly

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

reversible interframe compression of medical images a comparison of decorrelation methods the authors investigate whether data representing medical image sequences can be compressed more efficiently by taking into account the temporal correlation between the sequence frames the standard of comparison is intraframe hint the best known reversible decorrelation method for 2 d images in interframe decorrelation a distinction is made between extrapolation and interpolation based methods and methods based on local motion estimation block motion estimation and unregistered decorrelation these distinctions give six classes of interframe decorrelation methods all of which are described the methods are evaluated by applying them to sequences of coronary x ray angiograms ventricle angiograms and liver scintigrams as well as to a nonmedical videoconferencing image sequence for the medical image sequences 1 interpolation based methods are superior to extrapolation based methods 2 estimation of interframe motion is not advantageous for image compression 3 interframe compression yields entropies comparable to intraframe hint at higher computational costs and 4 two methods unregistered extrapolation and interpolation are nonetheless possibly interesting alternatives to intraframe hint

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 0 some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique

locally lipschitz functions cofinal completeness and uc spaces abstract let x d be a metric space we find necessary and sufficient conditions on the space for the locally lipschitz functions to coincide with each of two more restrictive classes of locally lipschitz functions studied by several authors the uniformly locally lipschitz functions and the lipschitz in the small functions in the first case we get the cofinally complete spaces and in the second the uc spaces we address this question to which family of subsets of x d is the restriction of each function in each class actually lipschitz finally we determine exactly when the class of uniformly locally lipschitz functions is uniformly dense in the cauchy continuous real valued functions a class that naturally contains them in fact our theorem is valid when the target space is any banach space our density theorem complements the uniform approximation results of garrido and jaramillo 12 13

the lipschitz metric for real valued continuous functions abstract for a continuous real function f defined on a metric space x let f denote its minimal lipschitz constant if f is lipschitz and put f otherwise we study the extended real valued metric on the continuous real functions defined by d f g max f x 0 g x 0 f g when x a b this metric provides new insight into a classical result regarding the derivative of a limit of a sequence of real valued functions defined on the interval

a computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers singularly perturbed turning point problems tpps for second order ordinary differential equations des exhibiting twin boundary layers are considered in order to obtain numerical solution of these problems a computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods in this method the given internal domain of definition of differential equation is divided into four subintervals and we solve the differential equation in each interval and combine the solution the implementation of the method on parallel architectures is mentioned error estimates are derived and numerical examples are given

strong uniform continuity abstract let b be an ideal of subsets of a metric space x d this paper considers a strengthening of the notion of uniform continuity of a function restricted to members of b which reduces to ordinary continuity when b consists of the finite subsets of x and agrees with uniform continuity on members of b when b is either the power set of x or the family of compact subsets of x the paper also presents new function space topologies that are well suited to this strengthening as a consequence of the general theory we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions

l valued bornologies on powersets in m abel and a ostak 2011 1 the concept of an l fuzzy bornology was introduced actually an l fuzzy bornology on a set x is a certain ideal in the family lx of l fuzzy subsets of a set x here we propose an alternative approach to fuzzification of the concept of bornology we define an l valued bornology on a set x as an l fuzzy subset b of the powerset 2x satisfying l valued analogues of the axioms of a bornology basic properties of l valued bornological spaces are studied our special interest concerns l valued bornologies induced by fuzzy metrics and relative compactness type l valued bornologies in changgoguen l topological spaces

asymptotic numerical methods for singularly perturbed fourth order ordinary differential equations of reaction diffusion type abstract singularly perturbed boundary value problems bvps for fourth order ordinary differential equations odes with a small positive parameter multiplying the highest derivative of the form ey iv x b x y x c x y x f x x d 0 1 y 0 p y 1 q y 0 r y 1 0 e 1 are considered the given fourth order bvp is transformed into a system of weakly coupled systems of two second order odes one without the parameter and the other with the parameter e multiplying the highest derivative and suitable boundary conditions in this paper computational methods for solving this system are presented in these methods we first find the zero order asymptotic approximation expansion of the solution of the weakly coupled system then the system is decoupled by replacing the first component of the solution by its zero order asymptotic approximation expansion of the solution in the second equation then the second equation is solved by the fitted operator method fitted mesh method and boundary value technique error estimates are derived and examples are provided to illustrate the methods

semicontinuous limits of nets of continuous functions in this paper we present a topology on the space of real valued functions defined on a functionally hausdorff space x that is finer than the topology of pointwise convergence and for which 1 the closure of the set of continuous functions mathcal c x is the set of upper semicontinuous functions on x and 2 the pointwise convergence of a net in mathcal c x to an upper semicontinuous limit automatically ensures convergence in this finer topology

a computational method for solving singular perturbation problems abstract a class of singularly perturbed two point boundary value problems for second order ordinary differential equations is considered in order to solve them a computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods the proposed method is distinguished by the following facts first we divide the given interval the domain of definition of differential equation into two subintervals called inner and outer regions then we solve the differential equation over both the regions as two point boundary value problems the terminal boundary condition of the inner region is obtained using the zero order asymptotic expansion of the solution some numerical examples are given to illustrate the method

convergence of partial maps abstract given metric spaces x d and y a partial map between x and y is a pair d u where d is a closed subset of x and u d y is a function we introduce a general convergence notion for nets of such partial functions while our initial description is variational in nature we show that this description amounts to bornological convergence of the associated net of graphs as defined by lechicki levi and spakowski 26 with respect to a natural bornology on x y and which places the work on continuous partial functions of brandi ceppitelli and hola 12 13 20 21 in a general framework

on walsh domain versus rdft filtering spectral filtering and the computation of fourier coefficients by the fast walsh transform fwt and the fast algorithm for the real discrete fourier transform frft are discussed on a comparative basis in all cases discussed the frft has fewer multiplications and additions as the comparisons show there is no good reason for using the walsh fourier method in spectral filtering or for the generation of fourier coefficients if the number of operations are the major criterion however the walsh fourier method may still be useful if both the walsh and the fourier coefficients are to be utilized in a particular application

positive solutions of nonlinear fourth order boundary value problems with local and non local boundary conditions we establish new existence results for multiple positive solutions of fourth order nonlinear equations which model deflections of an elastic beam we consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non local boundary conditions with a unified approach our method is to show that each boundary value problem can be written as the same type of perturbed integral equation in the space c 0 1 involving a linear functional u but although we seek positive solutions the functional is not assumed to be positive for all positive u the results are new even for the classic boundary conditions of clamped or hinged ends when u 0 because we obtain sharp results for the existence of one positive solution for multiple solutions we seek optimal values of some of the constants that occur in the theory which allows us to impose weaker assumptions on the nonlinear term than in previous works our non local boundary conditions contain multi point problems as special cases and for the first time in fourth order problems we allow coefficients of both signs

formation of boundary layers for singularly perturbed fourth order ordinary differential equations with the lidstone boundary conditions abstract in this paper we concentrate on the aspect of the boundary layer phenomenon that represents a typical asymptotic behavior mode of singularly perturbed systems at the endpoints of the considered interval we provide a detailed analysis of this phenomenon for the nonlinear fourth order ordinary differential equations subject to the lidstone boundary conditions by an analysis of the integral equation associated with an original boundary value problem

normality in terms of distances and contractions abstract the main purpose of this paper is to explore normality in terms of distances between points and sets we prove some important consequences on realvalued contractions i e functions not enlarging the distance showing that as in the classical context of closures and continuous maps normality in terms of distances based on an appropriate numerical notion of separation of sets has far reaching consequences on real valued contractive maps where the real line is endowed with the euclidean metric we show that normality is equivalent to 1 separation of separated sets by some urysohn contractive map 2 to kat tov tong s insertion stating that for bounded positive realvalued functions between an upper and a larger lower regular function there exists a contractive interpolating map and 3 to tietze s extension theorem stating that certain contractions defined on a subspace can be contractively extended to the whole space the appropriate setting for these investigations is the category of approach spaces but the results have quasi metric counterparts in terms of non expansive maps moreover when restricted to topological spaces classical normality and its equivalence to separation by a urysohn continuous map to kat tov tong s insertion for semicontinuous maps and to tietze s extension theorem for continuous maps are recovered

the asymptotic solution of a class of third order boundary value problems arising in the theory of thin film flows this paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third order boundary value problems which govern the motion of thin liquid films subject to viscous capillary and gravitational forces precise conditions specifying where and when the third order derivative terms in the differential equations can be neglected are derived and improved estimates for the actual solutions in terms of solutions of the lower order models are constructed the paper also contains a technique for replacing a third order problem with an asymptotically equivalent second order one that may have wider applicability

a mixed transform approach for efficient compression of medical images a novel technique is presented to compress medical data employing two or more mutually nonorthogonal transforms both lossy and lossless compression implementations are considered the signal is first resolved into subsignals such that each subsignal is compactly represented in a particular transform domain an efficient lossy representation of the signal is achieved by superimposing the dominant coefficients corresponding to each subsignal the residual error which is the difference between the original signal and the reconstructed signal is properly formulated adaptive algorithms in conjunction with an optimization strategy are developed to minimize this error both two dimensional 2 d and three dimensional 3 d approaches for the technique are developed it is shown that for a given number of retained coefficients the discrete cosine transform dct walsh mixed transform representation yields a more compact representation than using dct or walsh alone this lossy technique is further extended for the lossless case the coefficients are quantized and the signal is reconstructed the resulting reconstructed signal samples are rounded to the nearest integer and the modified residual error is computed this error is transmitted employing a lossless technique such as the huffman coding it is shown that for a given number of retained coefficients the mixed transforms again produces the smaller rms modified residual error the first order entropy of the error is also smaller for the mixed transforms technique than for the dct thus resulting in smaller length huffman codes

a differential index assignment scheme for tree structured vector quantization a differential index di assignment scheme is proposed for the image encoding system in which a variable length tree structured vector quantizer vltsvq is adopted each source vector is quantized into a terminal node of vltsvq and each terminal node is represented as a unique binary vector the proposed index assignment scheme utilizes the correlation between interblocks of the image to increase the compression ratio with the image quality maintained simulation results show that the proposed scheme achieves a much higher compression ratio than the conventional one does and that the amount of the bit rate reduction of the proposed scheme becomes large as the correlation of the image becomes large the proposed encoding scheme can be effectively used to encode mr images whose pixel values are in general highly correlated with those of the neighbor pixels

block hybrid method for the numerical solution of fourth order boundary value problems abstract a linear multistep block hybrid method with four off grid points is presented for the direct approximation of the solution of fourth order boundary value problems multiple finite difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem without the need to reduce it previously to a first order system the convergence of the proposed method is discussed the superiority of this method over existing methods is established numerically considering different problems that have appeared in the literature

modal interactions of a randomly excited hinged clamped beam abstract an investigation into the response statistics of a hinged clamped beam under broadband random excitation is made by using galerkin s method the governing equation is reduced to a system of non autonomous non linear ordinary differential equations the fokker planck equation is applied to generate a general first order differential equation in the dynamic moments of response co ordinates by means of the gaussian and non gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations the analytical results for two and three mode interactions are also compared with results obtained by monte carlo simulation

real valued lipschitz functions and metric properties of functions abstract the purpose of this article is to explore the very general phenomenon that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by an arbitrary real valued lipschitz function the composition has this property the key tools we use are the efremovic lemma 21 and a theorem of garrido and jaramillo 22 that says that a function h between metric spaces is lipschitz if and only if whenever it is followed by a lipschitz real valued function in a composition the composition is lipschitz we also present a streamlined proof of the garrido jaramillo result itself but one that still relies on their natural continuous linear operator from the lipschitz space for the target space to the lipschitz space for the domain separately we include a highly applicable uniform closure theorem that yields the most important uniform density theorems for lipschitz type functions as special cases

further examples of the boundary value technique in singular perturbation problems illustration de la technique des valeurs frontieres dans les problemes a perturbations singulieres par des exemples varies

arzela s theorem and strong uniform convergence on bornologies abstract in 1883 arzela 1983 1984 2 gave a necessary and sufficient condition via quasi uniform convergence for the pointwise limit of a sequence of real valued continuous functions on a compact interval to be continuous arzela s work paved the way for several outstanding papers a milestone was the p s alexandroff convergence introduced in 1948 to tackle the question for a sequence of continuous functions from a topological space not necessarily compact to a metric space in 2009 in the realm of metric spaces beer and levi 2009 10 found another necessary and sufficient condition through the novel notion of strong uniform convergence on finite sets we offer a direct proof of the equivalence of arzela alexandroff and beer levi conditions the proof reveals the internal gear of these important convergences and sheds more light on the problem we also study the main properties of the topology of strong uniform convergence of functions on bornologies initiated in beer and levi 2009 10

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 t 1 with the four point boundary conditions u 0 u 1 0 au 1 bu 1 0

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

numerical solution of singular perturbation problems via deviating arguments we present a new approach to numerically solving linear singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the interval the original problem is divided into outer and inner region problems a terminal boundary condition in the implicit form is derived then the outer region problem is solved as a two point boundary value problem tpbvp and an explicit terminal boundary condition is obtained in turn a new inner region problem is obtained and solved as a tpbvp using the explicit terminal boundary condition the proposed method is iterative on the terminal point of the inner region some numerical examples have been solved to demonstrate the applicability of the method

modulus of continuity and lipschitz approximation abstract given a uniformly continuous map f from a doubling metric space x to a normed linear space v and given a subadditive function we give a characterization of dominating the modulus of continuity of f in terms of lipschitz approximation as the main part of this characterization we give a constructive method of approximating a uniformly continuous map from x to v by lipschitz maps the corresponding approximation operation is linear

lipschitz type functions on metric spaces in order to find metric spaces x for which the algebra lip x of bounded lipschitz functions on x determines the lipschitz structure of x we introduce the class of small determined spaces we show that this class includes precompact and quasi convex metric spaces we obtain several metric characterizations of this property as well as some other characterizations given in terms of the uniform approximation and the extension of uniformly continuous functions in particular we show that x is small determined if and only if every uniformly continuous real function on x can be uniformly approximated by lipschitz functions

biseparating maps between lipschitz function spaces for complete metric spaces x and y a description of linear biseparating maps between spaces of vector valued lipschitz functions defined on x and y is provided in particular it is proved that x and y are bi lipschitz homeomorphic and the automatic continuity of such maps is derived in some cases besides these results are used to characterize the separating bijections between scalar valued lipschitz function spaces when y is compact