hypergeometric transforms of functions with derivative in a half plane let a be the class of normalized analytic functions in the unit disk f a b c z and a c z denote respectively the gaussian and confluent hypergeometric functions let r lcub a r rcub such that re ei z 0 z rcub for a we define the hypergeometric transforms va b c and ua c by the convolution va b c zf a b c z z and ua c z a c z z respectively the main aim of this paper is to find conditions on 1 2 and the parameters a b c such that each of the operators va b c and ua c maps r 1 into r 2 we also find conditions such that the fu cab f a b c z 1 or ca a c z 1 is in r

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

sharp bounds for generalized elliptic integrals of the first kind abstract in this paper we prove that the double inequality 1 r 2 k a r sin a log e r a 2 r 1 r 2 holds for all a 0 1 2 and r 0 1 if and only if r a sin a 1 and a 1 a where r 1 r 2 k a r is the generalized elliptic integral of the first kind and r x is the ramanujan constant function besides as the key tool the series expression for the ramanujan constant function r x is given

inequalities for the generalized elliptic integrals and modular functions abstract in this paper the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions such as m a r and a r making use of these results the authors obtain some sharp inequalities for the so called ramanujan s generalized modular functions

some properties of the difference between the ramanujan constant and beta function abstract the authors present the power series expansions of the function r a b a at a 0 and at a 1 2 show the monotonicity and convexity properties of certain familiar combinations defined in terms of polynomials and the difference between the so called ramanujan constant r a and the beta function b a b a 1 a and obtain asymptotically sharp lower and upper bounds for r a in terms of b a and polynomials in addition some properties of the riemann zeta function n n n and its related sums are derived

on hypergeometric functions and function spaces the aim of this paper is to discuss the role of hypergeometric functions in function spaces and to prove some new results for these functions the first part of this paper proves results such as monotone convexity and concavity properties of sums of products of hypergeometric functions the second part of our results deals with the space a of all normalized analytic functions f f 0 0 f 0 1 in the unit disk and the subspace r f a a n r such that re ei f z 0 z for f a we consider integral transforms of the type v f 01 t f tz t dt where t is a real valued nonnegative weight function normalized so that 01 t 1 we obtain conditions on and the function such that v f takes each member of r into a starlike function of order 0 1 2 these results extend and improve the earlier known results in these directions we end the paper with an open problem

heuristics for selecting pair wise elicitation questions in multiple criteria choice problems abstract we present a set of heuristic approaches for selecting pair wise elicitation questions in an interactive process for multiple criteria choice problems our heuristics aim at minimizing the number of question answer iterations leading to the univocal recommendation of the decision maker s dm s most preferred alternative to identify the myopically best question at a given stage of interaction the proposed approaches ask the dm to compare a pair of alternatives that contributes to the greatest reduction of uncertainty with respect to the indication of the best alternative by all compatible value functions this uncertainty is measured either in terms of the number of potentially optimal alternatives or the entropy of first rank acceptabilities while assuming different a priori unknown probabilities of the dm s answers we discuss results from the extensive experiments on artificially generated and real world decision problems depending on the complexity of the considered problem instances we either perform a comprehensive analysis of the question answer interaction trees constructed by the heuristics or traverse their paths randomly by simulating a numerous set of decision policies we demonstrate that the greatest benefits from using our questioning procedures can be observed for problems involving numerous alternatives and few criteria and when the applied piece wise linear value functions consist of a small number of characteristic points the study allows us to identify two approaches that perform well in the average or the least advantageous elicitation scenario

quantitative image quality analysis of a nonlinear spatio temporal filter digital temporal and spatial filtering of fluoroscopic image sequences can be used to improve the quality of images acquired at low x ray exposure in this study we characterized a nonlinear edge preserving spatio temporal noise reduction filter the bidirectional multistage bms median filter of arce 1991 to assess image quality signal detection and discrimination experiments were performed on stationary targets using a four alternative forced choice paradigm a measure of detectability d was obtained for filtered and unfiltered noisy image sequences at different signal amplitudes filtering gave statistically significant average d improvements of 20 detection and 31 discrimination a nonprewhitening detection model modified to include the human spatio temporal visual system contrast sensitivity underestimated enhancement predicting an improvement of 6 pixel noise standard deviation a commonly applied image quality measure greatly overestimated effectiveness giving 67 improvement in d we conclude that human testing is required to evaluate the filter effectiveness and that human perception models must be improved to account for the spatio temporal filtering of image sequences

supplements to a class of logarithmically completely monotonic functions associated with the gamma function abstract in this article the authors present a necessary condition a sufficient condition and a necessary and sufficient condition for a class of functions associated with the gamma function to be logarithmically completely monotonic as a consequence of these results supplements to the recent investigation by chen and qi c p chen f qi logarithmically completely monotonic functions relating to the gamma function j math anal appl 321 2006 405 411 are provided and a new keckic vasic type inequality is concluded

x ray fluoroscopy spatio temporal filtering with object detection one potential way to reduce patient and staff x ray fluoroscopy dose is to reduce the quantum exposure to the detector and compensate the additional noise with digital filtering a new filtering method spatio temporal filtering with object detection is described that reduces noise while minimizing motion and spatial blur as compared to some conventional motion detection filtering schemes this object detection method incorporates additional a priori knowledge of image content i e much of the motion occurs in isolated long thin objects catheters guide wires etc we create object likelihood images and use these to control spatial and recursive temporal filtering such as to reduce blurring the objects of interest we use automatically computed receiver operating characteristic roc curves to optimize the object likelihood enhancement method and determine that oriented matched filter kernels with 4 orientations are appropriate the matched filter kernels are simple projected cylinders we demonstrate the method on several representative x ray fluoroscopy sequences to which noise is added to simulate very low dose acquisitions with processing we find that noise variance is significantly reduced with slightly less noise reduction near moving objects we estimate an effective exposure reduction greater than 80

image sequence filtering in quantum limited noise with applications to low dose fluoroscopy clinical angiography requires hundreds of x ray images putting the patients and particularly the medical staff at risk dosage reduction involves an inevitable sacrifice in image quality in this work the latter problem is addressed by first modeling the signal dependent poisson distributed noise that arises as a result of this dosage reduction the commonly utilized noise model for single images is shown to be obtainable from the new model stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle the temporal versions of these filters as developed here are more suitable for filtering image sequences as correlations along the time axis can be utilized for these dynamic sequences the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur

convexity with respect to holder mean involving zero balanced hypergeometric functions in this note we investigate the convexity of zero balanced hypergeometric functions with respect to holder mean

accurate approximations for the complete elliptic integral of the second kind abstract in this paper we prove that the double inequality s 11 4 7 4 1 r e r s 11 4 7 4 1 r holds for all r 0 1 if and only if 2 1 570796 and 11 7 1 571428 where r 1 r 2 1 2 e r 0 2 1 r 2 sin 2 t d t is the complete elliptic integral of the second kind and s p q a b q a p b p p a q b q 1 p q is the stolarsky mean of a and b

functional inequalities for the quotients of hypergeometric functions letf a b c x be the gaussian hypergeometric series and for 0 r 1 let formula g d anderson m k vamanamurthy and m vuorinen raised recently the following problem for whicha b 0 1 does formula hold for allr s 0 1 they also proved this inequality fora b 1 2 the main purpose of this paper is to give an answer to this problem fora b 1 and to find a lower bound for the summ r m s fora 0 2 andb 0 2 a

an approximation for zero balanced appell function f1 near 1 1 abstract we suggest an approximation for the zero balanced appell hypergeometric function f 1 near the singular point 1 1 our approximation can be viewed as a generalization of ramanujan s approximation for zero balanced f 1 2 and is expressed in terms of f 2 3 we find an error bound and prove some basic properties of the suggested approximation which reproduce the similar properties of the appell function our approximation reduces to the approximation of carlson gustafson when the appell function reduces to the first incomplete elliptic integral

on applications of hypergeometric functions abstract this is a survey article on the author s involvement over the years with hypergeometric functions we discuss our counter example to one of m robertson s conjectures our results on the omitted values problems brannan s conjecture on the coefficients of a certain power series generalizations of ramanujan s asymptotic formulas for complete elliptic integrals and muir s 1883 approximation to the arc length of an ellipse involving an inequality for some 3f2 s

asymptotical bounds for complete elliptic integrals of the second kind abstract in this paper we establish several asymptotical bounds for the complete elliptic integrals of the second kind e r and improve the well known conjecture e r 1 1 r 2 3 4 2 2 3 2 for all r 0 1 proposed by m vuorinen

some gamma function inequalities a class of completely monotonic functions are presented involving the gamma function as well as the derivative of the psi function as a consequence new upper and lower bounds for the ratio f x 1 f x s are obtained and compared with related bounds given in part by j d keckic and p m vasic our results are further applied to obtain functions which are laplace transforms of infinitely divisible probability measures

exponential gamma and polygamma functions simple proofs of classical and new inequalities abstract some inequalities for the exponential gamma and polygamma functions are established by means of the mean value theorem of differential calculus in particular the cases of the ratio of gamma and polygamma functions are considered in some cases the results are new in some others classical results are recovered or extended

continued fraction estimates for the psi function we present continued fraction estimates for the psi function as a consequence we educe inequality for the euler mascheroni constant which improves a result of detemple

monotonicity of some functions involving the gamma and psi functions let l x x x t x s x 8 t 1 where x is euler s gamma function we determine conditions for the numbers s t so that the function x x s x t x t s 1 l x is strongly completely monotonic on 0 oo through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation we also give several other examples of strongly completely monotonic functions defined in terms of and functions some limiting and particular cases are also considered

iterative maximum likelihood displacement field estimation in quantum limited image sequences we develop an algorithm for obtaining the maximum likelihood ml estimate of the displacement vector field dvp from two consecutive image frames of an image sequence acquired under quantum limited conditions the estimation of the dvf has applications in temporal filtering object tracking stereo matching and frame registration in low light level image sequences as well as low dose clinical x ray image sequences in the latter case a controlled x ray dosage reduction may be utilized to lower the radiation exposure to the patient and the medical staff the quantum limited effect is modeled as an undesirable poisson distributed signal dependent noise artifact a fisher bayesian formulation is used to estimate the dvf and a block component search algorithm is employed in obtaining the solution several experiments involving a phantom sequence and a teleconferencing image sequence with realistic motion demonstrate the effectiveness of this estimator in obtaining the dvf under severe quantum noise conditions 20 25 events pixel

the effect of temporal image filters on observer dependent contrast metrics interframe correlation resulting from filtering diminishes eye integration signal to noise ratio snr improvement this reduces the snr improvement used to predict improved minimum resolvable contrast or temperature difference to approximately half of that achieved at the monitor results are included for mean and recursive filters versus filter delay and blurring parameters

linear quadratic noise smoothing filters for quantum limited images we consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum limited imaging conditions a volterra expansion is investigated from which a set of linear quadratic filters is derived using higher order statistics the filters are applicable for single frame and multiple frames of a single scene imaged under low light levels

limits and inequalities associated with the euler mascheroni constant i we present several limits associated with the euler mascheroni constant ii let c 0 577215 be the euler mascheroni constant and let t n k 1 n1k lnn 12 124n and p n k 1 n22k 1 ln 4n we determine the best possible constants a b a and b such that the inequalities148 n a 3 c t n 148 n b 3and124 n a 2 1

functional inequalities involving special functions ii this paper is motivated by an open problem of anderson vamanamurthy and vuorinen we prove a chain of inequalities for hypergeometric functions generalized and normalized bessel functions kummer functions and for some general power series some particular cases and refinements are given

some properties of the gamma and psi functions with applications in this paper some monotoneity and concavity properties of the gamma beta and psi functions are obtained from which several asymptotically sharp inequalities follow applying these properties the authors improve some well known results for the volume n of the unit ball b n r n the surface area n 1 of the unit sphere s n 1 and some related constants

monotonicity of asymptotic relations for generalized hypergeometric functions abstract in this paper we study monotonicity properties of asymptotic relations for the generalized hypergeometric function f p p 1 and the lauricella hypergeometric function f d n the results extend known monotonicity properties of the zero balanced gaussian hypergeometric function f 1 2

monotonicity criterion for the quotient of power series with applications abstract in this paper we present the necessary and sufficient condition for the monotonicity of the quotient of power series as applications some gaps and misquotations in certain published articles are pointed out and corrected and some known results involving the landen inequalities for zero balanced hypergeometric functions are improved

generalized convexity and inequalities abstract let r 0 and let m be the family of all mean values of two numbers in r some examples are the arithmetic geometric and harmonic means given m 1 m 2 m we say that a function f r r is m 1 m 2 convex if f m 1 x y m 2 f x f y for all x y r the usual convexity is the special case when both mean values are arithmetic means we study the dependence of m 1 m 2 convexity on m 1 and m 2 and give sufficient conditions for m 1 m 2 convexity of functions defined by maclaurin series the criteria involve the maclaurin coefficients our results yield a class of new inequalities for several special functions such as the gaussian hypergeometric function and a generalized bessel function

inequalities for the volume of the unit ball in rn abstract let n n 2 1 n 2 be the volume of the unit ball in rn we determine the best possible constants a b a b and such that the inequalities a n n 1 n 1 n b n n 1 n 1 n a 2 n 1 n n b 2 and 1 1 n 2 n n 1 n 1 1 1 n are valid for all integers n 1 our results refine and complement inequalities proved by g d anderson et al k h borgwardt and d a klain and g c rota

some properties of a class of elliptic partial differential operators abstract we prove schwarz pick type estimates and coefficient estimates for a class of functions induced by the elliptic partial differential operators then we apply these results to obtain a landau type theorem

monotonicity properties of functions related to the psi function abstract in this paper the monotonicity properties of functions related to the psi function are obtained a double inequality for the euler mascheroni constant is established relevant connections of the results presented here with those derived in earlier works are also pointed out

precise estimates for differences of the gaussian hypergeometric function abstract by showing certain combinations of the gaussian hypergeometric functions f a b a b 1 x c and f a b a b 1 x d to be monotone on 0 1 for given a b c d 0 a b and c d the authors study the problem of comparing these two functions they find sup 0 a f a b a b 1 x c f a b a b 1 x d for x 0 1 thus solving an open problem and a recent conjecture

inequalities for compound mean iterations with logarithmic asymptotes abstract we consider the compound means arising as limits from the arithmetic geometric mean iteration and related iterations each of these iterations possesses a logarithmic asymptote we show that these limit means satisfy very precise inequalities these can be deduced in a quite uniform fashion from a comparison lemma for compound means

perception of temporally filtered x ray fluoroscopy images for noisy x ray fluoroscopy image sequences the authors quantitatively evaluated image quality after digital temporal filtering to reduce noise using an experimental paradigm called a reference test adaptive forced choice method the authors compared detectability of stationary low contrast disks in filtered and un filtered computer generated image sequences in the first experiment a low pass first order recursive filter used in x ray fluoroscopy was found to be much less effective at enhancing detectability than predicted from the reduction of display noise variance a common measurement of filter effectiveness detectability was reasonably predicted by a nonprewhitening human observer model npw hvs that included an independently determined human temporal contrast sensitivity function in another experiment designed to test models over a range of temporal frequencies the authors used paired high pass and low pass temporal filters that both reduced noise variance by 25 the high pass filter was artificially applied to the noise only and greatly improved detectability while the low pass filter had little effect the human observer model quantitatively described the measurements but classical prewhitening and nonprewhitening signal detectors did not as compared to the nonprewhitening spatio temporal matched filter human observer efficiency was low and variable at 2 1 2 9 and 0 06 for 60 frames of un filtered low pass and high pass noise respectively as compared to this detector humans were not very effective at combining information across frames on the other hand signal to noise ratios snrs from the human observer model were comparable to human performance and efficiencies were reasonably constant at 40 52 and 32 respectively the authors conclude that it is imperative to include human observer models and experiments in the analysis of noise reduction filtering of noisy image sequences such as x ray fluoroscopy

inequalities for zero balanced hypergeometric functions the authors study certain monotoneity and convexity properties of the gaussian hypergeometric function and those of the euler gamma function

logarithmically completely monotonic functions and applications in this article we give a sufficient condition and a necessary and sufficient condition for a function class associated with the gamma function to be logarithmically completely monotonic some applications are also presented

asymptotical formulas for gaussian and generalized hypergeometric functions in this paper we present several generalizations and refinements for the asymptotic formulas of gaussian and generalized hypergeometric functions

on some inequalities for the gamma and psi functions we present new inequalities for the gamma and psi functions and we provide new classes of completely monotonic star shaped and superadditive functions which are related to and