integral inequalities for concave functions with applications to special functions in this paper we prove refinements extensions and counterparts of known integral inequalities for concave functions furthermore we apply our results to find new inequalities for some special functions and mean values

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

koszul divisors on moduli spaces of curves given a moduli space how can one construct the best in the sense of higher dimensional algebraic geometry effective divisor on it we show that at least in the case of the moduli space of curves the answer is provided by the koszul divisor defined in terms of the syzygies of the parameterized objects in this paper we find a formula for the slopes of all koszul divisors on overline cal m g in particular we obtain the first infinite series of counterexamples to the harris morrison slope conjecture and we prove the maximal rank conjecture in the case when the brill noether number of the corresponding linear series equals 0 we also find shorter proofs for the formulas of the class of the brill noether and gieseker petri divisors finally we improve most of logan s results on the kodaira dimension of the moduli spaces overline cal m g n of pointed stable curves

some mean values related to the quasi arithmetic mean in this article we study new mean values and their properties related to the quasi arithmetic mean and their properties in the spirit of h haruki and th m rassias

a refinement of the cauchy schwarz inequality abstract we prove if xk and yk k 1 n are real numbers satisfying 0 x 0 1 x 2 2 x n n and 0 n y n 1 y 1 then k 1 n x k y k 2 k 1 n y k k 1 n x 2 k 1 4 x k x k 1 y k with equality holding if and only if xk kx1 k 1 n and y1 yn inequality is valid in particular if the sequence xk is positive and convex

chebyshev type inequalities involving permanents and their applications abstract we extend the well known chebyshev s inequality to some new cases involving permanents under the proper hypotheses our main results are per a b n per a n per b n and per a i 1 n j 1 n a i j per b i 1 n j 1 n b i j as applications we consider the problem of finding bounds of the ratios of two functions involving permanents

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 incomplete gamma function abstract we present several inequalities for f a x a x a 0 a 0 x 0 where a x is the incomplete gamma function one of our theorems states that the inequalities f a s p x 1 x n f a x 1 f a x n f a s q x 1 x n p q 0 hold for all nonnegative real numbers x 1 x n n 2 if and only if p m i n a 1 and q m a x a 1 here s t x 1 x n denotes the power sum of order t this extends and complements a result published by ismail and laforgia in 2006

a new weighted metric the relative metric ii in the first part of this investigation we generalized a weighted distance function of r c li s and found necessary and sufficient conditions for it being a metric in this paper some properties of this so called m relative metric are established specifically isometries and quasiconvexity results are derived we also illustrate connections between our approach and generalizations of the hyperbolic metric

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

bounds for complete elliptic integrals of the second kind with applications in this paper we present some sharp bounds for complete elliptic integrals of the second kind as applications we establish several inequalities for the perimeter of an ellipse

a new approach for fuzzy information retrieval based on weighted power mean averaging operators an information retrieval system can help users to retrieve documents relevant to the users queries in recent years some researchers used averaging operators i e infinite one operators waller kraft operators p norm operators and gma operators to handle and and or operations of users fuzzy queries for fuzzy information retrieval but they still have some drawbacks e g sometimes query results do not coincide with the intuition of the human being in this paper we present new averaging operators called weighted power mean averaging wpma operators based on the weighted power mean for dealing with fuzzy information retrieval to overcome the drawbacks of the existing methods furthermore we also extend the proposed wpma operators into the extended wpma operators to handle weighted fuzzy queries for fuzzy information retrieval the proposed wpma operators are more flexible and more intelligent than the existing averaging operators to handle users fuzzy queries for fuzzy information retrieval

sharp inequalities between one parameter and power means for all a b 0 with a b we prove that j p a b m 1 2p 3 a b for p 2 1 2 u 1 and j p a b m 1 2p 3 a b for p 00 2 1 2 1 and the parameter 1 2p 3 in either case is the best possible here j p a b and m p a b are the one parameter and power means of order p of two positive numbers a and b respectively

aggregation operators for selection problems this paper describes and compares aggregation techniques for multi expert multi criteria decision making the process of selecting applicants for a ph d program using different aggregation operators is presented as a case study the focus is on applying these operators using only ordinal sorted information a heuristic for determining weights in these situations is discussed the results obtained with different aggregation methods are compared and analyzed

generalization and sharpness of the power means inequality and their applications abstract in this paper we generalize and sharpen the power means inequality by using the theory of majorization and the analytic techniques our results unify some optimal versions of the power means inequality as application a well known conjectured inequality proposed by janous et al is proven furthermore these results are used for studying a class of geometric inequalities for simplex from which some interesting inequalities including the refined euler inequality and the reversed finsler hadwiger type inequality are obtained

generalized convexity and inequalities involving special functions abstract in this paper the authors show a relation between the generalized convexity and super sub multiplicative property and discuss some generalized convexity and inequalities involving the gaussian hypergeometric function the generalized distortion function k a x and the generalized grotzsch function a r

concavity of the complete elliptic integrals of the second kind with respect to holder means abstract in this paper we establish a necessary and sufficient condition for the concavity of the complete elliptic integrals of the second kind with respect to holder means

a variant of jensen steffensen s inequality and quasi arithmetic means a variant of jensen steffensen s inequality is proved necessary and sufficient conditions for the equality in jensen steffensen s inequality are established several inequalities involving more than two monotonic functions and generalized quasi arithmetic means with not only positive weights are proved it is shown that such generalized quasi arithmetic means have the same comparability properties as those with positive weights

power geometric operators and their use in group decision making the power average pa operator and the power ordered weighted average powa operator are the two nonlinear weighted average aggregation tools whose weighting vectors depend on the input arguments in this paper we develop a power geometric pg operator and its weighted form which are on the basis of the pa operator and the geometric mean and develop a power ordered geometric pog operator and a power ordered weighted geometric powg operator which are on the basis of the powa operator and the geometric mean and study some of their properties we also discuss the relationship between the pa and pg operators and the relationship between the powa and powg operators then we extend the pg and powg operators to uncertain environments i e develop an uncertain pg upg operator and its weighted form and an uncertain power ordered weighted geometric upowg operator to aggregate the input arguments taking the form of interval of numerical values furthermore we utilize the weighted pg and powg operators respectively to develop an approach to group decision making based on multiplicative preference relations and utilize the weighted upg and upowg operators respectively to develop an approach to group decision making based on uncertain multiplicative preference relations finally we apply both the developed approaches to broadband internet service selection

a contribution to the study of the metric and euclidean structures of dissimilarities this paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their euclidean nature we present several particular transformations which preserve euclideanarity and we complete through the study of a one parameter family the current knowledge of the metric and euclidean structure of coefficients based on binary data these results are directly deduced from two theorems which prove the positive semi definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used

new characterizations of some mean values the purpose of this paper is to give new characterizations of some mean values of two positive real numbers the arithmetic geometric and harmonic means of two positive real numbers are the fundamentals of this paper

a general refinement of jordan type inequality in this work a general form of jordan s inequality p 2 n x a n 1 p 2 4x 2 n email protected email protected p 2 n x email protected n 0na email protected 2 email protected 2 n 1 p 2 4x 2 n 1 is established where email protected 0 p 2 p 2 n x email protected n 0 na n p 2 4x 2 n a email protected a email protected 3 a n 1 2n 12 n 1 p 2a n 116n n 1 p 2a n 1 and n 0 is a natural number the applications of the above result give the general improvement of the yang le inequality and a new infinite series sinx email protected n 0 a n p 2 4x 2 n for 0 x email protected 2

matrix quantizer design for lpc speech using the generalized llyod algorithm rate distortion theory provides the motivation for using data compression techniques on matrices of n lpc vectors this leads to a simple extension of speech coding techniques using vector quantization the effects of using the generalized lloyd algorithm on such matrices using a summed itakura saito distortion measure are studied and an extension of the centroid computation used in vector quantization is presented the matrix quantizers so obtained offer substantial reductions in bit rates relative to full search vector quantizers bit rates as low as 150 bits s for the lpc matrix information inclusive of gain but without pitch and voicing have been achieved for a single speaker having average test sequence and codebook distortions comparable to those in the equivalent full search vector quantizer operating at 350 bits s preliminary results indicate that higher quality or lower bit rates may be achieved with enough computational resources

theory of surround system and associated inequalities in this paper we define the surround system s m c l and the surround system with a center s 2 p c l under the proper hypotheses we establish several geometric inequalities for s 2 p c l as applications we give the background of the surround system with a center s 2 p c l in space science

curves and symmetric spaces ii let sym 3 c p k sym 3 k sym 3 k k p 13 a 1 a a det a be the veronese embedding of the space of symmetric matrices of degree 3 where a is the cofactor matrix of a the closure spg 3 6 of this image is a 6 dimensional homogeneous variety of the symplectic group sp 3 a canonical curve c 16 c p 8 of genus 9 over a perfect field k is isomorphic to a complete linear section of this projective variety spg 3 6 c p 13 unless c k k k being the algebraic closure is a covering of degree at most 5 of the projective line we prove this by means of linear systems of higher rank

on some further extensions of the characterizations of mean values by h haruki and th m rassias abstract the purpose of this paper is to give a characterization of some mean values of two positive real numbers in a real valued function m a b the arithmetic harmonic and some other means of two positive real numbers are the fundamentals of this paper

two optimal double inequalities between power mean and logarithmic mean for email protected r the power mean m p a b of order p the logarithmic mean l a b and the arithmetic mean a a b of two positive real values a and b are defined by m p a b a p b p2 1 p p 0 ab p 0 l a b b alogb loga a b a a b and a a b a b2 respectively in this article we answer the questions what are the greatest values p and r and the least values q and s such that the inequalities m p a b 13a a b 23l a b m q a b and m r a b 23a a b 13l a b m s a b hold for all a b 0

inequalities for means abstract a monotone form of l hospital s rule is obtained and applied to derive inequalities between the arithmetic geometric mean of gauss the logarithmic mean and stolarsky s identric mean some related inequalities are given for complete elliptic integrals

some properties of generalized exponential entropies with applications to data compression abstract the scale of exponential entropies of order is introduced it unifies a number of notions of generalized differential entropies for continuous distributions the properties of this scale are derived from results in the theory of means we show that the scale can represent the extent of a probability distribution i e its degree of concentration with regard to a reference measure this fact has several consequences that are of interest in the theory of data or signal compression the aspects of data compression considered are the intrinsic extent of a probability distribution introduced by l l campbell and the properties of entropy series we investigate specially the exponential families of distributions in particular the miller thomas or generalized gaussian family of distributions

a new segment quantization using lempel ziv algorithm and its application to quantization of line spectral frequencies a new segment quantization method using the lempel ziv algorithm is proposed and it is applied to quantize line spectral frequency parameters in speech codec the proposed segment quantizer can save four bits per frame compared with the itu t g 729 speech codec 18 bits frame without degradation of subjective or objective speech quality

the mercat conjecture for stable rank 2 vector bundles on generic curves we prove the mercat conjecture for rank 2 vector bundles on generic curves of every genus for odd genus we identify the effective divisor in mg where the mercat conjecture fails and compute its slope the clifford index of a smooth curve c defined as the non negative quantity cliff c min deg l 2r l l pic c h c l 2 deg l g 1 stratifies the moduli space mg of curves of genus g with the smallest stratum being that consisting of hyperelliptic curves which have clifford index zero while the definition is obviously inspired by the classical clifford theorem the notion came to real prominence in the works of green lazarsfeld g gl voisin v2 and many others in the context of syzygies of canonical curves for a general curve c of genus g one has cliff c bg 1 2 c the locus of curves c mg with cliff c bg 1 2 c is a subvariety of codimension 1 respectively 2 when g is odd respectively even much studied by harris and mumford hm it has been a long standing problem to find an adequate definition of the clifford index for higher rank vector bundles on curves a higher rank clifford index should not only capture the behavior of the generic curve from the point of view of special higher rank vector bundles but also provide a geometrically meaningful stratification ofmg an interesting definition has been put forward by lange and newstead ln1 for a semistable vector bundle e of rank 2 and slope e on a curve c of genus g one defines its clifford index as cliff e e h c e 2 0 the rank 2 clifford index of c is then defined as the quantity cliff2 c min cliff e e uc 2 d d 2g 2 h c e 4 observe that if l is a line bundle on c with deg l 2h0 c l 2 cliff c that is l computes the clifford index of c then cliff l l cliff c in particular the inequality cliff2 c cliff c holds for every curve c of genus g the main achievement of this paper is the proof of the following result theorem 1 for a general curve c of genus g the following equality holds cliff2 c cliff c g 1 2 equivalently if e is a semistable rank 2 vector bundle on c contributing to cliff2 c then h c e e 2 cliff c mercat me conjectured the equality cliff2 c cliff c for every smooth curve c mg counterexamples to this expectation have been found using noether lefschetz special k3 surfaces in fo1 fo2 and ln2 however these examples are special in moduli and theorem 1 proves mercat s conjecture for generic curves of every genus

gradient algorithms for designing predictive vector quantizers a predictive vector quantizer pvq is a vector extension of a predictive quantizer it consists of two parts a conventional memoryless vector quantizer vq and a vector predictor two gradient algorithms for designing a pvq are developed in this paper the steepest descent sd algorithm and the stochastic gradient sg algorithm both have the property of improving the quantizer and the predictor in the sense of minimizing the distortion as measured by the average mean squared error the differences between the two design approaches are the period and the step size used in each iteration to update the codebook and predictor the sg algorithm updates once for each input training vector and uses a small step size while the sd updates only once for a long period possibly one pass over the entire training sequence and uses a relatively large step size code designs and tests are simulated for both gauss markov sources and for sampled speech waveforms and the results are compared to codes designed using techniques that attempt to optimize only the quantizer for the predictor and not vice versa

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

sharp cusa type inequalities with two parameters and their applications in the article we present several sharp cusa type inequalities with two parameters as applications some new shafer fink type and carlson type inequalities for inverse sine and cosine functions and new inequalities for bivariate means are found

on the existence of certain families of curves introduction 25 w 1 generalities on families of curves in ip 28 w the map 0 d 33 w 3 the number of moduli of a family 40 w 4 plane curves existence of families with the expected number of moduli 43 w 5 smoothing certain reducible curves in ip r r 3 47 w 6 curves in ip r 3 existence of families with the expected number of moduli 52 w curves in ip3 a more general existence theorem 55

on approximating the arithmetic geometric mean and complete elliptic integral of the first kind abstract in the article we prove that the double inequalities 1 6 p 7 r p 5 p 6 r tanh 1 r 2 r k r 1 6 q 7 r q 5 q 6 r tanh 1 r 2 r q a 1 r 5 q 6 g 1 r a 1 r 6 q 7 g 1 r l 1 r a g m 1 r p a 1 r 5 p 6 g 1 r a 1 r 6 p 7 g 1 r l 1 r hold for all r 0 1 if and only if p 2 1 570796 and q 89 69 1 289855 where k r 0 2 1 r 2 sin 2 t 1 2 d t is the complete elliptic integral of the first kind tanh 1 r log 1 r 1 r 2 is the inverse hyperbolic tangent function r 1 r 2 and a 1 r 1 r 2 g 1 r r l 1 r r 1 log r and a g m 1 r are the arithmetic geometric logarithmic and gaussian arithmetic geometric means of 1 and r respectively

some inequalities involving means and their converses using an idea of j sandor and v e s szabo an inequality of ky fan and its generalizations are proved we also establish some converses of these inequalities as consequences some well known inequalities are obtained

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

lagrangian mean type mappings for which the arithmetic mean is invariant we determine the class of all pairs of the lagrangian means forming mean type mappings which are invariant with respect to the arithmetic mean

schur convexity and schur geometrically concavity of gini means the schur convexity and the schur geometric convexity with variables x y r 2 for fixed s t of gini means g r s x y are discussed some new inequalities are obtained

generalized golden ratios defined by means abstract golden ratio is defined by a proportion corresponding to the geometric mean we introduce a generalized golden ratio as a fixed point of an operator defined by an arbitrary mean satisfying certain conditions an algorithm for the evaluation of the generalized golden ratio is obtained using banach s fixed point theorem as applications we show that some problems in shape optimization correspond to some aesthetic standards introduced in the paper

why does the kronecker model result in misleading capacity estimates many recent works that study the performance of multiple input multiple output mimo systems in practice assume a kronecker model where the variances of the channel entries upon decomposition on to the transmit and the receive eigenbases admit a separable form measurement campaigns however show that the kronecker model results in poor estimates for capacity motivated by these observations a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better in this paper we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates the transmit and or the receive eigenbases using tools from random matrix theory we then establish the theoretical basis behind the kronecker mismatch at the low and the high snr extremes 1 sparsity of the dominant statistical degrees of freedom dof in the true channel at the low snr extreme and 2 nonregularity of the sparsity structure disparities in the distribution of the dof across the rows and the columns at the high snr extreme

monotonicity theorems and inequalities for the complete elliptic integrals we prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind k and e these results lead to sharp symmetrical bounds for k and e which improve recently discovered inequalities

sharp power mean bounds for the gaussian hypergeometric function sharp inequalities are established between the gaussian hypergeometric function and the power mean these results extend known inequalities involving the complete elliptic integral and the hypergeometric mean

a mean value theorem and its applications abstract for a function f defined in an interval i satisfying the conditions ensuring the existence and uniqueness of the lagrange mean l f we prove that there exists a unique two variable mean m f such that f x f y x y m f f x f y for all x y i x y the mean m f is closely related l f necessary and sufficient condition for the equality m f m g is given a family of means m t t r relevant to the logarithmic means is introduced the invariance of geometric mean with respect to mean type mappings of this type is considered a result on convergence of the sequences of iterates of some mean type mappings and its application in solving some functional equations is given a counterpart of the cauchy mean value theorem is presented some relations between stolarsky means and m t means are discussed