positive radial solutions and non radial bifurcation for semilinear elliptic equations in annular domains abstract we discuss the existence and multiplicity of positive radial solutions and the non radial bifurcation of u f u 0 in and u 0 on where is an annular domain of r n n 2 we prove that if f u 0 for u 0 and lim u f u u then there exists 0 such that there are at least two positive radial solutions for each 0 at least one for and none for if f 0 0 lim u 0 f u u 1 and uf u 1 e f u for u 0 e 0 then there exists a variational solution for 0 1 where 1 is the least eigenvalue of if f 0 0 lim u 0 f u u 0 and lim u f u u then there exists at least one positive radial solution for any 0 we obtain some precise multiplicity results for narrow annulus and show that the non radial bifurcation occurs if the growth of f u is rapid enough as u

on an efficient family of derivative free three point methods for solving nonlinear equations abstract new three step derivative free families of three point methods for solving nonlinear equations are presented first a new family without memory of optimal order eight consuming four function evaluations per iteration is proposed by using two weight functions the improvement of the convergence rate of this basic family even up to 50 is obtained without any additional function evaluation using a self accelerating parameter this varying parameter is calculated in each iterative step employing only information from the current and the previous iteration defining in this way a family with memory the self accelerating parameter is calculated applying newton s interpolating polynomials of degree scaling from 1 to 4 the corresponding r orders of convergence are increased from 8 to 10 11 6 4 2 11 66 and 12 providing very high computational efficiency of the proposed methods with memory another convenient fact is that these methods do not use derivatives numerical examples and comparison with the existing three point methods are included to confirm theoretical results

exact multiplicity results for a class of two point boundary value problems abstract this paper is concerned with the exact number of positive solutions for boundary value problems y p 2 y f y 0 and y 1 y 1 0 where p 1 and 0 is a positive parameter we consider the case in which the nonlinearity f is positive on 0 and p 1 f u u f u changes sign from negative to positive

bayesian inference for small sample capture recapture data we consider data on the survival of a population of cephalorhynchus hectori hector s dolphins in a marine area of new zealand to estimate survival probabilities of animal populations a multiple capture recapture sampling scheme can be used in this paper we propose a practical methodology to derive approximations to posterior distributions based on laplace methods we show how to calculate bayes estimates and credible intervals in this setting

new eighth order iterative methods for solving nonlinear equations in this paper three new families of eighth order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative this implies that the efficiency index of the developed methods is 1 682 which is optimal according to kung and traub s conjecture 7 for four function evaluations per iteration notice that bi et al s method in 2 and 3 are special cases of the developed families of methods in this study several new examples of eighth order methods with efficiency index 1 682 are provided after the development of each family of methods numerical comparisons are made with several other existing methods to show the performance of the presented methods

uniqueness and nonuniqueness for positive radial solutions of δu f u r 0 on considere le probleme de l unicite pour les solutions positives du probleme de dirichlet non lineaire u f u x 0 dans u 0 est une boule ou un anneau de r n et f 0 est superlineaire en u et satisfaisait f 0 x 0

solving nonlinear equations by a new derivative free iterative method we develop a new simple iteration formula which does not require any derivatives of f x for solving a nonlinear equation f x 0 it is proved that the convergence order of the new method is quadratic furthermore the new method can approximate complex roots by several numerical examples we show that the presented method will give desirable approximation to the root without a particularly good initial approximation and be efficient for all cases regardless of the behavior of f x

construction of optimal order nonlinear solvers using inverse interpolation abstract there is a vast literature on finding simple roots of nonlinear equations by iterative methods these methods can be classified by order by the information used or by efficiency there are very few optimal methods that is methods of order 2 m requiring m 1 function evaluations per iteration here we give a general way to construct such methods by using inverse interpolation and any optimal two point method the presented optimal multipoint methods are tested on numerical examples and compared to existing methods of the same order of convergence

a new family of optimal eighth order methods with dynamics for nonlinear equations we propose a simple yet efficient family of three point iterative methods for solving nonlinear equations each method of the family requires four evaluations namely three functions and one derivative per full iteration and possesses eighth order of convergence thus the family is optimal in the sense of kung traub conjecture and has the efficiency index 1 682 which is better than that of newton s and many other higher order methods various numerical examples are considered to check the performance and to verify the theoretical results computational results including the elapsed cpu time confirm the efficient and robust character of proposed technique moreover the presented basins of attraction also confirm better performance of the methods as compared to other established methods in literature

a family of three point methods of optimal order for solving nonlinear equations a family of three point iterative methods for solving nonlinear equations is constructed using a suitable parametric function and two arbitrary real parameters it is proved that these methods have the convergence order eight requiring only four function evaluations per iteration in this way it is demonstrated that the proposed class of methods supports the kung traub hypothesis 1974 3 on the upper bound 2 n of the order of multipoint methods based on n 1 function evaluations consequently this class of root solvers possesses very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed with only few function evaluations

semiparametric regression in capture recapture modeling capture recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time variation in survival may be explained by incorporating relevant covariates we propose nonparametric and semiparametric regression methods for estimating survival in capture recapture models a fully bayesian approach using markov chain monte carlo simulations was employed to estimate the model parameters the work is illustrated by a study of snow petrels in which survival probabilities are expressed as nonlinear functions of a climate covariate using data from a 40 year study on marked individuals nesting at petrels island terre adelie

new modifications of hansen patrick s family with optimal fourth and eighth orders of convergence in this paper we present two new second derivative free classes of iterative methods based on hansen patrick s family hansen and patrick 1977 4 for solving nonlinear equations numerically in terms of computational cost both families require only three and four functional evaluations to achieve optimal fourth and eighth orders of convergence respectively moreover the local convergence analysis of the proposed methods is also given using hypotheses only on the first derivative and lipschitz constants furthermore the proposed schemes can also determine the complex zeros without having to start from a complex initial guess as would be necessary with other methods numerical examples and comparisons with some existing methods are included to confirm the theoretical results and high computational efficiency

global branches of non radially symmetric solutions to a semilinear neumann problem in a disk let d r 2 be a disk and let f c 3 we assume that there is a r such that f a 0a ndf a 0 in this article we are concerned with the neumann problem u f u 0i nd u 0o n d we show the following there are unbounded continuums consisting of non radially symmetric solutions emanating from the second and third eigenvalues if f u u u u p 1 a 1 or if f is of bistable type then the unbounded branches emanating from non principal eigenvalues are unbounded in the positive direction of the branch emanating from the second eigenvalue is unique near the bifurcation point up to rotation the main tool of this article is the zero level set the nodal curve of u and ux

a minimax inequality and its applications to ordinary differential equations the aim of this paper is to investigate the minimax inequality which plays a fundamental role in the critical points theorem of b ricceri below equivalent formulations are shown and characterization is proved in particular for a special class of functionals as an application a multiplicity result for an ordinary dirichlet problem is emphasized

bayesian analyses for a multiple capture recapture model summary in multiple capture recapture surveys the probability of capture can vary between sampling occasions the model accounting for this variation is known as at bayes empirical bayes and bayes empirical bayes solutions are given to the problems of interval estimation decision making and point estimation of the population size n when the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate estimates obtained from empirical bayes and bayes empirical bayes methods compare closely to bayesian methods using a reference prior distribution for the capture probabilities however when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small inferences obtained using different reference priors can differ considerably

several improvements of the 2 point third order midpoint iterative method using weight functions abstract in this paper we improve the order of the midpoint iterative method from three to four with same number of function evaluations using weight functions to obtain a class of 2 point fourth order jarratt type methods then we prove a general result to further improve the order of the old methods through an additional function evaluation using weight functions in this way we develop two 3 point sixth order midpoint methods using different weights a family of n point i f s of order 2 n is proposed using weight functions we further improve the methods to obtain a 5 point sixteenth order midpoint method with same efficiency index as the optimal 2 point fourth order jarratt type methods two numerical examples using different starting are provided to test the robustness of the methods

some sixth order variants of ostrowski root finding methods abstract in this paper we present some sixth order class of modified ostrowski s methods for solving nonlinear equations per iteration each class member requires three function and one first derivative evaluations and is shown to be at least sixth order convergent several numerical examples are given to illustrate the performance of some of the presented methods

on non radially symmetric bifurcation in the annulus we discuss the radially symmetric solutions and the non radially symmetric bifurcation of the semilinear elliptic equation u 2 eu 0 in and u 0 on where x r2 a2 0 a the upper branch of radial solutions has a non radially symmetric bifurcation symmetry breaking at each k a k 1 as a 0 the radial solutions will tend to the radial solutions on the disk and 0 a 1 the critical number on the disk

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

some novel and optimal families of king s method with eighth and sixteenth order of convergence in this study our principle aim is to provide some novel eighth and sixteenth order families of king s method for solving nonlinear equations which should be superior than the existing schemes of same order the relevant optimal orders of the proposed families satisfy the classical kung traub conjecture which was made in 1974 the derivations of the proposed schemes are based on the weight function and rational approximation approaches respectively in addition convergence properties of the proposed families are fully investigated along with one lemma and two main theorems describing their order of convergence we consider a concrete variety of real life problems e g the trajectory of an electron in the air gap between two parallel plates chemical engineering problem van der waal s equation which explains the behavior of a real gas by introducing in the ideal gas equations and fractional conversion in a chemical reactor in order to check the validity applicability and effectiveness of our proposed methods further it is found from the numerical results that our proposed methods perform better than the existing ones of the same order when the accuracy is checked in the multi precision digits

existence of positive nonradial solutions for nonlinear elliptic equations in annular domains we study the existence of positive nonradial solutions of equation a f u 0 in sia u 0 on d la where s x 6 w a 2 and is positive and superlinear at both 0 and oo we use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak 0 1 for any positive integer k if is subcritical and for large k if is supercritical when is subcritical then a nehari type variational method can be used to prove that there exists a e 0 1 such that for any a e a 1 the equation has a nonradial solution on 0 a

on a general class of optimal order multipoint methods for solving nonlinear equations abstract we develop a class of n point iterative methods with optimal 2 n order of convergence for solving nonlinear equations newton s second order and ostrowski s fourth order methods are special cases corresponding to n 1 and n 2 eighth and sixteenth order methods that correspond to n 3 and n 4 of the class are special cases of the eighth and sixteenth order methods proposed by sharma et al 25 the methodology is based on employing the previously obtained n 1 step scheme and modifying the n th step by using rational hermite interpolation unlike that of existing higher order techniques the proposed technique is attractive since it leads to a simple implementation local convergence analysis is provided to show that the iterations are locally well defined and convergent theoretical results are verified through numerical experimentations the performance is also compared with already established methods in literature it is observed that new algorithms are more accurate than existing counterparts and very effective in high precision computations

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

derivative free two point methods with and without memory for solving nonlinear equations abstract two families of derivative free two point iterative methods for solving nonlinear equations are constructed these methods use a suitable parametric function and an arbitrary real parameter it is proved that the first family has the convergence order four requiring only three function evaluations per iteration in this way it is demonstrated that the proposed family without memory supports the kung traub hypothesis 1974 on the upper bound 2n of the order of multipoint methods based on n 1 function evaluations further acceleration of the convergence rate is attained by varying a free parameter from step to step using information available from the previous step this approach leads to a family of two step self accelerating methods with memory whose order of convergence is at least 2 5 4 236 and even 2 6 4 449 in special cases the increase of convergence order is attained without any additional calculations so that the family of methods with memory possesses a very high computational efficiency numerical examples are included to demonstrate exceptional convergence speed of the proposed methods using only few function evaluations

the global solution set for a class of semilinear problems we use bifurcation theory to study positive negative and sign changing solutions for several classes of boundary value problems depending on a real parameter we show the existence of infinitely many points of pitchfork bifurcation and study global properties of the solution curves

a fourth order iterative method for solving nonlinear equations the present paper illustrates an iterative numerical method to solve nonlinear equations of the form f x 0 especially those containing the partial and non partial involvement of transcendental terms comparative analysis shows that the present method is faster than newton raphson method hybrid iteration method new hybrid iteration method and others cost is also found to be minimum than these methods the beauty in our method can be seen because of the optimization in important effecting factors i e lesser number of iteration steps lesser number of functional evaluations and lesser value of absolute error in final as well as in individual step as compared to the other methods this work also demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative

an efficient optimal family of sixteenth order methods for nonlinear models abstract the principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ newton s method to further develop new interesting optimal scheme of order sixteen this scheme requires four evaluations of the involved function and one evaluation of its first order derivative at each step so it is being optimally consistent with the conjecture of kung traub in addition theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence moreover the conjugacy maps and the strange fixed points of some iterative methods are discussed their basins of attractions are also given to show their dynamical behavior around the simple roots from the numerical experiments we find that our methods perform better than the existing ones when we checked the performance on a concrete variety of nonlinear equations

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

third order derivative free sph iterative method for solving nonlinear systems the majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function in this paper based on the basic principle of the sph method s kernel approximation a kernel approximation was constructed to compute first and second order derivatives through taylor series expansion derivatives in our proposed method were replaced in a newton like iterative method to obtain a derivative free sph iterative method for solving nonlinear systems to illustrate that the new method has the same order of convergence as the considered iterative method some numerical examples are presented

symmetry breaking for solutions of semilinear elliptic equations with general boundary conditions we study the bifurcation of radially symmetric solutions of f u 0 onn balls into asymmetric ones we show that ifu satisfies homogeneous neumann boundary conditions the asymmetric components in the kernel of the linearized operators can have arbitrarily high dimension for general boundary conditions we prove some theorems which give bounds on the dimensions of the set of asymmetric solutions and on the structure of the kernels of the linearized operators

a family of optimal three point methods for solving nonlinear equations using two parametric functions abstract using an interactive approach which combines symbolic computation and taylor s series a wide family of three point iterative methods for solving nonlinear equations is constructed these methods use two suitable parametric functions at the second and third step and reach the eighth order of convergence consuming only four function evaluations per iteration this means that the proposed family supports the kung traub hypothesis 1974 on the upper bound 2 m of the order of multipoint methods based on m 1 function evaluations providing very high computational efficiency different methods are obtained by taking specific parametric functions the presented numerical examples demonstrate exceptional convergence speed with only few function evaluations

eighth order family of iterative methods for nonlinear equations and their basins of attraction abstract we present a new family of eighth order methods for solving nonlinear equations the order of convergence of the considered methods is proved and corresponding asymptotic error constants are expressed in terms of four parameters numerical examples obtained using mathematica with high precision arithmetic demonstrate convergence and efficacy of our family of methods for some combinations of parameter values the new eighth order methods produce very good results on tested examples compared to the results produced by some of the eighth order methods existing in the related literature an exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials

exact multiplicity results for a class of boundary value problems with cubic nonlinearities abstract we give an exact multiplicity result for a class of boundary value problems for cubic nonlinearities with an explicit x dependence moreover we provide a detailed analysis of global solution curves

a family of composite fourth order iterative methods for solving nonlinear equations in this paper we present a family of new fourth order iterative methods for solving nonlinear equations per iteration the methods consisting of the family require only two evaluations of the function and one evaluation of its derivative several numerical examples are given to illustrate the efficiency and performance of some of the presented methods

a variant of steffensen king s type family with accelerated sixth order convergence and high efficiency index first it is attempted to derive an optimal derivative free steffensen king s type family without memory for computing a simple zero of a nonlinear function with efficiency index 4 1 3 1 587 next since our without memory family includes a parameter in which it is still possible to increase the convergence order without any new function evaluations therefore we extract a new method with memory so that the convergence order rises to six without any new function evaluation and therefore reaches efficiency index 6 1 3 1 817 consequently derivative free and high efficiency index would be the substantial contributions of this work as opposed to the classical steffensen s and king s methods finally we compare some of the convergence planes with different weight functions in order to show which are the best ones

interpolatory multipoint methods with memory for solving nonlinear equations abstract a general way to construct multipoint methods for solving nonlinear equations by using inverse interpolation is presented the proposed methods belong to the class of multipoint methods with memory in particular a new two point method with memory with the order 5 17 2 4 562 is derived computational efficiency of the presented methods is analyzed and their comparison with existing methods with and without memory is performed on numerical examples it is shown that a special choice of initial approximations provides a considerably great accuracy of root approximations obtained by the proposed interpolatory iterative methods

improved chebyshev halley methods with sixth and eighth order convergence we present a second derivative free family of modified chebyshev halley methods with increasing order of convergence for solving nonlinear equations the idea is based on the recent development by li et al 2014 analysis of convergence shows that the family possesses at least sixth order of convergence in a particular case even eighth order of convergence is achieved per iteration each method of the family requires four evaluations namely three functions and one first derivative that means the eighth order method is optimal in the sense of kung traub hypothesis numerical tests are performed which confirm the theoretical results regarding order of convergence and efficiency of the new methods

capture recapture estimation via gibbs sampling capture recapture models are widely used in the estimation of population sizes based on data augmentation considerations we show how gibbs sampling can be applied to calculate bayes estimates in this setting as a result formulations which were previously avoided because of analytical and numerical intractability can now be easily considered for practical application we illustrate this potential by using gibbs sampling to calculate bayes estimates for a hierarchical capture recapture model in a real example

a new family of eighth order iterative methods for solving nonlinear equations a family of eighth order iterative methods with four evaluations for the solution of nonlinear equations is presented kung and traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2 n 1 the new family of eighth order methods agrees with the conjecture of kung traub for the case n 4 therefore this family of methods has efficiency index equal to 1 682 numerical comparisons are made with several other existing methods to show the performance of the presented methods

an improvement to ostrowski root finding method an improvement to the iterative method based on the ostrowski one to compute nonlinear equation solutions which increases the local order of convergence is suggested the adaptation of a strategy presented here gives a new iteration function with an additional evaluation of the function it also shows a smaller cost if we use adaptive multi precision arithmetic the numerical results computed using this system with a floating point system representing 200 decimal digits support this theory

a composite fourth order iterative method for solving non linear equations in this paper we present a new iterative method with order of convergence four for solving non linear equations per iteration the new method requires two evaluations of the function and one evaluation of its first derivative analysis of efficiency in term of function evaluations shows that the new method is superior its practical utility is demonstrated by numerical examples

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

exact multiplicity results for a p laplacian problem with concave convex concave nonlinearities we study the exact number of positive solutions of a two point dirichlet boundary value problem involving the p laplacian operator we consider the case p 2 as well as the case p 1 when the nonlinearity f satisfies f 0 0 and has two distinct simple positive zeros and such that f changes sign exactly twice on 0 note that we may allow that f changes sign more than twice on 0 some interesting examples of quartic polynomials are given in particular for f u u2 u 1 u 2 we study the evolution of the bifurcation curves of the p laplacian problem as p increases from 1 to infinity and hence are able to determine the exact multiplicity of positive solutions for each p 1

new modifications of potra ptak s method with optimal fourth and eighth orders of convergence in this paper we present two new iterative methods for solving nonlinear equations by using suitable taylor and divided difference approximations both methods are obtained by modifying potra ptak s method trying to get optimal order we prove that the new methods reach orders of convergence four and eight with three and four functional evaluations respectively so kung and traub s conjecture kung and traub 1974 2 that establishes for an iterative method based on n evaluations an optimal order p 2 n 1 is fulfilled getting the highest efficiency indices for orders p 4 and p 8 which are 1 587 and 1 682 we also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with potra ptak s method from which they have been derived and with other recently published eighth order methods

exact multiplicity results for boundary value problems with nonlinearities generalizing cubic using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type the first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u the second one deals with a class of nonlinearities with explicit x dependence

three point methods with and without memory for solving nonlinear equations abstract a new family of three point derivative free methods for solving nonlinear equations is presented it is proved that the order of convergence of the basic family without memory is eight requiring four function evaluations which means that this family is optimal in the sense of the kung traub conjecture further accelerations of convergence speed are attained by suitable variation of a free parameter in each iterative step this self accelerating parameter is calculated using information from the current and previous iteration so that the presented methods may be regarded as the methods with memory the self correcting parameter is calculated applying the secant type method in three different ways and newton s interpolatory polynomial of the second degree the corresponding r order of convergence is increased from 8 to 4 1 5 2 8 472 9 10 and 11 the increase of convergence order is attained without any additional function calculations providing a very high computational efficiency of the proposed methods with memory another advantage is a convenient fact that these methods do not use derivatives numerical examples and the comparison with existing three point methods are included to confirm theoretical results and high computational efficiency

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

exact multiplicity and ordering properties of positive solutions of a p laplacian dirichlet problem and their applications we study the exact multiplicity and ordering properties of positive solutions of the p laplacian dirichlet problem

a new highly efficient and optimal family of eighth order methods for solving nonlinear equations the principle aim of this manuscript is to present a new highly efficient and optimal eighth order family of iterative methods to solve nonlinear equations in the case of simple roots the derivation of this scheme is based on weight function and rational approximation approaches the proposed family requires only four functional evaluations viz f xn f xn f yn and f zn per iteration therefore the proposed family is optimal in the sense of kung traub hypotheses in addition we given a theorem which describing the order of convergence of the proposed family moreover we present a local convergence analysis using hypotheses only on the first order derivative since in our preceding theorem we used hypotheses on higher order derivatives that do not appear in these methods in this way we expand the applicability of these methods even further furthermore a variety of nonlinear equations is considered for the numerical experiments it is observed from the numerical experiments that our proposed methods perform better than the existing optimal methods of same order when the accuracy is checked in multi precision digits

a bayesian analysis of multiple recapture sampling for a closed population summary this paper considers from a bayesian viewpoint inferences about the size of a closed animal population from data obtained by a multiple recapture sampling scheme the method developed enables prior information about the population size and the catch probabilities to be utilized to produce considerable improvements in certain cases on ordinary maximum likelihood methods several ways of expressing such prior information are explored and a practical example of the uses of these ways is given the main result of the paper is an approximation to the posterior distribution of sample size that exhibits the contributions made by the likelihood and the prior ideas the multiple recapture sampling scheme involves taking samples from a population of animals at each stage counting the number of marked animals in the sample marking the previously unmarked animals and returning the sample to the population the literature is reviewed by cormack 1968 and the papers most relevant to our problem are those of chapman 1952 and darroch 1958 in these papers maximum likelihood estimates for the population parameters and variances for these estimates are given our approach differs from previous ones by introducing prior information about the population size and about the propensities of the animals to be captured called catch probabilities by some previous authors the incorporation of these propensities is a feature not shared by many previous approaches darroch 1958 found their introduction into his model does not change the maximum likelihood estimates of the population size our approach will show that strong prior knowledge about the catch probabilities can greatly affect inference about the population size and it is in this respect that the greatest difference from previous approaches lies although it is recognized that models of an open population incorporating death and immigration such as those of jolly 1965 and seber 1965 are more practically realistic we feel that our method which deals only with a closed population is worth investigating as a step towards providing a bayesian treatment of the open population problem

a family of modified ostrowski methods with accelerated sixth order convergence based on ostrowski fourth order multipoint method we derive a one parameter family of sixth order methods for solving equations each member of the family requires three evaluations of the given function and one evaluation of its derivative per iteration numerical examples are presented and performance is compared with ostrowski method

an analysis of a khattri s 4th order family of methods in this paper we analyze an optimal fourth order family of methods suggested by khattri and babajee 2013 we analyze the family using the information on the extraneous fixed points two measures of closeness to the imaginary axis of the set of extraneous points are considered and applied to the members of the family to find its best performer the results are compared to three best members of king s family of methods

generating function method for constructing new iterations abstract in this paper we propose a generating function method for constructing new two and three point iterations with p 3 p 8 order of convergence this approach allows us to derive a new family of the optimal order iterative methods that include well known methods as special cases the necessary and sufficient conditions for pth order convergence of the proposed iterations are given in terms of parameters n and n we also propose some generating functions for n and n we give the extension of a class of optimal fourth order jarratt s type iterations with a 2 3 we develop a unified representation of all optimal eighth order methods several numerical results are given to demonstrate the efficiency and the performance of the presented methods and compare them with some other existing methods

on the similarity of some three point methods for solving nonlinear equations abstract in this short note we discuss certain similarities between some three point methods for solving nonlinear equations in particular we show that the recent three point method published in r thukral a new eighth order iterative method for solving nonlinear equations appl math comput 217 2010 222 229 is a special case of the family of three point methods proposed previously in r thukral m s petkovic family of three point methods of optimal order for solving nonlinear equations j comput appl math 233 2010 2278 2284

three step iterative methods with eighth order convergence for solving nonlinear equations a family of eighth order iterative methods for the solution of nonlinear equations is presented the new family of eighth order methods is based on king s fourth order methods and the family of sixth order iteration methods developed by chun et al per iteration the new methods require three evaluations of the function and one evaluation of its first derivative therefore this family of methods has the efficiency index which equals 1 682 kung and traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n 1 thus we provide a new example which agrees with the conjecture of kung traub for n 4 numerical comparisons are made to show the performance of the presented methods

comparison of several families of optimal eighth order methods several families of optimal eighth order methods to find simple roots are compared to the best known eighth order method due to wang and liu 2010 we have tried to improve their performance by choosing the free parameters of each family using two different criteria

some variants of ostrowski s method with seventh order convergence in this paper we present a class of new variants of ostrowski s method with order of convergence seven per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore this class of methods has the efficiency index equal to 1 627 numerical tests verifying the theory are given and multistep iterations based on the present methods are developed