existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

multiple positive solutions for multipoint boundary value problems with one dimensional p laplacian abstract in this paper we consider the multiplicity of positive solutions for the one dimensional p laplacian differential equation p u q t f t u u 0 t 0 1 subject to some boundary conditions by means of a fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems

fine tuning some resistant rules for outlier labeling abstract a previous study examined the performance of a standard rule from exploratory data analysis which uses the sample fourths fl and fu and labels as outside any observations below fl k fu fl or above fu k fu fl customarily with k 1 5 in terms of the order statistics x 1 x 2 x n the standard definition of the fourths is fl x f and fu x n 1 f where f n 3 2 and denotes the greatest integer function the results of that study suggest that finer interpolation for the fourths might yield smoother behavior in the face of varying sample size in this article we show that using f i n 4 5 12 to define the fourths produces the desired smoothness corresponding to a common definition of quartiles fq n 4 1 4 leads to similar results instead of allowing the some outside rate per sample the probability that a sample contains one or more outside observations analogous to the experimentwise error rate in simultaneous inference to vary some us

a fourth order compact finite difference method for nonlinear higher order multi point boundary value problems a fourth order compact finite difference method is proposed for a class of nonlinear 2nth order multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as the three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term the convergence and the fourth order accuracy of the method are proved an efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems various sufficient conditions for the construction of upper and lower solutions are obtained some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach

comparing classical and resistant outlier rules abstract in this article we compare rosner s 1983 extension of the outlier t test the generalized esd procedure to the boxplot rules tukey s 1977 resistant outlier labeling approach the underlying principles are contrasted and the behavior of the procedures is compared in a variety of sampling situations to facilitate power type comparisons of procedures that are based on different paradigms the conditional outside rate a performance criterion for assessing outlier labeling procedures is introduced this quantity represents the probability that an observation yi is labeled an outlier conditional on its distance from the center e yi e some exact expressions as well as simple approximations and a monte carlo swindle are developed the conditional outside rate together with the outside rate per observation and the some outside rate per sample are applied to compare performance of the classical and boxplot rules based on monte carlo simulation of samples of sizes n 10 30 and 50

using simulated envelopes in the evaluation of normal probability plots of regression residuals we investigate properties of a diagnostic envelope method for evaluating normal probability plots of regression residuals that was proposed by atkinson 1981 implemented by bmdp hardwick 1987 and extended to logistic regression by landwehr pregibon and shoemaker 1984 the envelope s stability properties and joint residual vector inclusion levels undocumented so far in the literature are explored here with several examples alternative resistant techniques for creating envelopes are considered interpretations that can be derived from these plots are discussed a resistant version of the envelopes shows good stability and good sensitivity to outlying residuals both full normal and half normal probability plots with this envelope method provide useful information to the analyst

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

three positive solutions to a discrete focal boundary value problem abstract we are concerned with the discrete focal boundary value problem 3x t k f x t x a x t2 2x b 1 0 under various assumptions on f and the integers a t2 and b we prove the existence of three positive solutions of this boundary value problem to prove our results we use fixed point theorems concerning cones in a banach space

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

performance of some resistant rules for outlier labeling abstract the techniques of exploratory data analysis include a resistant rule for identifying possible outliers in univariate data using the lower and upper fourths fl and fu approximate quartiles it labels as outside any observations below fl 1 5 fu fl or above fu 1 5 fu fl for example in the ordered sample 5 2 0 1 8 fl 2 and fu 1 so any observation below 6 5 or above 5 5 is outside thus the rule labels 8 as outside some related rules also use cutoffs of the form fl k fu fl and fu k fu fl this approach avoids the need to specify the number of possible outliers in advance as long as they are not too numerous any outliers do not affect the location of the cutoffs to describe the performance of these rules we define the some outside rate per sample as the probability that a sample will contain one or more outside observations its complement is the all inside rate per sample we also define the outside rate per observation as the average fraction of outs

three point boundary value problems for difference equations in this paper the existence and nonexistence of positive solutions for three point nonlinear boundary value problems of difference equations are considered

existence and iteration of positive solutions for a multipoint one dimensional p laplacian boundary value problem abstract in this paper we study the existence and iteration of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following multipoint boundary condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i by applying a monotone iterative method we not only obtain the existence of positive solutions for the problem but also establish iterative schemes for approximating the solutions

on the number of positive solutions of a nonlinear algebraic system abstract in this paper we study the nonlinear algebraic system of the form e x af x where 0 is a parameter x and f x denote the column vectors col x 1 x 2 x n and col f 1 x 1 f 2 x 2 f n x n respectively with fk r r k 1 2 n 1 n and n is a positive integer a aij n n is an n n matrix and all its entries are positive numbers many problems in various areas such as difference equations boundary value problems dynamical networks stochastic process numerical analysis etc can be converted to system e applying fixed point theorems we prove results on existence uniqueness multiplicity and nonexistence of positive solutions for e

outlier labeling with boxplot procedures in this article we focus on the detection of possible outliers based on the widely used boxplot procedures the outliers in a set of data are defined to be a subset of observations that appear to be inconsistent with the remaining observations we identify the outliers by constructing a boxplot with its lower fence lf and upper fence uf either a satisfying the requirement that if the given sample is outlier free then the probability that one or more of the sample data would fall outside the region lf uf is equal to a prescribed small value or b taken to be the tolerance limits derived from an outlier free random sample within which a specified large proportion of the sampled population would be asserted to fall with a given large probability exact expressions that can be routinely used to evaluate the constants needed in the construction of the boxplot s outlier region for samples taken from the family of location scale distributions are obtained for both procedures this article sh

on numerical studies of multi point boundary value problem and its fold bifurcation based upon shooting method we set up a numerical method for approximating solutions and fold bifurcation solutions of second order multi point boundary value problems we prove the equivalence of the regularity of solutions and simple fold bifurcation solutions between the numerical method and the multi point boundary value problems many numerical experiments are carried out to illustrate the theoretical analysis from which we explore that the fold bifurcation phenomenon are generic in multi point boundary value problems although there is no theoretical analysis in the literature so far

successive iteration and positive symmetric solution for a sturm liouville like four point boundary value problem with a p laplacian operator abstract in this paper we consider the following sturm liouville like four point p laplacian boundary value problem with the nonlinear term f depending on the first order derivative p u t q t f t u t u t 0 0 t 1 subject to the boundary conditions u 0 u 0 u 1 u 0 by using a monotone iterative technique the existence of symmetric positive solutions and corresponding iterative schemes are obtained

matrix korteweg de vries and modified korteweg de vries hierarchies noncommutative soliton solutions the present work continues work on kdv type hierarchies presented by s carillo and c schiebold noncommutative korteweg de vries and modified korteweg de vries hierarchies via recursion methods j math phys 50 073510 2009 10 1063 1 3155080 general solution formulas for the kdv and mkdv hierarchies are derived by means of banach space techniques both in the scalar and matrix case a detailed analysis is given of solitons breathers their countable superpositions as well as of multisoliton solutions for the matrix hierarchies

positive solutions for some second order four point boundary value problems abstract in this paper the second order four point boundary value problem x t h t f t x t 0 0 t 1 x 0 a x x 1 b x is studied where 0 1 0 a b 1 and h 0 1 0 f 0 1 0 0 are nonnegative continuous functions by the use of the property of the corresponding green s function fixed point index theory leray schauder degree and upper and lower solution method some existence nonexistence and multiplicity results of positive solutions are acquired

positive solutions of a general discrete boundary value problem in this paper the existence of positive solutions for a nonlinear general discrete boundary value problem is established such results extend and improve some known facts for the two point and three point boundary value problems particularly the boundary value conditions can be nonlinear and the method is new for explaining the main results some numerical examples are also given

bounds for positive solutions for a focal boundary value problem we will be concerned with the focal boundary value problem 1 n n p t ny t n f h t y t n 1y t iy 0 n iy b 1 0 0 i n 1 using cone theory in a banach space we show that under certain assumptions on f this focal boundary value problem has two positive solutions in the special case 2y t 1 h2 y t y t y 0 b 1 0 where 0 1 we are able to exhibit upper and lower bounds for these two positive solutions

positive solutions for second order m point boundary value problems by using the schauder fixed point theorem and analysis method we establish the existence of solutions for the m point boundary value problem u t a t f u 0 u 0 0 u 1 i 1m 2kiu i b where b ki 0 i 1 2 m 2 0 b

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

eigenvalue and spectral intervals for a nonlinear algebraic system abstract this paper studies the nonlinear algebraic system of the form x af x where 0 a is a positive n n square matrix x x 1 x 2 x n t f x f x 1 f x 2 f x n t the nondecreasing continuous function f is defined on 0 and f u 0 for u 0 the system covers many problems that arise in applications such as difference equations boundary value problems and dynamical networks let f 0 lim u 0 cf u u and f lim u f u u we classify the system according to six pairs of possible values of f 0 and f with the assumption that both f 0 and f exist including for each case r 0 is divided into intervals for the value of intervals that corresponds to existence multiplicity and nonexistence of positive solutions of the system respectively we then obtain intervals that contain only the eigenvalues of the nonlinear operator t af also the resolvent and the spectrum of t are determined two examples are given to show the applications of the results

multiple positive solutions for second order m point boundary value problems abstract in this paper the second order m point boundary value problem u t f t u 0 0 t 1 u 0 0 u 1 i 1 m 2 k i u i 0 is studied where k i 0 i 1 2 m 2 0 1 2 m 2 1 we give at first the associated green s function and its properties for the m point boundary value problem and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

positive solutions of three point boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we study the three point boundary value problems for systems of nonlinear second order ordinary differential equations of the form u f t v t 0 1 v g t u t 0 1 u 0 v 0 0 u u 1 v v 1 under some conditions we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones

existence of multiple positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 0 1 2 m 2 1 a i 0 for i 1 2 m 3 and a m 2 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

necessary and sufficient conditions for the existence of solution to three point bvp abstract we study the existence of a solution of the three point boundary value problem p x x g x h x 0 0 x x we give sufficient and necessary conditions on g and h in order for p to have a real solution our conditions are of landesman lazer type and depend on the real values of and

existence and iteration of positive solutions for a generalized right focal boundary value problem with p laplacian operator abstract in the paper we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following third order generalized right focal boundary value problem with p laplacian operator p u t q t f t u t 0 t 1 u 0 i 1 m i u i u 0 u 1 i 1 n i u i the main tool is the monotone iterative technique

bivariate extensions of the boxplot the boxplot has proven to be a very useful tool for summarizing univariate data several options of bivariate boxplot type constructions are discussed these include both elliptic and asymmetric plots an inner region contains 50 of the data and a fence identifies potential outliers such a robust plot shows location scale correlation and a resistant regression line alternative constructions are compared in terms of efficiency of the relevant parameters additional properties are given and recommendations made emphasis is given to the bivariate biweight m estimator several practical examples illustrate that standard least squares ellipsoids can give graphically misleading summaries

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

positive solutions of singular three point boundary value problems for second order differential equations in this paper we study the existence of positive solutions of a singular three point boundary value problem for the following second order differential equation y ma t f t y t 0 t 0 1 y 0 by 0 0 y 1 ay h where m 0 is a parameter b 0 0 0 by constructing an available integral operator and combining fixed point index theory with properties of green s function under some conditions concerning the first eigenvalues corresponding to the relevant linear operator the sufficient conditions of the existence of positive solutions for the boundary value problems are established the interesting point of the results is that the term a t may be singular at t 0 and or t 1 moreover the nonlinear f t x is also allowed to have singularity at x 0