new existence theorems of positive solutions for sturm liouville boundary value problems by constructing available operators some new existence theorems of positive solutions are obtained for the sturm liouville boundary value problem p t u t email protected t f t u t 0 a 1u 0 email protected 1p 0 u 0 0 a 2u 1 email protected 2p 1 u 1 0 where a t 0 and l 0 is a parameter

solvability of second order nonlinear three point boundary value problems abstract we are interested in the existence of nontrivial solutions to the three point boundary value problem bvp u t f t u t 0 0 t 1 u 0 0 u 1 u u where 0 1 f t u c 0 1 r r and are real constants fixed point theorems and degree theory are frequently used to study such problems recently the authors demonstrated that in many situations the shooting method proves to be an effective approach often leading to better results with shorter proofs here we present another such example assume that f t 0 0 and that there exist nonnegative functions k h l 1 0 1 such that f t w k t w h t for all t w 0 1 r sun and liu 13 for the special case 0 and sun 14 for the special case 0 showed that if the l 1 norm k 1 is sufficiently small then there exists a nontrivial solution to the bvp in this paper their results are improved using the shooting method

causal diagrams for empirical research summary the primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject matter information in particular the paper develops a principled nonparametric framework for causal inference in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data if so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions otherwise the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained

existence and iteration of positive solutions to a class of sturm liouville like p laplacian boundary value problems abstract this paper deals with the existence and iteration of positive solutions for the following p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following sturm liouville like four point boundary condition u 0 u 0 u 1 u 0 where 0 1 by applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions we not only obtain the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

new fixed point theorems and applications to boundary value problems with p laplacian we obtain a new fixed point theorem in cone which extend the krasnosel skii s compression expansion theorem in cones under a quite relaxed condition two theorems for the existence of positive solutions of p laplacian boundary value problems are proved

some fixed point theorems and existence of positive solutions of two point boundary value problems abstract three theorems are obtained for the existence of at least one or three fixed points for a completely continuous mapping which extend the krasnoselskii s compression expansion theorem in cones based on them two theorems for the existence of positive solutions of two point boundary value problems are proved under a quite relaxed condition compared with the existing literature

positive solutions for a four point boundary value problem with the p laplacian abstract in this paper we study the nonlinear four point boundary value problem with the p laplacian p u f t u t 0 0 t 1 u 0 u 0 u 1 u 0 where p s s p 2 s p 1 0 0 1 by applying a fixed point theorem in cones sufficient conditions are given for the existence of a positive solution and multiple positive solutions the interesting point is the sturm liouville like boundary condition which was rarely treated until now

cohesive zone models higher order continuum theories and reliability methods for computational failure analysis a concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials the importance of the cohesive zone approach is emphasized and various ways to incorporate the cohesive zone methodology in discretization methods are discussed numerical representations of cohesive zone models suffer from a certain mesh bias for discrete representations this is caused by the initial mesh design while for smeared representations it is rooted in the ill posedness of the rate boundary value problem that arises upon the introduction of decohesion a proper representation of the discrete character of cohesive zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition of unity property of finite element shape functions the effectiveness of the approach is demonstrated for some examples at different scales moreover examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack true discontinuum when adhering to a continuum description of failure higher order continuum models must be used meshless methods are ideally suited to assess the importance of the higher order gradient terms as will be shown finally regularized strain softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes

conditional independence and chain event graphs graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure however it is not unusual for a model to be specified from a description of how a process unfolds i e via its event tree rather than through relationships between a given set of measurements here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships this graph is more expressive and flexible than either the bayesian network equivalent in the symmetric case or the probability decision graph various separation theorems are proved for the chain event graph these enable implied conditional independencies to be read from the graph s topology we also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree

existence of positive solutions for sturm liouville boundary value problems on the half line in this paper we establish sufficient conditions to guarantee the existence of at least one positive solution a unique positive solution and multiple positive solutions for the sturm liouville boundary value problem on the half line by using an effective operator the fixed point theorems in cone especially krasnoselskii fixed point theorem can be applied to such systems and then existence criteria are established the interesting point of the results is that the nonlinear term f can be sign changing

random walks and percolation on trees there is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree it equals the exponential of the hausdorff dimension of the boundary in an appropriate metric its importance for probabilistic processes on a tree is shown in several ways including random walk and percolation where it provides points of phase transition

computation causation and discovery in science business and policymaking anywhere data are used in prediction two sorts of problems requiring very different methods of analysis often arise the first problems of recognition and classification concerns learning how to use some features of a system to accurately predict other features of that system the second problems of causal discovery concerns learning how to predict those changes to some features of a system that will result if an intervention changes other features this book is about the second more difficult type of problem typical problems of causal discovery are how will a change in commission rates affect the total sales of a company how will a reduction in cigarette smoking among older smokers affect their life expectancy how will a change in the formula a college uses to award scholarships affect its dropout rate these sorts of changes are interventions that directly alter some features of the system and perhaps and this is the question indirectly alter others the contributors discuss recent research and applications using bayes nets or directed graphic representations including representations of feedback of recursive systems the book contains a thorough discussion of foundational issues algorithms proof techniques and applications to economics physics biology educational research and other areas

causal inference without counterfactuals abstract a popular approach to the framing and answering of causal questions relies on the idea of counterfactuals outcomes that would have been observed had the world developed differently for example if the patient had received a different treatment by definition one can never observe such quantities nor assess empirically the validity of any modeling assumptions made about them even though one s conclusions may be sensitive to these assumptions here i argue that for making inference about the likely effects of applied causes counterfactual arguments are unnecessary and potentially misleading an alternative approach based on bayesian decision analysis is presented properties of counterfactuals are relevant to inference about the likely causes of observed effects but close attention then must be given to the nature and context of the query as well as to what conclusions can and cannot be supported empirically in particular even in the absence of statistical uncertainty such inferences m

multiple solutions of impulsive sturm liouville boundary value problem via lower and upper solutions and variational methods abstract in this paper we prove the existence of multiple solutions for second order sturm liouville boundary value problem l u f x u x 0 1 r 1 u 0 r 2 u 0 where l u p x u q x u is a sturm liouville operator r 1 u u 0 u 0 r 2 u u 1 u 1 the technical approach is fully based on lower and upper solutions and variational methods the interesting point is that the existence of four solutions and seven solutions is given

successive iteration and positive symmetric solutions for some sturm liouville like four point p laplacian boundary value problems this paper deals with the existence of positive solutions for some sturm liouville like four point p laplacian boundary value problems our approach is based on the fixed point theorem and the monotone iterative technique without the assumption of the existence of lower and upper solution we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

multiple sign changing solutions to the sturm liouville boundary value problem with resonance abstract in this paper we study the sturm liouville boundary value problem p x u q x u f x u x 0 1 subject to u 0 u 0 u 1 u 1 0 by constructing a new sobolev space h 1 0 1 we discuss the existence of multiple solutions especially the existence of multiple sign changing solutions to this problem when the nonlinear f is resonant both at 0 and by combining the methods of the morse theory the topological degree and the fixed point index we establish a multiple solutions theorem which guarantees that the problem has at least six nontrivial solutions if this problem has only finitely many solutions then of these solutions there are two positive solutions two negative solutions and two sign changing solutions

causal analysis with chain event graphs as the chain event graph ceg has a topology which represents sets of conditional independence statements it becomes especially useful when problems lie naturally in a discrete asymmetric non product space domain or when much context specific information is present in this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains furthermore we demonstrate that as with causal bayesian networks cbns the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the ceg we close the paper with a proof of a back door theorem for cegs analogous to pearl s back door theorem for cbns

the existence of positive solutions for the sturm liouville boundary value problems abstract for the sturm liouville boundary value problem p t u t f t u t 0 0 t 1 1 u 0 1 p 0 u 0 0 2 u 1 2 p 1 u 1 0 where 0 we shall use a fixed point theorem in a cone to obtain the existence of positive solutions for on a suitable interval

sign changing and multiple solutions of the sturm liouville boundary value problem via invariant sets of descending flow abstract in this paper we prove the existence of sign changing and multiple solutions for the second order sturm liouville boundary value problem l u f x u x 0 1 r 1 u 0 r 2 u 0 where l u p x u q x u is the sturm liouville operator r 1 u u 0 u 0 and r 2 u u 1 u 1 the technical approach is fully based on minimax methods and invariant sets of descending flow

causal identifiability via chain event graphs we present the chain event graph ceg as a complementary graphical model to the causal bayesian network for the representation and analysis of causally manipulated asymmetric problems our focus is on causal identifiability finding conditions for when the effects of a manipulation can be estimated from a subset of events observable in the unmanipulated system ceg analogues of email protected s back door and front door theorems are presented applicable to the class of singular manipulations which includes both email protected s basic do intervention and the class of functional manipulations possible on bayesian networks these theorems are shown to be more flexible than their bayesian network counterparts both in the types of manipulation to which they can be applied and in the nature of the conditioning sets which can be used