Positive solutions of a nonlinear four-point boundary value problems
In this paper, by using the Krasnoselskii's theorem in a cone, we study the existence of at least one or two positive solutions to the four-point boundary value problemy^''(t)+a(t)f(y(t))=0,00. As an application, we also give some examples to demonstrate our results.

title: A singular integral of the composite operator
abstract: We establish the Poincare-type inequalities for the composition of the homotopy operator and the projection operator. We also obtain some estimates for the integral of the composite operator with a singular density.

title: Note on third-order boundary value problem for differential equations with deviating arguments
abstract: A third-order boundary value problem for differential equations with deviating arguments is considered in this note. An existence result is obtained by the help of the well-known Leray-Schauder Alternative. Also, a uniqueness result is given.

title: Solvability of multi-point boundary value problem at resonance (III)
abstract: In this paper, we consider the following second order ordinary differential equation(1.1)x^'^'=f(t,x(t),x^'(t))+e(t),t@?(0,1),subject to one of the following boundary value conditions: (1.2)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),(1.3)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x^'(1)=@?"j"="1^n^-^2@b"jx^'(@h"j),(1.4)x^'(0)=@?"i"="1^m^-^2@a"ix^'(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),where @a"i(1=

title: Positive solutions of three-point boundary value problems for the one-dimensional p-laplacian with infinitely many singularities
abstract: We consider thesingular three-point boundary value problems 
(φp(y′))′ + a(t)f(y(t)) = 0, 0 < t < 1, y′(0) = 0, y(1) = βy(ƞ), 
where φp(s) = |s|p−2s, p ≥ 2, 0 < β < 1, 0 < η < 1, f ϵ C([0, + ∞), [0, + ∞)), a: [0,1] → [0, + ∞), andhas countably many singularities in [0, frsol|1/2). We show that there exist countably many positive solutions by using the fixed-point index theory.

title: Solvability of multi-point boundary value problem at resonance--Part IV

title: Learning with Positive and Unlabeled Examples Using Weighted Logistic Regression
abstract: The problem of learning with positive and unlabeled examples arises frequently in retrieval applications. We transform the problem into a problem of learning with noise by labeling all unlabeled examples as negative and use a linear function to learn from the noisy examples. To learn a linear function with noise, we perform logistic regression after weighting the examples to handle noise rates of greater than a half. With appropriate regularization, the cost function of the logistic regression problem is convex, allowing the problem to be solved efficiently. We also propose a performance measure that can be estimated from positive and unlabeled examples for evaluating retrieval performance. The measure, which is proportional to the product of precision and recall, can be used with a validation set to select regularization parameters for logistic regression. Experiments on a text classification corpus show that the methods proposed are effective.

title: Building text classifiers using positive and unlabeled examples
abstract: We study the problem of building text classifiers using positive and unlabeled examples. The key feature of this problem is that there is no negative example for learning. Recently, a few techniques for solving this problem were proposed in the literature. These techniques are based on the same idea, which builds a classifier in two steps. Each existing technique uses a different method for each step. We first introduce some new methods for the two steps, and perform a comprehensive evaluation of all possible combinations of methods of the two steps. We then propose a more principled approach to solving the problem based on a biased formulation of SVM, and show experimentally that it is more accurate than the existing techniques.

title: Using Decision Tree Induction for Discovering Holes in Data
abstract: Existing research in machine learning and data mining has been focused on finding rules or regularities among the data cases. Recently, it was shown that those associations that are missing in data may also be interesting. These missing associations are the holes or empty regions. The existing algorithm for discovering holes has a number of shortcomings. It requires each hole to contain no data point, which is too restrictive for many real-life applications. It also has a very high complexity, and produces a huge number of holes. Additionally, the algorithm only works in a continuous space, and does not allow any discrete/nominal attribute. These drawbacks limit its applications. In this paper, we propose a novel approach to overcome these shortcomings. This approach transforms the holes-discovery problem into a supervised learning task, and then uses the decision tree induction technique for discovering holes in data.

title: Learning from Positive and Unlabeled Examples with Different Data Distributions
abstract: We study the problem of learning from positive and unlabeled examples. Although several techniques exist for dealing with this problem, they all assume that positive examples in the positive set P and the positive examples in the unlabeled set U are generated from the same distribution. This assumption may be violated in practice. For example, one wants to collect all printer pages from the Web. One can use the printer pages from one site as the set P of positive pages and use product pages from another site as U. One wants to classify the pages in U into printer pages and non-printer pages. Although printer pages from the two sites have many similarities, they can also be quite different because different sites often present similar products in different styles and have different focuses. In such cases, existing methods perform poorly. This paper proposes a novel technique A-EM to deal with the problem. Experiment results with product page classification demonstrate the effectiveness of the proposed technique.

title: Advances in Web Mining and Web Usage Analysis: 6th International Workshop on Knowledge Discovery on the Web, WEBKDD 2004Seattle, WA, USA, August 22-25, ... Papers (Lecture Notes in Computer Science)