Mathematician Robert Bosch never intended to become an artist. But 15 years ago, he started looking for ways to engage his students in optimization research, his field of expertise. Optimization is the mathematical quest for the best way to do something, from finding the shortest distance between two places to figuring out the best way to pack a suitcase. It often involves calculating the highe...

In this paper, we examine ways that participants in online math problemsolving chat sessions dis-attend and attend to postings by other participants and the ways that participants design their postings to elicit responses from recipients. This is consequential in terms of the design of CSCL systems that use chat as the basis of participant interaction. By developing a proper understanding of th...

According to the assignment, M may not be path-connected. Thus we decompose M into path-connected components. Since M is locally Euclidean, the path-connected components are the same as the connected components and are open subspaces of M . Thus each component itself is a smooth manifold. Then we will solve the problem on each of them separately but with the same method. This means we can assum...

Authorship detection is a challenging task due to many design choices the user has to decide on. The performance highly depends on the right set of features, the amount of data, in-sample vs. out-of-sample settings, and profilevs. instance-based approaches. So far, the variety of combinations renders off-the-shelf methods for authorship detection inappropriate. We propose a novel and generally ...

The present paper surveys the history of algebraic represetations of complete directed graphs, known in graph theory as tournaments, or equivalently, relational structures with a trichotomous binary relation. Essentially, two kinds of algebraizations of tournaments were studied in the literature: algebras with one binary operation (called groupoids of tournaments) and algebras with two binary o...

In this work we present a thread-based approach for analyzing synchronous collaborative math problem solving activities. Thread information is shown to be an important resource for analyzing collaborative activities, especially for conducting sequential analysis of interaction among participants of a small group. We propose a computational model based on thread information which allows us to id...

We use the recently-developed multiparameter theory of additive Lévy processes to establish novel connections between an arbitrary Lévy process X in R, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the folklore of the theory of Lévy processes. First, we compute the Hausdorff dimension of the image X(G) ...

We present a graph-based approach to discover and extend semantic relationships found in a mathematics curriculum to more general network structures that can illuminate relationships within the instructional material. Using words representative of a secondary level mathematics curriculum we identified in separate work, we constructed two similarity networks of word problems in a mathematics tex...

In this paper, motivated and inspired by Zegeye and Shahzad (Nonlinear Anal. 70:2707-2716, 2009), Qin et al. (J. Comput. Appl. Math. 225(1):20-30, 2009) and Kimura and Takahashi (J. Math. Anal. Appl. 357:356-363, 2009), we introduce a new hybrid projection iterative scheme that converges strongly to a common element of the solution set of a generalized mixed equilibrium problem, the solution se...

Atkinson, F. V. ,1972. 'Multiparameter Eigenvalue Problems', (Matrices and compact operators) Academic Press, New York, Vol. 1 Atkinson, F. V. , 1968. 'Multiparameter spectral theory', Bull. Am. Math. Soc. , Vol. 75, pp(1-28) Baruah, A. K. , 1987. 'Estimation of eigen elements in a two-parameter eigen value problem', Ph. D Thesis, Dibrugarh University, Assam. Bindi...