The hierarchical implicit modelling paradigm, as exemplified by the BlobTree, makes it possible to support not only Boolean operations and affine transformations, but also various forms of blending and space warping. Typically the resulting solid is converted to a boundary representation, a triangle mesh approximation for rendering. These triangles are obtained by evaluating the corresponding i...

A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · ·A s2 2 A s1 1 , where si ∈ {−1,+1} and (A1, . . . , Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matri...

g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining eigenvectors with a (potentially nonlinear) function of the unobservable population matrix. The optimal shape this reflects loss/risk that is to minimized. We solve problem estimation under variety loss functions motivated statistical precedent, probability and differential ge...

We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R(L) where R is a regular tree transducer and L is a regular tree language. The construction of this set is not possib...

The theory of regular and aperiodic transformations of finite strings has recently received a lot of interest. These classes can be equivalently defined using logic (Monadic second-order logic and first-order logic), two-way machines (regular two-way and aperiodic two-way transducers), and one-way register machines (regular streaming string and aperiodic streaming string transducers). These cla...