Given an rc-graph R of permutation w and an rc-graph Y of permutation v, we provide an insertion algorithm, which defines an rc-graph R ← Y in the case when v is a shuffle with the descent at r and w has no descents greater than r or in the case when v is a shuffle, whose shape is a hook. This algorithm gives a combinatorial rule for computing the generalized Littlewood-Richardson coefficients ...

Let I be a finite interval and r ∈ N. Denote by ∆ s + L q the subset of all functions y ∈ L q such that the s-difference ∆ s τ y(·) is nonnegative on I, ∀τ > 0. Further, denote by ∆ s + W r p , the class of functions x on I with the seminorm x (r) L p ≤ 1, such that ∆ s τ x ≥ 0, τ > 0. For s = 3,. .. , r + 1, we obtain two-sided estimates of the shape preserving widths

We present a method for factoring polynomials of the shape f(X)− f(Y ), where f is a univariate polynomial over a field k. We then apply this method in the case when f is a member of the infinite family of exceptional polynomials we discovered jointly with H. Lenstra in 1995; factoring f(X)−f(Y ) in this case was posed as a problem by S. Cohen shortly after the discovery of these polynomials.

Motivation Direct reconstruction of 3D face shape—solely based on a sparse set of 2D feature points localized by a facial landmark detector— offers an automatic, efficient and illumination-invariant alternative to the widely known analysis-by-synthesis framework, which is extremely timeconsuming considering the enormous parameter space for both shape and photometric properties. Given 2D landmar...

The present paper proposes a simultaneous estimation of both human head pose and shape. When head pose is estimated for a generic face model, a considerable estimation error is generated by the shape difference between the model and the target face. In the proposed framework, a specific face model is gradually created for the target face by deforming the generic model based on an error analysis...

Assume Xn is a random sample of n uniform, independent points from a triangle T . The longest convex chain, Y , of Xn is defined naturally (see the next paragraph). The length |Y | of Y is a random variable, denoted by Ln. In this article, we determine the order of magnitude of the expectation of Ln. We show further that Ln is highly concentrated around its mean, and that the longest convex cha...

Shape memory polymers of polyurethane series have been developed. These polymers have the following features. (1) They can be molded easily similar to conventional plastics, (2) their shape recovery temperature can be set arbitrarily, and (3) they can be colored as required because they are transparent, making a wide range of applications possible. In this paper. the basic characteristics of th...

We present an adjoint-based optimization for electromagnetic design. It embeds commercial Maxwell solvers within a steepest-descent inverse-design optimization algorithm. The adjoint approach calculates shape derivatives at all points in space, but requires only two "forward" simulations. Geometrical shape parameterization is by the level set method. Our adjoint design optimization is applied t...

2. VIRTUAL CLAY MODELER We have developed the interactive defonable clay modeler to provide a human designer with a rnethd to interact with the virtual objects. I n our model. the smoothness of the surface and the volume constancy are gu.mnteed even i f any dcSormation is applied, Our method consists of two fundamental rndcling concepts. One IS the representation of the objects by the sliced cy...