Various geometric operators have been playing an important role in surface processing. For example, many shape analysis algorithms have been developed based on eigenfunctions of the Laplace–Beltrami operator (LBO), which is defined based on the first fundamental form of the surface. In this paper, we introduce two new geometric operators based on the second fundamental form of the surface, name...

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

We study theL1-stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solut...

A famous result by McKinsey and Tarski ([5] and [6]) provides an interpretation of intuitionistic logic into the modal logic S4. The algebras for S4 are Boolean algebras with an interior operator. One wonders if it is possible to perform a similar construction starting from a logic which is different from classical logic, say a logic extending Full Lambek Calculus FL. The algebraic counterpart ...

We study the output-sensitive computation of all the combinations of edges and concave vertices of a simple polygon that allow an immobilizing grasp with less than four frictionless point contacts. More specifically, if n is the number of edges, and m is the number of concave vertices of the polygon, we show how to compute: • in O(m log m + K) time, all K combinations that allow a form-closure ...

In this paper we introduce improved rules for Catmull-Clark and Loop subdivision that overcome several problems with the original schemes (lack of smoothness at extraordinary boundary vertices, folds near concave corners). In addition, our approach to rule modification allows generation of surfaces with prescribed normals, both on the boundary and in the interior, which considerably improves co...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

(Here, we use the notation x > y and x 2 y to mean, respectively, x y E k” and x y E K”.) This result extends an earlier theorem of Smith [2] concerning “discrete dynamics of monotone, concave maps”; some interesting applications to differential equations can be found in [l, 21. Another extension of Smith’s theorem has been given by TakaE in [3]. In this paper we shall extend the above trichoto...

We investigate the properties of the operator ∆(σ∆·) : H0(Ω) → H−2(Ω), where σ is a given parameter whose sign can change on the bounded domain Ω. Here, H0(Ω) denotes the subspace of H2(Ω) made of the functions v such that v = ν · ∇v = 0 on ∂Ω. The study of this problem arises when one is interested in some configurations of the Interior Transmission Eigenvalue Problem. We prove that ∆(σ∆·) : H...

Many real life situations can be described using twice continuously differentiable functions over convex sets with interior points. Such functions have an interesting separation property: At every interior point of the set they separate particular classes of quadratic convex functions from classes of quadratic concave functions. Using this property we introduce new characterizations of the deri...