Fix ρ : GQ,S → GL2(k) absolutely irreducible, and let ρ : GQ,S → GL2(R) be the universal deformation. We’re interested in the map R → Tm for some Hecke algebra defined in terms of ρ. Note that the Hecke algebra is 1-dimensional, and even finite free over Zp. The universal deformation ring R, however, often has dimension > 1 and nonzero p-torsion. In other words, the surjection R ։ Tm is not eve...

An approach to the deformable registration of three-dimensional brain tumor images to a normal brain atlas is presented. The approach involves the integration of three components: a biomechanical model of tumor mass-effect, a statistical approach to estimate the model's parameters, and a deformable image registration method. Statistical properties of the sought deformation map from the atlas to...

In this paper we explore the dynamical behaviour of the qdeformed versions of widely studied 1D nonlinear map-the Gaussian map and another famous 2D nonlinear map-the Henon map. The Gaussian map is perhaps the only 1D nonlinear map which exhibits the co-existing attractors. In this study we particularly, compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a spec...

A variational method to non rigid registration of multi-modal image data is presented. A suitable deformation will be determined via the minimization of a morphological, i.e., contrast invariant, matching functional along with an appropriate regularization energy. The aim is to correlate the morphologies of a template and a reference image under the deformation. Mathematically, the morphology o...

In the metal forming process, a realistic frictional coefficient must be specified at the die/work piece interface. Several methods are developed to evaluate friction coefficient in large deformation processes. This paper presents the concept of friction calibration map to determine different frictional conditions between interfaces of die and billet in the upsetting process. One such map is ge...

そこで本研究では、FFD の格子を自動生成し、オリジ ナルの FFD の柔軟性を保ちつつ、ユーザによる 3 次元 モデルの変形を支援する手法を提案する。我々の手法 は、まずモデルのバウンディングボックスを生成し、 それを初期格子とする。その初期格子から階層的に新 たな格子を生成することで、多重解像度格子という格 子集合を作り出し、ユーザがその中から目的に沿った 適切な格子、すなわち大域的な変形のための少数の制 御点を持つ格子や、局所的な変形のための変形対象領 域の形状をよく近似する格子を選択できるようにする。 さらに、変形前の格子だけでなく、ユーザによって変 形された格子から新たな格子の生成を行うことで、階 層的変形を行うことができる。階層的変形を用いるこ とで、格子をバウンディングボックスから再定義する ことなく、大域的な変形から局所的な変形、またはそ の逆といったようにモデルを階...

In this work, we show that the eigenvalues of the problem  (∆2 + V (x) + λ)u(x) = 0 x ∈ Ω u(x) = ∆u(x) = 0 x ∈ ∂Ω are generically simple in the set of C4 regular regions of Rn, n ≥ 2. In fact, we prove that there exists a residual set of regions C4 diffeomorphic to a given Ω such that all the eigenvalues for a supported plate equation are simple.

With the increasing complexity of photo-realistic scenes, the question of building and placing objects in three-dimensional scenes is becoming ever more di cult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free-form deformation t...