We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weakly imposed symmetry of stress. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces...

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for H...

Large projection neurons in lamina III of the rat spinal cord that express the neurokinin 1 receptor are densely innervated by peptidergic primary afferent nociceptors and more sparsely by low-threshold myelinated afferents. However, we know little about their input from other glutamatergic neurons. Here we show that these cells receive numerous contacts from nonprimary boutons that express the...

Abstract. We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ–M∗–convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ–M∗–convolution body of the n–dimensional cube is homothetic to the unit ball of ln 1 .

We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ-M∗-convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ-M∗-convolution body of the n-dimensional cube is homothetic to the unit ball of `1 .

A 3D quasiperiodic pattern by projection from an nD lattice can be defined by an orthonormal n x n lattice matrix which produces basis vectors in pattern space with a prescribed arrangement and basis vectors in perpendicular or test space satisfying the quasicrystallographic condition. A 16 x 16 lattice matrix is derived which produces basis vectors in pattern space as a combination or mixing o...

We provide a projection-based analysis of a large class of finite element methods for second order elliptic problems. It includes the hybridized version of the main mixed and hybridizable discontinuous Galerkin methods. The main feature of this unifying approach is that it reduces the main difficulty of the analysis to the verification of some properties of an auxiliary, locally defined project...

We propose a novel second order in time numerical scheme for Cahn-Hilliard-NavierStokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, ...

Unilateral intraocular injections of either of two fluorescent carbocyanine dyes into the embryonic chick eye resulted in both retrograde staining of ganglion cells (GCs) in the eye contralateral to site of injection and anterograde labeling of axons whose cell bodies were located within the injected eye. This prominent retino-retinal projection formed by thousands of GCs having a nasal origin ...

A fixed 2-dimensional projection of a 3-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the 2-dimensional projections with probability one? Equivalently: 3-dimensional Brownian motion hits any infinite cylinder with probability one; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoi...