We consider the generalized elastica functional defined on L1(R2) as F(u) =  ∫ R2 |∇u|(α +β |div ∇u |∇u| |p)dx, if u ∈ C2(R2), +∞ else, where p > 1, α > 0, β ≥ 0. We study the L1-lower semicontinuous envelope F of F and we prove that, for any u ∈ BV(R2), F(u) can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the le...

an occlusive, diffuse, generalized lesion in medium and small-sized arteries, with particular involvement of the heart, skin, gastrointestinal tract, kidneys, pancreas, and liver. It showed a fibrous thickening of the intima; the internal lamina elastica, the media, and the adventitia remained unchanged. A pathogenic interpretation of the vascular lesions is attempted, and their asynchronism in...

At the submicron scale, an elastic fiber adheres to a rigid surface when the surface forces induced by electrostatic, capillary, or van der Waals interactions exceed the elastic restoring forces for bending. Adhesion is aided by the application of a shear load to the base of the fiber, which will initiate or increase the length of side contact. The presence of a shear force is necessary for the...

Recently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler’s elastica ...

Spherical neodymium-iron-boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chira...

A comparison of a number of texts, descriptive of the structure of the elastic intima-the fenestrated membrane of Henleof arteries, reveals the fact that the views concerning the structure of this layer are byno means unanimous. Schafer‘ speaks of the elastic intima as follows: “The elastic tissue is represented by one distinct lamina, which is separated from the endothelium by the subendotheli...

On quantization of a loop on a Riemannian sphere P with an energy functional, we must not evaluate its stationary points with respect to the energy but also all states. Thus in this paper, we have investigated moduli M of loops (a quantize loop) on P. Then we proved that its moduli is decomposed to equivalent classes determined by flows of the KdV hierarchy. Since the flows of the KdV hierarchy...

Multiple dissecting aneurysms were found in the course of an autopsy on a 52-year-old male patient who had expired suddenly as a result of a massive pericardial tamponade. Two of these aneurysms involved the aorta. The others involved muscular arteries, namely, the superior mesenteric and the splenic. In the case of the aorta, there was an absence of elastica from the entire inner half of the m...

Evidence from mass, nuclear-magnetic-resonance and infrared spectrometry and from gas-liquid and thin-layer chromatography is presented in favour of the presence of cis-trans-decaprenol, -undecaprenol and -dodecaprenol in the mixture of polyprenols (2.6mg./g.) isolated from leaf tissue of Ficus elastica. The trivial names ficaprenol-10, -11 and -12 are proposed. Nuclear-magnetic-resonance studi...