We explore some geometric aspects of compensation compactness associated to Jacobian determinants. We provide the optimal constant in Wente's inequality-the original motivation of this work-and go on to give various extensions to geometric situations. In fact we improve Wente's inequality somewhat, making it more appropriate for applications in which optimal results are required. This is demons...

A comprehensive error compensation system has been developed to correct geometric, thermal, and cutting forceinduced errors on a turning centre. The basic approach to error compensation is proposed in this paper. The implementation of error compensation control and o f hardware configuration of the system are also presented. A total of 11 geometric and thermal error components and 10 cutting fo...

In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, prove sharp first nonzero eigenvalue by reciprocal of size boundary and diameter respectively. We also similar estimates higher order eigenvalues.

Due to the small aperture of blood vessel, a considerable disadvantage to current intravascular ultrasound (IVUS) imaging transducers is that their lateral imaging resolution is much lower than their axial resolution. To solve this problem, a single-element, 50 MHz, 0.6 mm diameter IVUS transducer with a geometric focus at 3 mm was proposed in this paper. The focusing transducer was based on a ...

Aligned liquid crystalline nanowires within ordered porous alumina templates show a pronounced texture on a macroscopic scale. We have investigated the influence of the geometric confinement and the nature of the pore walls on the mesophase formation by means of X-ray diffraction. The apparent texture is the result of a complex interplay of the pore geometry, interfacial phenomena, and the ther...

We calculate the values of the trigonometric functions for angles: π3 and π 6 , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the d...

For a set S of n points in convex position in the plane, let P(S) denote the set of all plane spanning paths on S. The geometric path graph Gn of S is the graph with P(S) as its vertex set and two vertices P,Q ∈ P(S) are adjacent if one of the corresponding paths can be obtained from the other by means of a single edge replacement. Recently, Akl et al. [On planar path transformation, Inform. Pr...

A decomposition of a polygon P is a set of polygons whose geometric union is exactly P . We consider the problem of decomposing a polygon, which may contain holes, using subpolygons that have a bounded diameter. We show that this problem is NP-complete via a reduction from Planar 3, 4SAT .

It is well known that pebble diameter systematically decreases downstream in rivers. The contribution of abrasion is uncertain, in part because (1) diameter is insufficient to characterize pebble mass loss due to abrasion and (2) abrasion rates measured in laboratory experiments cannot be easily extrapolated to the field. A recent geometric theory describes abrasion as a curvature-dependent pro...

In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n− 1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (S, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) ac...