it is known that solutions locally belong to a slightly higher Sobolev space than assumed a priori. This self-improving property was first observed by Elcrat and Meyers in [ME] (see also [Gi] and [Str]). Their argument is based on reverse Hölder inequalities and a modification of Gehring’s lemma [Ge], which originally was developed to study the higher integrability of the Jacobian of a quasicon...

A survey of swept volume concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into five major categories: method with envelope theory, method with sweep differential equation (SDE)/sweep envelope differential equation (SEDE), method with Jacobian rank deficiency, Voxel-based method, and free-form solids’ sweeping met...

New combinatorial properties of Catalan trees are established and used to prove a number of algebraic results related to the Jacobian conjecture. Let F = (x1 + H1, x2 + H2, . . . , xn + Hn) be a system of n polynomials in C[x1, x2, . . . , xn], the ring of polynomials in the variables x1, x2, . . . , xn over the field of complex numbers. Let H = (H1,H2, . . . ,Hn). Our principal algebraic resul...

For p a prime number, let X0(p)Q be the modular curve, over Q, parametrizing isogenies of degree p between elliptic curves, and let J0(p)Q be its jacobian variety. Let f : X0(p)Q → J0(p)Q be the morphism of varieties over Q that sends a point P to the class of the divisor P − ∞, where ∞ is the Q-valued point of X0(p)Q that corresponds to PQ with 0 and ∞ identified, equipped with the subgroup sc...

The paper aims to analyze the kinematics of a three-degreeof-freedom (3-DOF) in-parallel actuated mechanism, which can be used as a wrist robotic device. Basic kinematic models are given. Due to symmetry in mechanism geometry, the input-output polynomial degree derived in position forward kinematics can be considerably reduced. By analyzing the relationship between the independent and dependent...

A (holomorphic) automorphism of an Enriques surface S is said to be numerically reflective if it acts on the cohomology group H(S,Q) by reflection. We shall show that there are two lattice-types of numerically reflective involutions, and describe one type geometrically in terms of curves of genus 2 and Göpel subgroups of their Jacobians. An automorphism of an Enriques surface S is numerically t...

for any given finite abelian group‎, ‎we give factorizations of the group determinant in the group algebra of any subgroups‎. ‎the factorizations is an extension of dedekind's theorem‎. ‎the extension leads to a generalization of dedekind's theorem‎.

Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtua...

We developed an immunogen to stimulate multivalent immunity against hepatitis B surface antigen (HBsAg) and hepatitis B core antigens (HBcAg). Immune responses specific for both HBsAg and HBcAg play an important role in controlling the infection. HBsAg-specific antibodies mediate elimination of virions at an early stage of infection and prevent the spread of virus. The immunogen was constructed...