This paper presents measurements of sound velocity and attenuation in olive oil, with known chemical composition, as a function of pressure, within the range of pressure up to 0.7 GPa. Dependencies of sound velocity, relative ultrasonic wave attenuation, volume, and adiabatic compressibility on pressure show discontinuities. This proves the existence of the first order phase transition in olive...

In a gravitational force field, a bounded orbit of an infinitesimal point mass is called a satellite orbit. The purpose of this paper is to establish a variational theory for the existence of some relative periodic satellite orbits in periodic gravitational force fields. The gravitation field can be generated by a relative equilibrium or a uniformly rotating asteroid. Our approach is to regard ...

We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, where the target has non-positive Gauss curvature and conic points with cone angles less than 2π. For a homeomorphism w of such a surface, we prove existence and uniqueness of minimizers in the homotopy class of w relative to the inverse images of the cone poin...

Let E be a subset of a convex, open, bounded, planar set G. Let P (E, G) be the relative perimeter of E (the length of the boundary of E contained in G). We obtain relative geometric inequalities comparing the relative perimeter of E with the relative diameter of E and with its relative inradius. We prove the existence of both extremal sets and maximizers for these inequalities and describe the...

The most common philosophical view about the notion of existence is that it is a second-order property or existential quantification. A less common view is that existence is a (first-order) property of 'existent' as opposed to 'nonexistent' (past or merely intentional) objects. An even less common view is that existence divides into different 'modes of being' for different sorts of entities. In...

A proper one-particle relative entropy is introduced for the ground state of trapped Bose particles and its asymptotic behavior under the GP scaling limit is investigated. Some peculiar properties of the relative entropy allow to prove an existence theorem for the probability measure associated to the GP functional and a related weak convergence result.

Let p be an odd prime. We first get some non-existence and structural results on (pn,p,pn,n) relative difference sets with gcd(p,n)= 1 through a group ring approach. We then give a construction of (p(p+ 1),p,p(p+ 1),p+ 1) relative difference sets with p a Mersenne prime.