We prove that the surface-diffusion flow and the volumepreserving mean curvature flow can drive embedded hypersurfaces to self-intersections.

We prove that for a generic measure preserving transformation T , the closed group generated by T is a continuous homomorphic image of a closed linear subspace of L0(λ,R), where λ is Lebesgue measure, and that the closed group generated by T contains an increasing sequence of finite dimensional toruses whose union is dense.

The search for fast unitary transforms and the need for data compression in linear systems are complementary issues. Compression requires the definition of a threshold dependent on the condition number, which is invariant over the unitary group. With respect tot this threshold it is shown that the SVD is the optimal tool. Considerations in connection with the Kronecker product and direct sum of...

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices of a unitary representation to canonical form, give a certain description of the representations of canonical form, and reduce the problem of classifying Eu...

We consider pseudo-unitary quantum systems and discuss various properties of pseudounitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of i = √ −1 times a pseudo-Hermitian matrix, and determine the structure of the L...

according to the reports of who, stability of rev.1 vaccine should take more than one year, while the expiring date for the vaccine produced in iran is 3 to 4 months, therefore any attempt to elongate the stability of this vaccine can solve many problems of the production including the request of veterinary organization of iran in this regard. the objective of this study was to increase the sta...

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...

The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a domain in 3-space, helicity is known to be invariant under volume-preserving diffeomorphisms of the domain that are homotopic to the identity. We...