This paper deals with the subject of infinitesimal variations Euclidean submanifolds arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar theory isometric immersions in space, we prove that system three equations certain pair tensors are integrability conditions differential equation determines variations. In addition, giv...

Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. We first review the long history of the infinit...

A passive orthonomic system of PDEs defines a submanifold in the corresponding jet manifold, coordinated by so called parametric derivatives. We restrict the total differential operators and the prolongation of an evolutionary vector field v to this submanifold. We show that the vanishing of their commutators is equivalent to v being a generalized symmetry of the system. 1 The standard symmetry...

In our last work, we formulate a Fourier transformation on the infinitedimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution exp ( −πξ ∞ −∞ α 2(t)dt ) for ξ ∈ C with Re(ξ) > 0, α ∈ L2(R), using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and defi...

between the K-theory of locally free modules on the non-commutative infinitesimal site and hypercohomology K-theory of free modules. These K-theory results are obtained as a very particular case of a general construction. The input of this construction consists of a category C equipped with a suitable notion of infinitesimal deformation, (e.g. C=rings, deformation=surjection with nilpotent kern...

Background: 99mTc is a widely used radioisotope in nuclear medicine centers which is obtained by elution from Mo-99/Tc-99m generators. Usually the generators are either supplied by the Iran Atomic Energy Agency or by private companies from foreign countries. In this study we have measured 99Mo contamination in 99mTc elute from different generators in a period of one year. Materials and...

Using a formalism of minitwistors, we derive infinitely many conserved charges for the sl(∞)-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions. E-mail address; be10@dk...