in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

Let G be a transitive group of permutations of a finite set Ω, and suppose that some element of G has at most two orbits on Ω. We prove that any two maximal chains of groups between G and a point-stabilizer of G have the same length, and the same sequence of relative indices between consecutive groups (up to permutation). We also deduce the same conclusion when G has a transitive quasi-Hamilton...

We note an error in [2]. This Erratum will not be published. The paper defines Ham(M,ω) to be the group of Hamiltonian automorphisms, equipped with the C∞-topology, and G as “the group of smooth based loops in Ham(M,ω)”. This is a misleading formulation, since what the paper really means is that elements of G are Hamiltonian loops. If one understands it in that way, then the proof of [2, Lemma ...

Abstract We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of theory over another: ceteris paribus , general fundamental. illustrate this criterion through novel interpretation classical mechanics, based on three physical conditions. Two these conditions suffice recovering A third ...

The theory of differential forms began with a discovery of Poincaré who found conservation laws of a new type for Hamiltonian systems—The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant differential forms: a symplectic two-form, or a contact one-form for geodesic flows. Some invariant forms can be naturally considered as “forms on the quotient....