This paper gives a classification up to isotopy of automorphisms (self-homeomorphisms) of 3-dimensional handlebodies and compression bodies, analogous to the Nielsen-Thurston classification of automorphisms of surfaces. Indecomposable automorphisms analogous to pseudo-Anosov automorphisms are identified and called generic. The first steps are taken towards understanding generic automorphisms us...

Abstract With the increasingly complex combat environment and diversity of tasks, important military targets are surrounded by multi-layer defense. Modern information warfare pays more attention to system confrontation multi-system cooperative operations,and missile formation attack is main research content this paper. For wing ideal trajectory generation problems, ensure Angle time meet design...

We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η+, and η+-pseudo-Hermitian operators acting in C 2. The latter represent the physical observables of a model whose Hamiltonian and Hilbert space are respectively H and C2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact...

We treat the problem of subsequence time-series clustering (STSC) from a group-theoretical perspective. First, we show that the sliding window technique introduces a mathematical artifact to the problem, which we call the pseudo-translational symmetry. Second, we show that the resulting cluster centers are necessarily governed by irreducible representations of the translational group. As a resu...

Publications in Refereed Journals 1. I numeri di Fermat, Periodico di Matematiche, VII, 5 (1998), no. 2-3, 63–68 2. Some observations on the statistical independence and the distribution of zeros in the Selberg Class, Rend. Circ. Mat. Palermo (2), 52 (2003), no. 2, 211–223 3. Extending the idea of compressed algebra to arbitrary socle-vectors, J. Algebra 270 (2003), no. 1, 181–198 4. When are T...

Given a free-by-cyclie group G = FN oφ Z determined by a hyperbolic and fully irreducible outer automorphism φ ∈ Out(FN ), with u0 : G → Z the homomorphism having ker(u0) = FN , we construct a K(G, 1) 2–complex X called the folded mapping torus of φ, and equip it with a semiflow. We show that X enjoys many similar properties to those proven by Thurston and Fried for the mapping torus of a pseud...

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...

An algebra generated by projections with relations of Temperley–Lieb type is considered. Knowledge of Gröbner basis of the ideal allows to find a linear basis of the algebra. Some questions of representation theory for this algebra were studied in [13]. Obtained in the present paper are the additional relations, which hold in all finite-dimensional irreducible ∗-representations, although they d...

Different properties of rings and fields are discussed. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R −→ S we have R/ker(f) ∼= Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and h...

We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a p-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and i...