Let A be an associative algebra over a field F of characteristic zero and let L Lie F. If acts on by derivations, then such action determines its universal enveloping U(L) in this case we refer to as with derivations or L-algebra. Here give characterization the ideal differential identities finite dimensional L-algebras corresponding sequence codimensions ${c_{n}^{L}} (A)$ , n ≥ 1, is polynomia...

The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and Zantema. Altho...

The algorithmic problem of whether a compressed string is accepted by a (nondeterministic) finite state automaton with compressed transition labels is investigated. For string compression, straight-line programs (SLPs), i.e., contextfree grammars that generate exactly one string, are used. Two algorithms for this problem are presented. The first one works in polynomial time, if all transition l...

We study a continuous time random walk X in an environment of dynamic random conductances in Zd. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X, and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic in...

By allowing measurement (read-out) of some, but not all, qubits, this paper shows that NP-complete problems are efficiently solvable by quantum computers in polynomial time with bounded probability (NP in BQP). This is demonstrated by describing a polynomially large network of quantum gates that solves the 3SAT problem with bounded probability in polynomial time. The “weak Church-Turing thesis”...

In 2007, Arkin et al. [3] initiated a systematic study of the complexity of the Hamiltonian cycle problem on square, triangular, or hexagonal grid graphs, restricted to polygonal, thin, superthin, degree-bounded, or solid grid graphs. They solved many combinations of these problems, proving them either polynomially solvable or NP-complete, but left three combinations open. In this paper, we pro...

Abstract We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragmén–Lindelöf theorem polynomially bounded functions on the right complex half-plane. interpolation leads to nonoptimal off-diagonal bounds.