Given a connected graph G = (V, E) with a nonnegative cost on each edge in E, a nonnegative prize at each vertex in V , and a target set V ′ ⊆ V , the Prize Collecting Steiner Tree (PCST) problem is to find a tree T in G interconnecting all vertices of V ′ such that the total cost on edges in T minus the total prize at vertices in T is minimized. The PCST problem appears frequently in practice ...

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a nonsurjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through t...

The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find corresponding Poisson brackets. Availability of these ingredients allows us to state the problem of a canonical quantization to these equations and disclose some im...

We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras.

Explicit expressions for three series of R matrices which are related to a “dilute” generalisation of the Birman–Wenzl–Murakami algebra are presented. Of those, one series is equivalent to the quantum R matrices of the D (2) n+1 generalised Toda systems whereas the remaining two series appear to be new. A “dilute” generalisation of the Birman–Wenzl–Murakami (BWM) algebra [1, 2] has recently bee...

The present article discusses the connection between exactly-solvable Schrödinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials, which includes the relatively recently introduced potentials of Natanzon and Ginocchio. As well, this class is shown to contain two new families of exactly solvable potentials. AMS classification sc...

A simple analytically solvable model exhibiting a 1/f spectrum in an arbitrarily wide frequency range was recently proposed by Kaulakys and Meškauskas (KM). Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is Brownian fluctuations of the average intervent time between subsequent pulses of the pulse sequence. We generalize the KM model to reproduce the variet...