On the equality of Hausdorff measure and Hausdorff content

We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for any subset of a self-similar set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any self-similar or graph-directed self-similar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `self-similar'. For example, it fails in general for self-conformal sets, self-affine sets and Julia sets. We also give applications of our results concerning Ahlfors regularity. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and $\delta$-approximate packing pre-measure coincide for sufficiently small $\delta>0$.Comment: 21 pages. This version includes applications concerning the weak separation property and Ahlfors regularity. To appear in Journal of Fractal Geometr

Semigroup analysis of structured parasite populations

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.Comment: to appear in Mathematical Modelling of Natural Phenomen

Connectivity-Based Self-Localization in WSNs

Efficient localization methods are among the major challenges in wireless sensor networks today. In this paper, we present our so-called connectivity based approach i.e, based on local connectivity information, to tackle this problem. At first the method fragments the network into larger groups labeled as packs. Based on the mutual connectivity relations with their surrounding packs, we identify border nodes as well as the central node. As this first approach requires some a-priori knowledge on the network topology, we also present a novel segment-based fragmentation method to estimate the central pack of the network as well as detecting so-called corner packs without any a-priori knowledge. Based on these detected points, the network is fragmented into a set of even larger elements, so-called segments built on top of the packs, supporting even more localization information as they all reach the central node

Bibliography and checklist of foliicolous lichenized fungi up to 1992

Bibliographic records are presented of 324 scientific papers on foliicolous lichenized fungi published subsequent to Santesson’s survey of 1952. The 482 species presently known are listed in an alphabetical checklist, with references to important descriptions, keys and illustrations published by or after Santesson (1952), and an indication of the distribution. Also added are all synonyms used after 1952. Introductory chapters deal with the present state of research on foliicolous lichens and its history. The following new combination is proposed: Strigula smaragdula Fr. var. stellata (Nyl. & Cromb.) Farkas

Analysis of Minimal LDPC Decoder System on a Chip Implementation

This paper presents a practical method of potential replacement of several different Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes with one, with the intention of saving as much memory as required to implement the LDPC encoder and decoder in a memory-constrained System on a Chip (SoC). The presented method requires only a very small modification of the existing encoder and decoder, making it suitable for utilization in a Software Defined Radio (SDR) platform. Besides the analysis of the effects of necessary variable-node value fixation during the Belief Propagation (BP) decoding algorithm, practical standard-defined code parameters are scrutinized in order to evaluate the feasibility of the proposed LDPC setup simplification. Finally, the error performance of the modified system structure is evaluated and compared with the original system structure by means of simulation

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

A Quantum-Gravity Perspective on Semiclassical vs. Strong-Quantum Duality

It has been argued that, underlying M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this letter we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.Comment: 10 page