Sampling of insect communities is very challenging and for reliable interpretation of results the effects of different sampling protocols and data processing on the results need to be fully understood. We compared three different commonly used methods for sampling forest beetles, freely hanging flight-intercept (window) traps (FWT), flight-intercept traps attached to trunks (TWT) and pitfall traps placed in the ground (PFT), in Scots pine dominated boreal forests in eastern Finland. Using altogether 960 traps, forming 576 sub-samples, at 24 study sites, 59760 beetles belonging to 814 species were collected over a period of a month. All of the material was identified to species, with the exception of a few species pairs, to obtain representative data for analyses. Four partly overlapping groups were used in the analyses: (1) all, (2) saproxylic, (3) rare and (4) red-listed species. In terms of the number of species collected TWTs were the most effective for all species groups and the rarer species the species group composed of (groups 1-2-3-4) the larger were the differences between the trap types. In particular, the TWTs caught most red-listed species. However, when sample sizes were standardized FWTs and TWTs caught similar number of species of all species groups. PFTs caught fewer species of all species groups, whether the sample sizes were standardized or not. In boreal forests they seem to be unsuitable for sampling saproxylic, rare and red-listed species. However, the PFTs clearly sampled different parts of species assemblages than the window traps and can be considered as a supplementary method. The abundance distribution of saproxylic species was truncated lognormal in TWT and pooled material, whereas unclassified material failed to reveal lognormal distribution in all the trap types and pooled material. The results show that even in boreal forests sample sizes of at least thousands, preferably tens of thousands of individuals, collected by a high number of traps are needed for community level studies. Relevant ecological classification of material is also very important for reliable comparisons. Differences in the performance of trap types should be considered when designing a study, and in particular when evaluating the results.
The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper presents two methods to handle the algebraic condition: the first one is based on iterative minimization of a cost functional defined as the integral of the square of the algebraic expression to be equal to zero. The second method converts the algebraic-differential equation into a singularly perturbed system of partial differential equations only. Both methods are compared and the simulation results are presented including on-line control implementation to some practically motivated laboratory models.
Let $\tilde{f}$, $\tilde{g}$ be ultradistributions in $\mathcal Z^{\prime }$ and let $\tilde{f}_n = \tilde{f} * \delta _n$ and $\tilde{g}_n = \tilde{g} * \sigma _n$ where $\lbrace \delta _n \rbrace $ is a sequence in $\mathcal Z$ which converges to the Dirac-delta function $\delta $. Then the neutrix product $\tilde{f} \diamond \tilde{g}$ is defined on the space of ultradistributions $\mathcal Z^{\prime }$ as the neutrix limit of the sequence $\lbrace {1 \over 2}(\tilde{f}_n \tilde{g} + \tilde{f} \tilde{g}_n)\rbrace $ provided the limit $\tilde{h}$ exist in the sense that \[ \mathop {\mathrm N\text{-}lim}_{n\rightarrow \infty }{1 \over 2} \langle \tilde{f}_n \tilde{g} +\tilde{f} \tilde{g}_n, \psi \rangle = \langle \tilde{h}, \psi \rangle \] for all $\psi $ in $\mathcal Z$. We also prove that the neutrix convolution product $f \mathbin {\diamondsuit \!\!\!\!*\,}g$ exist in $\mathcal D^{\prime }$, if and only if the neutrix product $\tilde{f} \diamond \tilde{g}$ exist in $\mathcal Z^{\prime }$ and the exchange formula \[ F(f \mathbin {\diamondsuit \!\!\!\!*\,}g) = \tilde{f} \diamond \tilde{g} \] is then satisfied.
We define various ring sequential convergences on $\mathbb{Z}$ and $\mathbb{Q}$. We describe their properties and properties of their convergence completions. In particular, we define a convergence $\mathbb{L}_1$ on $\mathbb{Z}$ by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields $\mathbb{Z}/(p)$. Further, we show that $(\mathbb{Z}, \mathbb{L}^\ast _1)$ is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.
A cytoskeletal network contributes significantly to intracellular regulation of mechanical stresses, cell motility and cellular mechanics. Thus, it plays a vital role in defining the mechanical behaviour of the cell. Among the wide range of models proposed for dynamic behaviour of cytoskeleton, the soft glassy rheology model has gained special attention due to the resemblance of its predictions with the mechanical data measured from experiment. The soft glassy material, theory of soft glassy rheology and experiment on cytoskeleton has been discussed, which leads to a discussion of the unique features and flaws of the model. The soft glassy rheological model provides a unique explanation of the cytoskeleton ability to deform, flow and remodel. and Obsahuje seznam literatury
In this paper an original algorithm for tlie choice of a relevaiit
belief formula is presented. Belief forinulas are treated as external representations of internal States of cognition directed at an ontologically existing atom object. This algorithrn is based on the idea of intentional semantics and uses soft methods based on the theory of consensus and choice.
For any d≥11 we construct graphs of degree d, diameter 2, and order 825d2+O(d), obtained as lifts of dipoles with voltages in cyclic groups. For Cayley Abelian graphs of diameter two a slightly better result of 925d2+O(d) has been known \cite{MSS} but it applies only to special values of degrees d depending on prime powers.
In this paper we use cohomology of Lie algebras to study the variety of laws associated with filiform Lie algebras of a given dimension. As the main result, we describe a constructive way to find a small set of polynomials which define this variety. It allows to improve previous results related with the cardinal of this set. We have also computed explicitly these polynomials in the case of dimensions 11 and 12.
In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions which guarantee that a policy is optimal for the problem if and only if it satisfies the EE. The problem is exemplified in two particular cases: for a logarithmic utility and for a Cobb-Douglas utility. In both cases explicit formulas for the optimal policy and the optimal value function are supplied.