Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Hydrotalcite-derived Co-containing mixed metal oxide catalysts for methanol incineration

The Co–Mg–Al mixed metal oxides were prepared by calcination of co-precipitated hydrotalcite-like precursors at various temperatures (600–800 °C), characterised with respect to chemical (AAS) and phase (XRD) composition, textural parameters (BET), form and aggregation of cobalt species (UV–vis-DRS) and their redox properties (H₂-TPR, cyclic voltammetry). Moreover, the process of thermal decomposition of hydrotalcite-like materials to mixed metal oxide systems was studied by thermogravimetric method combined with the analysis of gaseous decomposition products by mass spectrometry. Calcined hydrotalcite-like materials were tested as catalysts for methanol incineration. Catalytic performance of the oxides depended on cobalt content, Mg/Al ratio and calcination temperature. The catalysts with lower cobalt content, higher Mg/Al ratio and calcined at lower temperatures (600 or 700 °C) were less effective in the process of methanol incineration. In a series of the studied catalysts, the best results, with respect to high catalytic activity and selectivity to CO₂, were obtained for the mixed oxide with Co:Mg:Al molar ratio of 10:57:33 calcined at 800 °C. High activity of this catalyst was likely connected with the presence of a Co–Mg–Al spinel-type phases, containing easy reducible Co³⁺ cations, formed during high-temperature treatment of the hydrotalcite-like precursor.     

Self-maps of <Emphasis Type="Italic">S</Emphasis><Superscript>2</Superscript> homotopic to a smooth map with a single <Emphasis Type="Italic">n</Emphasis>-periodic point

We show for which (d,n) ∈ Z×N there exists a smooth self-map f:S² → S² so that deg(f)=d and Fix(fⁿ) is a point.     

Bounded sets structure of CpX and quasi‐(DF)‐spaces

For wide classes of locally convex spaces, in particular, for the space $C_p(X)$ of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of $(DF)$‐spaces have led us to introduce quasi‐ $(DF)$‐spaces, a class of locally convex spaces containing $(DF)$‐spaces that preserves subspaces, countable direct sums and countable products. Regular $(LM)$‐spaces as well as their strong duals are quasi‐ $(DF)$‐spaces. Hence the space of distributions $D^{\prime }(\mathrm{\Omega })$ provides a concrete example of a quasi‐ $(DF)$‐space not being a $(DF)$‐space. We show that $C_p(X)$ has a fundamental bounded resolution if and only if $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if the strong dual of $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if X is countable. If X is metrizable, then $C_k(X)$ is a quasi‐ $(DF)$‐space if and only if X is a σ‐compact Polish space.     

Weighted Influence Non-linear Gauge System (WINGS) – An analysis method for the systems of interrelated components

The WINGS method has been derived from DEMATEL and can be widely used as a structural model for analysis of intertwined factors and causal relations between them. Its novelty comes from an idea of including in one mathematical mechanism both strength (importance) and influence of the system components. In particular, WINGS can be applied as the MCDA method for evaluating alternatives when interrelations between criteria cannot be neglected. For the problem with independent criteria, WINGS reproduces the additive aggregation of preferences, a classical method in MCDA.