A note on vertex colorings of plane graphs

Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V , let c(v) denote the sum of the weight of v ∈ V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) 6= c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2

Modeling of Masonry Structures at Multiple Scales

Zdivo je materiál použitý ve většině stavebních památek na celém světě. Spolehlivé nástroje pro analýzu zděných konstrukcí jsou zapotřebí nejen pro vyhodnocení jejich seismické zranitelnosti, ale také při návrhu opatření směřujících k obnovení či zvýšení únosnosti existujících budov, které si zaslouží ochranu. Zdivo je nelineární, heterogenní a anizotropní materiál, jehož vlastnosti silně závisejí na základních stavebních jednotkách, tedy blocích (cihlách) a maltě, a na jejich prostorovém uspořádání. Pro simulaci mechanického chování zděných konstrukcí byla vyvinuta řada modelů, které se liší mírou rozlišení. Pro velké konstrukce vede snaha o výpočetní efektivitu ke zjednodušeným modelům, charakterizovaným rozdělením zděných stěn na makroprvky. Významným zástupcem této skupiny modelů je metoda ekvivalentního rámu. Její podstatou je nahrazení zděné stěny idealizovaným rámem, přičemž panely jsou modelovány jako nosníky charakterizované odpovídajícím mechanickým chováním. Míra rozlišení může být zvýšena tím, že se každý makroprvek uvažuje jako homogenizované kontinuum s vlastnostmi, které reprodukují celkovou odezvu určitého výseku heterogenní mikrostruktury. Formulace vhodného konstitutivního zákona ale není lehkou úlohou. Tento zákon by měl fenomenologicky reprodukovat mechanické chování materiálu, včetně vzniku tahových trhlin, smykového pokluzu, drcení v tlaku a dalších jevů. Navíc tento přístup vyžaduje těžkopádnou identifikaci mechanických parametrů, které není vždy snadné určit na základě běžných laboratorních testů materiálu. K popisu role základních stavebních jednotek a jejich interakce může posloužit model formulovaný na mikroúrovni, který explicitně bere v úvahu jednotlivé bloky, maltu a rozhraní mezi nimi. Tato práce se zabývá zděnými konstrukcemi na několika úrovních rozlišení. Problémy s formulací modelů ekvivalentního rámu v případě nepravidelného rozmístění otvorů se zkoumají na základě porovnání výsledků pro ekvivalentní rámy s výsledky získanými metodou konečných prvků, o které lze předpokládat, že lépe postihuje skutečné chování nepravidelných stěn. Provedená parametrická analýza zděných pilířů modelovaných jako homogenizované kontinuum je zaměřena na posouzení vlivu tvaru a svislého tlakového zatížení na nelineární statické chování. Pozornost se pak přesouvá na jemnější úrovně rozlišení, na nichž se zkoumá lokalizace nepružného přetváření, která ovlivňuje konstitutivní zákony pro modelování zdiva na makro a mikroúrovni. Provádí se lokalizační analýza ortotropního makroskopického modelu formulovaného podle teorie plasticity s více plochami plasticity, v jejímž rámci jsou odvozeny analytické podmínky lokalizace potvrzené simulacemi metodou konečných prvků. V závěru je vyvinut mikromechanický model pro pravidelné zdivo a pomocí něj se na reprezentativním objemu materiálu analyzují lokalizační vlastnosti, ovlivněné velikostí tohoto objemu a předpokládanými směry periodicityMasonry represents the material used in the great majority of the world building heritage structures. Reliable tools for analysis of masonry structures are needed not only for seismic vulnerability assessment but also to properly design interventions to restore and strengthen existing buildings, which deserve to be preserved. Masonry is a nonlinear, heterogeneous, and anisotropic material whose properties strongly depend on its microstructure, typically composed of two phases, blocks and mortar, and on the way it is assembled. To simulate the mechanical behavior of masonry structures, numerous models have been developed, characterized by different detailing levels. For large structures, the need for computational efficiency leads to simplified models characterized by the subdivision of masonry walls in macro-elements. A notable example of this group of models is the equivalent-frame method, which consists of identifying the masonry wall with an ideal frame, where panels are modeled as beams characterized by proper mechanical behavior. The detailing level can be increased by considering each macro-element as a homogenized continuum, assuming that, at the scale of representation, masonry can be treated as a continuum having mechanical properties that reproduce the overall response of a certain portion of the heterogeneous microstructure. However, the formulation of a suitable constitutive law is not an easy task. It should phenomenologically reproduce the material mechanics, including tension cracking, shear sliding, compressive crushing, and many other aspects. Moreover, this approach requires a cumbersome identification of mechanical parameters that are not always easy to determine from basic experimental tests on the material. To consider the role of each constituent and the effects of their interactions, a microscale model can be set up, where blocks, mortar joints, and mortar-block interfaces are represented explicitly. In this work, masonry structures are studied at several detailing levels. An issue affecting equivalent-frame models, namely the presence of irregularity in the wall opening layout, is addressed by comparing equivalent-frame results with finite-element ones, which are assumed to better represent the actual behavior of irregular walls. A parametric analysis on masonry piers, modeled as a homogenized continuum, is carried out, aimed to assess the influence of the height-to-width ratio and the vertical compression load on the nonlinear static behavior. The focus is then shifted to finer scales. The localization analysis of an orthotropic macro-scale model in the framework of multi-surface plasticity is presented, deriving analytical localization conditions corroborated by finite element simulations. Finally, a microscale model for regular masonry is developed to analyze the localization properties of the representative volume element, also by investigating the role of its size and periodicity directions

Radio emission of sea surface at centimeter wavelengths and is fluctuations

The eigen thermal radio emission of the sea was examined as well as the agitated surface of the sea when the reflection (scattering) is similar in nature to diffused scattering. The contribution of this emission to the total emission of the sea is practically constant in time, and the time fluctuations of the radio emissions of the sea are basically determined only by a change in the eigen emission of the sea, connected with the agitation

Theory and Design of Flight-Vehicle Engines

Papers are presented on such topics as the testing of aircraft engines, errors in the experimental determination of the parameters of scramjet engines, the effect of the nonuniformity of supersonic flow with shocks on friction and heat transfer in the channel of a hypersonic ramjet engine, and the selection of the basic parameters of cooled GTE turbines. Consideration is also given to the choice of optimal total wedge angle for the acceleration of aerospace vehicles, the theory of an electromagnetic-resonator engine, the dynamic characteristics of the pumps and turbines of liquid propellant rocket engines in transition regimes, and a hierarchy of mathematical models for spacecraft control engines

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

THE ENTIRE FACE IRREGULARITY STRENGTH OF A BOOK WITH POLYGONAL PAGES

A face irregular entire labeling is introduced by Baca et al. recently, as a modification of the well-known vertex irregular and edge irregular total labeling of graphs and the idea of the entire colouring of plane graph. A face irregular entire k-labeling ðœ†:ð‘‰âˆªð¸âˆªð¹â†’{1,2,⋯,ð‘˜} of a 2-connected plane graph ðº=(ð‘‰,ð¸,ð¹) is a labeling of vertices, edges, and faces of ðº such that for any two different faces ð‘“ and ð‘”, their weights ð‘¤ðœ†(ð‘“) and ð‘¤ðœ†(ð‘“) are distinct. The minimum 𑘠for which a plane graph ðº has a face irregular entire ð‘˜-labeling is called the entire face irregularity strength of ðº, denoted by ð‘’ð‘“ð‘ (ðº). This paper deals with the entire face irregularity strength of a book with ð‘š ð‘›-polygonal pages, where embedded in a plane as a closed book with ð‘›âˆ’sided external face

Surface Morphology of Porous Cementitious Materials Subjected to Fast Dynamic Fractures

This paper presents a study of the surface height irregularities of cement pastes subjected to fast dynamic fractures. The height irregularities are quantified by the values of the three-dimensional profile parameters. The studied dynamical irregularities show a similar analytical behavior to those obtained by static fractures

Particle Swarm Optimization Based Source Seeking

Signal source seeking using autonomous vehicles is a complex problem. The complexity increases manifold when signal intensities captured by physical sensors onboard are noisy and unreliable. Added to the fact that signal strength decays with distance, noisy environments make it extremely difficult to describe and model a decay function. This paper addresses our work with seeking maximum signal strength in a continuous electromagnetic signal source with mobile robots, using Particle Swarm Optimization (PSO). A one to one correspondence with swarm members in a PSO and physical Mobile robots is established and the positions of the robots are iteratively updated as the PSO algorithm proceeds forward. Since physical robots are responsive to swarm position updates, modifications were required to implement the interaction between real robots and the PSO algorithm. The development of modifications necessary to implement PSO on mobile robots, and strategies to adapt to real life environments such as obstacles and collision objects are presented in this paper. Our findings are also validated using experimental testbeds.Comment: 13 pages, 12 figure