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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublicationLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Equitable coloring of corona products of graphs
PublicationIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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International Network Optimization Conference, Warsaw, Poland 2015
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The final answer to the complexity of a basic problem in resilient network design
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Partial hyperbolicity and central shadowing
PublicationWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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From Pathwidth to Connected Pathwidth
PublicationW pracy przedstawiono dowód faktu, że spójna szerokość ścieżkowa grafu wynosi co najwyżek 2k+1, gdzie k jest jego szerokością ścieżkową. Dowód jest konstruktywny, tzn., został skonstruowany algorytm, który dla podanej na wejściu dekompozycji grafu o szerekości k zwraca dekompozycję spóją o szerekości co najwyżej 2k+1.
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On-line ranking of split graphs
PublicationA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Detecting coupling directions with transcript mutual information: A comparative study
PublicationCausal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...
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Subharmonic solutions for a class of Lagrangian systems
PublicationWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publicationn this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublicationThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
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Dynamic inequalities and equations of Volterra type on time scales
PublicationPraca dotyczy całkowo-różniczkowych równań dynamicznych typu Volterry z warunkami początkowymi. Stosując twierdzenie Banacha o punkcie stałym pokazano istnienie jedynego rozwiązania liniowego równania dynamicznego. Stosując metodę iteracji monotonicznych pokazano istnienie rozwiązań ekstremalnych dla problemów nieliniowych. Badano też nierówności dynamiczne. Praca zawiera również uwagi dotyczące zagadnień różniczkowych i różnicowych.
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Boundary value problems for dynamic equations of Volterra type on time scales
PublicationPraca dotyczy równań i nierówności dla problemów dynamicznych typu Volterry. Podano warunki dostateczne na istnienie ekstremalnych rozwiązań w obszarze ograniczonym przez dolne i górne rozwiązania. Praca zawiera również pewne uwagi dla konkretnych zagadnień różniczkowych i dyskretnych.
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On integro-differential equations with delayed arguments
PublicationPraca dotyczy problemów różniczkowo-całkowych z warunkami początkowymi oraz brzegowymi typu okresowego. Podano warunki na istnienie i jednoznaczność rozwiązania. Badania dotyczyły również nierówności różniczkowo-całkowych z argumentami typu opóżnionego. Podano przykłady, które mogą mieć zastosowanie w problemach inżynierskich.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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Positive solutions to second order four-point impulsive problems with deviating arguments
PublicationStosując tw. Leggetta-Williamsa, podano warunki dostateczne na istnienie dodatnich rozwiązań dla czteropunktowych problemów brzegowych dla równań różniczkowych rzędu drugiego z odchylonymi argumentami. Dyskutowane były problemy gdy argument odchylony był typu opóźnionego lub wyprzedzonego.
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Airborne wear particle emission from train brake friction materials with different contents of steel and copper fibres
PublicationThis study investigated the influence of the amount of steel and copper fibres in a train brake friction material on the tribological performance, emission intensity and characteristics of airborne wear particles. The particles were generated on a pin-on-disc tribometer under controlled friction and environmental conditions. It was found that the steel fibre results in a more intensive emission of 0.3–10 μm particles compared to...
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A spice equivalent circuit for modeling the performance of dual frequency echo-sounder
PublicationThe paper presents novel network equivalent circuit of piezoceramic circular disc transducers that takes into account thickness and radial mode of vibrations. The starting point of the analysis is 4-port description of circular disc element representing the solution of wave equation set in radial and thickness directions. The approximate solution for harmonic case is represented in the form of 4x4 matrix, which is synthesised and...
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A LUMPED-CIRCUIT MODEL OF CIRCULAR PISTON TRANSDUCER FOR MODELING ITS PERFORMANCE IN DUAL FREQUENCY OPERATING MODES
PublicationThe paper presents novel network equivalent circuit of piezoceramic circular disc transducer that takes into account thickness and ra dial mode of vibrations. The starting point of the analysis is 4-port description of circular disc element representing the solution of wave equation set in radial and thickness directions. Th e approximate solution for harmonic case is represented in the form of 4x4 matrix, which is syn thesized...
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Correlations between the wear of car brake friction materials and airborne wear particle emissions
PublicationAirborne wear particles emitted from transport vehicle brakes are one of the main sources of toxic metals in inhalable particulate matter. Prediction of wear particle emissions may become more accurate if the relationship between the wear and particle emission characteristics is known. An experimental study was performed to investigate proportional correlations between the mass wear, 0.01–0.42 μm particle emission measured by a NanoScan...
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Numerical Test for Stability Evaluation of Analog Circuits
PublicationIn this contribution, a new numerical test for the stability evaluation of analog circuits is presented. Usually, if an analog circuit is unstable then the roots of its characteristic equation are localized on the right half-plane of the Laplace s- plane. Because this region is unbounded, we employ the bilinear transformation to map it into the unit disc on the complex plane. Hence, the existence of any root inside the unit disc...
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Functionalization of indium-tin-oxide electrodes by laser-nanostructured gold thin films for biosensing applications
Publicationof a relatively large area formed by pulsed laser nanostructuring of thin gold films arereported and discussed. The SEM inspection of modified electrodes reveals the presence of the nearlyspherical and disc-shaped particles of dimensions in the range of 40–120 nm. The NP-array geometry canbe controlled by selection of the laser processing conditions. It is shown that particle size and packingdensity of the array are important factors...
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A concept for reducing PM 10 emissions for car brakes by 50%
PublicationWith regard to airborne particles with an aerodynamic diameter of less than 10 μm (PM10), in countries in the European Union, the mass of brake emissions equals approximately 8–27% of the total traffic-related emissions. Using a research methodology combining tests at different scale levels with contact mechanics simulations and PM10 chemical characterization, the REBRAKE EU-financed project had the following aims: i) to demonstrate...
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Comparison of properties of the new electro-mechanical model and circumferential model of the inductive-dynamic drive
PublicationThe article presents a new electromechanical model of inductive-dynamic drive. The model is implemented in two environments: Maxwell for analyzing electrodynamic phenomena including moving of the disc and Ansys which allows for stress analysis on the basis of the volume forces imported from Maxwell. Additionally, a model validation by comparing with the existing circumferential model was carried out.
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Technological Problems in Lapping on Flat Surfaces of Ceramic Parts
PublicationThis paper will present the results of research on single-disc lapping of flat surfaces of small ceramic elements. Machining with the use of different tools such as metallic, two-metallic and abrasive-metallic will be analyzed. The basics and techniques of reinforcement of laps will be discussed. The results of the influence of parameters on the surface quality of ceramic conponents (sealing) for three treatments on lapping machines...
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Suitability study of hybrid model of electrodynamic actuator
PublicationThis paper presents the proposal of the hybrid circuit-field model of an electrodynamic actuator. The field model uses the inductor current as the input data which is obtained from the circuit model or experimentally. The field model implemented using the FLUX program makes it possible to easily determine the pressure distribution acting on the disc. The results have been verified experimentally.
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Effective density of airborne wear particles from car brake materials
PublicationPeople living in urban environments are subject to high health risks due to various anthropogenic sources of airborne particulate matter, including wear of transport vehicle brakes. Studies of airborne particles often require an estimate of the effective particle density, a property that allows correct matching of mass and size characteristics measured by different aerosol instruments. In this study we investigated the effective...
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Influence of Flat Lapping Kinematics on Machinability of Ceramics
PublicationNew tools for flat grinding of ceramics are presented in the paper. Electroplated CBN tools (B64 and B107) were used in a modified single-disc lapping machine configuration. The results from experiments, such as the material removal rate and surface roughness parameters are presented and analyzed. Numerical simulations, based on the model for the shape error and tool wear estimation in machining with flat lapping kinematics, are...
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Numerical Method for Stability Testing of Fractional Exponential Delay Systems
PublicationA numerical method for stability testing of fractional exponential systems including delays is presented in this contribution. We propose the numerical test of stability for a very general class of systems with a transfer function, which includes polynomials and exponentials of fractional powers of the Laplace variable s combined with delay terms. Such a system is unstable if any root of its characteristic equation, which usually...
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Cavitation wearing of the SUPERSTON alloy after laser treatment at cryogenic conditions
PublicationThe purpose of this paper is to demonstrate the method of laser remelting at cryogenic conditions of the SUPERSTON alloy and its influence on microstructure and cavitation wearing. The cavitation test was performed using the rotating disc facility in IPM PAN Gdansk. During the cavitation test, the mass loss of the material with different parameters of laser remelting was determined. Surface and cross-section microstructure of the...
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Fretting wear of materials - methodological aspects of research
PublicationW artykule przedstawiono metodyczne aspekty frettingowego zużywania materiałów. Rezultaty badań przeprowadzonych na stanowisku typu ''pin on disc'' wykonanym w Katedrze Inżynierii Materiałowej i Biomedycznej Politechniki Białostockiej potwierdziły decydujący wpływ amplitudy oscylacji i wartości obciążenia na przebieg i charakter procesu zużywania. Wzrost wartości amplitudy powodował zmiany w warunkach tarcia. Wzrost wartości obciążenia...
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Comparison of antimicrobial activity of selected, commercially available wound dressing materials
PublicationOBJECTIVE: The aim of our study was to examine the antimicrobial potential of eight selected, commercially available wound dressings containing different antimicrobial agents: silver, chlorhexidine acetate, povidone-iodine, and manuka honey. METHOD: The materials were tested against four reference strains of bacteria: Staphylococcus aureus (PCM 2051), Staphylococcus epidermidis (PCM 2118), Pseudomonas aeruginosa (ATCC 27853),...
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A Study on Emission of Airborne Wear Particles from Car Brake Friction Pairs
PublicationThe emission of airborne wear particles from friction material / cast iron pairs used in car brakes was investigated, paying special attention to the influence of temperature. Five low-metallic materials and one non-asbestos organic material were tested using a pin-on-disc machine. The machine was placed in a sealed chamber to allow airborne particle collection. The concentration and size distribution of 0.0056 to 10 μm particles...
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MODELOWANIE TURBINY WIATROWEJ Z DWOMA PRZECIWBIEŻNIE OBRACAJĄCYMI SIĘ WIRNIKAMI
PublicationW artykule przedstawiono sposoby modelowania dwuwirnikowej turbiny wiatrowej z wykorzystaniem technik Obliczeniowej Mechaniki Płynów. Omówiono uproszczone metody modelowania Actuator Disc i Actuator Line Method oraz aspekty związane z dokładnym odwzorowaniem turbiny na siatce obliczeniowej. Zaprezentowano przykładowe wyniki obliczeń turbiny dwuwirnikowej złożonej z wirników NREL o mocy nominalnej 5 MW każdy. Do wykonania badań...
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Vertical vibration reduction and audible sound analysis in surface grinding with electroplated tools
PublicationOne of the first approaches to the development of a grinding process monitoring system based on audible sound sensors is presented in the paper. Electroplated diamond tools (abrasive D64 and D107) were used in a modified single-disc lapping machine configuration for flat grinding of ceramics (Al2O3). The main aim of the machine modification was to reduce the vertical vibration in order to decrease the tool wear and to increase...
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Reliability of acicular grindable thermocouples for transient temperature measurements at sliding contacts
PublicationAcicular grindable thermocouples represent an interesting and prospective technique of temperature measurements at sliding contacts. This study aimed at the investigation of their reliability and accuracy as applied to the friction materials of various classes in contact with steel. The tests were conducted on a pin-on-disc tribometer under stationary and transient regimes. The experimental results were validated by comparing the...
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Synergistic Effects of Bitumen Plasticization and Microwave Treatment on Short-Term Devulcanization of Ground Tire Rubber
PublicationGround tire rubber (GTR) was mechano-chemically modified with road bitumen 160/220 and subsequently treated using a microwave radiation. The combined impact of bitumen 160/220 content and microwave treatment on short-term devulcanization of GTR was studied by thermal camera, wavelength dispersive X-ray fluorescence spectrometry (WD-XRF), static headspace, and gas chromatography-mass spectrometry (SHS-GC-MS), thermogravimetric analysis...
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Inverse determination of sliding surface temperature based on measurements by thermocouples with account of their thermal inertia
PublicationThis study developed an inverse heat conduction algorithm to determine temperature at a sliding surface taking account of thermocouple thermal inertia. The direct heat conduction problem was solved analytically based on the Laplace integral transform approach. The inverse algorithm was applied to the problem of friction of a brake material against a steel. The experiments were conducted on a pin-on-disc tribometer for three short-time...
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Flavones in cocoa defence against Phytophthora megakarya
PublicationCross-pollination of suitable genotypes and earlier selection of elite offspring using adequate plants-associated defence markers in plantlets leaves are decisive for development of T. cacao genotypes tolerant to black pods disease (BPD). T. cacao plantlets from manual cross-pollination of ♀SNK64 × ♂UPA143 were analyzed for their susceptibility to BPD using leaf disc test. Subsequently, leaves (healthy, wounded and wound+infected)...
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Emission and properties of airborne wear particles from train brake friction materials based on novolac phenolic resins and butadiene rubbers
PublicationThe emission of airborne particulate matter from a train brake depends on the formulation of its friction material. This study investigates the emission and properties of wear particles from train brake friction materials based on straight or resorcinol-modified novolac phenolic resin and nitrile or styrene butadiene rubber used as binding ingredients. The wear particles are generated by a pin-on-disc tribomachine inside an aerodynamic...
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Modification of Ground Tire Rubber—Promising Approach for Development of Green Composites
PublicationGround tire rubber (GTR) was mechano-chemically modified using a road bitumen 100/150 and two types of organic peroxides: di-(2-tert-butyl-peroxyisopropyl)-benzene (BIB) and dicumyl peroxide (DCP). The impact of used additives on reactive sintering efficiency and physico-mechanical properties of modified GTR was investigated using oscillating disc rheometer measurements, followed by tensile tests and swelling behavior studies....
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Performance of acicular grindable thermocouples for temperature measurements at sliding contacts
PublicationThe present study investigates the performance of acicular grindable thermocouples based on a constantan wire / steel hollow cylinder construction. The experiments showed that the measuring junction electrical resistance, temperature–voltage characteristic, measuring junction rise time and signal noise standard deviation of the acicular thermocouples are comparable to those of conventional J-type thermocouples with bare wire diameter...
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Sandwich Biobattery with Enzymatic Cathode and Zinc Anode Integrated with Sensor
PublicationCarbon paper covered with side-naphthylated multi walled carbon nanotubes was used as the conducting support for the construction of a biocathode in a hybrid biofuel cell. Laccase Carrena unicolor enzyme was employed as the catalyst for the 4e reduction of oxygen and a zinc disc covered with hopeite was used as the anode. Derivatized carbon nanotubes increase the working surface of the electrode and provide direct contact with...
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Tribological Properties of Ni-P/Si3N4 Nanocomposite Layers Deposited by Chemical Reduction Method on Aluminum Alloy AW-7075
PublicationThe article presents the results of tribological tests of Ni-P/Si3N4 nanocomposite and Ni-P nickel layers deposited on the AW-7075 aluminum alloy by chemical reduction method, and the AW-7075 alloy without coating. Nanocomposite layers were produced using Si3N4 siliconnitride in the form of a polydisperse powder whose particle sizes ranged from 20 to 25 nm. The influence of the content of the dispersion phase layer material on...
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Badania tribologicznych właściwości nanokompozytowych warstw Ni-P/Si3N4 osadzanych metodą redukcji chemicznej na stopie aluminium AW-7075
PublicationPrzedstawiono wyniki tribologicznych badań warstw nanokompozytowych Ni-P/Si3N4 i niklowych Ni-P osadzonych na stopie aluminium AW-7075 metodą redukcji chemicznej, a także stopu AW-7075 bez powłoki. Warstwy nanokompozytowe wytworzono, stosując azotek krzemu Si3N4 w postaci polidyspersyjnego proszku o wielkości cząstek 20–25 nm. Analizowano wpływ zawartości w materiale warstwy fazy dyspersyjnej na twardość i zużycie ścierne, którą...
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Hydrographic echosounder for sounding inland waters.
PublicationNowy model echosondy zaprojektowanej specjalnie dla instytucji administrującymi śródlądowymi drogami wodnymi, sztucznymi i naturalnymi zbiornikami oraz morskimi wodami przybrzeżnymi jest opisany. Podstawowym wymogiem wynikającym z sondażu wód płytkich jest pomiar możliwie najmniejszych głębokości. Przez zastosowanie oddzielnych przetworników (nadawczego i odbiorczego) i ich wytłumienie oraz przez wprowadzenie układu TVG o dużej...