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Evaluation of vegetable and petroleum based diesel fuels in the aspect of lubricity in steel-aluminium association
B. Batko,T.K. Dobek,A. Koniuszy
International Agrophysics , 2008,
Abstract: The paper presents the results of a study on wear resistance of elements of injection system operating in steelaluminium friction system with relation to the kind of fuel used. The fuels used in the study included regular petroleum-based diesel fuel, esters of colza oil, and their mixtures. The study, of a laboratory character, was done using a friction machine with a roller-ring friction couple. Such a combination allows to obtain the border friction which is based on the rule of transition from friction on the material surface to friction on the surface of adsorbed polar compounds. The persistence of lubricating film was evaluated as ability to counteract the wear of a sample made of aluminium. On the basis of the research it was found that a small supplement of RME to diesel fuel causes a sudden increase of sample wear. The highest wear value was obtained with a 20% supplement of RME. The smallest value of wear of aluminium sample was obtained with the use of pure diesel fuel.
Stability of the Exponential Functional Equation in Riesz Algebras
Bogdan Batko
Abstract and Applied Analysis , 2014, DOI: 10.1155/2014/848540
Abstract: We deal with the stability of the exponential Cauchy functional equation in the class of functions mapping a group ( , +) into a Riesz algebra . The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem. 1. Introduction In 1979 Baker et al. (cf. [1]) proved that the exponential functional equation in the class of functions mapping a vector space to the real numbers is superstable; that is, any function satisfying, with given , the inequality is either bounded or exponential (satisfies (1)). Then Baker generalized this famous result in [2]. We quote this theorem here since it will be used in the sequel. Theorem 1 (cf. [2, Theorem？？1]). Let be a semigroup and let be given. If a function satisfies the inequality for all , then either for all or for all . After that the stability of the exponential functional equation has been widely investigated (cf., e.g., [3–6]). This paper will primarily be concerned with the question if similar result holds true in the class of functions taking values in Riesz algebra with the common notion of the absolute value of an element stemming from the order structure of . The main aim of the present paper is to show that the superstability phenomenon does not hold in such an order setting. However, we prove that the exponential functional equation (1) is stable in the Ulam-Hyers sense; that is, for any given satisfying inequality (3) there exists an exponential function which approximates uniformly on in the sense that the set is bounded in . As a method of investigation we apply spectral representation theory for Riesz spaces; to be more precise, we use the Yosida Spectral Representation Theorem for Riesz spaces with a strong order unit. For some recent results concerning stability of functional equations in vector lattices we refer the interested reader to [7–12]. 2. Preliminaries Throughout the paper , , , and are used to denote the sets of all positive integers, integers, real numbers and nonnegative real numbers, respectively. For the readers convenience we quote basic definitions and properties concerning Riesz spaces (cf. [13]). Definition 2 (cf. [13, Definitions？？11.1 and？？22.1]). We say that a real linear space , endowed with a partial order , is a Riesz space if exists for all and We define the absolute value of by the formula . A Riesz space is called Archimedean if, for each , the inequality holds whenever the set is bounded above.
Controlling of Violations of the Basic Assumptions of the Recurrent Assessment Model of Long-Term Noise Indicators
Wojciech Batko, Renata Bal
Archives of Acoustics , 2010, DOI: 10.2478/v10168-010-0030-4
Abstract: The function of a new estimation procedure of long-term noise indicators is considered in this study. New possibilities are related to the stochastic modelling of the control data formation mechanism. Assuming the mathematical formalism based on the adaptive model of exponential smoothing of control data, the need of controlling at each estimation stage of long-term noise indicators, the adherence to the model assumptions is formulated. The procedure of its realisation is described in the paper. The tracking signal method referred to the tested errors of the assumed model was applied. The ratio of the sum of model errors in relation to the average absolute error, generated by the assumed approximation, was selected as the representative of the tracking signal. Conditions for the acceptation of the model assumption were defined. The analysis of functionality of the developed solution was illustrated by the results of a continuous noise monitoring recorded at one of the main arteries in Kraków.
Determination of the Probability Distribution of the Mean Sound Level
Wojciech Batko, Bartosz Przysucha
Archives of Acoustics , 2010, DOI: 10.2478/v10168-010-0041-1
Abstract: Assessment of several noise indicators are determined by the logarithmic mean , from the sum of independent random results L1; L2; : : : ; Ln of the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.
New Approach to the Uncertainty Assessment of Acoustic Effects in the Environment
Wojciech Batko, Pawe Pawlik
Archives of Acoustics , 2012, DOI: 10.2478/v10168-012-0008-5
Abstract: The acoustic climate assessment needed for the selection of solutions (technical, legal and organisational), which will help to minimise the acoustic hazards in the analysed areas, is realised on the basis of acoustic maps. The reference computational algorithms, assigned to them, require very thorough preparation of input data for the considered noise source model representing - in the best possible way - the acoustic climate. These input data are burdened with certain uncertainties in this class of computational tasks. The uncertainties are related to the problem of selecting proper argument values (from the interval of their possible variability) for the modelled processes. This situation has a direct influence on the uncertainty of acoustic maps. The idea of applying the interval arithmetic for the assessment of acoustic models uncertainty is formulated in this paper. The computational formalism assigned to the interval arithmetic was discussed. The rules of interval estimations for the model solutions determining the sound level distribution around the analysed noise source - caused by possible errors in the input data - were presented. The application of this formalism was illustrated in uncertainty assessments of modelling acoustic influences of the railway noise linear source on the environment.
Uncertainty Analysis in the Noise Parameters Estimation
Batko W.,Pawlik P.
MATEC Web of Conferences , 2012, DOI: 10.1051/matecconf/20120101005
Abstract: The new approach to the uncertainty estimation in modelling acoustic hazards by means of the interval arithmetic is presented in the paper. In the case of the noise parameters estimation the selection of parameters specifying the acoustic wave propagation in an open space as well as parameters which are required in a form of average values – often constitutes a difficult problem. In such case, it is necessary to determine the variance and then, related strictly to it, the uncertainty of model parameters. The application of the interval arithmetic formalism allows to estimate the input data uncertainties without the necessity of the determination their probability distribution, which is required by other methods of uncertainty assessment. A successive problem in the acoustic hazards estimation is a lack of the exact knowledge of the input parameters. In connection with the above, the analysis of the modelling uncertainty in dependence of inaccuracy of model parameters was performed. To achieve this aim the interval arithmetic formalism – representing the value and its uncertainty in a form of an interval – was applied. The proposed approach was illustrated by the example of the application the Dutch RMR SRM Method, recommended by the European Union Directive 2002/49/WE, in the railway noise modelling.
SmB$_6$: Topological insulator or semiconductor with valence-fluctuation induced hopping transport?
I. Batko,M. Batkova
Physics , 2007, DOI: 10.1016/j.ssc.2014.07.014
Abstract: We advert to the fact that presence of valence fluctuations (VFs) in semiconductors with in-gap impurity bands unconditionally leads to dynamical changes (fluctuations) of energies of localized impurity states. We provide arguments that in the impurity subnetwork consisting of centers having energy levels fluctuating around the Fermi energy there exist favorable conditions for hops from occupied states to empty states of less energy. Consequently, we propose original valence-fluctuation induced hopping mechanism as a new possibility to explain unusual metallic-like conduction of SmB$_6$ and other Kondo insulators experimentally observed at lowest temperatures. Interestingly, the proposed mechanism infers enhanced metallic-like surface conductivity of SmB$_6$, what resembles a characteristic property of topological insulator, and is in agreement with experimental observations attempting to prove the existence of topologically protected surface state in SmB$_6$.
Observation of drift and diffusion processes in Ti/TiOx/Ti memristive devices prepared by local anodic oxidation
I. Batko,M. Batkova
Physics , 2011, DOI: 10.1051/epjap/2012120102
Abstract: We demonstrate that memristive devices can be fabricated by tip-induced oxidation of thin metallic films using atomic force microscope. Electrical measurements of such prepared Ti/TiOx/Ti test structures confirmed their memristive behavior and inferred diffusion of oxygen vacancies in the TiOx barrier. Consequent Kelvin probe force microscopy studies provided evidence for the diffusion, as well as for expected oxygen vacancy drift. Time evolution of the space distribution of the vacancies due to the diffusion process revealed minute-scale (at least) retention times of the devices. The work presents technology alternative for fabrication of memristive nanodevices in geometry favouring advantageous scanning probe microscopy studies of their in-barrier processes, as well as widely utilizable approach to search for novel oxide materials for perspective memristive applications.
Calorimetric tunneling study of heat generation in metal-vacuum-metal tunnel junction
I. Batko,M. Batkova
Physics , 2004, DOI: 10.1051/epjap:2005045
Abstract: We have proposed novel calorimetric tunneling (CT) experiment allowing exact determination of heat generation (or heat sinking) in individual tunnel junction (TJ) electrodes which opens new possibilities in the field of design and development of experimental techniques for science and technology. Using such experiment we have studied the process of heat generation in normal-metal electrodes of the vacuum-barrier tunnel junction (VBTJ). The results show there exists dependence of the mutual redistribution of the heat on applied bias voltage and the direction of tunnel current, although the total heat generated in tunnel process is equal to Joule heat, as expected. Moreover, presented study indicates generated heat represents the energy of non-equilibrium quasiparticles coming from inelastic electron processes accompanying the process of elastic tunneling.
Weak index pairs and the Conley index for discrete multivalued dynamical systems
Bogdan Batko,Marian Mrozek
Mathematics , 2015,
Abstract: Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive definition of the isolating neighbourhood. It turns out that then the main tool for the construction of the index, i.e. the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs.
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