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Search results for: BUCKINGHAM THEOREMS
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublicationUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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Can architecture be 11-dimensional? The nature of space in the architecture of the digital world era
PublicationThis research aims to explore the development of architectural theories about ‘architectural dimensions’ and look at architecture as a multidimensional space. It is important to understand that with today's development of virtual reality technology and through the combination of theories of physics and architecture, a new possibility of creating space has emerged. The arguments are made through inductive reasoning and grounded...
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In search of a new relationship between nature and society
PublicationWe live in an era of breakthrough- not only in the literal sense of the word, but the breakthrough of the century or the millennium. New discoveries and the crisis present in the economy, society, religion and ecology forces a review of all universally accepted theories. Nature, ecology and environment are the key words used in every area of human activity. It has led to the development of a new scientific field- the philosophy...
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Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
PublicationWe consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Georg Simmel’s The Philosophy of Money and the Modernization Paradigm
PublicationThis article examines Georg Simmel’s contribution to the understanding of how money functions in modern society, mainly scrutinizing his most important work on that topic, The Philosophy of Money, in the context of modernization theories. Modernization theories, as developed (most notably) by Marx, Weber, Durkheim, and Elias, attempted to explain the transition from feudalism and a closed agrarian economy to capitalism and industrial...
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An Analysis of Elliptical-Rectangular Patch Structure on Multilayer Elliptic Cylinders
PublicationThe resonance frequency problem of an ellipticalrectangular patch mounted on multilayered dielectric coated elliptic conducting cylinder, is investigated in this paper. A fullwave analysis and a moment-method calculation are employed. The analysis is carried out considering the expansion of the field as a series of Mathieu functions. An additional theorem for Mathieu functions is utilized to investigate the non-confocal ellipse...
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The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
PublicationWe show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Subadditivity of the minimum output entropy and superactivation of the classical capacity of quantum multiple access channels
PublicationWe study subadditivity of the minimum output entropy (Hmin) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for Hmin known in classical information theory. Our result is based on a fundamental property of MACs, i.e., independence of each sender. The channels used in the example can be constructed explicitly. On the basis of subadditivity of Hmin we also provide an example...
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RNS/TCS CONVERTER DESIGN USING HIGH-LEVEL SYNTHESIS IN FPGA
PublicationAn experimental high-level synthesis (HLS) of the residue number system (RNS) to two’s-complement system (TCS) converter in the Vivado Xilinx FPGA environment is shown. The assumed approach makes use of the Chinese Remainder Theorem I (CRT I). The HLS simplifies and accelerates the design and implementation process, moreover the HLS synthesized architecture requires less hardware by about 20% but the operational frequency is smaller...
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On the interspike-intervals of periodically-driven integrate-and-fire models
PublicationWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Integrable zero-range potentials in a plane
PublicationWe examine general statements in the Wronskian representation of Darboux transformations for plane zero-range potentials. Such expressions naturally contain scattering problem solution. We also apply Abel theorem to Wronskians for differential equations and link it to chain equations for Darboux transforms to fix conditions for further development of the underlying distribution concept. Moutard transformations give a convenient...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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Space syntax analysis - methodology of understanding the space
PublicationNowadays space is considered as a net of connections between different areas. The questions how to delineate its character and how it is possible to objectively compare two spaces is the matter under consideration. This was the reason for creating new theories about the structure of place. "Space syntax analysis" (SSA) or simply "Space Syntax" defines a number of theories and research areas devoted to the analysis of space configuration....
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Qualia: About Personal Emotions Representing Temporal Form of Impressions - Implementation Hypothesis and Application Example
PublicationThe aim of this article is to present the new extension of the xEmotion system as a computerized emotional system, part of an Intelligent System of Decision making (ISD) that combines the theories of affective psychology and philosophy of mind. At the same time, the authors try to find a practical impulse or evidence for a general reflection on the treatment of emotions as transitional states, which at some point may lead to the...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Critical Remarks on Landauer’s principle of erasure– dissipation: Including notes on Maxwell demons and Szilard engines
PublicationWe briefly address Landauer’s Principle and some related issues in thermal demons. We show that an error-free Turing computer works in the zero-entropy limit, which proves Landauer’s derivation incorrect. To have a physical logic gate, memory or information-engine, a few essential components necessary for the operation of these devices are often neglected, such as various aspects of control, damping and the fluctuation–dissipation...
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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Usage of Memi-Markov Process in Operation Evaluation of Diesel Engine
PublicationIn paper, the proposition of quantitative evaluation of operation using semi-Markov processes theories has been presented. Basic assumptions, essential for creating mathematical model on example of diesel engine were shown. Special attention was given to practical aspects of using established mathematical model. Example of characteristic of analysed process - temporary distribution of probability was assigned.
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain
PublicationWe study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on the whole $\R^n$. To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $\WLPhispace(\R^n)$. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden...
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublicationThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...
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Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body
PublicationGeneralized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or...
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On jump conditions at non-material singular curves in the resultant shell thermomechanics
PublicationThe global, refined, resultant, two-dimensional (2D) balance laws of mass, linear and angular momenta, and energy as well as the entropy inequality were formulated by Pietraszkiewicz (2011) as exact implications of corresponding laws of 3D rational thermomechanics. In case of a shell with the regular base surface and all resultant surface fields differentiable everywhere on it and at any time instant, the local laws of the resultant...
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Limiting distribution of Lempel Ziv'78 redundancy
PublicationWe show that the Lempel Ziv'78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ'78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences....
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On the Limiting distribution of Lempel Ziv'78 Redundancy for Memoryles Sources
PublicationWe show that the Lempel Ziv'78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ'78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences....
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Electromagnetic-based derivation of fractional-order circuit theory
PublicationIn this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order...
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Gender, education and motivation of onwers of small firms and their growth
PublicationAlmost every article on the growht of SMEs begins with noting the lack of a unified theory or a model of growth in thei group of companies, although the growth of small and medium sized enterprises has been the subject of research for many years and early theories about it appeared already before the Second World War. In the paper some conlusions about the relation between gender, education and motivation of owner and the small...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublicationIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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Simulation of Signal Propagation Along Fractional-Order Transmission Lines
PublicationIn this paper, the simulation method of signal propagation along fractional-order (FO) transmission lines is presented. Initially, fractional calculus and the model of FO transmission line are introduced. Then, the algorithm allowing for simulation of the nonmonochromatic wave propagation along FO transmission lines is presented. It employs computations in the frequency domain, i.e., an analytical excitation is transformed to the...
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Speed Observer Structure of Induction Machine Based on Sliding Super-Twisting and Backstepping Techniques
PublicationThis paper presents an analysis of the two speed observer structures which are based on the backstepping and sliding super twisting approach. The observer stabilizing functions result from the Lyapunov theorem. To obtain the observer tuning gains the observer structure is linearized near the equilibrium point. The rotor angular speed is obtained from non-adaptive dependence. In the sensorless control system structure the classical...
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Equivalent Single Layer Models in Free Vibration Analysis of Laminated Multi-Layered Plates
PublicationThe performance of selected equivalent single-layer (ESL) models is evaluated within several classical benchmark tests for small amplitude free vibration analysis of multi-layered plates. The authors elaborated their own Finite Element software based on the first-order shear deformation (FOSD) theory with some modifications incorporated including a correction of the transverse shear stiffness and an application of zigzag type functions....
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Torsion of restrained thin-walled bars of open constant bisymmetric cross-section
PublicationElastic and geometric stiffness matrices were derived using Castigliano's first theorem, for the case of torsion of restrained thin-walled bars of open constant bisymmetric cross-section. Functions which describe the angles of torsion were adopted from the solutions of thedifferential equation for restrained torsion. The exact solutions were simplified by expanding them in a power series. Numerical examples were taken from Kujawa...
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Wstępna analiza zagrożenia podtopieniami w zlewni Potoku Strzyża w Gdańsku.
PublicationCharakterystyka sieci hydrograficznej Potoku Strzyża. Analiza zagrożenia podtopie - niami z wykorzystaniem hydraulicznego modelu potoku. Przedstawienie oraz analiza wyników obliczeń. Wstępne określenie odcinków newralgicznych z punktu widze - nia zagrożenia powodziowego. Wstępna analiza możliwych przyczyn występowania podtopień na terenie zlewni Potoku Strzyża.
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Asymmetric Renyi Problem and > PATRICIA Tries
PublicationIn 1960 R´enyi asked for the number of random queries necessary to recover a hidden bijective labeling of n distinct objects. In each query one selects a random subset of labels and asks, what is the set of objects that have theselabels? Weconsider here anasymmetric version of the problem in which in every query an object is chosenwith probability p > 1/2 and we ignore “inconclusive” queries. We study the number of queries needed...
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Average Redundancy of the Shannon Code for Markov Sources
PublicationIt is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend these findings, concerning the Shannon...
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Understanding Knowledge-Intensive Business Services. Identification, Systematization, and Characterization of Knowledge Flows
PublicationThis book contributes to an improved understanding of knowledge-intensive business services and knowledge management issues. It offers a complex overview of literature devoted to these topics and introduces the concept of ‘knowledge flows’, which constitutes a missing link in the previous knowledge management theories. The book provides a detailed analysis of knowledge flows, with their types, relations and factors influencing...
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Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2
PublicationWe will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this...
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Research on protection mechanisms of Resilient Packet Ring Network.
PublicationPaper describes iSteering - a new method to control traffic in case of RPR network failure. There's comparison of packet wrapping, steering and our proposed method iSteering, which can be used in case of transmitter/receiver or fiber failure. Numerical analysis for even and random traffic flow has been made in order to compare packet wrapping, steering and iSteering. The results of all the tests are included.
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Modelling the time-dependent behaviour of soft soils
PublicationTime-dependence of soft soils has already been thoroughly investigated. The knowledge on creep and relaxation phenomena is generally available in the literature. However, it is still rarely applied in practice. Regarding the organic soils, geotechnical engineers mostly base their calculations on the simple assumptions. Yet, as presented within this paper, the rate-dependent behaviour of soft soils is a very special and important...
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Hat problem on a graph
PublicationThe topic of our paper is the hat problem. In that problem, each of n people is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color looking at the hat colors of the other people. The team wins if at least one person guesses his hat color correctly and no one guesses his hat color wrong, otherwise the team loses. The aim is to maximize the probability of win. In this version every...
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Visual Dimensions of Modeling Languages in Interdisciplinary Perspective
PublicationUżyteczność języków modelowania wizualnego zależy od notacji. Notacja może być postrzegana jako zestaw wizualnych komponentów, które w określony sposób oddziałują na ludzkie oko i ludzki mózg. Referat przedstawia analizę interdyscyplinarną wykonaną w celu lepszego zrozumienia wizualnych wymiarów języków modelowania. Wizualne wymiary pochodzą z teorii opisujących percepcję wzrokową, wizualizację danych oraz reprezentacje poznawcze....
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On FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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Computational issues of solving the 1D steady gradually varied flow equation
PublicationIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....