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Search results for: history of mathematic
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Almost homoclinic solutions for a certain class of mixed type functional differential equations
PublicationW pracy opisano pewną metodę aproksymacyjną szukania rozwiązań prawie homoklinicznych dla równań różniczkowo funkcyjnych z opóźnionym i przyśpieszonym argumentem. Podano również przykłady zastosowań tej metody.
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Chromatic cost coloring of weighted bipartite graphs
PublicationGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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Generic invariant measures for iterated systems of interval homeomorphisms
PublicationIt is well known that iterated function systems generated by orientation preserving homeomorphisms of the unit interval with positive Lyapunov exponents at its ends admit a unique invariant measure on (0, 1) provided their action is minimal. With the additional requirement of continuous differentiability of maps on a fixed neighbourhood of {0,1} { 0 , 1 } , we present a metric in the space of such systems which renders it complete....
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On the super domination number of lexicographic product graphs
PublicationThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines
PublicationWe consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s1, s2, and s3 to minimize the schedule length. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We how that if the graph is 2-chromatic then the problem can be solved in O(n^2) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1>s2=s3.
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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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A spline-based FE approach to modelling of high frequency dynamics of 1-D structures
PublicationIn this paper a computational methodology leading to the development of a new class of FEs, based on the application of continuous and smooth approximation polynomials, being splines, has been presented. Application of the splines as appropriately defined piecewise elemental shape functions led the authors to the formulation of a new approach for FEM, named as spFEM, where contrary to the well-known NURBS approach, the boundaries...
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The law of the Iterated Logarithm for random interval homeomorphisms
PublicationA proof of the law of the iterated logarithm for random homeomorphisms of the interval is given.
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Infinite chromatic games
PublicationIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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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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A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems
PublicationIn this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on...
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Laplace domain BEM for anisotropic transient elastodynamics
PublicationIn this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained....
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Maximum transportation growth in energy and solute particles in Prandtl martial across a vertical 3D-heated surface: Simulations achieved using by finite element approach
PublicationThe goal of this study is to determine the maximum energy and solute particles' transportation growth in a 3D-heated region of Prandtl martial through a dynamic magnetic field. The effects of this field on the properties of solvent molecules and heat conduction are studied. A correctly stated functional method and a finite element approach are comparable to a certain type of differential equations. In order demonstrate the effects...
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A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers
PublicationThis work presents a generalized Kirchhoff–Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for heterogeneous and fibrous materials such as textiles, biomaterials, composites and pantographic structures. The presented theory is a direct extension of classical Kirchhoff–Love shell theory to incorporate...
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Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations
PublicationAbstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version...
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Local material symmetry group for first- and second-order strain gradient fluids
PublicationUsing an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients....
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Global edge alliances in graphs
PublicationIn the paper we introduce and study a new problem of finding a minimum global edge alliance in a graph which is related to the global defensive alliance (Haynes et al., 2013; Hedetniemi, 2004) and the global defensive set (Lewoń et al., 2016). We proved the NP-completeness of the global edge alliance problem for subcubic graphs and we constructed polynomial time algorithms for trees. We found the exact values of the size of the...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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A chemo-mechano-thermodynamical contact theory for adhesion, friction, and (de)bonding reactions
PublicationThis work presents a self-contained continuum formulation for coupled chemical, mechanical, and thermal contact interactions. The formulation is very general and, hence, admits arbitrary geometry, deformation, and material behavior. All model equations are derived rigorously from the balance laws of mass, momentum, energy, and entropy in the framework of irreversible thermodynamics, thus exposing all the coupling present in the...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
PublicationIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily...
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Minimal surfaces and conservation laws for bidimensional structures
PublicationWe discuss conservation laws for thin structures which could be modeled as a material minimal surface, i.e., a surface with zero mean curvatures. The models of an elastic membrane and micropolar (six-parameter) shell undergoing finite deformations are considered. We show that for a minimal surface, it is possible to formulate a conservation law similar to three-dimensional non-linear elasticity. It brings us a path-independent...
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Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere
PublicationA class of dissipative orientation preserving homeomorphisms of the infinite annulus,pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere isconsidered. We prove that in some isotopy classes the local behavior of such homeomor-phisms at a fixed point, namely the existence of so-called inverse saddle, impacts thetopology of the attractor — it cannot be arcwise connected
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Equitable coloring of hypergraphs
PublicationA hypergraph is equitablyk-colorable if its vertices can be partitioned into k sets/colorclasses in such a way that monochromatic edges are avoided and the number of verticesin any two color classes differs by at most one. We prove that the problem of equitable 2-coloring of hypergraphs is NP-complete even for 3-uniform hyperstars. Finally, we apply the method of dynamic programming for designing a polynomial-time algorithm to...
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Surface effects of network materials based on strain gradient homogenized media
PublicationThe asymptotic homogenization of periodic network materials modeled as beam networks is pursued in this contribution, accounting for surface effects arising from the presence of a thin coating on the surface of the structural beam elements of the network. Cauchy and second gradient effective continua are considered and enhanced by the consideration of surface effects. The asymptotic homogenization technique is here extended to...
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Inverse shadowing and related measures
PublicationWe study various weaker forms of the inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called ergodic inverse shadowing property (Birkhoff averages of continuous functions along an exact trajectory and the approximating one are close). We demonstrate that this property implies the continuity of the set of invariant measures in the Hausdorff metric. We show that the...
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Biomimetic torene shells
PublicationThe genome inside the eukaryotic cells is guarded by a unique shell structure, called the nuclear envelope (NE), made of lipid membranes. This structure has an ultra torus topology with thousands of torus-shaped holes that imparts the structure a high flexural stiffness. Inspired from this biological design, here we present a novel ‘‘torene’’ architecture to design lightweight shell structures with ultra-stiffness for engineering...
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Remarks on evaluation of spectral radius of operators arising in WR methods for linear systems of ODEs
PublicationW pracy omawiane są różne metody oszacowania promienia spektralnego. Do oszacowań tych użyto elementarnych metod. Jedną z nich jest metoda wykorzystująca normę Bieleckiego. Jedną z zalet takich metod wyraźnie widać na przykładzie równań różniczkowych z opóźnieniem, gdzie oszacowania promienia spektralnego zależą od charakteru opóźnienia.
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Wolność gospodarcza w Polsce- istota i kierunki zmian
PublicationCelem artykulu jest przedstawienie istoty i znaczenia pojęcia''wolnośc gospodarcza'' w Polsce poprzez analizę dokonywanych zmian w prawie gospodarczym, ewolucję znaczenia tego pojęcia oraz ocenę stopnia realnej swobody gospodarczej polskich podmiotów gospodarczych na tle innych krajów
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Teleopieka domowa w systemie opieki nad osobami starszymi – doświadczenia gmin województwa pomorskiego
PublicationCelem opracowania jest przedstawienie istoty teleopieki domowej oraz dotychczasowych doświadczeń w zakresie jej wdrażania w gminach województwa pomorskiego. Autorka artykułu omówiła założenia idei gminnych powszechnych systemów teleopieki domowej oraz zidentyfikowała warunki konieczne do ich efektywnego funkcjonowania.
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Koncepcja i modelowanie silnika o wirującym tworniku oraz magneśnicy do zastosowania w napędzie miejskiego samochodu elektrycznego
PublicationW artykule zaprezentowano koncepcję, model oraz prototyp silnika z wirującym twornikiem oraz magneśnicą. Opisano historię powstania i zastosowania tego typu silników w motoryzacji. Przedstawiono nowoczesne rozwiązania konstrukcyjne i zastosowania we współczesnych samochodach elektrycznych i hybrydowych. Opracowano model silnika z wirującym twornikiem i magneśnicą oraz przedstawiono wybrane wyniki symulacji przeprowadzone w programie...
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WiMAX - nowy standard szerokopasmowych sieci bezprzewodowych (Cześć 1)
PublicationW artykule przedstawiono historię powstania i rozwoju, główne założenia oraz modele zastosowania standardu IEEE 802.16 (WiMAX). Zaprezentowano architekturę standardu, obejmującą rozwiązania warstwy fizycznej oraz warstwy łącza danych, w obecnej wersji 802.16-2004. Opisano perspektywy rozwoju standardu do wersji mobilnej oraz prognozy dotyczące wejścia rozwiązania na rynek w najbliższych latach.
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Przebudowy gdańskich kościołów
PublicationW historii architektury świątyń gdańskich wystąpiły działania budowlane mające na celu zmodernizowanie ich bryły. Polegały one na: powiększeniu planu, dobudowie kaplic, translokacji. Inne działania polegały na dostawieniu wieży, ich nadbudowie, a także zmianie układu przestrzennego naw. Do radykalnych przedsięwzięć należała zmiana funkcji sakralnej na świecką wraz z niezbędnymi przekształceniami architektonicznymi.
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Filozofia jako krytyka poznania. Wprowadzenie do transcendentalizmu Ernsta Cassirera
PublicationRdzeń monografii stanowią założenia metodologiczne i refleksja nad zasadami poznania wyrastające z tradycji filozofii krytycznej i przedstawione przez Cassirera jako „krytyka poznania”. Ma ona na celu przedstawienie oraz omówienie historii i teorii transcendentalizmu w jego marburskiej postaci oraz pokazanie jego potencjału wyjaśniającego jako metody współczesnych nauk ścisłych i humanistycznych.
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Orłowo: Dzieje, krajobraz, architektura : Perła międzywojennej Gdyni
PublicationKsiążka przedstawia bogato ilustrowaną historię trzech obecnych dzielnic Gdyni: Orłowa, Kolibek i Małego Kacka. Ukazuje dzieje tych miejscowości od czasów najdawniejszych (archeologia), poprzez średniowiecze, nowożytność, aż do 1 połowy XX wieku. Ważnym aspektem monografii jest całościowe przedstawienie architektury i urbanistyki tego terenu, jak również jego unikalnych walorów krajobrazowych.
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Numerical simulations of space-time conditional random fields of ground motions
PublicationArtykuł przedstawia metodę modelowania stochastycznego efektu propagacji fali sejsmicznej z wykorzystaniem przestrzenno-czasowej funkcji korelacji pola losowego trzęsienia ziemi. Metodę wykorzystano do generacji nieznanych historii czasowych trzęsienia w wybranych punktach na podstawie znanego rejestru w jednym miejscu. Wyniki pokazały, iż zastosowanie zaproponowanej metody prowadzi do relatywnie małych błędów symulacji.
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Enhancing seismic performance of rigid and semi-rigid connections equipped with SMA bolts incorporating nonlinear soil-structure interaction
PublicationNowadays, using smart connections can improve the performance of buildings with some recentering features that are from the superelastic behavior of Shape Memory Alloys (SMAs). It seems that there is different rigidity between the designed connection and the real one in Steel Moment-Resisting Frames (SMRFs), which can be considered as a problematic issue due to the importance of connections in seismic performance assessment. This...
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Bezczujnikowe sterowanie trakcyjnym silnikiem IPMSM małej mocy
PublicationThis paper describes an algorithm for estimation of IPMSM angular rotor position. The algorithm uses derivatives of motor phase currents resulting from PWM modulation to obtain the rotor position. Control of the IPMSM electromagnetic torque requires a precise estimation of the rotor angular position throughout the wide speed range. This involves using a set of estimation methods switched with the dependence on the actual rotor...
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Incomplete Cross-Bonding in the MV Line. Experience from the Operation of MV Single Cable Lines
PublicationCable lines are one of the basic components of power systems. Medium and high voltage cables mainly comprise a metallic sheath, which is concentric to the main core conductor. There are several operating schemes of such cable lines, which differ in the place of earthing of sheaths and the possible use of the sheaths and/or conductors crossing. The sheaths cross-bonding is typically done in two places of one cable line section,...
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An automatic selection of optimal recurrent neural network architecture for processes dynamics modelling purposes
PublicationA problem related to the development of algorithms designed to find the structure of artificial neural network used for behavioural (black-box) modelling of selected dynamic processes has been addressed in this paper. The research has included four original proposals of algorithms dedicated to neural network architecture search. Algorithms have been based on well-known optimisation techniques such as evolutionary algorithms and...
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VOLTAMMETRIC DETERMINATION OF DEOXYRIBONUCLEIC ACID PRESENCE ON A CARBON ELECTRODE
PublicationThis paper presents a voltammetry as a useful method to analyse DNA from different species. This electrochemical method is well know and used in different analyses. The influence of an area of working electrode and the capacity component, is shown at equals and the measurement. In voltammetry DNA measurement the capacity component is very important and must be taken into consideration. All mathematical analyses were verify at laboratory.
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A reactive algorithm for deducing nodal forwarding behavior in a multihop ad-hoc wireless network in the presence of errors
PublicationA novel algorithm is presented to deduce individual nodal forwarding behavior from standard end-to-end acknowledgments. The algorithm is based on a well-established mathematical method and is robust to network related errors and nodal behavior changes. The proposed solution was verified in a network simulation, during which it achieved sound results in a challenging multihop ad-hoc network environment.
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Rhythm and Colours of the Angles
PublicationABSTRACT The game of space was and still is a crucial aspect of visual arts. The aim of this study is to examine how the arrangement of hues, rhythms and angles of various polygons can create an impression of depth and movement on a flat surface. The so-called Penrose tiling and Ulam's spiral are mathematical models that have been applied for the painting experiment. There is a vast amount of evidence gathered over the ages that...
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Data on LEGO sets release dates and worldwide retail prices combined with aftermarket transaction prices in Poland between June 2018 and June 2023
PublicationThe dataset contains LEGO bricks sets item count and pricing history for AI-based set pricing prediction. The data spans the timeframe from June 2018 to June 2023. The data was obtained from three sources: Brickset.com (LEGO sets retail prices, release dates, and IDs), Lego.com official web page (ID number of each set that was released by Lego, its retail prices, the current status of the set) and promoklocki.pl web page (the retail...
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The Origins of the Concept of Ideology
PublicationThe concept of "ideology" as, firstly, a term that points at non-epistemological conditioning of cognitive processes, and, secondly, as a term which aimed at disclosing the ancillary role of given ideas in regard to specific political interests of certain groups, has long history. Since Francis Bacon's theory of idols modern philosophy endavoured to create a comprehensive classification of systematic cognitive errors which divert...
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Numerical study on pounding between two adjacent buildings under earthquake excitation
PublicationSeismic excitation, which results in large horizontal relative displacements, may cause collisions between two adjacent structures due to insufficient separation distance between them. Such collisions, known as earthquake-induced structural pounding, may induce severe damages. In this paper, the case of pounding between two adjacent buildings is studied by the application of single degree-of-freedom structural models. Impact is...
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Analysis of Transparent Concrete as an Innovative Material Used in Civil Engineering
PublicationSince the dawn of history concrete has been, right behind stone and brick, one of the oldest building materials. The ancient Romans took advantage of its opportunities. They constructed amazing architectural objects, which survived centuries as whole buildings or parts of them. Concrete is so ubiquitous, that when we are walking in a newer districts of cities we are virtually surrounded by concrete from everywhere. Sometimes...
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Memory and Imagination: Artwork as a Form of Testimony
PublicationAs the generation of witnesses is passing away and the testimonies of Shoah survivors are replaced by an inherited, culturally constructed memory - post-memory – art becomes a meaningful landmark in the landscape of memory. Although the narration of history - being the researchers’ discourse rather than an objective view - has been considered to a certain extent fictitious, the difference between real and fictional, between remembering...