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Search results for: UNIQUENESS
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On a comparison principle and the uniqueness of spectral flow
PublicationThe spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...
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Uniqueness or uniformity - studies of media architecture
PublicationA development of media architecture is presented in light of to such phenomena as aesthetization, consumerism and digitization. This article deals with media architecture in commercial spaces. Media solutions impact on the architectural skin, making it into visible and dynamic points of the image of a post-modern city. This article presents the specificity of media solutions, depending on the function of commercial activity buildings...
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On the Conley index in Hilbert spaces in the absence of uniqueness
PublicationW artykule podana jest konstrukcja indeksu Conley`a w przestrzeniach nieskończonego wymiaru dla równań różniczkowych bez jednoznaczności rozwiązań. Celem pracy jest przygotowanie właściwej teorii do badań ilościowych i jakościowych pewnych typów nieliniowych układów eliptycznych.
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Existence and uniqueness for neutral equations with state dependent delays
PublicationW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Existence and uniqueness for neutral equations with delay dependant on a solution and its derivative
PublicationDla wykazania istnienia i jednoznaczności w pracy została zaprezentowana metoda porównawcza.
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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublicationWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...
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Non-uniqueness of fracture parameter choice in simulations of concrete cracking at mesoscale level
PublicationIn the paper a non-uniqueness of fracture parameter choice in simulations of cracking process in plain concrete specimens at mesoscale level under monotonic static loading is analysed. The Finite Element Method is used, where cracks are defined in a discrete way using interface cohesive elements with nonlinear material law including softening. The concrete mesostructure (such as: cement matrix, air voids, aggregates, and Interfacial...
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Theory versus experiment for vacuum Rabi oscillations in lossy cavities. II. Direct test of uniqueness of vacuum
PublicationThe paper continues the analysis of vacuum Rabi oscillations we started in part I [Phys. Rev. A 79, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic-oscillator Lie algebras. The zero-temperature master equation, derived in part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublicationDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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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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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Equations with Separated Variables on Time Scales
PublicationWe show that the well-known theory for classical ordinary differential equations with separated variables is not valid in case of equations on time scales. Namely, the uniqueness of solutions does not depend on the convergence of appropriate integrals.
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Existence of unbounded solutions to parabolic equations with functional dependence
PublicationThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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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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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublicationWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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Remote Stateful Autoconfiguration for Mobile IPv6 Nodes with Server Side Duplicate Address Detection
PublicationDuring interdomain handover, IPv6 node requires new address at its new location. Once the L2 handover procedure is completed, mobile node (MN) starts its IPv6 configuration, using stateless (router advertisements) or stateful (DHCPv6 communication) mode. Once the address is obtained, its uniqueness has to be verified, using Duplicate Address Detection (DAD) procedure. Depending on the interface type, this procedure may easily take...
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Knowledge-Based Management as the Key Success Factor for Research and Development Organizations
PublicationA key to achieving success in project organizations lies in exemplary management of processes within those organizations, while the ongoing projects are mainly characterized by their uniqueness. The situation is no different in commercial research and development organizations (R&D) where accuracy and repeatability of elementary processes guarantees efficient and productive realization of all enterprises. R&D organizations are...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Stock Markets’ Reactions to the Announcement of the Hosts. An Event Study in the Analysis of Large Sporting Events in the Years 1976–2032
PublicationThis study attempts to estimate the impact of the announcements of hosts of large sporting events on domestic stock markets. The research problem is to establish a connection between the uniqueness of a sporting event and investors’ beliefs through stock price behavior. Using appropriate estimation windows, 13 different sporting events classified as large, including mega and major events, were tested. The obtained results show...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Rotating rod and ball
PublicationWe consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublicationThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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Distinctive facades of commercial buildings and the quality of public space,
PublicationMutual relations between the retail center and public spaces of the city are varied. They depend on the type and size of the commercial structure. Other ones are for multifunctional shopping centers and other for high streets. In megastores and shopping malls the essential for their functioning is their interior and entrance, which is sometimes the only place of interpenetration of the commercial structure with the surrounding...
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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....
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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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Billiard in a rotating half-plane
PublicationThe main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic...
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The Laboratory Stand for the Evaluation of Heat Dissipation from the Power Cable in a Casing Pipe
PublicationThe current carrying capacity of a power cable determines its efficiency, which depends on its capability to dissipate heat produced inside the cable, as a result of current flow, into the surrounding. The studies were conducted to determine how the characteristics of the medium around the cable affected its temperature and, as a result, its ability to transport electricity. The experimentation in the lab and real measurements...
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The interaction of the pulsed laser irradiation with titania nanotubes - Theoretical studies on the thermal effect
PublicationThis paper reports temperature dispersion simulations of titania nanotubes irradiated by the 355 nm, pulsed, nanosecond laser. The modelling with the use of Finite Elements Method concerns titania nanotubes of the length and the wall thickness in the range of 0.5–2 μm and 5–20 nm, respectively. The uniqueness of the morphology was preserved by ensuring the wall thickness variation along the height of the tube, which was determined...
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Kultura jakości, doskonałości i bezpieczeństwa w organizacji
PublicationKultura jakości, bezpieczeństwa oraz doskonałości to ważne, kategorie zasobów każdej organizacji, decydujące o jej niepowtarzalności. Kształtują one nie tylko tożsamość danej organizacji, ale także mają wpływ na jej zdolność do spełniania potrzeb różnych grup interesariuszy oraz na szeroko rozumianą reputację na rynku. Każda z tych kultur wyraża się poprzez swoiste założenia, normy, wartości oraz artefakty. Stanowią one fundament...
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Man in Early Islamic Philosophy: Al-Kindi and Al-Farabi
PublicationMan was, neither for Al-Kindi, nor for Al-Farabi, a clearly isolated object of philosophical reflection. This does not mean, however, that both Islamic philosophers were not at all concerned with the uniqueness of man, his nature or the purpose of his existence. In order to understand and analyze in depth the philosophies of man voiced by Al-Kindi and Al-Farabi, one must focus primarily on their epistemologies, on their philosophical...
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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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Numerical and quantitative analysis of HIV/AIDS model with modified Atangana-Baleanu in Caputo sense derivative
PublicationFractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu’s of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels....
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3D MODELLING OF CYLINDRICAL-SHAPED OBJECTS FROM LIDAR DATA - AN ASSESSMENT BASED ON THEORETICAL MODELLING AND EXPERIMENTAL DATA
PublicationDespite the increasing availability of measured laser scanning data and their widespread use, there is still the problem of rapid and correct numerical interpretation of results. This is due to the large number of observations that carry similar information. Therefore, it is necessary to extract from the results only the essential features of the modelled objects. Usually, it is based on a process using filtration, followed by...
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Linking optical and electronic properties to photoresponse of heterojunctions based on titania nanotubes and chromium, molybdenum, and tungsten oxides
PublicationThe development of photosensitization strategies for titanium dioxide is necessary for the enhancement of its optical and electronic properties towards its application potential in solar photoelectrochemistry. In this work, significant differences in the photosensitizing capability of the 6th group transition metal oxides applied on the surface of titania nanotubes are reported. For the first time, correlations between the experimentally...
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Succinite, Baltic Amber: A Chemical Masterpiece of Nature
PublicationSuccinite, Baltic amber, is one of the most appreciated fossil resins. Its beauty has fascinated people since prehistoric times. It is a substance, and also gemstone, whose uniqueness is due to its compelling, though still not fully understood, physicochemical nature. In this article, some facts about the physical and chemical properties of succinite in order to find an answer for questions about the unique properties of this resin,...
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Rapid Design of 3D Reflectarray Antennas by Inverse Surrogate Modeling and Regularization
PublicationReflectarrays (RAs) exhibit important advantages over conventional antenna arrays, especially in terms of realizing pencil-beam patterns without the employment of the feeding networks. Unfortunately, microstrip RA implementations feature narrow bandwidths, and are severely affected by losses. A considerably improved performance can be achieved for RAs involving grounded dielectric layers, which are also easy to manufacture using...
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WPŁYW OCENY WARTOŚCI ZACHOWANEGO KULTUROWEGO DZIEDZICTWA MATERIALNEGO NA PROCES INWESTYCYJNY NA TERENACH STOCZNI GDAŃSKIEJ OBJĘTYCH PROGRAMEM REWITALIZACYJNYM
PublicationRewitalizacja terenów poprzemysłowych i obiektów poprzemysłowych jest procesem długoterminowym i wieloetapowym. W pierwszym etapie rewitalizacji ważna jest ocena materialnej, emocjonalnej i użytkowej wartości zachowanego dziedzictwa kulturowego. Na przykładzie projektu rewitalizacyjnego, który trwa od 1996 r., Na dawnych obszarach Stoczni Gdańskiej, w których znajdują się pozostałości Stoczni Cesarskiej i Stoczni Schichau, przedstawiono...
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Timber - material of the future. Examples of small wooden architecture structures.
PublicationThe aim of this article is to present various types of wood-based products, classified as engineered timber, while specifying the implications of their structural properties for their forms. Timber is used as a construction material due to its fire resistance, good structural characteristics and insulating properties. The advent of new technologies of wood processing and wood-based materials production has converted timber into...
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ARCHITECTURE IN BRANDING AND OVERBRANDING PROCESS. HOW GLOBALIZATION INFLUENCED ARCHITECTURE QUALITY.
PublicationGlobalization is unification. In the field of architecture and in the social structure alike, the globalization leads to a blending of economies and cultures that produces uniformly branded public space as a response to universal assumptions of integration and correlation. While branding consists in creating a recognizable and outstanding image a strong contradiction exists between both of these approaches. As a result, regional...
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Dynamic host configuration protocol for IPv6 improvements for mobile nodes
PublicationIn wireless networks mobile clients change their physical location, which results in changing point of attachment to the network. Such handovers introduce unwanted periods, when node does not have communication capabilities. Depending on many conditions, such events may require reconfiguration of layer 2 (e.g. IEEE 802.16) or both 2 and 3 layers (IPv6). This paper investigates delays introduced in the latter type of handover. IPv6...
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Exploring the impact of cultural context on eye-tracking studies of architectural monuments in selected European cities: Sustainable heritage management.
PublicationSustainable management of architectural heritage requires conducting an inclusive diagnosis of users’ opinions, considering both residents and tourists as the recipients of urban space. Given the cultural diversity within these groups, proposing the use of eye-trackers (ET) as an alternative to traditional public consultation prompts the need to assess the method’s advantages and disadvantages. It remains uncertain whether individuals...
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CONTRASTING MODERNISMS - ARCHITECTURE OF HARBOUR CITIES GDYNIA AND ALTONA
PublicationThe presentation of the exhibition “Architect Gustav Oelsner – Light, Air, Colour,”, which took place in Gdynia 1.04-29.05.2011, showed the clinker architecture of Gustav Oelsner in Altona. As a contrast to the white-plastered architecture of Gdynia, it provided an interesting background for the comparison of two different faces of modernism. The most important feature of the aesthetics of modernism was its cosmopolitan character,...
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublicationIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...