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Search results for: EXISTENCE
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A reliable synthesis of discrete-time H-inf control. Part I: basic theorems and J-lossless conjugators
PublicationThe paper gives a basis for solving many problems of numerically reliable synthesis of sub-optimal discrete-time control in H-inf. The approach is based on J-lossless factorisation of the delta-domain chain-scattering description of continuous-time plants being controlled. Relevant properties of poles and zeroes of chain-scattering models are given. Necessary and sufficient conditions for the existence of stabilising J-lossless...
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TRAVELLING WAVES FOR LOW–GRADE GLIOMA GROWTH AND RESPONSE TO A CHEMOTHERAPY MODEL
PublicationLow-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the...
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The cohomological span of LS-Conley index
PublicationIn this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula...
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Apparent molar volumes, expansibilities, and isentropic compressibilities of selected electrolytes in methanol
PublicationDensities of solutions of sodium bromide, sodium perchlorate, sodium tetraphenylborate, and tetraphenylphosphonium bromide in methanol at the temperatures ranging from 283.15 to 313.15 K have been measured. Ultrasound velocities for the above systems at T = 298.15 K have been determined. From the obtained data, the partial molar volumes and the partial molar isentropic compressibilities for electrolytes in solution have been estimated....
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Completely entangled subspaces of entanglement depth k
PublicationWe introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth k (k-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least k. We present an efficient construction of k-CESs of any achievable dimensionality in any multipartite scenario. Further, we discuss the relation between these subspaces and unextendible product bases (UPBs)....
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublicationA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Fragment prywatnego księgozbioru gdańskiego kupca George'a Tönnigesa zachowany w zbiorach Biblioteki Gdańskiej PAN
PublicationIn the present holdings of the Gdańsk Library of the Polish Academy of Sciences beside the historical book collections once belonging to Gdańsk patricians (e.g. J. Uphagen, M. Hanow, W. Schlieff and A. Rosenberg), there are remains of a less known private book collection belonging in the 18th century to George Tönniges, a representative of the Gdańsk patriciate. On the one side, these several prints, fortunately survived up till...
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Examples of AFM applications in liquid environment
Open Research DataImportant advantage of atomic force microscopy (also tunneling microscopy) is the ability to work in different environments (vacuum, controlled atmosphere, liquid environment). The last one, open interesting possibilities, such as imaging of delicate biological materials in their natural state. The use of electrochemical mode allows for the modification...
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Quenching of bright and dark excitons via deep states in the presence of SRH recombination in 2D monolayer materials
PublicationTwo-dimensional (2D) monolayer materials are interesting systems due to an existence of optically non-active dark excitonic states. In this work, we formulate a theoretical model of an excitonic Auger process which can occur together with the trap-assisted recombination in such 2D structures. The interactions of intravalley excitons (bright and spin-dark ones) and intervalley excitons (momentum-dark ones) with deep states located...
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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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Dot-com and AI bubbles: Can data from the past be helpful to match the price bubble euphoria phase using dynamic time warping?
PublicationThe article investigates the existence of a price bubble in the artificial intelligence market, employing the Generalised Supremum Augmented Dickey-Fuller test and dynamic time warping methodology. It proposes a method to detect the end of the price bubble euphoria phase, generating an average profit of close to 7% over 5 days and over 10.5% over 20 days, with almost 90% effectiveness. The study found that the AI market experienced...
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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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Nilpotent singularities and chaos: Tritrophic food chains
PublicationLocal bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...
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Hopf bifurcation in time‐delayed gene expression model with dimers
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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Marcinkiewicz Averages of Smooth Orthogonal Projections on Sphere
PublicationWe construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank lattice \Gamma ⊂ R^d , a smooth projection is localized in a neighborhood of an arbitrary precompact fundamental domain R^d / \Gamma. We also show the existence of a highly localized smooth orthogonal projection, whose Marcinkiewicz average under the...
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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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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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Recurrent bowel-blood translocations of Escherichia coli with the unique virulence characteristics over three-year period in the patient with acute myeloid leukaemia – case report
PublicationIn patients with haematological malignancies, the bowel remains the main source of Escherichia coli bloodstream infections. We present the clinical example of recurrent bowel-blood translocations of E. coli with the unique virulence characteristics in a 55-year-old male with the diagnosis of acute myeloid leukaemia. The virulent factors profile of examined strains confirmed that the co-existence of genes papC, sfa, usp and cnf1,...
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Controlling the europium oxidation state in diopside through flux concentration
PublicationThis paper explores the connection between the H3BO3 flux concentration and the co-existence of Eu2+ and Eu3+ dopants within CaMgSi2O6 crystals (diopside). The samples were synthesised using a solid-state synthesis method under varying atmospheric conditions, including oxidative (air), neutral (N2), and reductive (H2/N2 mixture) environments. Additionally, some materials underwent chemical modification by partially substituting...
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Steady magnetohydrodynamic flow in a diverging channel with suction or blowing
PublicationAn analysis is made of steady two-dimensional divergent flow of an electrically conducting incompressible viscous fluid in a channel formed by two non-parallel walls, the flow being caused by a source of fluid volume at the intersection of the walls. The fluid is permeated by a magnetic field produced by an electric current along the line of intersection of the channel walls. The walls are porous and subjected to either suction...
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DIAGNOSIS OF MALIGNANT MELANOMA BY NEURAL NETWORK ENSEMBLE-BASED SYSTEM UTILISING HAND-CRAFTED SKIN LESION FEATURES
PublicationMalignant melanomas are the most deadly type of skin cancer but detected early have high chances for successful treatment. In the last twenty years, the interest of automated melanoma recognition detection and classification dynamically increased partially because of public datasets appearing with dermatoscopic images of skin lesions. Automated computer-aided skin cancer detection in dermatoscopic images is a very challenging task...
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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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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublicationStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Bi-based halide perovskites: Stability and opportunities in the photocatalytic approach for hydrogen evolution
PublicationIn this study, we successfully prepared Bi-based single perovskites of the A3Bi2I9 type (A = Cs, Rb, MA, FA), and, for the first time, attempted to experimentally obtain double perovskites Cs2B’BiI6 type (B′ = Ag, Au, In, Cu). Despite the premises available in theoretical studies, our research has proven the impossibility of the existence of double perovskites of this type. Nevertheless, both types of obtained materials were subjected...
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POLITECHNIKA GDAŃSKA W LITERATURZE
PublicationW artykule przedstawiono w jaki sposób Politechnika Gdańska funkcjonuje w literaturze pięknej. Politechnika ukazywana jest jako miejsce nauki, ale także miejsce wydarzeń historycznych i kulturalnych, jej istnienie jest zakorzenione w świadomości gdańszczan, a przede jest to miejsce w którym spędziło się najlepiej wspominany okres w życiu – okres studiów i pracy zawodowej. Wymienione zostały publikacje informacyjne, ale przede wszystkim...
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Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
PublicationIn this work we will consider a class of second order perturbed Hamiltonian systems with a superquadratic growth condition on a time periodic potential and a small aperiodic forcing term. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system...
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Cation sensing by diphenyl-azobenzocrowns
PublicationMetal cations complexation and proton binding by 13- and 16-membered diphenyl-azobenzocrowns and diphenyl-hydroxyazobenzocrowns were studied in acetonitrile using spectroscopic methods: UV–vis spectroscopy, spectrofluorimetry, and 1H NMR spectroscopy. Phenyl moieties in benzene rings were found to affect binding strength alkali and alkaline earth metal cations and hydrogen ion, and affect tautomeric equilibrium of hydroxyazobenzocrowns....
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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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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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CSR and innovation or CSR as non-technological innovation
PublicationThis chapter investigates the relationship between Corporate Social Responsibility (CSR) and innovation process. There is an ongoing discussion in the literature regarding this relationship, in particular on its one- or bidirectional nature and possible antecedents or mediating factors. This research addresses this gap and aims to provide more conceptual clarity and synthesize the different types of relationships between CSR and...
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Finite-window RLS algorithms
PublicationTwo recursive least-squares (RLS) adaptive filtering algorithms are most often used in practice, the exponential and sliding (rectangular) window RLS algorithms. This popularity is mainly due to existence of low-complexity versions of these algorithms. However, these two windows are not always the best choice for identification of fast time-varying systems, when the identification performance is most important. In this paper, we...
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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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Euro 2012 in Gdańsk, Poland. Is it worth using public funds?
PublicationThe aim of this study is to estimate the willingness - to - pay (WTP) among the community of the Pomeranian region, Poland in connection with intangible benefits and costs st emming from hosting the Euro 2012 in Gdansk. A survey conducted among 407 respondents was the source of information. The results of the study show that the average value of WTP benefit for the whole sample was 45,72 PLN2012 and WTP cost...
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The use of Markov chains in the social convergence analysis
PublicationThe main goal of this article is to analyze the social convergence process using Markov chains. In this research, term social convergence refers to the reduction of dispersion in the standard of living among countries. The use of Markov chains in the social convergence analysis allowed describing movements of observational units within the distribution and providing more details about the mechanism of the convergence process. A...
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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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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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The Method of a Two-Level Text-Meaning Similarity Approximation of the Customers’ Opinions
PublicationThe method of two-level text-meaning similarity approximation, consisting in the implementation of the classification of the stages of text opinions of customers and identifying their rank quality level was developed. Proposed and proved the significance of major hypotheses, put as the basis of the developed methodology, notably about the significance of suggestions about the existence of analogies between mathematical bases of...
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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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Why the solvation water around proteins is more dense than bulk water
PublicationThe main aim of this work is to propose a rational explanation of commonly observed phenomenon of increasing water density within solvation shell of proteins. We have observed that geometry of the water-water hydrogen bond network within solvation layer differs from the one in bulk water and it is the effect of interactions of water molecules with protein surface. Altered geometry of the network reflects changes in the structure...
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Why the Solvation Water around Proteins Is More Dense than Bulk Water
PublicationThe main aim of this work is to propose a rational explanation of the commonly observed phenomenon of increasing water density within solvation shell of proteins. We have observed that the geometry of the water–water hydrogen bond network within solvation layer differs from the one in bulk water, and it is the result of interactions of water molecules with protein surface. Altered geometry of the network reflects changes in the...
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Aktualność "Sporu o istnienie świata" Romana Ingardena w świetle współczesnych mu stanowisk filozoficznych
PublicationParadoksalnie Ingarden nie jest w stanie wykazać, że świat realny istnieje w pewnym zasadniczym sensie „istnienia”, bo przyjmuje taki sam jak Husserl egologiczny, przeżyciowy model czystej świadomości i sam podążając za Husserlem przyjmuje istnienie dwóch dziedzin przedmiotów indywidualnych: dziedzinę czystej świadomości (rozumianej po husserlowsku jako strumień przeżyć) i dziedzinę świata realnego za punkt wyjścia swoich rozważań....
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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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Shadow Economy in Poland Recent Evidence Based on Survey Data
PublicationThe book provides an estimate of the size of the shadow economy in Poland. Using analogous data, it traces core determinants of the existence of the shadow economy in Poland. It compares results with neighbouring countries, and if possible, the remaining Central-Eastern economies. The book tells why the problem of the unreported economic activity matters; it presents the problem from different angles―economic, social and institutional....
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Parseval Wavelet Frames on Riemannian Manifold
PublicationWe construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...
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Index filtrations and Morse decomposition for discrete dynamical systems
PublicationOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Roofing Materials as Pollution Emiters - Concentration Changes During Runoff
PublicationThe influence of roofing material on concentration of pollutants in roof runoff waters and changes of pollution concentration in time were investigated. In field studies four roofing material types were taken into consideration - ceramic tile, bituminous membrane, asbestos tile and zinc sheeting. Samples were collected since November 2007 to March 2008, anions, cations, metals, PAHs, pesticides and PCB were determined. The existence...
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FINITE GROUND CPW-FED UWB ANTENNA OVER THE METALLIC CYLINDRICAL SURFACES
PublicationThe investigation of finite ground coplanar fed ultra-wideband (UWB) antenna and the influence of its curvature and the proximity of circular metallic screen on the reflection coefficients and radiation characteristics is presented. The antenna is composed of two circular coplanar strips which enclose slot aperture of similar shape and is designed on a thin and flexible substrate which allows its bending. The antenna configuration...
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A subset of two adherence systems, acute pro-inflammatory pap genes and invasion coding dra, fim, or sfa, increases the risk of Escherichia coli translocation to the bloodstream
PublicationAn analysis of the phylogenetic distribution and virulence genes of Escherichia coli isolates which predispose this bacteria to translocate from the urinary tract to the bloodstream is presented. One-dimensional analysis indicated that the occurrence of P fimbriae and α-hemolysin coding genes is more frequent among the E. coli which cause bacteremia. However, a two-dimensional analysis revealed that a combination of genes coding...
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A Canonical Switched Capacitor DC-DC Converter. A look at how the historical SC synthesis problem is getting solved
PublicationWe reconsider a solution to the historical problem in switched capacitor (SC) DC-DC converter synthesis. Specifically, we retackle the problem of constructing an SC twophase network realizing arbitrary voltage conversion ratio within rational bounds defined. Theoretical foundations are available in our earlier research [3] where a nonconstructive proof of existence was given. We briefly review and comment on known circuit solutions...
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Estimation and Prediction of Vertical Deformations of Random Surfaces, Applying the Total Least Squares Collocation Method
PublicationThis paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling...