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Search results for: SUBCRITICAL BIFURCATION
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Through the looking-glass of the grazing bifurcation
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The Conley index, cup-length and bifurcation
PublicationZastosowano strukturę modułu w indeksie kohomologicznym Conleya do dowodu twierdzenia o minimalnej ilości rozwiązań okresowych dla układów Hamiltonowskich. Wykazano też ogólne twierdzenia dotyczące nietrywialności struktury mudułu.
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Extremal thermal loading of a bifurcation pipe
PublicationThe subject of considerations is a spherical bifurcation pipe of a live steam made of steel P91, which is an element of a block of coal-fired power plant working with a 18K370 turbine. As experience shows, it is a very sensitive element of the boiler pipelines. An extreme work scenario for such a block has been adopted, in which the turbine is shutting down to a warm state three times in 24 hours. This is an action dictated by...
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Subcritical Thermodynamic Cycles with Organic Medium and Isothermal Expansion
PublicationThe efffciencies of the Organic Rankine Cycle (ORC) are not very high and only very seldom do they exceed 20%. The increase and optimization of initial parameters and certain modifications of the thermodynamic cycle make it possible to overcome these drawbacks. A new modified cycle has been described and analyzed in detail in the paper. Similarly to the Ericsson cycle for gas turbines, isothermal expansion in the turbine is suggested...
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Green products from herbal medicine wastes by subcritical water treatment
PublicationHerbal medicine wastes (HMWs) are byproducts of medicine factories, which are mainly landfilled for their environmental problems. Only bearing in mind the contamination and concerns caused by the COVID-19 pandemic and environmental emissions, the worth of herbal medicine wastes management and conversion to green products can be understood. In this work, subcritical water treatment was carried out batch-wise in a stainless tube...
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Pressure drop and heat transfer during boiling and condensation at subcritical region
PublicationMost of the data presented in the literature relate to saturation temperatures in the range - 20°C to 40°C due to the application in refrigeration technology. There is necessity to extend databases to higher values of saturation temperature due to new applications such as Organic Rankine Cycle and high temperature heat pumps. Only few papers contain data for high reduced pressure for low boiling point liquids. This paper focus...
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Chaotic Dynamics and Bifurcations in Impact Systems
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Rich Bifurcation Structure in a Two-Patch Vaccination Model
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Arterial stiffness in relation to subclinical atherosclerosis
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A thermodynamic criterion for selection of working fluid for subcritical and supercritical domestic micro CHP
PublicationW pracy przedstawiono kryterium termodynamiczne doboru czynnika roboczego dla mikrosiłowni pracującej w warunkach podkrytycznych i nadkrytycznych. Przeanalizowano 20 płynów możliwych do wykorzystania w mikrosiłowni ORC. Z analizy wynika, że najlepszym płynem roboczym jest etanol, R123 oraz R141b.
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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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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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Stable and unstable bifurcation in the von Karman problem for a circular plate
PublicationW niniejszej pracy badamy równania von Karmana dla cienkiej, sprężystej, kołowej płyty, która znajduje się na sprężystym podłożu, pod działaniem sił ściskających wzdłuż swojego brzegu.Stosując metody analizy nieliniowej, dowodzimy istnienia stabilnychi niestabilnych punktów bifurkacji w zbiorze rozwiązań badanych równań.
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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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A note on simple bifurcation of equilibrium forms of an elastic rod on a deformable foundation
PublicationWe study bifurcation of equilibrium states of an elastic rod on a two-parameter Winkler foundation. In the article "Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation" [Nonlinear Anal., Real World Appl. 39 (2018) 451-463] the existence of simple bifurcation points was proved by the use of the Crandall-Rabinowitz theorem. In this paper we want to present an alternative proof of this fact based...
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Multiple bifurcation in the solution set of the von Karman equations with S^{1}-symmetries
PublicationRozważmy cienką, sprężystą, kołową płytę, położoną na sprężystym podłożu, poddawaną działaniu sił ściskających koncentrycznie wzdłuż jej brzegu. Formy równowagi takiej płyty są rozwiązaniami równań von Karmana z dwoma parametrami określonych na dysku w R^{2}. Są to równania różniczkowe cząstkowe rzędu czwartego. Można je zapisać jako równanie operatorowe F(x,p)=0 w przestrzeniach Höldera, gdzie zmienna x odpowiada formom równowagi...
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Grazing bifurcation and chaotic oscillations of vibro-impact systems with one degree of freedom
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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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Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point.
PublicationW niniejszej pracy badamy problem istnienia bifurkacji w zbiorze rozwiązań równania F(x,p)=0, gdzie F jest odwzorowaniem klasy C^2z iloczynu kartezjańskiego X i R^k do Y, X i Y są przestrzeniami Banacha takimi, że X jest podprzestrzenią liniową Y. Co więcej, dany jest iloczyn skalarny w Y, ciągły względem norm w X i Y. Pokazujemy, że pod pewnymi warunkami (0,p) jest punktem bifurkacji i opisujemyzbiór rozwiązań równania F(x,p)=0...
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Bifurcation of equilibrium forms of a gas column rotating with constant speed around its axis of symmetry
PublicationWe will be concerned with the problem of deformation of the lateral surface of a column that rotates with constant speed around its axis of symmetry. The column is filled by a gas and our goal is to investigate the deformation of the lateral surface depending on the pressure of the gas.
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Aortic excess pressure and arterial stiffness in subjects with subclinical white matter lesions
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Bifurcation in von Karman problem for rectangular, thin, elastic plate resting on elastic foundation of Winkler type
PublicationPraca poświęcona jest utracie stateczności prostokątnej, cienkiej płyty sprężystej spoczywającej na podłożu liniowo sprężystym typu Winklera. Płyta jest ściskana równomiernie rozłożonymi obciążeniami na dwóch równoległych brzegach. Wyznaczono obciążenia krytyczne, formy utraty stateczności płyty oraz początkowe zachowanie pokrytyczne. Analizę prowadzono za pomocą analizy funkcjonalnej przy zachowaniu precyzyjnego matematycznego...
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Description of the solution set of the von Karman equations for a circular plate in a small neighbourhood of a simple bifurcation point
PublicationW niniejszej pracy badamy równania von Karmana dla cienkiej, sprężystej, kołowej płyty na sprężystym podłożu, poddawanej działaniu sił ściskających wzdłuż brzegu. Są to równania różniczkowe cząstkowe IV rzędu. Stosując metody analizy nieliniowej, opisujemy zbiór rozwiązań równań von Karmana w małym otoczeniu jednokrotnego punktu bifurkacji.Badania były finansowane przez grant nr 1 P03A 042 29.
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Subclinical Mood and Cognition Impairments and Blood Pressure Control in a Large Cohort of Elderly Hypertensives
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Adipokine and cytokine levels in patients with adrenocortical cancer, subclinical Cushing's syndrome and healthy controls
PublicationIntroduction In recent years researchers have focused at hormonal activity in Cushing’s syndrome (CS) in connection with metabolic disorders and the role of adipokines and cytokines secreted by the adipose tissue. The aim of the study was to investigate levels of adipokines and cytokines in patients with: subclinical CS (SCS) – in relation to hormonal parameters of hypercortisolemia, and, adrenocortical cancer (ACC). Materials...
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Virulence gene profiles in Staphylococcus aureus isolated from cows with subclinical mastitis in eastern Poland
PublicationStaphylococcus aureus is arguably the most important pathogen involved in bovine mastitis. The aim of this study was to determine the virulence gene profiles of 124 Staph. aureus isolates from subclinical mastitis in cows in eastern Poland. The presence of 30 virulence genes encoding adhesins, proteases and superantigenic toxins was investigated by PCR. The 17 different combinations of adhesin genes were identified. Occurrence...
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Activity-based protein profiling guided identification of urine proteinase 3 activity in subclinical rejection after renal transplantation
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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
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Late subclinical hemolysis and long-term outcomes after aortic valve replacement with On-X mechanical prostheses – a preliminary single-center report
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 85
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 70
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 95
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 90
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Joanna Janczewska prof. dr hab.
PeopleJoanna Janczewska obtained her PhD degree at the University of Gdansk in 2002. From October 1999 to September 2004 she was an assistant at the University of Gdansk. Since October 2004 she has been an assistant professor at the Gdansk University of Technology. Moreover, from October 2008 to September 2010 she had a visiting position in the Institute of Mathematics of the Polish Academy of Sciences. Her mathematical interests...
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Analysis of Organic Rankine Cycle efficiency and vapor generator heat transfer surface in function of the reduced pressure
PublicationIn the paper presented is analysis of the influence of reduced pressure on efficiency and heat transfer area of vapor generator of Organic Rankine Cycle (ORC) in case of subcritical and supercritical parameters of operation. Compared are two cases of subcritical and supercritical ORC featuring a similar arrangement of heat source supply and heat removal, that is featuring the same temperatures of working fluid before the turbine,...
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Dynamics of S-unimodal maps used in population modeling.
Open Research DataS-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence...
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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APPLICATION OF COHEN'S CLASS TIME-FREQUENCY DISTRIBUTIONS IN THE BELOUSOV–ZHABOTINSKY REACTION ANALYSIS
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Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect
PublicationGalerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material...
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublicationWe give a complete description of possible sequences ofindices of iterations of f at an isolated fixed point, answering inaffirmative the Chow, Mallet-Paret and Yorke conjecture posed in[S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index whichis a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983,pp. 109-131].
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On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate
PublicationWe shall be concerned with the buckling of a thin circular elastic plate simply supported along a boundary, subjected to a radial compressive load uniformly distributed along its boundary. One of the main engineering concerns is to reduce deformations of plate structures. It is well known that von Karman equations provide an established model that describes nonlinear deformations of elastic plates. Our approach to study plate deformations...
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Module structure in Conley theory with some applications
PublicationA multiplicative structure in the cohomological versjon of Conley index is described . In the case of equivariant flows we apply the normalization procedure known from equivariant degree theory and we propose a new continuation invariant. The theory is then applied to obtain a mountain pass type theorem. Another application is a result on multiple bifurcations for some elliptic PDE.
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Analysis of a gene expression model
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...
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Visualizing Carotid Bodies With Doppler Ultrasound Versus CT Angiography: Preliminary Study
PublicationOBJECTIVE. The purpose of this article is to evaluate the utility of ultrasound in identifying carotid bodies (CBs) in patients with drug-resistant arterial hypertension. SUBJECTS AND METHODS. We enrolled 13 patients with drug-resistant hypertension into a trial for surgical CB excision. CT angiography (CTA) and Doppler ultrasound (DUS) of the cervical arteries were performed before surgery. CBs were identified in a blind manner...
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublicationWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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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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The Economic Legacy of Mega Sporting Events. The Impact of Hosting European Olympic Games on GDP Growth Through Infrastructure Development
PublicationIntroduction. The positive legacy of the Olympics is often cited by the International Olympic Committee and national or-ganizers. Some scholars, however, question an uncritical approach to an exclusively positive economic legacy. The aim of this study is to evaluate the impact of hosting the Olympics on infrastructure development, with a potential impact on economic growth in the form of Gross Domestic Product (GDP) in three phases...
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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...