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Search results for: HOPF BIFURCATION
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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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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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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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The Hopf theorem for gradient local vector fields on manifolds
PublicationWe prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.
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The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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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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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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Projekt Hoff
PublicationRozdział w monografii dotyczy działalności projektowej Barbary Hoff, od 1956 roku kiedy w "Przekroju" prezentowała pojedyncze projekty sukienek, poprzez pierwszą "kolekcję masową" w 1967 roku aż do powstania marki Hoffland i stoiska " z kolekcją własną Hoff" w Juniorze w Domach towarowych Centrum w warszawie w 1977 roku
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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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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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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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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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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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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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Analysis of the reliability of any-hop star network
PublicationZałożono, że sieć ma wielostopniową strukturę gwiaździstą. Jako oceny niezawodności tych sieci przyjęto: 1) średnią liczbę sprawnych par węzłów, które mogą komunikować się wzajemnie; 2) średnią liczbę sprawnych par węzłów, które mogą komunikować się poprzez węzeł centralny; 3) średnią liczbę sprawnych par węzłów, które mogą komunikować się z węzłem centralnym; 4) prawdopodobieństwo zdarzenia, że sprawne węzły mogą komunikować...
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Analysis of the reliability 0f any-hop star network.
PublicationZałożono, że sieć ma wielostopniową strukturę gwiaździstą. Jako oceny niezawodności tych sieci przyjęto: 1) średnią liczbę sprawnych par węzłów, które mogą komunikować się wzajemnie; 2)średnią liczbę sprawnych par węzłów, które mogą komunikować się poprzez węzeł centralny; 3) średnią liczbę sprawnych par węzłów, które mogą komunikować się z węzłem centralnym; 4) prawdopodobieństwo zdarzenia, że sprawne węzły mogą komunikować się...
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The Relationship of Purpose in Life and Hope in Shaping Happiness Among Patients with Cancer in Poland
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Lung Protection by Cathepsin C Inhibition: A New Hope for COVID-19 and ARDS?
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Can a man also be afraid? Partner communication, anxiety and hope in parents of premature infants
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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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The reliability of any-hop star networks with respect to failures of communication nodes.
PublicationThis paper investigated the reliability of any-hop star networks. The any-hop star topology is used in centralized computer networks. We will assume that the all nodes fail independently, links are failure-free. Following measures of network reliability are assumed: the expected number of nodes, which can communicate with the central node; the expected number of node pairs, which are connected by a path through the central node;...
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Mitigating Traffic Remapping Attacks in Autonomous Multi-hop Wireless Networks
PublicationMultihop wireless networks with autonomous nodes are susceptible to selfish traffic remapping attacks (TRAs). Nodes launching TRAs leverage the underlying channel access function to receive an unduly high Quality of Service (QoS) for packet flows traversing source-to-destination routes. TRAs are easy to execute, impossible to prevent, difficult to detect, and harmful to the QoS of honest nodes. Recognizing the need for providing...
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The Indirect Relationship Between Spiritual Experiences and Subjective Wellbeing Through Hope? A Sample of Chilean Students
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Composition and In Vitro Effects of Cultivars of Humulus lupulus L. Hops on Cholinesterase Activity and Microbial Growth
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Research Protocol of the Polish Adaptation and Validation of HOPE Scale: Qualitative Measurement of Patients' Spiritual Needs
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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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Indirect Relationship between Alcoholics Anonymous Spirituality and Their Hopelessness: The Role of Meaning in Life, Hope, and Abstinence Duration
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Resilience through multicast – An optimization model for multi-hop wireless sensor networks
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Selfish Attacks in Two-Hop IEEE 802.11 Relay Networks: Impact and Countermeasures
PublicationIn IEEE 802.11 networks, selfish stations can pursue a better quality of service through selfish MAC-layer attacks. Such attacks are easy to perform, secure routing protocols do not prevent them, and their detection may be complex. Two-hop relay topologies allow a new angle of attack: a selfish relay can tamper with either source traffic, transit traffic, or both. We consider the applicability of selfish attacks and their variants...
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Modeling a Traffic Remapping Attack Game in a Multi-hop Ad Hoc Network
PublicationIn multi-hop ad hoc networks, selfish nodes may unduly acquire high quality of service (QoS) by assigning higher priority to source packets and lower priority to transit packets. Such traffic remapping attacks (TRAs) are cheap to launch, impossible to prevent, hard to detect, and harmful to non-selfish nodes. While studied mostly in single-hop wireless network settings, TRAs have resisted analysis in multi-hop settings. In this paper...
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Distributed protection against non-cooperative node behavior in multi-hop wireless networks
PublicationAn important security problem in today's distributed data networks is the prevention of non-cooperative behavior i.e., attacks consisting in the modification of standard node operation to gain unfair advantage over other system nodes. Such a behavior is currently feasible in many types of computer networks whose communication protocols are designed to maximize the network performance assuming full node cooperation. Moreover, it...
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Maximization of multicast periodic traffic throughput in multi-hop wireless networks with broadcast transmissions
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Throughput vs. Resilience in Multi-hop Wireless Sensor Networks with Periodic Packet Traffic
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A Reputation Scheme to Discourage Selfish QoS Manipulation in Two-Hop Wireless Relay Networks
PublicationIn wireless networks, stations can improve their received quality of service (QoS) by handling packets of source flows with higher priority. Additionally, in cooperative relay networks, the relays can handle transit flows with lower priority. We use game theory to model a two-hop relay network where each of the two involved stations can commit such selfish QoS manipulation. We design and evaluate a reputation-based incentive scheme...
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Religious–spiritual sources of hope and the meaning of life in alcohol co-dependent subjects receiving support in self-help groups
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Nodal cooperation equilibrium analysis in multi-hop wireless ad hoc networks with a reputation system
PublicationMotivated by the concerns of cooperation security, this work examines selected principles of state-of-the-art reputation systems for multi-hop ad hoc networks and their impact upon optimal strategies for rational nodes. An analytic framework is proposed and used for identification of effective cooperation-enforcement schemes. It is pointed out that optimum rather than high reputation can be expected to be sought by rational nodes.
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HOPE-3, SPRINT, VALUE and a meta-analysis of trials in patients with diabetes support treatment of hypertension to a target below 140 mmHg
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More than just a beer – Brewers' spent grain, spent hops, and spent yeast as potential functional fillers for polymer composites
PublicationBeer is among the most popular beverages in the world, with the production distributed uniformly between the biggest continents, so the utilization of brewing by-products is essential on a global scale. Among their potential recipients, the plastics industry offers extensive range of potential products. Herein, the presented study investigated the application of currently underutilized solid brewing by-products (brewers' spent...
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Effect of the Concentration of Hop Cone Extract on the Antibacterial, Physico-Chemical and Functional Properties of Adhesive Toilet Cleaners
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The Health Outcomes Prevention and Evaluation 4 (HOPE 4) project: A successful community-based intervention to lower cardiovascular risk in people with hypertension
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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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Use of hop cone extract obtained under supercritical CO2 conditions for producing antibacterial all-purpose cleaners
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