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Search results for: ergodic theorem
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On the Limiting Distribution of Lempel-Ziv’78 Redundancy for Memoryless Sources
PublicationWe study the Lempel-Ziv'78 algorithm and show that its (normalized) redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper, in particular, by presenting a new simplified proof of the central limit theorem (CLT) for the number of phrases in the LZ'78 algorithm. We first analyze the asymptotic behavior of the total path length in the associated digital search...
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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 FEM analysis of Cosserat-type stiffened shells. Static and stability linear analysis
PublicationThe present research investigates the theory and numerical analysis of shells stiffened with beams in the framework based on the geometrically exact theories of shells and beams. Shell’s and beam’s kinematics are described by the Cosserat surface and the Cosserat rod respectively, which are consistent including deformation and strain measures. A FEM approximation of the virtual work principle leads to the conforming shell and beam...
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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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NON-STATIONARY THERMAL SELF-ACTION OF ACOUSTIC BEAMS CONTAINING SHOCK FRONTS IN THERMOCONDUCTING FLUID
PublicationNon-stationary thermal self-action of a periodic or impulse acoustic beam containing shock fronts in a thermoconducting Newtonian fluid is studied. Self-focusing of a saw-tooth periodic and impulse sound is considered, as well as that of a solitary shock wave which propagates with the linear sound speed. The governing equations of the beam radius are derived. Numerical simulations reveal that the thermal conductivity weakens the...
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Centrifuge modelling of tapered wall jacked into dense sand
PublicationA series of static penetration tests of trapezoidal walls in dense Fontainebleau sand were performed in the geotechnical centrifuge at Gustave Eiffel University. The models of wall with three different shapes (straight profile with thickness D=16mm, 0.75 degree and 1.5 degree of taper angle) but with the same volume were used. The soil mass was instrumented with five stress cells located at two levels at 2D, 4D and 6D distance...
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Opracowanie wyników pomiaru przemieszczeń pionowych i odchyleń od pionu słupów w halach "Mostostalu Gdańsk S.A." przy ulicy Marynarki Polskiej 96 w Gdańsku
PublicationPomiary okresowe osiadania i wychylenia słupów hali o konstrukcji szkieletowej
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One-dimensional chaos in a system with dry friction: analytical approach
PublicationWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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Multi-Agent Signal Filtering for Electrical Energy Demand Management
PublicationConsumers participating in electrical energy Demand Response (DR) programs may be exposed to energy-use related decisions at instants of time which are generally hard to predict. This is especially cumbersome to residential consumers who are less capable of investing in special equipment, or devoting significant time to analyze information and take decisions. To ease residential consumer participation, a multi-agent system proposed...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublicationIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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Computational analysis of an infinite magneto-thermoelastic solid periodically dispersed with varying heat flow based on non-local Moore–Gibson–Thompson approach
PublicationIn this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining...
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Free trade with the former COMECON Countries as Unequal Exchange
PublicationTwo authors of this chapter were born to the East of what was once The Iron Curtain and two to the West. From both angles, the two systems – capitalism and communism – seemed to be as contrary to each other as possible. Few people are aware that in terms of industrial and trade policy, both classical capitalism and communism had a common root in the theories of German economist Friedrich List (1789-1846) (List, 1841). In fact,...
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Informal work in Poland - a regional approach
PublicationIn our paper we try to combine the theories explaining the prevalence of informal work, using a regional approach. Reviewing the literature, we observe that, there is no evidence to confirm that the relationships that occur in cross-country comparisons remain significant when we use regional data and analyse cross-regional variations. Our general question is therefore whether there is simply more informal work in less-developed...
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The Maslov index and the spectral flow—revisited
PublicationWe give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...
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Analysis of Corrugated Coaxial Line with the Use of Body of Revolution and Finite Element Method
PublicationA combination of the body-of-revolution and finite element methods is utilized to the analysis of coaxial lines with corrugated rod and wall. Both periodic and non-periodic structures can be investigated. As the structure is axially symmetrical the two dimensional scalar-vector finite element method can be used, which allows for the investigation of complex geometries and is computationally efficient. A generalized impedance matrix...
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On the regularity of the displacement sequence of an orientation preserving circle homeomorphism
PublicationWe investigate the regularity properties of the displacemnet sequence of an orientation preserving circle homeomorphism. is rational, then ηn(z) is asymptotically periodic with semi-period q. This
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Evolutionary benefits of personality traits when facing workplace bullying
PublicationFacing workplace bullying negatively affects physical and mental health, and consequently quality of life and well-being. Personality traits that can help an individual survive and reproduce entail more benefits than costs. Building on two evolutionary theories, Life History Theory and Costly Signaling Theory, this study aims to provide novel insights into how and why personality traits are associated with facing workplace bullying...
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublicationWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Nonlinear Excitation of the Non-Wave Perturbations by the Magnetoacoustic Waves in the Non-Isentropic Plasma
PublicationNonlinear excitation of slow modes by the planar magnetosonic perturbations in a plasma is discussed. Plasma is an open system due to radiation and external heating. This may stipulate enhancement of wave perturbations and hence the acoustical activity of plasma. Plasma is assumed to be a homogeneous ideal gas with infinite electrical conductivity. The straight magnetic field is orthogonal to the velocity of fluid’s...
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Homoclinic orbits for an almost periodically forced singular Newtonian system in R^3
Publication. This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in R^3 which are subjected to almost periodic forcing in time variable
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Nonlinear Influence of Sound on the Vibrational Energy of Molecules in a Relaxing Gas
PublicationDynamics of a weakly nonlinear and weakly dispersive flow of a gas where molecular vibrational relaxation takes place is studied. Variations in the vibrational energy in the field of intense sound is considered. These variations are caused by a nonlinear transfer of the acoustic energy into energy of vibrational degrees of freedom in a relaxing gas. The final dynamic equation which describes this is instantaneous, it includes a...
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Weak forms of shadowing in topological dynamics
PublicationWe consider continuous maps of compact metric spaces. It is proved that every pseudotrajectory with sufficiently small errors contains a subsequence of positive density that is point-wise close to a subsequence of an exact trajectory with the same indices. Also, we study homeomor- phisms such that any pseudotrajectory can be shadowed by a finite number of exact orbits. In terms of numerical methods this property (we call it multishadowing)...
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Bearing capacity of monotonically installed tapered piles in medium dense Fontainebleau sand
PublicationA series of installation of tapered piles in medium-dense Fontainebleau sand were performed in the geotechnical centrifuge at Gustave Eiffel University. The models of piles with three different shapes - straight profile (S), and with taper angle of 0.70 degrees (T1), and 1.4 degrees (T2) were used. The piles were instrumented with fiber optic wires on the shaft and load cell at the base. After monotonic installation, the models were...
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Interaction of Acoustic and Thermal Modes in the Gas with Nonequilibrium Chemical Reactions: Possibilities of Acoustic Cooling
PublicationNonlinear generation of thermal mode during propagation of dominative sound in a chemically reacting gas is considered. The dynamic equation of excess temperature associated with the thermal mode is derived. It is instantaneous and includes quadratic nonlinear acoustic source reflecting the nonlinear character of interaction between acoustic and non-acoustic types of gas motion. Both periodic and aperiodic sound may be considered...
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ENERGY ANALYSIS OF THE PROPULSION SHAFT FATIGUE PROCESS IN A ROTATING MECHANICAL SYSTEM PART III DIMENSIONAL ANALYSIS
PublicationThis article presents the third and last part of the problem of diagnosing the fatigue of marine propulsion shafts in terms of energy with the use of the action function, undertaken by the authors. Even the most perfect physical models of real objects, observed under laboratory conditions and developed based on the results of their research, cannot be useful in diagnostics without properly transferring the obtained results to the...
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Adaptacyjny algorytm filtracji sygnału fonokardiograficznego wykorzystujący sztuczną sieć neuronową
PublicationPodstawowym problemem podczas projektowania systemu autodiagnostyki chorób serca, bazującego na analizie sygnału fonokardiograficznego (PCG), jest konieczność zapewnienia, niezależnie od warunków zewnętrznych, sygnału o wysokiej jakości. W artykule, bazując na zdolności Sztucznej Sieci Neuronowej (SSN) do predykcji sygnałów periodycznych oraz quasi-periodycznych, został opracowany adaptacyjny algorytm filtracji dźwięków serca....
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On the deformation and frequency analyses of SARS-CoV-2 at nanoscale
PublicationThe SARS-CoV-2 virus, which has emerged as a Covid-19 pandemic, has had the most significant impact on people's health, economy, and lifestyle around the world today. In the present study, the SARS-CoV-2 virus is mechanically simulated to obtain its deformation and natural frequencies. The virus under analysis is modeled on a viscoelastic spherical structure. The theory of shell structures in mechanics is used to derive the governing...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Morse cohomology in a Hilbert space via the Conley index
PublicationThe main theorem of this paper states that Morse cohomology groups in a Hilbert space are isomorphic to the cohomological Conley index. It is also shown that calculating the cohomological Conley index does not require finite-dimensional approximations of the vector field. Further directions are discussed.
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Partial hyperbolicity and central shadowing
PublicationWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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Computational Study of Molecular Interactions in ZnCl2(urea)2 Crystals as Precursors for Deep Eutectic Solvents
PublicationDeep eutectic solvents (DESs) are now enjoying an increased scientific interest due to their interesting properties and growing range of possible applications. Computational methods are at the forefront of deciphering their structure and dynamics. Type IV DESs, composed of metal chloride and a hydrogen bond donor, are among the less studied systems when it comes to their understanding at a molecular level. An important example...
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On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
PublicationWe study the existence of homoclinic type solutions for a class of inhomogenous Lagrangian systems with a potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and a square integrable forcing term. A homoclinic type solution is obtained as a limit of periodic solutions of an approximative sequence of second order differential equations.
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A new concept of contemporary marketing
PublicationPurpose: This conceptual paper aims to propose a new concept of marketing that responds well to the needs of a changing world, taking into account the continuous development of the service economy and the revolution in the development of the Internet and related tools. Methodology/Approach: The proposed concept is based on well-researched theories: service marketing, experience marketing, relationship marketing and digital marketing...
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On the plastic buckling of curved carbon nanotubes
PublicationThis research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stress-strain is concerned...
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Interpretation and modeling of emotions in the management of autonomous robots using a control paradigm based on a scheduling variable
PublicationThe paper presents a technical introduction to psychological theories of emotions. It highlights a usable ideaimplemented in a number of recently developed computational systems of emotions, and the hypothesis thatemotion can play the role of a scheduling variable in controlling autonomous robots. In the main part ofthis study, we outline our own computational system of emotion – xEmotion – designed as a key structuralelement in...
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Comparative analysis of the theoretical models of ideal propulsor, ideal fluid brake, ideal screw propeller and ideal axial wind turbine
PublicationThe article presents a detailed discussion of four different fluid dynamics devices.These devices are presented with all relevant mathematical formulae regarding the forces, the power and the efficiency. It is demonstrated that application of the Betz theorem to axial wind turbines is not correct and it underestimates the maximujm achievable efficiency. This conclusion is supported by numerical calculations.
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Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy
PublicationThe majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included...
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas
PublicationTwo dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place. are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Convergence or divergence in the European Union
PublicationThe disparities in economic prosperity revealed both from inter-country and inter-region perspective are one of the main problem in the modern economy. They consist of the dispersion in the real values such as incomes, GDP or productivity, but also nominal values such as prices and costs. The European Union is aware of this problem hence the role of the regional and structural policy aiming enhancing the cohesion between member...
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No Quantum Realization of Extremal No-Signaling Boxes
PublicationThe study of quantum correlations is important for fundamental reasons as well as for quantum communication and information processing tasks. On the one hand, it is of tremendous interest to derive the correlations produced by measurements on separated composite quantum systems from within the set of all correlations obeying the no-signaling principle of relativity, by means of information-theoretic principles. On the other hand,...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublicationOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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Empirically adjusted and consistent set of EHT valence orbital parametersfor all elements of the periodic table. Modelling Simul. Mater. Sci. Eng. [online]. 2004 vol. 12 [dostęp..] s. 21-32, 3 rys. 3 tab. bibliogr. 35 poz. Dostępny w Internecie stacks.iop.org/MSMSE/12/21.ISSN 0965-0393 Jednorodny skorygowany empirycznie zbiór parametrów EHT dla orbitali walen- cyjnych pierwiastków.
PublicationModel atomu HFS został zmodyfikowany poprzez przypisanie każdemu z atomówindywidualnego parametru ŕ. Wartości ŕ dobrano w oparciu o pierwszy poten-cjał jonizacji atomu. Parametry EHT wyznaczono w oparciu o tak zmodyfikowa-ny model HFS.
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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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The impact of global value chains on wages, employment, and productivity: a survey of theoretical approaches
PublicationThis study presents a systematic literature review to provide a collection of theories explaining the impact of global value chains (GVCs) on labour market outcomes. Due to the complex nature of GVCs and the interconnectedness of wages, employment, and productivity, many direct and indirect effects are at play. To ensure a transparent and systematic flow of the review process, I follow the PRISMA guide. Eventually, 36 records out...
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MODELOWANIE ODDZIAŁYWAŃ DYNAMICZNYCH POCIĄGU TYPU PENDOLINO NA KONSTRUKCJE ZABYTKOWYCH MOSTÓW KOLEJOWYCH W POLSCE
PublicationW artykule przedstawiono badania i symulacje numeryczne dotyczące modelowania oddziaływań dynamicznych przejeżdżających pociągów Pendolino po zabytkowych mostach kolejowych w Polsce. Zakres prac obejmuje badania doświadczalne, rozwiązanie problemu dotyczącego poprawnego rozwiązania funkcji dynamicznej uwzględniającej model zależności między mostem, torem i taborem, tzw. model RBT oraz symulacje numeryczne dla obiektu zabytkowego...
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Parabolic Equations with Functional Dependence
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublicationIn this paper, we retrieve some traveling wave, periodic solutions, bell shaped, rational, kink and anti-kink type and Jacobi elliptic functions of Burger’s equation and Shallow water wave equation with the aid of various integration schemes like improved -expansion scheme and Jacobi elliptic function method respectively. We also present our solutions graphically in various dimensions.