Relevant bibliographies by topics / Difference equation system

Academic literature on the topic 'Difference equation system'

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Published: 11 March 2023

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Journal articles on the topic "Difference equation system"

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Pasáčková, Jana. "Neutral Difference System and its Nonoscillatory Solutions." Tatra Mountains Mathematical Publications 71, no. 1 (December 1, 2018): 139–48. http://dx.doi.org/10.2478/tmmp-2018-0012.

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Abstract The paper deals with a system of four nonlinear difference equations where the first equation is of a neutral type. We study nonoscillatory solutions of the system and we present sufficient conditions for the system to have weak property B.
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Pogrebkov, Andrei. "Hirota Difference Equation and Darboux System: Mutual Symmetry." Symmetry 11, no. 3 (March 25, 2019): 436. http://dx.doi.org/10.3390/sym11030436.

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We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R 3 . We demonstrated that specific properties of solutions of the HDE with respect to independent variables enabled introduction of an infinite set of discrete symmetries. We showed that degeneracy of the HDE with respect to parameters of these discrete symmetries led to the introduction of continuous symmetries by means of a specific limiting procedure. This enabled consideration of these symmetries on equal terms with the original HDE independent variables. In particular, the Darboux system appeared as an integrable equation where continuous symmetries of the HDE served as independent variables. We considered some cases of intermediate choice of independent variables, as well as the relation of these results with direct and inverse problems.
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Khaliq, Abdul, Muhammad Adnan, and Abdul Qadeer Khan. "Global Dynamics of Sixth-Order Fuzzy Difference Equation." Mathematical Problems in Engineering 2021 (October 5, 2021): 1–16. http://dx.doi.org/10.1155/2021/9769093.

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Across many fields, such as engineering, ecology, and social science, fuzzy differences are becoming more widely used; there is a wide variety of applications for difference equations in real-life problems. Our study shows that the fuzzy difference equation of sixth order has a nonnegative solution, an equilibrium point and asymptotic behavior. y i + 1 = D y i − 1 y i − 2 / E + F y i − 3 + G y i − 4 + H y i − 5 , i = 0,1,2 , … , where y i is the sequence of fuzzy numbers and the parameter D , E , F , G , H and the initial condition y − 5 , y − 4 , y − 3 , y − 2 , y − 1 , y 0 are nonnegative fuzzy number. The characterization theorem is used to convert each single fuzzy difference equation into a set of two crisp difference equations in a fuzzy environment. So, a pair of crisp difference equations is formed by converting the difference equation. The stability of the equilibrium point of a fuzzy system has been evaluated. By using variational iteration techniques and inequality skills as well as a theory of comparison for fuzzy difference equations, we investigated the governing equation dynamics, such as its boundedness, existence, and local and global stability analysis. In addition, we provide some numerical solutions for the equation describing the system to verify our results.
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MIHAILOVIĆ, DRAGUTIN T., and GORDAN MIMIĆ. "KOLMOGOROV COMPLEXITY AND CHAOTIC PHENOMENON IN COMPUTING THE ENVIRONMENTAL INTERFACE TEMPERATURE." Modern Physics Letters B 26, no. 27 (September 24, 2012): 1250175. http://dx.doi.org/10.1142/s0217984912501758.

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In this paper, we consider the chaotic phenomenon and Kolomogorov complexity in computing the environmental interface temperature. First, the environmental interface is defined in the context of the complex system, in particular for autonomous dynamical systems. Then we consider the following issues in modeling procedure: (i) how to replace given differential equations by appropriate difference equations in modeling of phenomena in the environmental world? (ii) whether a mathematically correct solution to the corresponding differential equation or system of equations is always physically possible and (iii) phenomenon of chaos in autonomous dynamical systems in environmental problems, in particular in solving the energy balance equation to calculate environmental interface temperature. The difference form of this equation for computing the environmental interface temperature is discussed and analyzed depending on parameters of equation, using the Lyapunov exponent and sample entropy. Finally, the Kolmogorov complexity of time series obtained from this difference equation is analyzed.
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İnan, B., and A. R. Bahadir. "Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method." Journal of Applied Mathematics, Statistics and Informatics 11, no. 2 (December 1, 2015): 57–67. http://dx.doi.org/10.1515/jamsi-2015-0012.

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Abstract In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then linear equations system is obtained. Finally, linear equations system is solved using Gauss elimination method at each time-step. The numerical solutions obtained by this way are compared with the exact solutions and obtained by other methods to show the efficiency of the method.
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Porter, D., and N. R. T. Biggs. "SYSTEMS OF INTEGRAL EQUATIONS WITH WEIGHTED DIFFERENCE KERNELS." Proceedings of the Edinburgh Mathematical Society 47, no. 1 (February 2004): 205–30. http://dx.doi.org/10.1017/s0013091503000269.

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AbstractExplicit expressions are derived for the inverses of operators of a particular class that includes the operator corresponding to a system of coupled integral equations having weighted difference kernels. The inverses are expressed in terms of a finite number of functions and a systematic way of generating different sets of these functions is devised. The theory generalizes those previously derived for a single integral equation and an integral-equation system with pure difference kernels. The connection is made between the finite generation of inverses and embedding.AMS 2000 Mathematics subject classification: Primary 45A05
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Potts, R. B., and X. H. Yu. "Difference equation modelling of a variable structure system." Computers & Mathematics with Applications 28, no. 1-3 (August 1994): 281–89. http://dx.doi.org/10.1016/0898-1221(94)00116-2.

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Uslu, K. "GENERALIZED PERIOD OF NON-LINEAR DIFFERENCE EQUATION SYSTEM." Far East Journal of Applied Mathematics 95, no. 6 (January 4, 2017): 451–57. http://dx.doi.org/10.17654/am095060451.

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Ma, Junxia, Qiuling Fei, Fan Guo, and Weili Xiong. "Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems." Mathematics 7, no. 12 (November 22, 2019): 1143. http://dx.doi.org/10.3390/math7121143.

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Many basic laws of physics or chemistry can be written in the form of differential equations. With the development of digital signals and computer technology, the research on discrete models has received more and more attention. The estimates of the unknown coefficients in the discretized difference equation can be obtained by optimizing certain criterion functions. In modern control theory, the state-space model transforms high-order differential equations into first-order differential equations by introducing intermediate state variables. In this paper, the parameter estimation problem for linear difference equation systems with uncertain noise is developed. By transforming system equations into state-space models and on the basis of the considered priors of the noise and parameters, a variational Bayesian iterative estimation algorithm is derived from the observation data to obtain the parameter estimates. The unknown states involved in the variational Bayesian algorithm are updated by the Kalman filter. A numerical simulation example is given to validate the effectiveness of the proposed algorithm.
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Kodipaka, Mamatha, Siva Prasad Emineni, and Phaneendra Kolloju. "Difference Scheme for Differential-Difference Problems with Small Shifts Arising in Computational Model of Neuronal Variability." International Journal of Applied Mechanics and Engineering 27, no. 1 (March 1, 2022): 91–106. http://dx.doi.org/10.2478/ijame-2022-0007.

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Abstract The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.
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Dissertations / Theses on the topic "Difference equation system"

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Zhou, Bo. "The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/14255.

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In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applying forward and backward Gronwall inequality and coupling method.
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Bou, Saba David. "Analyse et commande modulaires de réseaux de lois de bilan en dimension infinie." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI084/document.

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Les réseaux de lois de bilan sont définis par l'interconnexion, via des conditions aux bords, de modules élémentaires individuellement caractérisés par la conservation de certaines quantités. Des applications industrielles se trouvent dans les réseaux de lignes de transmission électriques (réseaux HVDC), hydrauliques et pneumatiques (réseaux de distribution du gaz, de l'eau et du fuel). La thèse se concentre sur l'analyse modulaire et la commande au bord d'une ligne élémentaire représentée par un système de lois de bilan en dimension infinie, où la dynamique de la ligne est prise en considération au moyen d'équations aux dérivées partielles hyperboliques linéaires du premier ordre et couplées deux à deux. Cette dynamique permet de modéliser d'une manière rigoureuse les phénomènes de transport et les vitesses finies de propagation, aspects normalement négligés dans le régime transitoire. Les développements de ces travaux sont des outils d'analyse qui testent la stabilité du système, et de commande au bord pour la stabilisation autour d'un point d'équilibre. Dans la partie analyse, nous considérons un système de lois de bilan avec des couplages statiques aux bords et anti-diagonaux à l’intérieur du domaine. Nous proposons des conditions suffisantes de stabilité, tant explicites en termes des coefficients du système, que numériques par la construction d'un algorithme. La méthode se base sur la reformulation du problème en une analyse, dans le domaine fréquentiel, d'un système à retard obtenu en appliquant une transformation backstepping au système de départ. Dans le travail de stabilisation, un couplage avec des dynamiques décrites par des équations différentielles ordinaires (EDO) aux deux bords des EDP est considéré. Nous développons une transformation backstepping (bornée et inversible) et une loi de commande qui, à la fois stabilise les EDP à l'intérieur du domaine et la dynamique des EDO, et élimine les couplages qui peuvent potentiellement mener à l’instabilité. L'efficacité de la loi de commande est illustrée par une simulation numérique
Networks of balance laws are defined by the interconnection, via boundary conditions, of elementary modules individually characterized by the conservation of physical quantities. Industrial applications of such networks can be found in electric (HVDC networks), hydraulic and pneumatic (gas, water and oil distribution) transmission lines. The thesis is focused on modular analysis and boundary control of an elementary line represented by a system of balance laws in infinite dimension, where the dynamics of the line is taken into consideration by means of first order two by two coupled linear hyperbolic partial differential equations. This representation allows to rigorously model the transport phenomena and finite propagation speed, aspects usually neglected in transient regime. The developments of this work are analysis tools that test the stability, as well as boundary control for the stabilization around an equilibrium point. In the analysis section, we consider a system of balance laws with static boundary conditions and anti-diagonal in-domain couplings. We propose sufficient stability conditions, explicit in terms of the system coefficients, and numerical by constructing an algorithm. The method is based on reformulating the analysis problem as an analysis of a delay system in the frequency domain, obtained by applying a backstepping transform to the original system. In the stabilization work, couplings with dynamic boundary conditions, described by ordinary differential equations (ODE), at both boundaries of the PDEs are considered. We develop a backstepping (bounded and invertible) transform and a control law that at the same time, stabilizes the PDEs inside the domain and the ODE dynamics, and eliminates the couplings that are a potential source of instability. The effectiveness of the control law is illustrated by a numerical simulation
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Clark, Rebecca G. "A Study of the Effect of Harvesting on a Discrete System with Two Competing Species." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4497.

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This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.
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Halfarová, Hana. "Slabě zpožděné lineární rovinné systémy diskrétních rovnic." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2014. http://www.nusl.cz/ntk/nusl-233648.

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Dizertační práce se zabývá slabě zpožděnými lineárními rovinnými systémemy s konstantními koeficienty. Charakteristická rovnice těchto systémů je identická s charakteristickou rovnicí systému, který neobsahuje zpožděné členy. V takovém případě se počáteční dimenze prostoru řešení mění po několika krocích na menší. V jistém smyslu je tato situace analogická podobnému jevu v teorii lineárních diferenciálních systémů s konstantními koeficienty a speciálním zpožděním, kdy původně nekonečně rozměrný prostor řešení (na počátečním intervalu) přejde po několika krocích do konečného prostoru řešení. V práci je pro každý možný případ kombinace kořenů charakteristické rovnice konstruováno obecné řešení daného systému a jsou formulovány výsledky o dimenzi prostoru řešení. Také je zkoumána stabilita řešení.
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Šafařík, Jan. "Slabě zpožděné systémy lineárních diskrétních rovnic v R^3." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2018. http://www.nusl.cz/ntk/nusl-378908.

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Dizertační práce se zabývá konstrukcí obecného řešení slabě zpožděných systémů lineárních diskrétních rovnic v ${\mathbb R}^3$ tvaru \begin{equation*} x(k+1)=Ax(k)+Bx(k-m), \end{equation*} kde $m>0$ je kladné celé číslo, $x\colon \bZ_{-m}^{\infty}\to\bR^3$, $\bZ_{-m}^{\infty} := \{-m, -m+1, \dots, \infty\}$, $k\in\bZ_0^{\infty}$, $A=(a_{ij})$ a $B=(b_{ij})$ jsou konstantní $3\times 3$ matice. Charakteristické rovnice těchto systémů jsou identické s charakteristickými rovnicemi systému, který neobsahuje zpožděné členy. Jsou získána kriteria garantující, že daný systém je slabě zpožděný a následně jsou tato kritéria specifikována pro všechny možné případy Jordanova tvaru matice $A$. Systém je vyřešen pomocí metody, která ho transformuje na systém vyšší dimenze, ale bez zpoždění \begin{equation*} y(k+1)=\mathcal{A}y(k), \end{equation*} kde ${\mathrm{dim}}\ y = 3(m+1)$. Pomocí metod lineární algebry je možné najít Jordanovy formy matice $\mathcal{A}$ v závislosti na vlastních číslech matic $A$ and $B$. Tudíž lze nalézt obecné řešení nového systému a v důsledku toho pak odvodit obecné řešení počátečního systému.
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Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.

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Clinger, Richard A. "Stability Analysis of Systems of Difference Equations." VCU Scholars Compass, 2007. http://hdl.handle.net/10156/1318.

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Luís, Rafael Domingos Garanito. "Nonautonomous difference equations with applications." Doctoral thesis, Universidade da Madeira, 2011. http://hdl.handle.net/10400.13/206.

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This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.
Henrique Oliveira and Saber Elaydi
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Xue, Fei. "Asymptotic solutions of almost diagonal differential and difference systems." Morgantown, W. Va. : [West Virginia University Libraries], 2006. https://eidr.wvu.edu/etd/documentdata.eTD?documentid=4556.

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Kama, Phumezile. "Non-standard finite difference methods in dynamical systems." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-07132009-163422.

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Books on the topic "Difference equation system"

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Kikuchi, Tetsuya. Studies on commuting difference systems arising from solvable lattice models. Sendai, Japan: Tohoku University, 2000.

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Ahlbrandt, Calvin D. Discrete Hamiltonian systems: Difference equations, continued fractions, and Riccati equations. Dordrecht: Kluwer Academic Publishers, 1996.

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Bohner, Martin, Yiming Ding, and Ondřej Došlý, eds. Difference Equations, Discrete Dynamical Systems and Applications. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24747-2.

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Alsedà i Soler, Lluís, Jim M. Cushing, Saber Elaydi, and Alberto A. Pinto, eds. Difference Equations, Discrete Dynamical Systems and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-52927-0.

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Elaydi, Saber, Christian Pötzsche, and Adina Luminiţa Sasu, eds. Difference Equations, Discrete Dynamical Systems and Applications. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20016-9.

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Arendt, Wolfgang, Joseph A. Ball, Jussi Behrndt, Karl-Heinz Förster, Volker Mehrmann, and Carsten Trunk, eds. Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0.

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Layton, Richard A. Principles of Analytical System Dynamics. New York, NY: Springer New York, 1998.

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Elaydi, Saber, Yoshihiro Hamaya, Hideaki Matsunaga, and Christian Pötzsche, eds. Advances in Difference Equations and Discrete Dynamical Systems. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6409-8.

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Bohner, Martin, Stefan Siegmund, Roman Šimon Hilscher, and Petr Stehlík, eds. Difference Equations and Discrete Dynamical Systems with Applications. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35502-9.

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Baigent, Steve, Martin Bohner, and Saber Elaydi, eds. Progress on Difference Equations and Discrete Dynamical Systems. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60107-2.

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Book chapters on the topic "Difference equation system"

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Buică, Adriana, Isaac A. García, and Susanna Maza. "Centers in a Quadratic System Obtained from a Scalar Third Order Differential Equation." In Differential and Difference Equations with Applications, 405–10. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_34.

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Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Classical System Identification." In Regularized System Identification, 17–31. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_2.

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AbstractSystem identification as a field has been around since the 1950s with roots from statistical theory. A substantial body of concepts, theory, algorithms and experience has been developed since then. Indeed, there is a very extensive literature on the subject, with many text books, like [5, 8, 12]. Some main points of this “classical” field are summarized in this chapter, just pointing to the basic structure of the problem area. The problem centres around four main pillars: (1) the observed data from the system, (2) a parametrized set of candidate models, “the Model structure”, (3) an estimation method that fits the model parameters to the observed data and (4) a validation process that helps taking decisions about the choice of model structure. The crucial choice is that of the model structure. The archetypical choice for linear models is the ARX model, a linear difference equation between the system’s input and output signals. This is a universal approximator for linear systems—for sufficiently high orders of the equations, arbitrarily good descriptions of the system are obtained. For a “good” model, proper choices of structural parameters, like the equation orders, are required. An essential part of the classical theory deals with asymptotic quality measures, bias and variance, that aim at giving the best mean square error between the model and the true system. Some of this theory is reviewed in this chapter for estimation methods of the maximum likelihood character.
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Paunonen, Lassi. "The Infinite-dimensional Sylvester Differential Equation and Periodic Output Regulation." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 515–31. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_31.

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Zhao, Xiao, and Vasilis Z. Marmarelis. "Equivalence between Nonlinear Differential and Difference Equation Models Using Kernel Invariance Methods." In Advanced Methods of Physiological System Modeling, 219–27. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-9024-5_12.

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Nolasco, A. P., and F. O. Speck. "On Some Boundary Value Problems for the Helmholtz Equation in a Cone of 240º." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 497–513. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_30.

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Hommel, Angela. "A Useful Transformation for Solving the Discrete Beltrami Equation and Reducing a Difference Equation of Second Order to a System of Equations of First Order." In Trends in Mathematics, 487–503. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23854-4_23.

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Elaydi, Saber N. "Systems of Difference Equations." In An Introduction to Difference Equations, 105–53. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3110-1_3.

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Elaydi, Saber N. "Systems of Difference Equations." In An Introduction to Difference Equations, 113–62. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-9168-6_3.

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Gay, Simon J., Diogo Poças, and Vasco T. Vasconcelos. "The Different Shades of Infinite Session Types." In Lecture Notes in Computer Science, 347–67. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99253-8_18.

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AbstractMany type systems include infinite types. In session type systems, infinite types are important because they specify communication protocols that are unbounded in time. Usually infinite session types are introduced as simple finite-state expressions "Equation missing" or by non-parametric equational definitions "Equation missing". Alternatively, some systems of label- or value-dependent session types go beyond simple recursive types. However, leaving dependent types aside, there is a much richer world of infinite session types, ranging through various forms of parametric equational definitions, to arbitrary infinite types in a coinductively defined space. We study infinite session types across a spectrum of shades of grey on the way to the bright light of general infinite types. We identify four points on the spectrum, characterised by different styles of equational definitions, and show that they form a strict hierarchy by establishing bidirectional correspondences with classes of automata: finite-state, 1-counter, pushdown and 2-counter. This allows us to establish decidability and undecidability results for type formation, type equivalence and duality in each class of types. We also consider previous work on context-free session types (and extend it to higher-order) and nested session types, and locate them on our spectrum of infinite types.
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Tu, Pierre N. V. "Review of Difference Equations." In Dynamical Systems, 39–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-78793-5_3.

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Conference papers on the topic "Difference equation system"

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Shen, Fu, Ping Ju, Liling Gu, Xiaoming Huang, Boliang Lou, and Hongyang Huang. "Mechanism analysis of power load using difference equation approach." In 2016 IEEE International Conference on Power System Technology (POWERCON). IEEE, 2016. http://dx.doi.org/10.1109/powercon.2016.7753937.

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Esmaeili, Mansoureh, and Mansour Shirvani. "Detecting of zeros locations in a linear differential-difference equation." In 2011 IEEE International Conference on System Engineering and Technology (ICSET). IEEE, 2011. http://dx.doi.org/10.1109/icsengt.2011.5993421.

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Watanabe, Hitoshi, Yutaka Ishibashi, and Pingguo Huang. "A Formulization of Remote Robot System by Using Difference Differential Equation." In 2018 3rd International Conference on Computer and Communication Systems (ICCCS). IEEE, 2018. http://dx.doi.org/10.1109/ccoms.2018.8463335.

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Ruimin Zhao, Wenzhang He, and Geyang Guo. "Finite difference parallel schemes based on follow-flow scheme for KdV equation." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5622840.

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Rahman, Kaysar, Nurmamat Helil, and Rahmatjan Yimin. "Some new semi-implicit finite difference schemes for numerical solution of Burgers equation." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5622119.

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Nobuya Yao, T. Takubo, K. Ohara, Y. Mae, and T. Arai. "Gait planning for a biped robot by a nonholonomic system with difference equation constraints." In 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010). IEEE, 2010. http://dx.doi.org/10.1109/iros.2010.5651683.

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Tanaka, Toshiyuki, and Chikara Sato. "Stability of the Second Order Difference Equation With Time-Varying Parameter." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0129.

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Abstract This paper deals with the stability of the second order difference equation possessing periodic parameter, which characterizes discrete periodic system. Discrete periodic system corresponding to Mathieu equation is expressed as second order difference equation with small parameter ε in the time-varying term. This parameter ε plays an important role in stability. For the fundamental equation without damping, stability boundary curves are analytically obtained with respect to parameters in the equation by using McLachlan’s method, which is based on Floquet’s theory and perturbation method. The boundary curves are computed by pursuing periodic solutions on the boundaries and letting secular term zero. The boundary curves are expressed as the power series of ε. When periodic parameter consists of even function of Fourier series, stability boundary curves are obtained. For the fundamental equation with damping, stability criterion is shown in the neighbor of important resonant points. This criterion is obtained by computing points on the boundary curves.
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Mironova, Tatiana, Andrey Prokofiev, and Victor Sverbilov. "The Finite Difference Technique for Modelling of Pipe System Vibroacoustical Characteristics." In 9th FPNI Ph.D. Symposium on Fluid Power. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fpni2016-1533.

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The finite difference technique of vibroacoustical pipeline characteristics are developed. The technique allows calculations vibroacoustical characteristics of pipe with the axial line lying in one plane under force excitation by oscillating fluid flow. The technique is based on the solving differential equation system of interaction between solid and oscillating fluid in the pipeline. Solution was done for transient non-stationary nonlinear differential equation system. The boundary conditions for fluid is a parameter combination of complex pressure oscillation amplitude of pipeline inlet section, complex pressure oscillation amplitude of pipeline outlet section, complex velocity oscillation amplitude of pipeline inlet section, complex velocity oscillation amplitude of pipeline outlet section, load impedance, input impedance. The boundary conditions for solid is bonding of the pipeline. Time response of the pipeline vibration are resulted of these techniques. The mathematical technique computational coast is 3 orders less than Ansys technique. The method is developed for pipeline diameter much smaller than acoustic wavelength in a fluid. It is actual for aircraft pipelines, pipes of power plants, mobile machines and pipes of stationary processing machines.
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Wang, Songling, Xuelei Zhang, Haiping Chen, and Lanxin Zhou. "General Calculation Model on the Influence of Heater Terminal Temperature Difference on Turbine Power." In ASME 2005 Power Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pwr2005-50300.

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Assessing exactly the influence of heater terminal temperature difference on turbine power is significant meaning for the design, operation and repair of thermodynamic system. The method adopted is based on heat balance equation and turbine power equation of thermodynamic system. Take the partial derivative of outlet water enthalpy on both sides of the above equations, the law of the formulas can be found. So, for different heater type, the general calculation model on the influence of heater terminal temperature difference on turbine power is derived in the paper. One important conception, which is called as terminal temperature difference equivalent enthalpy drops, is defined in the paper. The model discussed in the paper is proved to be possessed of the character of accurate, simple and more universal. Especially, it is suitable for on-line monitoring system of unit heat economy.
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Silalahi, Fitriani Tupa R., and I. Gde Eka Dirgayussa. "Numerical solution of Laplace equation for ship problem in the sea using finite difference method." In THE 2016 CONFERENCE ON FUNDAMENTAL AND APPLIED SCIENCE FOR ADVANCED TECHNOLOGY (CONFAST 2016): Proceeding of ConFAST 2016 Conference Series: International Conference on Physics and Applied Physics Research (ICPR 2016), International Conference on Industrial Biology (ICIBio 2016), and International Conference on Information System and Applied Mathematics (ICIAMath 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4953984.

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Reports on the topic "Difference equation system"

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Li, Guangye. The Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada453093.

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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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Dennis, Jr, Li J. E., and Guangye. The Combined Schubert/Secant Finite-Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada453834.

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Wadlinger, E. A. Parameter scaling to produce different charged-particle beam-transport systems having identical equations of motion. Office of Scientific and Technical Information (OSTI), April 1988. http://dx.doi.org/10.2172/5303564.

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Warrick, Arthur W., Gideon Oron, Mary M. Poulton, Rony Wallach, and Alex Furman. Multi-Dimensional Infiltration and Distribution of Water of Different Qualities and Solutes Related Through Artificial Neural Networks. United States Department of Agriculture, January 2009. http://dx.doi.org/10.32747/2009.7695865.bard.

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The project exploits the use of Artificial Neural Networks (ANN) to describe infiltration, water, and solute distribution in the soil during irrigation. It provides a method of simulating water and solute movement in the subsurface which, in principle, is different and has some advantages over the more common approach of numerical modeling of flow and transport equations. The five objectives were (i) Numerically develop a database for the prediction of water and solute distribution for irrigation; (ii) Develop predictive models using ANN; (iii) Develop an experimental (laboratory) database of water distribution with time; within a transparent flow cell by high resolution CCD video camera; (iv) Conduct field studies to provide basic data for developing and testing the ANN; and (v) Investigate the inclusion of water quality [salinity and organic matter (OM)] in an ANN model used for predicting infiltration and subsurface water distribution. A major accomplishment was the successful use of Moment Analysis (MA) to characterize “plumes of water” applied by various types of irrigation (including drip and gravity sources). The general idea is to describe the subsurface water patterns statistically in terms of only a few (often 3) parameters which can then be predicted by the ANN. It was shown that ellipses (in two dimensions) or ellipsoids (in three dimensions) can be depicted about the center of the plume. Any fraction of water added can be related to a ‘‘probability’’ curve relating the size of the ellipse (or ellipsoid) that contains that amount of water. The initial test of an ANN to predict the moments (and hence the water plume) was with numerically generated data for infiltration from surface and subsurface drip line and point sources in three contrasting soils. The underlying dataset consisted of 1,684,500 vectors (5 soils×5 discharge rates×3 initial conditions×1,123 nodes×20 print times) where each vector had eleven elements consisting of initial water content, hydraulic properties of the soil, flow rate, time and space coordinates. The output is an estimate of subsurface water distribution for essentially any soil property, initial condition or flow rate from a drip source. Following the formal development of the ANN, we have prepared a “user-friendly” version in a spreadsheet environment (in “Excel”). The input data are selected from appropriate values and the output is instantaneous resulting in a picture of the resulting water plume. The MA has also proven valuable, on its own merit, in the description of the flow in soil under laboratory conditions for both wettable and repellant soils. This includes non-Darcian flow examples and redistribution and well as infiltration. Field experiments were conducted in different agricultural fields and various water qualities in Israel. The obtained results will be the basis for the further ANN models development. Regions of high repellence were identified primarily under the canopy of various orchard crops, including citrus and persimmons. Also, increasing OM in the applied water lead to greater repellency. Major scientific implications are that the ANN offers an alternative to conventional flow and transport modeling and that MA is a powerful technique for describing the subsurface water distributions for normal (wettable) and repellant soil. Implications of the field measurements point to the special role of OM in affecting wettability, both from the irrigation water and from soil accumulation below canopies. Implications for agriculture are that a modified approach for drip system design should be adopted for open area crops and orchards, and taking into account the OM components both in the soil and in the applied waters.
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Willits, Daniel H., Meir Teitel, Josef Tanny, Mary M. Peet, Shabtai Cohen, and Eli Matan. Comparing the performance of naturally ventilated and fan-ventilated greenhouses. United States Department of Agriculture, March 2006. http://dx.doi.org/10.32747/2006.7586542.bard.

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The objectives of this project were to predict the performance of naturally and fan-ventilated greenhouses as a function of climate, type of crop, evaporative cooling and greenhouse size, and to estimate the effects of the two cooling systems on yield, quality and disease development in the different crops under study. Background In the competitive field of greenhouse cultivation, growers and designers in both the US and Israel are repeatedly forced to choose between naturally ventilated (NV) and fan ventilated (FV) cooling systems as they expand their ranges in an effort to remain profitable. The known advantages and disadvantages of each system do not presently allow a clear decision. Whether essentially zero operating costs can offset the less dependable cooling of natural ventilation systems is question this report hopes to answer. Major Conclusions US It was concluded very early on that FV greenhouses without evaporative pad cooling are not competitive with NV greenhouses during hot weather. During the first year, the US team found that average air temperatures were always higher in the FV houses, compared to the NV houses, when evaporative pad cooling was not used, regardless of ventilation rate in the FV houses or the vent configuration in the NV houses. Canopy temperatures were also higher in the FV ventilated houses when three vents were used in the NV houses. A second major conclusion was that the US team found that low pressure fogging (4 atm) in NV houses does not completely offset the advantage of evaporative pad cooling in FV houses. High pressure fog (65 atm) is more effective, but considerably more expensive. Israel Experiments were done with roses in the years 2003-2005 and with tomatoes in 2005. Three modes of natural ventilation (roof, side and side + roof openings) were compared with a fan-ventilated (with evaporative cooling) house. It was shown that under common practice of fan ventilation, during summer, the ventilation rate is usually lower with NV than with FV. The microclimate under both NV and FV was not homogeneous. In both treatments there were strong gradients in temperature and humidity in the vertical direction. In addition, there were gradients that developed in horizontal planes in a direction parallel to the direction of the prevailing air velocity within the greenhouse. The gradients in the horizontal direction appear to be larger with FV than with NV. The ratio between sensible and latent heat fluxes (Bowen ratio) was found to be dependent considerably on whether NV or FV is applied. This ratio was generally negative in the naturally ventilated house (about -0.14) and positive in the fan ventilated one (about 0.19). Theoretical models based on Penman-Monteith equation were used to predict the interior air and crop temperatures and the transpiration rate with NV. Good agreement between the model and experimental results was obtained with regard to the air temperature and transpiration with side and side + roof ventilation. However, the agreement was poor with only roof ventilation. The yield (number of rose stems longer than 40 cm) was higher with FV
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Shani, Uri, Lynn Dudley, Alon Ben-Gal, Menachem Moshelion, and Yajun Wu. Root Conductance, Root-soil Interface Water Potential, Water and Ion Channel Function, and Tissue Expression Profile as Affected by Environmental Conditions. United States Department of Agriculture, October 2007. http://dx.doi.org/10.32747/2007.7592119.bard.

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Constraints on water resources and the environment necessitate more efficient use of water. The key to efficient management is an understanding of the physical and physiological processes occurring in the soil-root hydraulic continuum.While both soil and plant leaf water potentials are well understood, modeled and measured, the root-soil interface where actual uptake processes occur has not been sufficiently studied. The water potential at the root-soil interface (yᵣₒₒₜ), determined by environmental conditions and by soil and plant hydraulic properties, serves as a boundary value in soil and plant uptake equations. In this work, we propose to 1) refine and implement a method for measuring yᵣₒₒₜ; 2) measure yᵣₒₒₜ, water uptake and root hydraulic conductivity for wild type tomato and Arabidopsis under varied q, K⁺, Na⁺ and Cl⁻ levels in the root zone; 3) verify the role of MIPs and ion channels response to q, K⁺ and Na⁺ levels in Arabidopsis and tomato; 4) study the relationships between yᵣₒₒₜ and root hydraulic conductivity for various crops representing important botanical and agricultural species, under conditions of varying soil types, water contents and salinity; and 5) integrate the above to water uptake term(s) to be implemented in models. We have made significant progress toward establishing the efficacy of the emittensiometer and on the molecular biology studies. We have added an additional method for measuring ψᵣₒₒₜ. High-frequency water application through the water source while the plant emerges and becomes established encourages roots to develop towards and into the water source itself. The yᵣₒₒₜ and yₛₒᵢₗ values reflected wetting and drying processes in the rhizosphere and in the bulk soil. Thus, yᵣₒₒₜ can be manipulated by changing irrigation level and frequency. An important and surprising finding resulting from the current research is the obtained yᵣₒₒₜ value. The yᵣₒₒₜ measured using the three different methods: emittensiometer, micro-tensiometer and MRI imaging in both sunflower, tomato and corn plants fell in the same range and were higher by one to three orders of magnitude from the values of -600 to -15,000 cm suggested in the literature. We have added additional information on the regulation of aquaporins and transporters at the transcript and protein levels, particularly under stress. Our preliminary results show that overexpression of one aquaporin gene in tomato dramatically increases its transpiration level (unpublished results). Based on this information, we started screening mutants for other aquaporin genes. During the feasibility testing year, we identified homozygous mutants for eight aquaporin genes, including six mutants for five of the PIP2 genes. Including the homozygous mutants directly available at the ABRC seed stock center, we now have mutants for 11 of the 19 aquaporin genes of interest. Currently, we are screening mutants for other aquaporin genes and ion transporter genes. Understanding plant water uptake under stress is essential for the further advancement of molecular plant stress tolerance work as well as for efficient use of water in agriculture. Virtually all of Israel’s agriculture and about 40% of US agriculture is made possible by irrigation. Both countries face increasing risk of water shortages as urban requirements grow. Both countries will have to find methods of protecting the soil resource while conserving water resources—goals that appear to be in direct conflict. The climate-plant-soil-water system is nonlinear with many feedback mechanisms. Conceptual plant uptake and growth models and mechanism-based computer-simulation models will be valuable tools in developing irrigation regimes and methods that maximize the efficiency of agricultural water. This proposal will contribute to the development of these models by providing critical information on water extraction by the plant that will result in improved predictions of both water requirements and crop yields. Plant water use and plant response to environmental conditions cannot possibly be understood by using the tools and language of a single scientific discipline. This proposal links the disciplines of soil physics and soil physical chemistry with plant physiology and molecular biology in order to correctly treat and understand the soil-plant interface in terms of integrated comprehension. Results from the project will contribute to a mechanistic understanding of the SPAC and will inspire continued multidisciplinary research.
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EXPERIMENTAL, NUMERICAL, AND THEORETICAL STUDY ON STATIC BEHAVIOUR OF NOVEL STEEL DOVETAIL JOINT SUBJECTED TO AXIAL TENSILE LOAD. The Hong Kong Institute of Steel Construction, March 2022. http://dx.doi.org/10.18057/ijasc.2022.18.1.4.

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In this study, two types of socket joints manufactured based on a simple design concept and bearing load principle are proposed. The design concept, design method, test program, and FE modelling method for a novel steel dovetail joint without teeth pattern (Interlock type I) and with teeth pattern (Interlock type II) are also discussed. In addition, the tests and numerical analyses of four specimens were conducted to investigate the bearing capacities and failure modes of the new joint systems under axial tensile loads. The test results indicated that the specimens with and without teeth patterns exhibited different tensile bearing capacities: the specimens with teeth patterns generated twice the tensile load capacity of those without teeth patterns. This result can be attributed to the fact that the interlock type-II specimens rely on the teeth pattern, edges of the hub keyway, and hub ring to bear the load, whereas interlock type-I specimens rely only rely on the edges of the hub keyway and hub rings. Further, the two types of specimens have the same failure modes when the beam-inserted end (tail) is pulled out of the hub keyway. In addition, shear failure occurs on the teeth pattern of the hub keyways and beam-inserted ends of the interlock type-II specimens. Two FE models are established to verify the results of the tests, and the related equations are derived and calculated. The results obtained from the numerical analysis using the equations were compared with the test results. Finally, it was concluded that the results obtained using the three analysis methods adopted in this study agree very well, with high calculation validity and efficiency.
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