Journal articles: 'Incidence theorem'

1

Fisher, J. Chris, Larry Hoehn, and Eberhard M. Schröder. "A 5-Circle Incidence Theorem." Mathematics Magazine 87, no. 1 (February 2014): 44–49. http://dx.doi.org/10.4169/math.mag.87.1.44.

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Helfgott, Harald Andrés, and Misha Rudnev. "AN EXPLICIT INCIDENCE THEOREM IN." Mathematika 57, no. 1 (December 13, 2010): 135–45. http://dx.doi.org/10.1112/s0025579310001208.

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Solymosi, József, and Terence Tao. "An Incidence Theorem in Higher Dimensions." Discrete & Computational Geometry 48, no. 2 (March 21, 2012): 255–80. http://dx.doi.org/10.1007/s00454-012-9420-x.

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Fokkema, Jacob T., and Anton Ziolkowski. "The critical reflection theorem." GEOPHYSICS 52, no. 7 (July 1987): 965–72. http://dx.doi.org/10.1190/1.1442365.

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In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

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Kelarev, A. V. "Minimum distances of error-correcting codes in incidence rings." International Journal of Mathematics and Mathematical Sciences 2003, no. 13 (2003): 827–33. http://dx.doi.org/10.1155/s0161171203204063.

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Sánchez Salcán, N. J., and F. P. Londo Yachambay. "Incidence of Lamy’s Theorem in static learning: Balance of forces." Journal of Physics: Conference Series 1043 (June 2018): 012051. http://dx.doi.org/10.1088/1742-6596/1043/1/012051.

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Adam, Jean-Pierre, Jean-Christophe Joly, Bernard Pecqueux, and Didier Asfaux. "The reciprocity theorem applied to finding the best coupling incidence." Comptes Rendus Physique 10, no. 1 (January 2009): 65–69. http://dx.doi.org/10.1016/j.crhy.2009.02.003.

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KELAREV, A. V. "ON THE STRUCTURE OF INCIDENCE RINGS OF GROUP AUTOMATA." International Journal of Algebra and Computation 14, no. 04 (August 2004): 505–11. http://dx.doi.org/10.1142/s0218196704001888.

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The Jacobson radical is one of the major tools used in the investigation of the structure of rings and ring constructions. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of group automata for all finite nilpotent groups.

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Manea, Adrian, and Dragoş Ştefan. "On Koszulity of finite graded posets." Journal of Algebra and Its Applications 16, no. 07 (July 17, 2016): 1750139. http://dx.doi.org/10.1142/s0219498817501390.

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In this paper, we continue our research on Koszul rings, started in [P. Jara, J. López-Peña and D. Ştefan, Koszul pairs and applications, to appear in J. Noncommut. Geom., http://arxiv.org/pdf/1011.4243.pdf ]. In Theorem 1.9, we prove in a unifying way several equivalent descriptions of Koszul rings, some of which being well known in the literature. Most of them are stated in terms of coring theoretical properties of [Formula: see text]. As an application of these characterizations, we investigate the Koszulity of the incidence rings for finite graded posets, see Theorems 2.8 and 2.9. Based on these results, we describe an algorithm to produce new classes of Koszul posets (i.e. graded posets, whose incidence rings are Koszul). Specific examples of Koszul posets are included.

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Kelarev, Andrei V., Willy Susilo, Mirka Miller, and Joe Ryan. "Ideals of Largest Weight in Constructions Based on Directed Graphs." Bulletin of Mathematical Sciences and Applications 15 (May 2016): 8–16. http://dx.doi.org/10.18052/www.scipress.com/bmsa.15.8.

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We introduce a new construction based on directed graphs. It provides a common generalization of the incidence rings and Munn semirings. Our main theorem describes all ideals of the largest possible weight in this construction. Several previous results can be obtained as corollaries to our new main theorem.

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Brusamarello, Rosali, Érica Zancanella Fornaroli, and Ednei Aparecido Santulo. "Classification of involutions on finitary incidence algebras." International Journal of Algebra and Computation 24, no. 08 (December 2014): 1085–98. http://dx.doi.org/10.1142/s0218196714500477.

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Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI (X), to be equivalent in the case when every multiplicative automorphism of FI (X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181–188] for finitary incidence algebras.

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12

Li, Jun Hong, Ning Cui, Liang Cui, and Cai Juan Li. "Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate." Applied Mechanics and Materials 155-156 (February 2012): 23–26. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.23.

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In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the an- alytical results.

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Li, Jun Hong, Ning Cui, and Hong Kai Sun. "Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate." Advanced Materials Research 479-481 (February 2012): 1495–98. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1495.

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An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

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Cui, Ning, Jun Hong Li, Jiao Qu, and Hong Dan Xue. "Dynamics Analysis of an SEIQS Model with a Nonlinear Incidence Rate." Applied Mechanics and Materials 157-158 (February 2012): 1220–23. http://dx.doi.org/10.4028/www.scientific.net/amm.157-158.1220.

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This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.

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Bernoussi, Amine, Abdelilah Kaddar, and Said Asserda. "Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence." International Journal of Engineering Mathematics 2014 (December 7, 2014): 1–6. http://dx.doi.org/10.1155/2014/487589.

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In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.

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Nazeer, Irfan, Tabasam Rashid, Muhammad Tanveer Hussain, and Juan Luis García Guirao. "Domination in Join of Fuzzy Incidence Graphs Using Strong Pairs with Application in Trading System of Different Countries." Symmetry 13, no. 7 (July 16, 2021): 1279. http://dx.doi.org/10.3390/sym13071279.

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Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), are an applicable and well-organized tool to epitomize and resolve multiple real-world problems in which ambiguous data and information are essential. In this article, we extend the idea of domination of FGs to the FIG using strong pairs. An idea of strong pair dominating set and a strong pair domination number (SPDN) is explained with various examples. A theorem to compute SPDN for a complete fuzzy incidence graph (CFIG) is also provided. It is also proved that in any fuzzy incidence cycle (FIC) with l vertices the minimum number of elements in a strong pair dominating set are M[γs(Cl(σ,ϕ,η))]=⌈l3⌉. We define the joining of two FIGs and present a way to compute SPDN in the join of FIGs. A theorem to calculate SPDN in the joining of two strong fuzzy incidence graphs is also provided. An innovative idea of accurate domination of FIGs is also proposed. Some instrumental and useful results of accurate domination for FIC are also obtained. In the end, a real-life application of SPDN to find which country/countries has/have the best trade policies among different countries is examined. Our proposed method is symmetrical to the optimization.

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Zhang, Hui, Li Yingqi, and Wenxiong Xu. "Global Stability of an SEIS Epidemic Model with General Saturation Incidence." ISRN Applied Mathematics 2013 (April 11, 2013): 1–11. http://dx.doi.org/10.1155/2013/710643.

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We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

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18

Green, J. J. "Banach algebras of topologically bounded index." Bulletin of the Australian Mathematical Society 56, no. 1 (August 1997): 51–62. http://dx.doi.org/10.1017/s0004972700030720.

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We consider normed and Banach algebras satisfying a condition topologically analogous to bounded index for rings. We investigate stability properties, prove a topological version of a theorem of Jacobson, and find in many cases co-incidence with well-known finiteness properties.

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Zhang, Zizhen, Yougang Wang, and Luca Guerrini. "Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence." Advances in Mathematical Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/7619074.

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This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.

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Zaki, A. S., A. M. Yousef, S. Z. Rida, and Y. Gh Gouda. "On the dynamics of an SIR epidemic model with a saturated incidence rate." Journal of Advanced Studies in Topology 8, no. 1 (September 15, 2017): 97. http://dx.doi.org/10.20454/jast.2017.1333.

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In this paper, discrete-time epidemic model with a saturated incidence rate is considered. Firstly, we introduce the local stability analysis of the system by details. Next, we study the bifurcation phenomena and the sufficient condition to verify flip bifurcation and Neimark-sacker bifurcation by using bifurcation theory and the center manifold theorem. Finally, numerical simulation including bifurcation diagrams, phase portraits and Chaotic attractors is carried out by using matlab to verify theoretical results obtained.

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21

Sun, Li Hong. "Properties of Weighted Geometric Means Combination Forecasting Model Based on Absolute of Grey Incidence." Advanced Materials Research 490-495 (March 2012): 442–46. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.442.

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weighted geometric means combination forecasting is a kind of nonlinear combination forecasting model. Based on absolute of grey incidence, a weighted geometric means combination forecasting model is proposed. Superior combination forecasting, dominant forecasting method and redundant degree are put forward. Under certain conditions the sufficient condition of existence of non-inferior combination and superior combination forecasting are discussed, redundant information is pointed out in a judging theorem.

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Tian, Xiaohong, and Rui Xu. "Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/795320.

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A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

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Li, Junhong, and Ning Cui. "Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives." Scientific World Journal 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/871393.

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An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compound matrix theory. Furthermore, the method of direct numerical simulation of the system shows that there is a periodic solution, when the system has three equilibrium points.

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Wu, Kuilin, and Kai Zhou. "Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission." Mathematics 7, no. 7 (July 18, 2019): 641. http://dx.doi.org/10.3390/math7070641.

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In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator.

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King, A. D., and W. K. Schief. "Application of an incidence theorem for conics: Cauchy problem and integrability of the dCKP equation." Journal of Physics A: Mathematical and General 39, no. 8 (February 8, 2006): 1899–913. http://dx.doi.org/10.1088/0305-4470/39/8/008.

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Zhou, Kai, and Qi-Ru Wang. "Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/369072.

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This paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By careful analyzsis, we derive the existence of traveling waves connecting the disease-free steady state and the endemic steady state through the establishment of the suitable upper-lower solutions.

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Liu, Juan. "Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate." Discrete Dynamics in Nature and Society 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2340549.

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This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results.

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Kodokostas, Dimitrios. "Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space." Geometry 2014 (December 18, 2014): 1–7. http://dx.doi.org/10.1155/2014/276108.

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With the use of only the incidence axioms we prove and generalize Desargues’ two-triangle Theorem in three-dimensional projective space considering an arbitrary number of points on each one of the two distinct planes allowing corresponding points on the two planes to coincide and three points on any of the planes to be collinear. We provide three generalizations and we define the notions of a generalized line and a triangle-connected plane set of points.

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Sakamoto, Haruhisa, and Koji Morioka. "Proposal of Micro Removal Process with Pulsed Laser Irradiation Based on Form Generation Theorem." Advanced Materials Research 1017 (September 2014): 825–30. http://dx.doi.org/10.4028/www.scientific.net/amr.1017.825.

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In general, the form generation theorem of laser removal processes has not yet been established. The cause of this is that laser is a light source and has no tool shape as conventional machining tools. Therefore, its transcription characteristics could not be determined. In this paper, the application of the form generation theorem to laser removal process is examined experimentally. In order to establish the form generation theorem, first the “equivalent tool shape” of the focused beam is determined. To determine the equivalent tool shape, a groove is machined with the laser intensity just above the removal threshold of the work piece material. From the machining result, the cross-section of the groove is machined in to a V-shape. The V-shape is peculiar to the workpiece material, thus can be determined as equivalent tool shape of laser machining. The groove shape can be simulated numerically by considering the removal threshold and dependence of absorption characteristics to incidence angle. The numerical simulation and the experimental result were in good agreement. Based on the equivalent tool shape and the form generation theorem, a rectangular cross-section groove is experimented. As a result the groove was finished with a flat bottom having ruggedness like a saw-blade. This result indicates that the laser shaping based on the form generation theorem can be possible by laser irradiation with properly suppressed intensity.

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Zhang, Jinhong, Jianwen Jia, and Xinyu Song. "Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/910421.

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The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.

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Yan, Mei, and Zhongyi Xiang. "Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination." Discrete Dynamics in Nature and Society 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/262535.

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We consider a nonautonomous SEIR endemic model with saturation incidence concerning pulse vaccination. By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. Finally, numerical simulations are given to illustrate the main theoretical results and it shows that pulse vaccination plays a key role in the disease control.

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Kung, Joseph P. S. "Matchings and Radon transforms in lattices II. Concordant sets." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 2 (March 1987): 221–31. http://dx.doi.org/10.1017/s0305004100066573.

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AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.

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Zhang, Qiu, and Shi-Liang Wu. "Wave propagation of a discrete SIR epidemic model with a saturated incidence rate." International Journal of Biomathematics 12, no. 03 (April 2019): 1950029. http://dx.doi.org/10.1142/s1793524519500293.

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This paper is concerned with the traveling wave solutions for a discrete SIR epidemic model with a saturated incidence rate. We show that the existence and non-existence of the traveling wave solutions are determined by the basic reproduction number [Formula: see text] of the corresponding ordinary differential system and the minimal wave speed [Formula: see text]. More specifically, we first prove the existence of the traveling wave solutions for [Formula: see text] and [Formula: see text] via considering a truncated initial value problem and using the Schauder’s fixed point theorem. The existence of the traveling wave solutions with speed [Formula: see text] is then proved by using a limiting argument. The main difficulty is to show that the limit of a decreasing sequence of the traveling wave solutions with super-critical speeds is non-trivial. Finally, the non-existence of the traveling wave solutions for [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] is proved.

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Zhai, Yanhui, Ying Xiong, Xiaona Ma, and Haiyun Bai. "Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/242410.

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The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.

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Lee, Kwang Sung, and Abid Ali Lashari. "Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/219173.

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Based on classical epidemic models, this paper considers a deterministic epidemic model for the spread of the pine wilt disease which has vector mediated transmission. The analysis of the model shows that its dynamics are completely determined by the basic reproduction numberR0. Using a Lyapunov function and a LaSalle's invariant set theorem, we proved the global asymptotical stability of the disease-free equilibrium. We find that ifR0≤1, the disease free equilibrium is globally asymptotically stable, and the disease will be eliminated. IfR0>1, a unique endemic equilibrium exists and is shown to be globally asymptotically stable, under certain restrictions on the parameter values, using the geometric approach method for global stability, due to Li and Muldowney and the disease persists at the endemic equilibrium state if it initially exists.

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Walden, Andrew, and Roy White. "On: “The critical reflection theorem” by J. T. Fokkema and A. Ziolkowski (GEOPHYSICS, 52, 965–972, July 1987)." GEOPHYSICS 53, no. 11 (November 1988): 1490–91. http://dx.doi.org/10.1190/1.1442430.

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In this paper, Fokkema and Ziolkowski consider precritical and postcritical incidence and resulting implications for the reflection response of the earth. The ideas are interesting and thought provoking, but their inferences with regard to the whiteness assumption in standard deconvolution are misleading. We will endeavor to show why.

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Batistela, Rosemeire De Fatima, Maria Aparecida Viggiani Bicudo, and Henrique Lazari. "Cenário do Surgimento e o Impacto do Teorema da Incompletude de Gödel na Matemática." Jornal Internacional de Estudos em Educação Matemática 10, no. 3 (February 6, 2018): 198. http://dx.doi.org/10.17921/2176-5634.2017v10n3p198-207.

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Este artigo trata do panorama das discussões matemáticas mantidas entre os matemáticos à época em que Gödel apresentou à comunidade matemática seu teorema da incompletude. Argumenta-se que o Teorema da Incompletude de Gödel (TIG) é um teorema mais para a alma do que para as mãos dos matemáticos. Afirma-se ser ele importante porque mostra que a Matemática não pode comunicar (provar) todas as suas verdades. Porém, as provas de que a aritmética básica dos naturais é incompleta e incompletável e da impossibilidade de demonstrar a sua não contradição não impossibilita que a Matemática continue sendo produzida. A linha de argumentação exposta segue apresentando: o cenário matemático vigente no momento da publicação do TIG; o ponto de incidência deste resultado na Matemática, o impacto deste teorema nesta ciência, bem como, como ele foi compreendido e acolhido pelos matemáticos.Palavras-chave: Teorema da Incompletude de Gödel (TIG). Problema da Compatibilidade da Aritmética. Programa de Hilbert. Método Axiomático.AbstractThis article deals with the panorama of the mathematical discussions held among mathematicians at the time when Gödel introduced his incompleteness theorem to the mathematical community. It is argued that Gödel’s Incompleteness Theorem (TIG) is a more theorem for the soul than for the hands of mathematicians. It is said to be important because it shows that Mathematics can’t communicate (prove) all its truths. However, evidence that the basic arithmetic of the natural is incomplete and incomplete and that it is impossible to demonstrate its non-contradiction does not preclude mathematics from being produced. The line of argument exposed continues presenting: the mathematical scenario in force at the time of the publication of the TIG; The point of incidence of this result in Mathematics, the impact of this theorem on this science, as well as how it was understood and welcomed by mathematicians.Keywords: Gödel’s Incompleteness Theorem. Hilbert’s Second Problem. Hibert’s Program. Axiomatic Method.

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Wang, Xiaoyan, Yuming Chen, and Junyuan Yang. "Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects." Complexity 2019 (June 16, 2019): 1–20. http://dx.doi.org/10.1155/2019/5842942.

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We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method.

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Peng, Miao, Zhengdi Zhang, C. W. Lim, and Xuedi Wang. "Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response." Mathematical Problems in Engineering 2018 (June 7, 2018): 1–12. http://dx.doi.org/10.1155/2018/6052503.

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Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

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Richter, William, Adam Grabowski, and Jesse Alama. "Tarski Geometry Axioms." Formalized Mathematics 22, no. 2 (June 30, 2014): 167–76. http://dx.doi.org/10.2478/forma-2014-0017.

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Summary This is the translation of the Mizar article containing readable Mizar proofs of some axiomatic geometry theorems formulated by the great Polish mathematician Alfred Tarski [8], and we hope to continue this work. The article is an extension and upgrading of the source code written by the first author with the help of miz3 tool; his primary goal was to use proof checkers to help teach rigorous axiomatic geometry in high school using Hilbert’s axioms. This is largely a Mizar port of Julien Narboux’s Coq pseudo-code [6]. We partially prove the theorem of [7] that Tarski’s (extremely weak!) plane geometry axioms imply Hilbert’s axioms. Specifically, we obtain Gupta’s amazing proof which implies Hilbert’s axiom I1 that two points determine a line. The primary Mizar coding was heavily influenced by [9] on axioms of incidence geometry. The original development was much improved using Mizar adjectives instead of predicates only, and to use this machinery in full extent, we have to construct some models of Tarski geometry. These are listed in the second section, together with appropriate registrations of clusters. Also models of Tarski’s geometry related to real planes were constructed.

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Dai, Yunxian, Yiping Lin, Huitao Zhao, and Chaudry Masood Khalique. "Global stability and Hopf bifurcation of a delayed computer virus propagation model with saturation incidence rate and temporary immunity." International Journal of Modern Physics B 30, no. 28n29 (November 10, 2016): 1640009. http://dx.doi.org/10.1142/s0217979216400099.

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In this paper, a delayed computer virus propagation model with a saturation incidence rate and a time delay describing temporary immune period is proposed and its dynamical behaviors are studied. The threshold value [Formula: see text] is given to determine whether the virus dies out completely. By comparison arguments and iteration technique, sufficient conditions are obtained for the global asymptotic stabilities of the virus-free equilibrium and the virus equilibrium. Taking the delay as a parameter, local Hopf bifurcations are demonstrated. Furthermore, the direction of Hopf bifurcation and the stabilities of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations (FDEs). Finally, numerical simulations are carried out to illustrate the main theoretical results.

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Yang, Fei-Ying, Wan-Tong Li, and Jia-Bing Wang. "Wave propagation for a class of non-local dispersal non-cooperative systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (March 14, 2019): 1965–97. http://dx.doi.org/10.1017/prm.2019.4.

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AbstractThis paper is concerned with the travelling waves for a class of non-local dispersal non-cooperative system, which can model the prey-predator and disease-transmission mechanism. By the Schauder's fixed-point theorem, we first establish the existence of travelling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations, whose bounds are deduced from a precise analysis. Further, we characterize the minimal wave speed of travelling waves and obtain the non-existence of travelling waves with slow speed. Finally, we apply the general results to an epidemic model with bilinear incidence for its propagation dynamics.

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Kumar, Abhishek, and Nilam. "Dynamic Behavior of an SIR Epidemic Model along with Time Delay; Crowley–Martin Type Incidence Rate and Holling Type II Treatment Rate." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 7-8 (November 18, 2019): 757–71. http://dx.doi.org/10.1515/ijnsns-2018-0208.

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Abstract In this article, we propose and analyze a time-delayed susceptible–infected–recovered (SIR) mathematical model with nonlinear incidence rate and nonlinear treatment rate for the control of infectious diseases and epidemics. The incidence rate of infection is considered as Crowley–Martin functional type and the treatment rate is considered as Holling functional type II. The stability of the model is investigated for the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. From the mathematical analysis of the model, we prove that the model is locally asymptotically stable for DFE when the basic reproduction number {R_0} is less than unity ({R_0} \lt 1) and unstable when {R_0} is greater than unity ({R_0} \gt 1) for time lag \tau \ge 0. The stability behavior of the model for DFE at {R_0} = 1 is investigated using Castillo-Chavez and Song theorem, which shows that the model exhibits forward bifurcation at {R_0} = 1. We investigate the stability of the EE for time lag \tau \ge 0. We also discussed the Hopf bifurcation of EE numerically. Global stability of the model equilibria is also discussed. Furthermore, the model has been simulated numerically to exemplify analytical studies.

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Montoya, Oscar Danilo, Walter Gil-González, and Diego Armando Giral. "On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence." Applied Sciences 10, no. 17 (August 21, 2020): 5802. http://dx.doi.org/10.3390/app10175802.

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This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations. The convergence test is performed using the Banach fixed-point theorem while considering the dominant diagonal structure of the demand-to-demand admittance matrix. A numerical example is presented in tutorial form using the MATLAB interface, which aids beginners in understanding the basic concepts of power-flow programming in distribution system analysis. Two classical test feeders comprising 33 and 69 nodes are used to validate the proposed formulation in comparison with conventional methods such as the Gauss–Seidel and Newton–Raphson power-flow formulations.

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Jang, Paeksan, Yongguk Ri, Songchol Ri, Cholho Pang, and Changson Ok. "Scattering of SH Wave by a Semi-Circle Inclusion Embedded in Bi-Material Half Space Surface." Journal of Mechanics 36, no. 4 (April 3, 2020): 497–506. http://dx.doi.org/10.1017/jmech.2019.72.

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ABSTRACTInvestigation of SH wave scattering by inclusions in bi-material half space is an important issue in engineering. The purpose of this work is to study the dynamic response of a semi-circle inclusion embedded in bi-material half space surface by SH wave. Graf's addition theorem, Green function method and region-matching technique are used to determine the displacement fields in the bi-material half space and the inclusion. The distributions of dynamic stress concentration factor (DSCF) around the semi-circle inclusion are depicted graphically considering different material parameters. The results show that the frequency and the incidence angle of SH wave, the rigidities of the inclusion and bi-material half space, and the distance from the inclusion to the interface have a great effect on the distribution of DSCF around the inclusion.

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Hamid, A.-K., I. R. Ciric, and M. Hamid. "Analytic solutions of the scattering by two multilayered dielectric spheres." Canadian Journal of Physics 70, no. 9 (September 1, 1992): 696–705. http://dx.doi.org/10.1139/p92-112.

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The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

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GLYNN, DAVID G. "THEOREMS OF POINTS AND PLANES IN THREE-DIMENSIONAL PROJECTIVE SPACE." Journal of the Australian Mathematical Society 88, no. 1 (February 2010): 75–92. http://dx.doi.org/10.1017/s1446788708080981.

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AbstractWe discuss n4 configurations of n points and n planes in three-dimensional projective space. These have four points on each plane, and four planes through each point. When the last of the 4n incidences between points and planes happens as a consequence of the preceding 4n−1 the configuration is called a ‘theorem’. Using a graph-theoretic search algorithm we find that there are two 84 and one 94 ‘theorems’. One of these 84 ‘theorems’ was already found by Möbius in 1828, while the 94 ‘theorem’ is related to Desargues’ ten-point configuration. We prove these ‘theorems’ by various methods, and connect them with other questions, such as forbidden minors in graph theory, and sets of electrons that are energy minimal.

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Teleman, Andrei. "Analytic cycles in flip passages and in instanton moduli spaces over non-Kählerian surfaces." International Journal of Mathematics 27, no. 07 (June 2016): 1640009. http://dx.doi.org/10.1142/s0129167x16400097.

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Let [Formula: see text] ([Formula: see text]) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with [Formula: see text] and let [Formula: see text] be a pure [Formula: see text]-dimensional analytic set. We prove a general formula for the homological boundary [Formula: see text] of the Borel–Moore fundamental class of [Formula: see text] in the boundary of the blown up moduli space [Formula: see text]. The proof is based on the holomorphic model theorem of [A. Teleman, Instanton moduli spaces on non-Kählerian surfaces, Holomorphic models around the reduction loci, J. Geom. Phys. 91 (2015) 66–87] which identifies a neighborhood of a boundary component of [Formula: see text] with a neighborhood of the boundary of a “blown up flip passage”. We then focus on a particular instanton moduli space which intervenes in our program for proving the existence of curves on class VII surfaces. Using our result, combined with general properties of the Donaldson cohomology classes, we prove incidence relations between the Zariski closures (in the considered moduli space) of certain families of extensions. These incidence relations are crucial for understanding the geometry of the moduli space, and cannot be obtained using classical complex geometric deformation theory.

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Chukhovskii, F. N. "On the optical theorem applicability using a self-consistent wave approximation model for the grazing-incidence small-angle X-ray scattering from rough surfaces." Acta Crystallographica Section A Foundations of Crystallography 68, no. 4 (May 30, 2012): 505–12. http://dx.doi.org/10.1107/s0108767312017448.

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Meidow, J., H. Hammer, and L. Lucks. "DELINEATION AND CONSTRUCTION OF 2D GEOMETRIES BY FREEHAND DRAWING AND GEOMETRIC REASONING." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-5-2020 (August 3, 2020): 77–84. http://dx.doi.org/10.5194/isprs-annals-v-5-2020-77-2020.

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Abstract. The creation of accurate and consistent line drawings is the subject of various applications. Prominent examples are the delineation of human-made objects in aerial images and the construction of technical line drawings, flow-charts, or diagrams. Interactive solutions usually restrict the user’s interaction during the design process to enforce geometric relations such as orthogonality or incidence. To avoid the time-consuming selection of operational modes, a freehand approach is desirable using strokes as the only user input. In this case, the construction principles have to be inferred automatically by geometric reasoning with uncertain observations. We present and discuss the corresponding methods in the context of educational technology. By introducing and utilizing a user-friendly software tool, we offer a hands-on approach to explore the feasibility and usability of the procedure. The experiments comprise the polygonal approximation of 2D shapes, theorem proving, and the construction of human-made figures.

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Journal articles on the topic 'Incidence theorem'

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