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Relevant bibliographies by topics / Degenerate PDE

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Academic literature on the topic 'Degenerate PDE'

Author: Grafiati

Published: 10 August 2024

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Journal articles on the topic "Degenerate PDE"

1

Rocca, Elisabetta, and Riccarda Rossi. "A degenerating PDE system for phase transitions and damage." Mathematical Models and Methods in Applied Sciences 24, no. 07 (2014): 1265–341. http://dx.doi.org/10.1142/s021820251450002x.

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In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns ϑ (absolute temperature), u (displacement), and χ (phase/damage parameter) are strongly nonlinearly coupled. Moreover, the momentum equation for u contains χ-dependent elliptic operators, which degenerate at the pure phases (corresponding to the values χ = 0 and χ = 1), making the whole system degenerate. That is why, we have to resort to a suitable weak solvability notion for the analysis of the problem: it c

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Nytrebych, Zinovii, and Oksana Malanchuk. "The conditions of existence of a solution of the degenerate two-point in time problem for PDE." Asian-European Journal of Mathematics 12, no. 03 (2019): 1950037. http://dx.doi.org/10.1142/s1793557119500372.

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The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its characteristic determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.

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Kubo, Masahiro, and Quqin Lu. "Evolution equations for nonlinear degenerate parabolic PDE." Nonlinear Analysis: Theory, Methods & Applications 64, no. 8 (2006): 1849–59. http://dx.doi.org/10.1016/j.na.2005.07.027.

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Spence, S., G. Rena, G. Sweeney, and M. D. Houslay. "Induction of Ca2+/calmodulin-stimulated cyclic AMP phosphodiesterase (PDE1) activity in Chinese hamster ovary cells (CHO) by phorbol 12-myristate 13-acetate and by the selective overexpression of protein kinase C isoforms." Biochemical Journal 310, no. 3 (1995): 975–82. http://dx.doi.org/10.1042/bj3100975.

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The cAMP phosphodiesterase (PDE) activity of CHO cells was unaffected by the addition of Ca2+ +calmodulin (CaM), indicating the absence of any PDE1 (Ca2+/CaM-stimulated PDE) activity. Treatment with the tumour promoting phorbol ester phorbol 12-myristate 13-acetate (PMA) led to the rapid transient induction of PDE1 activity which attained a maximum value after about 13 h before slowly decreasing. Such induction was attenuated by actinomycin D. PCR primers were designed to hybridize with two regions identified as being characteristic of PDE1 forms found in various species and predicted to ampli

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PARDOUX, ÉTIENNE, and AHMADOU BAMBA SOW. "HOMOGENIZATION OF A PERIODIC DEGENERATE SEMILINEAR ELLIPTIC PDE." Stochastics and Dynamics 11, no. 02n03 (2011): 475–93. http://dx.doi.org/10.1142/s0219493711003401.

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In this paper, a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of ℝd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion processes.

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Elshegmani, Zieneb Ali, and Rokiah Rozita Ahmad. "Fourier Transform of the Continuous Arithmetic Asian Options PDE." ISRN Applied Mathematics 2011 (September 26, 2011): 1–8. http://dx.doi.org/10.5402/2011/643749.

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Price of the arithmetic Asian options is not known in a closed-form solution, since arithmetic Asian option PDE is a degenerate partial differential equation in three dimensions. In this work we provide a new method for computing the continuous arithmetic Asian option price by means of partial differential equations. Using Fourier transform and changing some variables of the PDE we get a new direct method for solving the governing PDE without reducing the dimensionality of the PDE as most authors have done. We transform the second-order PDE with nonconstant coefficients to the first order with

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Katzourakis, Nikos. "On linear degenerate elliptic PDE systems with constant coefficients." Advances in Calculus of Variations 9, no. 3 (2016): 283–91. http://dx.doi.org/10.1515/acv-2015-0004.

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AbstractLet ${\mathbf{A}}$ be a symmetric convex quadratic form on ${\mathbb{R}^{Nn}}$ and Ω $\subset$$\mathbb{R}^{n}$ a bounded convex domain. We consider the problem of existence of solutions u: Ω $\subset$$\mathbb{R}^{n}$$\to$$\mathbb{R}^{N}$ to the problem${}\left\{\begin{aligned} \displaystyle\sum_{\beta=1}^{N}\sum_{i,j=1}^{n}% \mathbf{A}_{\alpha i\beta j}D^{2}_{ij}u_{\beta}&\displaystyle=f_{\alpha}&&% \displaystyle\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\text{on }\partial\Omega,\end{% aligned}\right.\phantom{\}}$when ${f\in L^{2}(\Omega,\

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Biswas, Imran H., Espen R. Jakobsen, and Kenneth H. Karlsen. "Difference-Quadrature Schemes for Nonlinear Degenerate Parabolic Integro-PDE." SIAM Journal on Numerical Analysis 48, no. 3 (2010): 1110–35. http://dx.doi.org/10.1137/090761501.

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Antil, Harbir, and Shawn W. Walker. "Optimal Control of a Degenerate PDE for Surface Shape." Applied Mathematics & Optimization 78, no. 2 (2017): 297–328. http://dx.doi.org/10.1007/s00245-017-9407-3.

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Ivochkina, Nina, Neil Trudinger, and Xu-Jia Wang. "The Dirichlet Problem for Degenerate Hessian Equations." Communications in Partial Differential Equations 29, no. 1-2 (2005): 219–35. http://dx.doi.org/10.1081/pde-120028851.

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Dissertations / Theses on the topic "Degenerate PDE"

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Hatami, Farhad. "Configurations of Wardrop's equilibrium and application to traffic analysis." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/565891.

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This thesis consists of two parts, and the connection between them is the so-called Wardrop's equilibrium. In the rst part of this thesis, which is the theoretical part, we study the congested transport dynamics arising from a non-autonomous tra c optimization problem. In this setting, we prove one can nd an optimal tra c strategy with support on the trajectories of a DiPerna-Lions ow. The proof follows the scheme introduced by Brasco, Carlier and Santambrogio in the autonomous setting, applied to the case of supercritical Sobolev dependence in the spatial variable. This requires bot

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Gerencsér, Máté. "Stochastic PDEs with extremal properties." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20445.

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We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of regularity of the coeffcients, the minimal assumption is boundedness and measurability, and a unique L2- valued solution is then readily available. We investigate its further properties, such as higher order integrability, boundedness, and continuity. The other class of equations considered here are the ones whose leading operators do not satisfy the strong coercivity condition, but

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Grundling, Hendrik. "Algebraic structure of degenerate systems /." Title page, table of contents and summary only, 1986. http://web4.library.adelaide.edu.au/theses/09PH/09phg888.pdf.

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Moss, Jonathan. "Linear degeneracy in multidimensions." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20171.

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Linear degeneracy of a PDE is a concept that is related to a number of interesting geometric constructions. We first take a quadratic line complex, which is a three parameter family of lines in projective space P3 specified by a single quadratic relation in the Plucker coordinates. This complex supplies us with a conformal structure in P3. With this conformal structure, we associate a three-dimensional second order quasilinear wave equation. We show that any PDE arising in this way is linearly degenerate, furthermore, any linearly degenerate PDE can be obtained by this construction. We classif

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Branco, Meireles Joao. "Singular Perturbations and Ergodic Problems for degenerate parabolic Bellman PDEs in R^m with Unbounded Data." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424194.

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In this thesis we treat the first singular perturbation problem of a stochastic model with unbounded and controlled fast variables with success. Our methods are based on the theory of viscosity solutions, homogenisation of fully nonlinear PDEs and a careful analysis of the associated ergodic stochastic control problem in the whole space R^m. The text is divided in two parts. In the first chapter, we investigate the existence and uniqueness as well as a suitable stability of the solution to the associated ergodic problem that are crucial to characterize the effective Hamiltonian of the lim

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Peillon, Etienne. "Simulation and analysis of sign-changing Maxwell’s equations in cold plasma." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAE004.

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De nos jours, les plasmas sont principalement utilisés à des fins industrielles. L'un des exemples les plus fréquemment cités d'utilisation industrielle est la production d'énergie électrique via des réacteurs nucléaires à fusion. Pour contenir le plasma correctement à l'intérieur du réacteur, un champ magnétique est imposé en arrière-plan, et la densité et la température du plasma doivent être précisément contrôlées. Cela est effectué en envoyant des ondes électromagnétiques à des fréquences et dans des directions spécifiques en fonction des caractéristiques du plasma.La première partie de ce

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Ikeda, Katsumoto. "Magnetothermoelectric properties of the degenerate semiconductor Hg1-xFexSe." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ53000.pdf.

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Maizurna, Isna. "Semigroup methods for degenerate cauchy problems and stochastic evolution equations /." Title page, abstract and contents only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09phm2328.pdf.

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Zhan, Yi. "Viscosity solutions of nonlinear degenerate parabolic equations and several applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49931.pdf.

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Hiller, Christine Louise. "'Daddy's girls', 'degenerate daughters', tracing interconnected violences within women's 'survivor' narratives." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/MQ40649.pdf.

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Books on the topic "Degenerate PDE"

1

The method of intrinsic scaling: A systematic approach to regularity for degenerate and singular PDEs. Springer, 2008.

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Urbano, José Miguel. The Method of Intrinsic Scaling: A Systematic Approach to Regularity for Degenerate and Singular PDEs (Lecture Notes in Mathematics Book 1930). Springer, 2008.

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Alexandrowicz, C. H. The Partition of Africa by Treaty (1974). Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780198766070.003.0020.

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This chapter analyses the partition of the African continent via treaties. It begins with an introductory examination of pre-nineteenth-century European–African treaty-making and references some classic writers to Africa. It then discusses relevant documents on the ‘scramble’ for titles to African territory. These demonstrate the extent to which normal institutions of the law of nations as originally applied to European–African relations degenerated into instruments of colonial penetration in the second half of the nineteenth century, particularly after the Berlin Conference of 1884–85, which

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Shahane, Shantanu. Osteoarthritis of the elbow joint. Oxford University Press, 2011. http://dx.doi.org/10.1093/med/9780199550647.003.005.005.

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♦ Symptomatic, primary osteoarthritis of the elbow usually occurs in young men involved in heavy manual labour.♦ Common causes of secondary osteoarthritis of the elbow are trauma, infection, bleeding disorders and neuropathic conditions.♦ Clinically, the commonest presenting symptom is loss of motion. Patients can also complain of pain, locking and ulnar nerve symptoms.♦ Plain X-rays are usually sufficient for diagnosis. They show reduction in joint space and osteophytes at the tip of olecranon and coronoid processes. Loose bodies are also frequently seen.♦ Symptoms in early stages of arthriti

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Flower, Oliver, and Matthew Mac Partlin. Pathophysiology, causes, and management of non-traumatic spinal injury. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0242.

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Non-traumatic spinal cord injury (NTSCI) is at least as common as traumatic spinal cord injury (TSCI). It affects both sexes equally and an older population than TSCI. It is a devastating condition with immense functional implications for the individuals involved. There is a wide spectrum of aetiologies with varying pathophysiology and knowledge of these is important to avoid delay in diagnosis and time-critical treatment. The most common causes described in case series in developed countries are degenerative disc disease, canal stenosis, tumours, vascular diseases and inflammatory conditions.

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Baglietto-Vargas, David, Rahasson R. Ager, Rodrigo Medeiros, and Frank M. LaFerla. Animal Models of Neurodegenerative Diseases. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780190233563.003.0014.

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The incidence and prevalence of neurodegenerative disorders (e.g., Alzheimer’s disease (AD), Parkinson’s disease (PD), and Huntington’s disease (HD), etc.) are growing rapidly due to increasing life expectancy. Researchers over the past two decades have focused their efforts on the development of animal models to dissect the molecular mechanisms underlying neurodegenerative disorders. Existing models, however, do not fully replicate the symptomatic and pathological features of human diseases. This chapter focuses on animal models of AD, as this disorder is the most prevalent of the brain degen

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Book chapters on the topic "Degenerate PDE"

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Rabinowitz, Paul H. "Multibump Solutions of a Semilinear Elliptic PDE on Rn." In Degenerate Diffusions. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_12.

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Efendiev, Messoud. "ODE-PDE coupling arising in the modelling of a forest ecosystem." In Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/11.

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Efendiev, Messoud. "On a class of PDEs with degenerate diffusion and chemotaxis: Autonomous case." In Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/09.

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Efendiev, Messoud. "On a class of PDEs with degenerate diffusion and chemotaxis: Nonautonomous case." In Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/192/10.

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Teixeira, Eduardo V., and José Miguel Urbano. "Geometric Tangential Analysis and Sharp Regularity for Degenerate pdes." In Harnack Inequalities and Nonlinear Operators. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73778-8_9.

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Düzgün, Fatma Gamze, Sunra Mosconi, and Vincenzo Vespri. "Harnack and Pointwise Estimates for Degenerate or Singular Parabolic Equations." In Contemporary Research in Elliptic PDEs and Related Topics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18921-1_8.

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Andreianov, Boris. "Time Compactness Tools for Discretized Evolution Equations and Applications to Degenerate Parabolic PDEs." In Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_3.

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Veske, A., U. Orth, K. Rüther, et al. "Mutations in the Gene for the B-Subunit of Rod Photoreceptor Cgmp-Specific Phosphodiesterase (PDEB) in Patients with Retinal Dystrophies and Dysfunctions." In Degenerative Diseases of the Retina. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1897-6_35.

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Nussbaum, M., I. Reider, and A. D. Korczyn. "Vascular Dementia (VD) and Primary Degenerative Dementia (PDD): Criteria for Differential Diagnosis." In Basic, Clinical, and Therapeutic Aspects of Alzheimer’s and Parkinson’s Diseases. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-5847-3_28.

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Efendiev, Messoud, and Anna Zhigun. "On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension." In Recent Trends in Dynamical Systems. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0451-6_9.

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Conference papers on the topic "Degenerate PDE"

1

Ogawa, Takayoshi. "Decay and asymptotic behavior of solutions of the Keller–Segel system of degenerate and nondegenerate type." In Self-Similar Solutions of Nonlinear PDE. Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc74-0-10.

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Pollmann, René, Franz Roeder, Victor Quiring, et al. "Integrated bright broadband PDC source for quantum metrology." In Frontiers in Optics. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/fio.2022.jw5a.57.

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We demonstrate a broadband quantum light source employing non-degenerate type II parametric down conversion in a 40 mm long periodically poled LiNbO3 waveguide, pumped with a narrowband CW laser. Therefore maximising time frequency entanglement while maintaining high brightness.

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Fotsing, Yannick Kengne, and Xiaobo Tan. "Bias-Dependent Impedance Model for Ionic Polymer-Metal Composite Actuators." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-5011.

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Ionic polymer-metal composites (IPMCs) are a novel class of soft sensing and actuation materials with promising applications in robotic and biomedical systems. In this paper we present a model for nonlinear electrical dynamics of IPMC actuators, by applying perturbation analysis on the dynamics-governing partial differential equation (PDE) around a given bias voltage. By approximating the steady-state electric field under the bias with a piecewise linear function, we derive a linear PDE for the perturbed charge dynamics, which has piecewise constant coefficients and coefficients linear in the

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Shimizu, Shimpei, Takushi Kazama, Takeshi Umeki, et al. "PPLN-Based Polarization-Diverse Phase-Sensitive Amplification of 96-Gbaud PDM-PCS-64QAM Signal with Carrier-Phase-Locked Phase-Conjugated Twin Waves." In Optical Fiber Communication Conference. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/ofc.2024.th1f.3.

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We demonstrated non-degenerate phase-sensitive amplification (PSA) of a 96-Gbaud PDM-PCS-64QAM signal. Phase-conjugated twin waves (PCTWs) with a polarization-independent carrier phase provided low-noise PSA of a 2.5-dB black-box noise figure without polarization tracking of the PCTWs.

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Serkland, D. K., M. M. Fejer, R. L. Byer, and Y. Yamamoto. "Squeezed Vacuum Generation using a Quasiphasematched LiNbO3 Waveguide Parametric Amplifier." In Nonlinear Guided Waves and Their Applications. Optica Publishing Group, 1995. http://dx.doi.org/10.1364/nlgw.1995.pd6.

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We have measured phase-sensitive amplification and quadrature squeezing using a quasiphasematched LiNbO3 waveguide degenerate parametric amplifier. We observed a 14% reduction in the noise in one quadrature, compared to the vacuum state, which is in quantitative agreement with our phase-sensitive amplification measurements.

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Russell, P. St J. "Nonlinear holography for wave-front conversion, frequency doubling, and parametric amplification." In Integrated Photonics Research. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/ipr.1990.wc5.

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When beams at frequencies ω0 and 2ω0 are mixed in a medium with third-order nonlinearity χ(3) a pattern of dc polarization fringes Pdc(3) results whose grating vector is K = kso − 2kpo, where kpo(r) and kso(r) are the wave vectors at ω0 and ω0. In germanosilicate optical fibers, Pdc(3) breaks the centrosymmetry of the amorphous core material (possibly by color-center alignment), creating a periodically modulated χ(2) = χ m (2)cos(K · r). This χ(2) structure automatically phase matches the fundamental light to its second harmonic (SH).1,2 Because the wave fronts of the participating beams do no

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Flom, Steven R., J. R. Lindle, R. G. S. Pong, F. J. Bartoli, and Z. H. Kafafi. "Fluence Dependent Dynamics Observed in the Resonant Third-Order Optical Response of C60 and C70 Films." In Nonlinear Optics. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.pd7.

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The fullerenes, C60 and C70, are molecules whose properties have been receiving increasing attention. Their high degree of symmetry and their three dimensional π—electron systems make them intriguing candidates for their potential nonlinear optical (NLO) properties. In order to investigate the resonant third—order optical response we have performed time resolved degenerate four—wave mixing (DFWM) experiments on films of pure C60 and pure C70 at 597 and 675 nm using an amplified ps laser system. The films were made by vapor deposition and characterized by FTIR and UV—Visible absorption spectros

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Medrano, C., M. Ingold, and P. Günter. "Self Pumped Phase Conjugation and Optical Light Oscillation in Fe Doped KNbO3." In Photorefractive Materials, Effects, and Devices II. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/pmed.1990.pd7.

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In recent years, self-pumped phase conjugation and self-induced photorefractive light oscillation have been reported, using different photorefractive materials. The main photorefractive materials used in these experiments are BaTiO3 and Bi12SiO20. In ferroelectric BaTiO3 the high electro-optic coefficients give rise to large reflectivities. In photoconductive and paraelectric Bi12SiO20 phase shifting techniques lead to enhanced self-diffracted intensities and phase conjugate reflectivities. KNbO3 is such a material which in addition to its high photorefractive sensitivity3 and large beam coupl

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Cook, Daniel J., Matthew S. Yeager, and Boyle C. Cheng. "Facet Translation Analysis in the Lumbar Spine: An Application in Posterior Dynamic Stabilization." In ASME 2012 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/sbc2012-80319.

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Facet articulation in the human lumbar spine has not been thoroughly characterized with regard to the effects of degeneration or surgical intervention. Kozanek et al. investigated the translation and rotation of the facets in 11 healthy adult subjects during maximal voluntary bending [1]. Li et al. used the same measurement technique on a cohort of 10 patients with degenerative disc disease (DDD) and found some significant differences in facet motion compared to a cohort of healthy patients [2]. Jegapragasan et al. investigated facet translations in intact lumbar spines in vitro and found the

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Reports on the topic "Degenerate PDE"

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Wang, Xiao, Hong Shen, Yujie Liang, Yixin Wang, Meiqi Zhang, and Hongtao Ma. Effectiveness of Tango Intervention on Motor Symptoms in Patients with Parkinson's Disease: A Protocol for Systematic Review and Meta-Analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, 2022. http://dx.doi.org/10.37766/inplasy2022.5.0009.

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Review question / Objective: Parkinson's disease (PD) is a degenerative neurological disease caused by the loss of dopaminergic neurons in the pars compacta of the substantia nigra of the brain, resulting in lesions in the basal ganglia. The main motor symptoms of PD include resting tremor, rigidity, akinesia or bradykinesia and postural instability. As an exercise intervention based on musical accompaniment, tango dance has shown positive effects on the rehabilitation of motor symptoms in PD patients in recently. In this study, we systematically reviewed the efficacy of tango intervention in

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Ni, Jiachun, Qiong Jiang, Gang Mao, et al. The effectiveness and safety of acupuncture for constipation associated with Parkinson’s disease: Protocol for a systematic review and meta-analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, 2022. http://dx.doi.org/10.37766/inplasy2022.2.0091.

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Review question / Objective: Is acupuncture a safe and effective therapy for constipation associated with Parkinson’s disease? Our aim is to assess the effectiveness and safety of acupuncture for constipation associated with PD and give guidance to future research direction. Condition being studied: Parkinson’s disease (PD) is a prevalent degenerative disease of nervous system characterized mainly by static tremor, bradykinesia, myotonia, postural gait disorders and other non-motor symptoms. According to variations on race, ethnicity, age and sex, the incidence of PD ranges from 8 to 20.5 per

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Eyal, Yoram, and Sheila McCormick. Molecular Mechanisms of Pollen-Pistil Interactions in Interspecific Crossing Barriers in the Tomato Family. United States Department of Agriculture, 2000. http://dx.doi.org/10.32747/2000.7573076.bard.

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During the evolutionary process of speciation in plants, naturally occurring barriers to reproduction have developed that affect the transfer of genes within and between related species. These barriers can occur at several different levels beginning with pollination-barriers and ending with hybrid-breakdown. The interaction between pollen and pistils presents one of the major barriers to intra- and inter-specific crosses and is the focus of this research project. Our long-term goal in this research proposal was defined to resolve questions on recognition and communication during pollen-pistil

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