There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This research is part of an effort that the ICT (Institute of Tropical Cultivation) has been doing for several years tending to develop superior genotypes of cocoa (Theobroma cacao L.). That is why this study aims to find tolerant or moderately tolerant cocoa genotypes and accessions to water stress with resistance to pests and diseases and high production and industrial quality. Twenty genotypes of cocoa seedlings were investigated, during the period of 6 months, in a soil with sandy-loam texture under nursery conditions, of controlled irrigation. A split plot design was used, with 40 treatments and 3 repetitions. In addition, daily data of the micro climatic characteristics (T °, HR) were taken, in which different indicators of variable were evaluated such as the stomatal conductance (CE) that is greatly influenced by the T ° and HR. The results obtained indicate that the genotypes that showed moderate tolerance to water stress were UNG - 77, UNG - 53, ICT - 1281 and ICT - 1112; the non-tolerant ones were PAS - 93, CEPEC - 2002, ICT - 2142, ICT - 1092, CP - 2005 - C10, TSH - 1188, CCN - 51, IMC - 67, PH - 17, AYP - 15, ICS - 6, BN - 34, ICT - 1506, PAS - 91, PH - 990 and ICS - 1. Under optimal conditions, the most outstanding genotype was ICS-1, both in plant height, number of leaves, and stomatal conductance, this being proof that this genotype develops excellently and stands out if it has the right conditions and water availability.

Stomatal conductance and photosynthesis

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

We present a theoretical model which is used to explain the intersegmental coordination of the neural networks responsible for generating locomotion in the isolated spinal cord of lamprey.

The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model.

1 Lindstedt's Method.- 2 Center Manifolds.- 3 Normal Forms.- 4 Two Variable Expansion Method.- 5 Averaging.- 6 Lie Transforms.- 7 Liapunov-Schmidt Reduction.- Appendix Introduction to MACSYMA.- References.

Perturbation Methods, Bifurcation Theory and Computer Algebra

This manuscript is among the initial offerings being published as part of a new approach to scholarly publishing. The manuscript is freely available from the The online version of this work is available on an open access basis, without fees or restrictions on personal use. A professionally printed and bound version may be purchased through Cornell Business Services by contacting: All mass reproduction, even for educational or not-for-profit use, requires permission and license. For more information, please contact dcaps@cornell.edu. We will provide a downloadable version of this document from the Internet-First

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Lecture Notes on Nonlinear Vibrations

https://hal.archives-ouvertes.fr/hal-01510818/document

Modal analysis of a cracked beam

We study a pair of weakly coupled van der Pol oscillators and investigate the bifurcations of phase-locked periodic motions which occur as the coupling coefficients are varied. Perturbation methods are used and their relation to the topological structure of solutions in the four dimensional phase space is discussed. While the problem is formulated for general linear coupling, the case of detuning plus diffusive coupling via displacement and velocity is discussed in more detail. It is shown that up to four phase-locked periodic motions can exist in this case.

Richard H. Rand

Papers

The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model.

Perturbation Methods, Bifurcation Theory and Computer Algebra

Lecture Notes on Nonlinear Vibrations

Modal analysis of a cracked beam

Bifurcation of periodic motions in two weakly coupled van der Pol oscillators