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Mathematical Theory (mathematical + theory)
Selected AbstractsEffect of genetic variance in plant quality on the population dynamics of a herbivorous insectJOURNAL OF ANIMAL ECOLOGY, Issue 4 2009Nora Underwood Summary 1Species diversity can affect many ecological processes; much less is known about the importance of population genetic diversity, particularly for the population dynamics of associated species. Genetic diversity within a host species can create habitat diversity; when associated species move among hosts, this variation could affect populations additively (an effect of average habitat) or non-additively (an effect of habitat variance). Mathematical theory suggests that non-additive effects of variance among patches should influence population size, but this theory has not been tested. 2This prediction was tested in the field by asking whether aphid population dynamics parameters on strawberry plant genotype mixtures were additive or non-additive functions of parameters on individual plant genotypes in monoculture using model fitting. 3Results show that variance in quality among plant genotypes can have non-additive effects on aphid populations, and that the form of this effect depends on the particular plant genotypes involved. 4Genetic variation among plants also influenced the spatial distribution of aphids within plant populations, but the number of plant genotypes per population did not affect aphid populations. 5These results suggest that predicting the behaviour of populations in heterogeneous environments can require knowledge of both average habitat quality and variance in quality. [source] The evolutionary psychology of left and right: Costs and benefits of lateralizationDEVELOPMENTAL PSYCHOBIOLOGY, Issue 6 2006Giorgio VallortigaraArticle first published online: 2 AUG 200 Abstract Why do the left and right sides of the vertebrate brain play different functions? Having a lateralized brain, in which each hemisphere carries out different functions, is ubiquitous among vertebrates. The different specialization of the left and right side of the brain may increase brain efficiency,and some evidence for that is reported here. However, lateral biases due to brain lateralization (such as preferences in the use of a limb or, in animals with laterally placed eyes, of a visual hemifield) usually occur at the population level, with most individuals showing similar direction of bias. Individual brain efficiency does not require the alignment of lateralization in the population. Why then are not left- and right-type individuals equally common? Not only humans, but most vertebrates show a similar pattern. For instance, in the paper I report evidence that most toads, chickens, and fish react faster when a predator approaches from the left. I argue that invoking individual brain efficiency (lateralization may increase fitness), evolutionary chance or direct genetic mechanisms cannot explain this widespread pattern. Instead, using concepts from mathematical theory of games, I show that alignment of lateralization at the population level may arise as an "evolutionarily stable strategy" when individually asymmetrical organisms must coordinate their behavior with that of other asymmetrical organisms. Thus, the population structure of lateralization may result from genes specifying the direction of asymmetries which have been selected under "social" pressures. © 2006 Wiley Periodicals, Inc. Dev Psychobiol 48: 418,427, 2006. [source] Assessing environmental risks of transgenic plantsECOLOGY LETTERS, Issue 2 2006D. A. Andow Abstract By the end of the 1980s, a broad consensus had developed that there were potential environmental risks of transgenic plants requiring assessment and that this assessment must be done on a case-by-case basis, taking into account the transgene, recipient organism, intended environment of release, and the frequency and scale of the intended introduction. Since 1990, there have been gradual but substantial changes in the environmental risk assessment process. In this review, we focus on changes in the assessment of risks associated with non-target species and biodiversity, gene flow, and the evolution of resistance. Non-target risk assessment now focuses on risks of transgenic plants to the intended local environment of release. Measurements of gene flow indicate that it occurs at higher rates than believed in the early 1990s, mathematical theory is beginning to clarify expectations of risks associated with gene flow, and management methods are being developed to reduce gene flow and possibly mitigate its effects. Insect pest resistance risks are now managed using a high-dose/refuge or a refuge-only strategy, and the present research focuses on monitoring for resistance and encouraging compliance to requirements. We synthesize previous models for tiering risk assessment and propose a general model for tiering. Future transgenic crops are likely to pose greater challenges for risk assessment, and meeting these challenges will be crucial in developing a scientifically coherent risk assessment framework. Scientific understanding of the factors affecting environmental risk is still nascent, and environmental scientists need to help improve environmental risk assessment. [source] Scaling of geological discontinuity normal load,deformation response using fractal geometryINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2001Michael E. Plesha Abstract The mechanical behaviour of discontinuities in rock, such as joints, is known to be size-dependent. It is also suspected that the behaviour of larger size features, such as faults, is also size-dependent. This size dependence has serious implications for performing numerical response simulations of geological media. In this paper, we develop a new mathematical theory for scaling of one particular discontinuity property, namely the interface normal stiffness. To accomplish this, we idealize an interface to have fractal geometry, and we develop analytical relations which show that the interface normal stiffness, which is commonly thought to be a size-independent property, is in fact a size-dependent property and has fractal characteristics that may be exploited to develop a fundamental theory for scaling. Copyright © 2001 John Wiley & Sons, Ltd. [source] Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right-hand side in Lp (p,1)MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2009Pierre-Étienne Druet Abstract Accurate modelling of heat transfer in high-temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L1. In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and Lp right-hand side, with p,1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the Lp norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley & Sons, Ltd. [source] Elastic,ideally plastic beams and Prandtl,Ishlinskii hysteresis operatorsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2007Pavel Krej Abstract The one-dimensional equation for transversal vibrations of an elastoplastic beam is derived from a general three-dimensional system with a single-yield tensorial von Mises plasticity model. It leads after dimensional reduction to a multiyield scalar Prandtl,Ishlinskii hysteresis model whose weight function is explicitly given. The use of Prandtl,Ishlinskii operators in elastoplasticity is thus not just a questionable phenomenological approach, but in fact quite natural. The resulting partial differential equation with hysteresis is transformed into an equivalent system for which the existence and uniqueness of a strong solution is proved. The proof employs techniques from the mathematical theory of hysteresis operators. Copyright © 2007 John Wiley & Sons, Ltd. [source] Index transforms associated with generalized hypergeometric functionsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2004Semyon B. Yakubovich Abstract We deal with a class of integral transformations whose kernels contain the Clausenian hypergeometric function 3F2(a1,a2,a3;b1,b2;z). These transforms are defined in terms of integrals with respect to their parameters. It involves as particular cases the familiar Olevskii and generalized Mehler,Fock transforms which are key tools in the methods of the mathematical theory of elasticity. The main theorem of boundedness of these operators as a map of L2(,+)L2(,+;x,1 dx) is proved. Some examples of the Olevskii and Mehler,Fock type integrals are given. Copyright © 2003 John Wiley & Sons, Ltd. [source] Wetting of a fiber bundle in fibrous structuresPOLYMER COMPOSITES, Issue 3 2003David Lukas In this paper we dealt with the problem of wetting and ascending of a liquid along a fiber bundle. Two issues are first addressed including the criterion for complete wetting of the fiber bundle and the ascension liquid profile on a partially dipped vertical fiber bundle. Both topics are studied theoretically by deriving a mathematical theory by which predictions are generated and important parametric analyses are carried out. Further, a 3D Ising model is used for computer modeling to simulate the fiber wetting and liquid ascending processes on a partially dipped single fiber. The significance and potential applications of the study are also summarized. [source] Foundations of Mathematics: Metaphysics, Epistemology, StructureTHE PHILOSOPHICAL QUARTERLY, Issue 214 2004Stewart Shapiro Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics. [source] The eastward displacement of a freely falling body on the rotating Earth: Newton and Hooke's debate of 1679ANNALEN DER PHYSIK, Issue 8 2010W. Dittrich Abstract In this article I would like to tell the story of the beginning of modern theoretical physics, freed from all kinds of questionable anecdotes which have entered the scientific literature over the centuries. It all began in the seventeenth century when the mathematical theory of astronomy began to take shape. A major step in the history of modern science was taken when a few members of The Royal Society in London realized that the laws ruling the motions of heavenly bodies as manifested in Kepler's three laws are also effective in the dynamics of Earth-bound particle motion. Everything started, not with I. Newton, but with R. Hooke. Not Newton's falling apple (Voltaire's invention), but a far-reaching response by R. Hooke to a letter by I. Newton, dated November 28, 1679, ignited Newton's interest in gravity. That letter contained the famous spiral which a falling body would follow when released from a certain height above the surface of the Earth. Hooke's answer, based on Keplerian orbits, expressed the opinion that the body's trajectory would rather follow an elliptical path. In his spiral sketch Newton, however, predicted correctly that the falling body would be found to suffer an eastward deviation from the vertical in consequence of the Earth's rotation. In the course of time, many a researcher, including Hooke himself, was able to verify this conjecture. But it took until 1803 for the first satisfactory calculation of the eastward displacement of a freely falling body to be performed, and was provided by C.F. Gauss. [source] ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUEAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009Ian R. Gordon Summary In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, , say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ,, > ,1' or ,, < ,1', where ,1 is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that,, > ,1,is to replace an estimator,,, of , by the maximum of,,and ,1. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality,, > ,1, which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint,, > ,1, strictly exceed ,1 except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which,,is close to ,1, and more generally produces estimators that respect the constraint in a smooth, realistic fashion. [source] Link, twist, energy, and the stability of DNA minicirclesBIOPOLYMERS, Issue 2 2003Kathleen A. Hoffman Abstract We describe how the stability properties of DNA minicircles can be directly read from plots of various biologically intuitive quantities along families of equilibrium configurations. Our conclusions follow from extensions of the mathematical theory of distinguished bifurcation diagrams9, 21 that are applied within the specific context of an elastic rod model of minicircles. Families of equilibria arise as a twisting angle , is varied. This angle is intimately related to the continuously varying linking number Lk for nicked DNA configurations that is defined as the sum of Twist and Writhe. We present several examples of such distinguished bifurcation diagrams involving plots of the energy E, linking number Lk, and a twist moment m3, along families of cyclized equilibria of both intrinsically straight and intrinsically curved DNA fragments. © 2003 Wiley Periodicals, Inc. Biopolymers 70: 145,157, 2003 [source] The Mathematical Contributions of Francesco Maurolico to the Theory of Music of the 16th Century (The Problems of a Manuscript)CENTAURUS, Issue 3 2006Tito M. Tonietti Here, in part I, his main results are presented and also their differences compared with the classical tradition of the mathematical theory of music. These results are a new proof of the number of commas in the tone, the theory of ,ictus', and a new notation for the composition of proportions. This is followed, in part II, by an explanation of how the original corpus of these folios was put together. Finally, part III discusses the complex puzzle of the manuscripts (one still extant, another probably lost, ,) and of their possible connections with the 1575 edition of a part of the corpus. Possible scenarios of the story of the manuscripts and probable interventions of the Jesuits on this edition are described. [source] | ||||||||||||||||