Search results for "Numbers"

Kompleksi skaitļi. Determinanti. Alģebraiski nolīdzinājumi. Parciāldaļas: lekcijas lasītas Latvijas Universitātes Inženierzinātņu un mechanikas fakul…

1931

“TEACHING REAL NUMBERS IN THE HIGH SCHOOL: AN ONTO-SEMIOTIC APPROACH TO THE INVESTIGATION AND EVALUATION OF THE TEACHERS' DECLARED CHOICES”

The thesis addresses the topics of investigating teachers' declared choices of practices concerning real numbers and the continuum in the high school in Italy, evaluating their didactical suitability and the impact of a deep reflexion about some historical and didactical issues on the teachers' decision-making process. Our research hypothesis was that teachers' choices of teaching sequences concerning real numbers, with particular attention to the representations of real numbers, could be very relevant in order to interpret some of the well-known students' difficulties. After a pilot study in form of a teaching experiment and a literature review concerning students' and teachers' difficulti…

From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters

2017

International audience; We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N −1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N(N +1) in x, y and t depending on 2N−2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.

Hybridization selects for prime‐numbered life cycles in Magicicada: An individual‐based simulation model of a structured periodical cicada population

2020

Abstract We investigate competition between separate periodical cicada populations each possessing different life‐cycle lengths. We build an individual‐based model to simulate the cicada life cycle and allow random migrations to occur between patches inhabited by the different populations. We show that if hybridization between different cycle lengths produces offspring that have an intermediate life‐cycle length, then predation acts disproportionately to select against the hybrid offspring. This happens because they emerge in low densities without the safety‐in‐numbers provided by either parent population. Thus, prime‐numbered life cycles that can better avoid hybridization are favored. How…

Common variants conferring risk of schizophrenia

2009

Schizophrenia is a complex disorder, caused by both genetic and environmental factors and their interactions. Research on pathogenesis has traditionally focused on neurotransmitter systems in the brain, particularly those involving dopamine. Schizophrenia has been considered a separate disease for over a century, but in the absence of clear biological markers, diagnosis has historically been based on signs and symptoms. A fundamental message emerging from genome-wide association studies of copy number variations (CNVs) associated with the disease is that its genetic basis does not necessarily conform to classical nosological disease boundaries. Certain CNVs confer not only high relative ris…

Decay and Fission Hindrance of Two- and Four-QuasiparticleKIsomers inRf254

2015

Two isomers decaying by electromagnetic transitions with half-lives of 4.7(1.1) and 247(73) μs have been discovered in the heavy ^{254}Rf nucleus. The observation of the shorter-lived isomer was made possible by a novel application of a digital data acquisition system. The isomers were interpreted as the K^{π}=8^{-}, ν^{2}(7/2^{+}[624],9/2^{-}[734]) two-quasineutron and the K^{π}=16^{+}, 8^{-}ν^{2}(7/2^{+}[624],9/2^{-}[734])⊗8^{-}π^{2}(7/2^{-}[514],9/2^{+}[624]) four-quasiparticle configurations, respectively. Surprisingly, the lifetime of the two-quasiparticle isomer is more than 4 orders of magnitude shorter than what has been observed for analogous isomers in the lighter N=150 isotones. …

The Vlasov Limit for a System of Particles which Interact with a Wave Field

2008

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.

Self-diffusion coefficients in plastic crystals by multiple-pulse NMR in large static field gradients.

1996

Measurements of self-diffusion coefficients in solids with the gradient spin echo technique have until now been limited due to short spin-spin relaxation times. Here we make use of multiple-pulse sequences, which average out the nuclear dipole interaction, to expand the measurable range for macroscopic self-diffusion coefficients by 2 orders of magnitude. By combining multiple-pulse NMR, in our case using the MREV-8 sequence, with a high static gradient we measured the self-diffusion coefficient in a molecular crystal of camphene down to a value of $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{m}}^{2}{\mathrm{s}}^{\en…

Nucleation kinetics in deionized charged colloidal model systems: A quantitative study by means of classical nucleation theory

2007

We have studied the nucleation kinetics of charged colloidal model systems under salt free conditions crystallizing in bcc structure covering a wide range of particle number densities $18\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}3}\ensuremath{\le}n\ensuremath{\le}66.3\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}{\mathrm{m}}^{\ensuremath{-}3}$. We employed direct video-microscopic observation of individual nucleation events to obtain time resolved nucleation rate densities. Polarization microscopy and static light scattering on the resulting solids in combination with Avrami theory is used to determine the steady state nucleation rate at high unde…

Nuclear charge radii and electromagnetic moments of radioactive scandium isotopes and isomers

2011

International audience; Collinear laser spectroscopy experiments with the Sc + transition 3d4s 3 D 2 → 3d4p 3 F 3 at λ = 363.1 nm were performed on the 42−46 Sc isotopic chain using an ion guide isotope separator with a cooler-buncher. Nuclear magnetic dipole and electric quadrupole moments as well as isotope shifts were determined from the hyperfine structure for five ground states and two isomers. Extensive multi-configurational Dirac-Fock calculations were performed in order to evaluate the specific mass-shift, M SMS, and field-shift, F, parameters which allowed evaluation of the charge radii trend of the Sc isotopic sequence. The charge radii obtained show systematics more like the Ti r…