Multiperiod Function Research Articles

A Study of Functions on the Torus and Multi-periodic Functions

In this paper, we are concerned with functions defined on the cube Qm = [−π, π] m and functions defined on the torus T m. Especially, the harmonic analysis of Sobolev-type spaces is carefully studied. We analyze in particular periodic distributions and distributions on the torus. We introduce a space similar to H1 0 , for which we prove a Poincaré-Wirtinger inequality. We prove that the usual Rellich-Kondrachov result does not hold for these last space because of the lack of compactness. A result of absolute continuity and density of regular functions is then established and a theorem of traces is obtained.

Integrating multiperiodic functions along the periodic characteristics of the diagonal differentiation operator

Integrating multiperiodic functions along the periodic characteristics of the diagonal differentiation operator

Parameter identification for multiperiodic functions

In this paper, we first present the idea of multiperiodic extension for a given function. These functions called the multiperiodic or the extended period functions have more than one period or a vector period instead of a scalar number. We present a method to estimate the parameters of these multiperiodic functions using the data collected from their given functions. The results on the parameter estimation, sensitivity functions and generalized sensitivity analysis of the multiperiodic extensions of the functions show that this method is useful for estimating the parameters of a larger model describing a more complex system on the basis of the parameter estimation of the smaller model describing a simpler or a smaller system.

Strong Aharonov-Bohm quantum interference in simply connected LaAlO3/SrTiO3 structures

We report Aharonov-Bohm (AB)-type quantum interference in simply-connected devices created at the LaAlO$_3$/SrTiO$_3$ interface using conductive-atomic force microscope (c-AFM) lithography. The oscillations are multi-periodic functions of magnetic field strength, and they exhibit a substantial magnetic hysteresis with frequencies that depends on the magnetic sweep direction. The oscillation amplitude for the lowest two frequencies approaches $e^2/h$, consistent with the theoretical maximum for the AB effect, and harmonics up to third order are observable. Broadband quasiperiodic behavior is reported in a fraction of simply-connected electron waveguide devices that exhibit magnetic asymmetries. Curiously, nanoscale ring devices that are multiply-connected lack signatures of AB quantum interference. The interference phenomena are associated with an inhomogeneous magnetic landscape within the LaAlO$_3$/SrTiO$_3$ nanostructures.

ARE TIME CONSISTENT VALUATIONS INFORMATION MONOTONE?

Multi-period risk functionals assign a risk value to discrete-time stochastic processes. While convexity and monotonicity extend in straightforward manner from the single-period case, the role of information is more problematic in the multi-period situation. In this paper, we define multi-period functionals in such a way that the development of available information over time (expressed as a filtration) enters explicitly the definition of the functional. This allows to define and study the property of information monotonicity, i.e. monotonicity w.r.t. increasing filtrations. On the other hand, time consistency of valuations is a favorable property and it is well-known that this requirement essentially leads to compositions of conditional mappings. We demonstrate that generally spoken the intersection of time consistent and information monotone valuation functionals is rather sparse, although both classes alone are quite rich. In particular, the paper gives a necessary and sufficient condition for information monotonicity of additive compositions of positively homogeneous risk/acceptability mappings. Within the class of distortion functionals only compositions of expectation or essential infima are information monotone. Furthermore, we give a sufficient condition and examples for compositions of nonhomogeneous mappings exhibiting information monotonicity.

On the Navier–Stokes equations with free convection in three‐dimensional unbounded triangular channels

AbstractThe quaternionic calculus is a powerful tool for treating the Navier–Stokes equations very elegantly and in a compact form, through the evaluation of two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. In this paper, we use special variants of quaternionic‐holomorphic multiperiodic functions in order to obtain explicit formulas for unbounded three‐dimensional parallel plate channels, rectangular block domains and regular triangular channels. Copyright © 2007 John Wiley & Sons, Ltd.

Asymptotic behaviour of multiperiodic functions scaled by Pisot numbers

Let β > 1 be a Pisot number andg be a positive Holder continuous function with period one and g(0) = 1. The multiperiodic functionG(ξ)=Π n=0 ∞ g(ξ/βn) is studied and the asymptotic behaviour ofI G(T) = ∫ 0 T G(ξ)dξ investigated. We prove that the limit of logI(T)/ logT exists asT tends to infinity. We also provide a method to calculate this limit for the caseg(ξ) = cos2 2πξ, corresponding to the Fourier transform of the Bernoulli convolution associated to the golden number (or some of its generalizations).

Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis

AbstractIn this paper, we consider rectangular domains in real Euclidean spaces of dimension at least 2, where the sides can be finite, semi‐infinite, or fully infinite. The Bergman reproducing kernel for the space of monogenic and square integrable functions on such a domain is obtained in closed form as a finite sum of monogenic multiperiodic functions. The reproducing property leads to an estimate of the first derivative of the single‐periodic cotangent function in terms of the classical real‐valued Eisenstein series. Copyright © 2002 John Wiley Sons, Ltd.

INTERACTIVE DESIGN OF SMOOTH GENUS N OBJECTS USING MULTIPERIODIC FUNCTIONS AND APPLICATIONS

A new method for interactive design of infinitely smooth genus n objects using multiperiodic functions is presented. Comparing with the existing geometric design methods, it provides many advantages: simpler data structure, compact data set, and infinite continuity. Moreover, it provides an user interface with interactive control for designing free form genus n objects. This is achieved by incorporating a radial basis scattered data interpolating function with a multiperiodic function of genus n objects over a single domain. As one of applications, the homeomorphic transformation from an unlinked double torus to a linked double torus is visualized. In order to make it control easier, the constrained Delaunay triangulation over the unstructured given data on the single domain is activated. This allows visualization of the polygonized genus n object in object space as well as providing an interactive data control behavior in object space. This method is characterized by the unconstrained control points inside boundaries and by the small-size data set designing a free form genus n object.

Exact two-particle matrix elements in S-matrix preserving deformation of integrable QFTs

In a recent paper it was shown that the response of an integrable QFT under variation of the Unruh temperature can be computed from a S-matrix preserving deformation of the form factor approach. We give explicit expressions for the deformed two-particle form factors for various integrable models: The Sine-Gordon and SU(2) Thirring model, several perturbed minimal CFTs and the real coupling affine Toda series. A uniform pattern is found to emerge when both the S-matrix and the deformed form factors are expressed in terms Barnes' multi-periodic functions.

Self-Similarity in Harmonic Analysis

This is a survey of recent work involving concepts of self-similarity that relate to harmonic analysis. Perhaps the main theme is the question: how does the fractal or self-similar nature of an object express itself on the Fourier transform side? A wide range of related topics are discussed, including self-similar measures and distributions, fractal Plancherel theorems, Lp dimensions and densities of measures, multiperiodic functions and their asymptotic behavior, convolution equations with self-similar measures, self-similar tilings, and the development of self-similar analysis on stratified nilpotent Lie groups.

The Growth of Populations

Previous articleNext article No AccessDecade One: 1926-1935The Growth of PopulationsRaymond Pearl and Lawrence SlobodkinRaymond Pearl Search for more articles by this author and Lawrence Slobodkin Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Quarterly Review of Biology Volume 51197650th Anniversary Special Issue, 1926-1976 Published in association with Stony Brook University Article DOIhttps://doi.org/10.1086/408971 Views: 42Total views on this site Citations: 11Citations are reported from Crossref Copyright 1976 Stony Brook Foundation, Inc.PDF download Crossref reports the following articles citing this article:Gary D. Hachtel, John D. Stack, Jordan A. Hachtel Forecasting and modeling of the COVID-19 pandemic in the USA with a timed intervention model, Scientific Reports 12, no.11 (Mar 2022).https://doi.org/10.1038/s41598-022-07487-8Mohammad Munir, Nasreen Kausar, Mohammad Shakil Parameter identification for multiperiodic functions, Technological Forecasting and Social Change 173 (Dec 2021): 121134.https://doi.org/10.1016/j.techfore.2021.121134Joaquín Mulero-Cerezo, Álvaro Briz-Redón, Ángel Serrano-Aroca Saccharomyces Cerevisiae Var. Boulardii: Valuable Probiotic Starter for Craft Beer Production, Applied Sciences 9, no.1616 (Aug 2019): 3250.https://doi.org/10.3390/app9163250Zachary Dockstader, Chris Bauch, Madhur Anand Interconnections Accelerate Collapse in a Socio-Ecological Metapopulation, Sustainability 11, no.77 (Mar 2019): 1852.https://doi.org/10.3390/su11071852Jerónimo Chirivella-Martorell, Álvaro Briz-Redón, Ángel Serrano-Aroca Modelling of Biomass Concentration, Multi-Wavelength Absorption and Discrimination Method for Seven Important Marine Microalgae Species, Energies 11, no.55 (Apr 2018): 1089.https://doi.org/10.3390/en11051089Thiparat Chotibut, David R. Nelson Evolutionary dynamics with fluctuating population sizes and strong mutualism, Physical Review E 92, no.22 (Aug 2015).https://doi.org/10.1103/PhysRevE.92.022718A. Bejan, S. Lorente, B. S. Yilbas, A. Z. Sahin Why solidification has an S-shaped history, Scientific Reports 3, no.11 (Apr 2013).https://doi.org/10.1038/srep01711E. Cetkin, S. Lorente, A. Bejan The steepest S curve of spreading and collecting flows: Discovering the invading tree, not assuming it, Journal of Applied Physics 111, no.1111 (Jun 2012): 114903.https://doi.org/10.1063/1.4721657Adrian Bejan, Sylvie Lorente The physics of spreading ideas, International Journal of Heat and Mass Transfer 55, no.44 (Jan 2012): 802–807.https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.029A. Bejan, S. Lorente The constructal law origin of the logistics S curve, Journal of Applied Physics 110, no.22 (Jul 2011): 024901.https://doi.org/10.1063/1.3606555S. A. SHEPHERD The epifauna of megaripples: species' adaptations and population responses to disturbance, Austral Ecology 8, no.11 (Mar 1983): 3–8.https://doi.org/10.1111/j.1442-9993.1983.tb01513.x

Multiperiod consumption-investment decisions and risk preference

The decision problem of a consumer who must make regular allocations of wealth to consumption expenditures and to risky investment is considered. Sufficient conditions for the consumer's multiperiod utility function to exhibit both decreasing absolute and increasing relative risk aversion are determined. Essentially, the multiperiod utility function exhibits decreasing absolute risk aversion if each period's utility of consumption exhibits decreasing absolute risk aversion; the multiperiod function exhibits increasing relative risk aversion for large levels of wealth if each period's utility exhibits increasing relative risk aversion and if consumption of wealth is approximately linear.