Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Implementation aspects of interactive multiobjective optimization for modeling environments: The case of GAMS-NIMBUS
2014
Abstract. Interactive multiobjective optimization methods have provided promising results in the literature but still their implementations are rare. Here we introduce a core structure of interactive methods to enable their convenient implementation. We also demonstrate how this core structure can be applied when implementing an interactive method using a modeling environment. Many modeling environments contain tools for single objective optimization but not for interactive multiobjective optimization. Furthermore, as a concrete example, we present GAMS-NIMBUS Tool which is an implementation of the classification-based NIMBUS method for the GAMS modeling environment. So far, interactive met…
Deducing the USLE mathematical structure by dimensional analysis and self-similarity theory
2010
The Universal Soil Loss Equation (USLE) was originally deduced by a statistical analysis of a large data set of soil loss measurements. The multiplicative structure of the model has been criticised due to the considerable interdependence between the variables. Using the soil erosion representative variables and the reference condition adopted in the USLE, the aim of this paper was to apply dimensional analysis and self-similarity theory to deduce the functional relationship among the selected variables. The analysis yielded a multiplicative equation, similar to the USLE. Therefore, this study suggested that the USLE has a logical structure with respect to the variables used to simulate the …
Special interpretation of formal measurement scales for the case of multiple heterogeneous properties
2001
A formal model of measurement is constructed and its components are outlined in this paper. An integrated hierarchical formal four-level structure which allows description of the multiple heterogeneous properties of a complex object under measurement is developed in order to have a uniform tool for the selection of specific scales for the measurement of these properties. A special treatment of a measurement scale defined on the space of the object states is offered, and corresponding structures of basic types of scales are explained permitting to take into consideration distances between relations on these states. Our approach can serve as the uniform formalised basis for development of mea…
Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions
2019
Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.
Filament sets and homogeneous continua
2007
Abstract New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament , non-filament , and ample , with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.
Annihilation Operators for Exponential Spaces in Subdivision
2022
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
On new means with interesting practical applications: Generalized power means
2021
Means of positive numbers appear in many applications and have been a traditional matter of study. In this work, we focus on defining a new mean of two positive values with some properties which are essential in applications, ranging from subdivision and multiresolution schemes to the numerical solution of conservation laws. In particular, three main properties are crucial—in essence, the ideas of these properties are roughly the following: to stay close to the minimum of the two values when the two arguments are far away from each other, to be quite similar to the arithmetic mean of the two values when they are similar and to satisfy a Lipchitz condition. We present new means with these pr…
Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators
1985
Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
ANALYSIS OF SUNSPOT NUMBER FLUCTUATIONS
2004
Monthly averages of the sunspot number visible on the sun, observed from 1749, Zurich Observatory, and from 1848 other observatories, have been analyzed. This time signal presents a frequency power spectra with a clear 1/fα behavior with α≃0.8±0.2. The well-known cycle of approximately 11 years, clearly present in the spectrum, does not produce a sensible distortion of that behavior. The eventual characterization of the sunspot time series as a fractal is analyzed by means of the detrended fluctuation analysis (DFA). The jump-size distribution of the signal is also studied.