The aim of this work is to propose a numerical method for solving different types of partial and ordinary differential equations. The equations share the same common property for their solutions to become infinite (blow up behaviour) or to become null (extinction behaviour) in finite time. This type of equations is solved using a sliced time computing technique, combined with rescaling both the variable time and the solution of the differential system. The main criterion under which the slice of time is defined, consists in imposing that the rescaled solution should not be greater than a preset cut off value. Another selection criterion for the method is based on the invariance and similarity conditions, enforced on the rescaled model in each of the time slices
Följande studie är utförd på uppdrag av företaget Nilar som tillverkar Nickel-Metallhydridbatterier (NiMH-batterier) vid sin produktionanläggning i Gävle. Den nuvarande beräkningen av State of Charge (SoC) sker på deras Battery Management Unit (BMU) och är implementerad i Structured Text i exekveringsmiljön CODESYS. Nilar vill flytta SoC-beräkningen från BMU:n så att den kan exekveras på en Interface Control Unit (ICU). Motiveringen till detta är för att distribuera SoC-beräkningen då ett flertal ICU:er finns tillgängliga per Battery Management System (BMS) men även för att i framtiden helt byta ut CODESY. Syftet med denna studie är att migrera implementationen av SoC-algoritmen till programmeringsspråket C så att algoritmen senare kan exekveras på ICU:n. Därefter optimeras algoritmen för att sänka exekveringstiden. Studien utforskar kodstrukturella och funktionella skillnader mellan implementationerna samt metoder för att optimera SoC-algoritmen. Migreringen av algoritmen fullföljdes utan större inverkan på noggrannheten. Algoritmen optimerades genom att skapa en variant av en LU-faktorisering som var specifikt anpassad för det aktuella problemet. Optimeringen av algoritmen resulterade i en minskning på 25% av den totala exekveringstiden för algoritmen. De nya implementationerna tar markant längre tid att exekvera då batteriet befinner sig under laddning jämfört när det befinner sig under urladdning, någonting som inte kan noteras för den gamla implementationen.
Syftet med denna studie var undersöka hur innovativa lösningar inom offentlig upphandling gällande äldre med biståndsbeslut påverkar välmående och ekonomiskt resultat. Många beslut gällande mänskliga resurser tas utan några ekonomiska underlag. Detta gör att åtgärder för att nå förbättring inom detta endast räknas som ekonomiska kostnader istället för investeringar då eventuella positiva effekter på lönsamhet inte beräknas. För att kunna förutse lönsamheten av åtgärder gällande mänskliga resurser finns det ett behov av att kunna mäta ekonomisk påverkan från dessa och då få en bild av totala kostnader för åtgärden. I Söderhamns kommun har matförsörjningen till hemmaboende äldre i Trönö/Norrala överlåtits till ett privat företag. För att mäta effekten av detta samlades empirisk data från kommunen gällande kostnader och de äldres näringsstatus. Intervjuer och egna beräkningar har även utförts för att uppskatta kostnader som kommunen inte har med i sina kostnadsberäkningar. Resultatet av denna studie visade en trend mot ökat välmående hos de äldre, vilket kan innebära en kostnadsreduktion i medicinska kostnader i framtiden. Det tillsammans med ökade skatteintäkter på grund av att Tempo utökat sin personal innebär en lägre totalkostnad för det nya systemet jämfört med tidigare beräkningar av kommunen. För att få en mer precis kostnadsbild krävs det fler och mer omfattande beräkningar. Denna studie är dock ett steg på vägen i hur denna typ av åtgärder kan mätas ekonomiskt.
A new method of signal processing by smart antennas is proposed and justified. It allows to improve the accuracy of angle measurement and to restore the image of the object with superresolution. The method is based on the extrapolation of the signals received by each element of the antenna array, outside the aperture. This allows introducing new virtual elements and thus synthesizing significantly larger antenna array. The method is tested in numerical experiments using a mathematical model and the maximum effective angular resolution is found for different cases and objects. Algorithms based on the method of digital aperture synthesis provide angular superresolution 3-7 times greater than that according to the Rayleigh criterion for a signal/noise ratio of 12-13 dB.
The results of theoretical studies and mathematical modeling indicate the possibility of obtaining the angular superresolution and its limits by using algebraic methods of imaging. The necessary algorithms are created on the basis of solution to inverse problems. The limiting levels of the achieved angular superresolution are found depending on the signal‐to‐noise ratio for objects of various types. A number of specific advantages of the method are shown as applied to the solution of two‐dimensional problems. Capabilities of the method are illustrated by examples. High performance of the proposed approach allows one to use it in real time when scanning and tracking targets.
Rogue waves are unexpectedly high waves of 2.5X the significant wave height and which occur in nearly all phases of nature, from oceans, to fiber-optic cables and atmospheric air-masses. In the ocean, rogue waves pose a significant danger to shipping and fishing vessels and have been found to reach 27.8 meters in height, and attain velocities of up to 100 km/hr. Mechanisms on naval structures for the real-time prediction of rogue waves are currently non-existent, and their development requires a) a good equation for simulating rogue waves and b) a deep study of the wave-trains of rogue waves. In this work, we consider the time-series of four rogue wave trains collected from various sources, including the U.S. Coastal Data Information Program. The method of study encompasses the development piece-wise constant functions from the rogue wave readings by laser/buoys. We use these piece-wise constant functions to form regularized functions as Fourier series, which we consider as weak solutions to the stationary nonlinear Schrödinger equation. The resulting force functions are quantified and compared to physical data of the rogue wave trains. The results show that we obtain a good correlation between the norms of the obtained force functions and the rogue wave height $H_{max}$ and the wave-velocity. The methods developed in the study build a potentially useful foundation for the development of a prediction model in a future study.
In this paper, we present a new approach to simulate time-dependent initial value differential equations which solutions have a common property of blowing-up in a finite time. For that purpose, we introduce the concept of “sliced-time computations”, whereby, a sequence of time intervals (slices) {[Tn − 1, Tn]| n ≥ 1} is defined on the basis of a change of variables (re-scaling), allowing the generation of computational models that share symbolically or numerically “similarity” criteria. One of these properties is to impose that the re-scaled solution computed on each slice do not exceed a well-defined cut-off value (or threshold) S. In this work we provide fundamental elements of the method, illustrated on a scalar ordinary differential equation y′ = f(y) where f(y) verifies $\int_0^\infty {f(y)dy} < \infty$. Numerical results on various ordinary and partial differential equations are available in [7], some of which will be presented in this paper.
The classical Quadratic Programming (QP) formulation of the well-known portfolio selection problem has traditionally been regarded as cumbersome and time consuming. This paper formulates two additional models, (i) maximin, and (ii) minimization of mean absolute deviation. Data from 67 securities over 48 months are used to examine to what extent all three formulations provide similar portfolios. As expected, the maximin formulation yields the highest return and risk, while the QP formulation provides the lowest risk and return, which also creates the efficient frontier. The minimization of mean absolute deviation is close to the QP formulation. When the expected returns are confronted with the true ones at the end of a six months period, the maximin portfolios seem to be the most robust of all.
Problems of electromagnetic wave scattering on 3D dielectric structures in the presence of bounded perfectly conducting surfaces are reduced to a system of singular integral equations. We study this system mathematically and suggest a numerical solution method.
Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of the 3D singular integral equations of electromagnetism by the Galerkin method and the collocation method.
An inverse problem of reconstructing real permittivity of a plane‐parallel layer in a perfectly conducting rectangular waveguide or in free space from experimental data using an explicit expression for the scattering matrix is considered. In general, this problem is improperly posed and may be unsolvable due to inaccuracy of the experimental data, and for a perfect noiseless experiment the solution may be not unique because the scattering coefficients curve has self‐intersection points. It is shown that the traditional multi‐frequency method of measurements applied in vector network analyzers can be justified. The following facts are rigorously proved in the paper: nonuniqueness of the solution can be removed if the frequency resolution is sufficiently small; and an algorithm for processing measurement results using least squares provides an approximate solution to the problem that converges to the exact one when the quality of the experiment improves, the convergence rate depends on the number of frequencies used in the experiment.
Existence of resonance frequencies (RFs) is validated for open metal–dielectric scatterers formed by a homogeneous dielectric cylinder of arbitrary cross-section partially covered by a perfectly conducting strip. The approach involves application of the spectral theory of integral operator-valued functions and semi-regularization and leads to the approximate RF determination.
Existence of symmetric complex waves in a dielectric rod (DR) - a dielectric waveguide of circular cross section - is proved by analyzing functional properties of the dispersion equations (DEs) using the theory of functions of several complex variables and validating the existence of complex roots of DE. A closed-form iteration procedure for calculating the roots in the complex domain supplied with efficient choice of initial approximation is proposed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.
The use of UWB radars makes it possible to detect, recognize, and carry out measurements of coordinate and velocities of hardly noticeable radar targets. The variational problems of searching for the maximum range of UWB-radar operation using optimization of the shape and duration of UWB-pulses are justified and solved.
This work is devoted to the analysis of inverse problems of permittivity reconstruction of diaphragms loaded in a rectangular waveguide including justification of the solution to a benchmark inverse problem of reconstructing permittivity of a one-sectional diaphragm. We perform comparison of theoretical and numerical results based on the measurement data to validate the efficiency of the proposed technique. The obtained solutions can be implemented in practical measurements for investigation of new artificial materials and media and can be applied in optics, nanotechnology, and design of microwave devices.
In this work, we study TE-polarized electromagnetic waves propagating in an inhomogeneous dielectric waveguide of circular cross section filled with a medium; the nonlinearity is simulated by Kerr’s law. For the numerical solution of the problem, an iterative algorithm is proposed, and its convergence is proved.
Consider a perfectly electrically conducting waveguide of constant cross-section ∂D and axis aligned with the z-axis. Any time-harmonic propagating mode has the form u(x,y)e -iωt-iyz where the function u satisfies the two-dimensional Helmholtz equation (Δ + λ)u = 0, with k denoting the wavenumber and λ = k 2 - γ 2 . Propagating modes occur at values λ 1 ≤ λ 2 ≤ λ 3 … of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. If the waveguide is perturbed by the insertion of axially aligned PEC structures, of cross-section Γ, the propagation constants are perturbed to values λ 1 + Δλ 1 , λ 2 +Δλ 2 ,…, with corresponding perturbations to the cutoff wavenumbers of the empty waveguide.
The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguides filled with inhomogeneous medium is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are found with a projection method. The comparison with known exact solutions (for particular values of parameters) is made.
The propagation of monochromatic electromagnetic TE waves in the Goubau line (conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is considered. Two types of nonlinearity are studied. A physical problem is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation. Eigenvalues of the problem correspond to propagation constants of the waveguide. A method is proposed for finding approximate eigenvalues of the nonlinear problem based on solving an auxiliary Cauchy problem (by the shooting method). The existence of eigenvalues that correspond to a new propagation regime is predicted. A comparison with the linear case is given.
Least-squares collocation (LSC) is a widely used method applied in physical geodesy to separate observations into a signal and noise part but has received only little attention when interpolating velocity fields. The advantage of the LSC is the possibility to filter and interpolate as well as extrapolate the observations. Here, we will present several extensions to the traditional LSC technique, which allows the combined interpolation of both horizontal velocity components (horizontal velocity (HV)-LSC), the separation of velocity observations on different tectonic plates, and the removal of stationarity by moving variance (the latter as HV-LSC-ex(tended)22). Furthermore, the covariance analysis, which is required to find necessary input parameters for the LSC, is extended by finding a suitable variance and correlation length using both horizontal velocity components at the same time. The traditional LSC and all extensions are tested on a synthetic dataset to find the signal at known as well as newly defined points, with stations separated on four different plates with distinct plate velocities. The methodologies are evaluated by calculation of a misfit to the input data, and implementation of a leave-one-out cross-validation and a Jackknife resampling. The largest improvement in terms of reduced misfit and stability of the interpolation can be obtained when plate boundaries are considered. In addition, any small-scale changes can be filtered out using the moving-variance approach and a smoother velocity field is obtained. In comparison with interpolation using the Kriging method, the fit is better using the new HV-LSC-ex2 technique.
Det tog tio år för den marockanske matematikern och matematikläraren - och en sån lärare! - Georges Ifrah att fara runt jorden och leta reda på siffror och tal och skriva den Räknekonstens kulturhistoria i två delar som nu även finns på svenska. (Del 1 anmäld i GD 9 september förra året.)
Owing to the recent research a method of estimating transmission coefficients for a waveguide of rectangular cross-section loaded with multi-layered parallel-plane dielectrics is found. Consequently, the analysis of the transmitted and reflected fields in terms of the scattering matrix formalism can be performed explicitly. This article is mainly based on comparisons between real measured and computed transmission coefficients of a waveguide filter. the computation employs analysis of closed-form solutions and numerical multi-parameter optimization. the presented waveguide filter is formed by multi-sectional diaphragms placed in a waveguide of rectangular cross-section. Comparison of the computed and measured transmission coefficients demonstrates that the difference is very low, rather marginal and thus the output of the work is considerably promising.