Functions In Plane Research Articles

Multi-temporal polarimetry in land-cover classification

ABSTRACTThis study uses time-series Sentinel-1(S-1) synthetic aperture radar images to evaluate the impact of multi-temporal polarimetric processing on land-cover classification. Various polarimetric processing methods are applied to multi-temporal S-1 data set in order to obtain several inputs parameters for land-cover classification: e.g. time-series coherence matrices from dual-polarization data (shows coherence among polarizations in matrix for separated time points t1, t2, to tn); scatter zone time series; multi-temporal single and dual-polarization coherence matrices (reveal coherences among time points for one or two polarizations); and parameters from the H/α decomposition. Then, the classification potential of each polarimetric data set is compared to a reference classification, which was derived from time series of dual-polarization backscatter (σ0) images. We evaluate if polarimetric processing of dual-polarization images brings better classification results than alone classification of backscatter image. Finally, we evaluate the impact of segment size and the classifier on classification accuracy.The classification based on polarimetric data sets is consistently better than that of backscatter time series. A maximum overall accuracy of 93.2% was achieved for the classification of four basic land-cover classes (urban, agriculture, forest, and water) using a composite data set made up time series of scatter zone derived from the H/α plane and scatter zone temporal stability maps. This accuracy was 4.5% better compared to our reference classification based on σ0 time series. Similar trends were observed for more detailed land-cover classes. Classification accuracy is heavily influenced by segment size and can drop by about 15% for very small segments. The most suitable classifier proved to be the Support Vector Machine, which performed up to 12% better than the worst one. This study demonstrates the suitability of multi-temporal polarimetry processing for land--cover classification.

On derivatives of planar mappings and their connections to complete mappings

Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well.

Study of solar radiation in the equinoxes and solstices in the City of Havana, Cuba

Solar radiation is of utmost importance for life on earth and for carrying out different human and natural activities, such as the studies carried out for agriculture. The objective of this work is to calculate, from formulations, the incidence of solar radiation. Solar energy will be calculated in Havana City, Cuba, during the equinoxes and solstices, as well as the variation that exists during the different seasons of the year. A study was carried out every 3 hours: 6am, 9am, 12m, 3pm and 6pm, (average solar time) creating a table with real values of this energy, obtaining maps of light and shadow planes.

Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components

We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.

Strict limits of planar BV homeomorphisms

We introduce a new class of planar mappings that allows for cavitations and fractures. The class is the set of strict limits of planar BV homeomorphisms. Each mapping from this class has a proper pointwise representative which is a multifunction, we show that it maps disjoint sets to essentially disjoint sets and that they have an inverse as a proper multifunction. We also characterize and study cavities and fractures of these mappings.

Linear combinations of a class of harmonic univalent mappings

A planar harmonic mapping is a complex-valued function f : U ? C of the form f (x + iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as f = h + g?, where h and g are both analytic; the function ? = g'=h' is called the dilatation of f. We consider the linear combinations of planar harmonic mappings that are the vertical shears of the asymmetrical vertical strip mappings j(z) = 1/2isin?j log (1+zei?j/ 1+ze-i?j) with various dilatations, where ?j ? [?/2,?), j=1,2. We prove sufficient conditions for the linear combination of this class of harmonic univalent mappings to be univalent and convex in the direction of the imaginary axis.

Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Bi-lipschitz property and distortion theorems for planar harmonic mappings with M-linearly connected holomorphic part

Nonlinear dynamic analysis of SWNTs conveying fluid using nonlocal continuum theory

By employing the nonlocal continuum field theory of Eringen and Von Karman nonlinear strains, this paper presents an analytical model for linear and nonlinear dynamics analysis of single-walled carbon nanotubes (SWNTs) conveying fluid with different boundary conditions. In the linear analysis the natural frequencies and critical flow velocities of SWNTs are computed. However, in the nonlinear analysis the effect of nonlocal parameter on nonlinear dynamics of cantilevered SWNTs conveying fluid is investigated by using bifurcation diagram, phase plane and Poincare map. Numerical results confirm existence of chaos as well as a period-doubling transition to chaos.

Harmonic mappings of bounded boundary rotation

The purpose of this paper is to investigate the valency of planar harmonic mappings of bounded boundary rotation of the open unit disc D . \mathbb {D}. The paper is motivated by the earlier work of the first two authors [Complex Analysis Oper. Theory 5 (2011), 767–774] and the recent work of T. Hayami [Complex Var. Elliptic Equ. 59 (2014), 1214–1222]. First, the authors give a counterexample showing that both the main result of Hayami, Theorem 2.1, and the related conjecture, Conjecture 4.1, are false. Second, the authors give a valency criterion for planar harmonic mappings of bounded boundary rotation of D \mathbb {D} , proving an ameliorated statement of Theorem 2.1 and settling a modified version of Conjecture 4.1.

A synthetic visual plane algorithm for visibility computation in consideration of accuracy and efficiency

Visibility computation is of great interest to location optimization, environmental planning, ecology, and tourism. Many algorithms have been developed for visibility computation. In this paper, we propose a novel method of visibility computation, called synthetic visual plane (SVP), to achieve better performance with respect to efficiency, accuracy, or both. The method uses a global horizon, which is a synthesis of line-of-sight information of all nearer points, to determine the visibility of a point, which makes it an accurate visibility method. We used discretization of horizon to gain a good performance in efficiency. After discretization, the accuracy and efficiency of SVP depends on the scale of discretization (i.e., zone width). The method is more accurate at smaller zone widths, but this requires a longer operating time. Users must strike a balance between accuracy and efficiency at their discretion. According to our experiments, SVP is less accurate but more efficient than R2 if the zone width is set to one grid. However, SVP becomes more accurate than R2 when the zone width is set to 1/24 grid, while it continues to perform as fast or faster than R2. Although SVP performs worse than reference plane and depth map with respect to efficiency, it is superior in accuracy to these other two algorithms.

Invariant curves of smooth quasi-periodic mappings

In this paper we are concerned with the existence of invariant curves of planar mappings which are quasi-periodic in the spatial variable, satisfy the intersection property, $\mathcal{C}^{p}$ smooth with $p>2n+1$, $n$ is the number of frequencies.

Harmonic mappings with hereditary starlikeness

We study a hereditary starlikeness property for planar harmonic mappings on a disk and on an annulus. While such a property is a common trait of conformal mappings, it may be absent in harmonic mappings. It turns out that a sufficient condition for a harmonic mapping f to possess this hereditary property is to have a harmonic argument — a striking feature of conformal mappings that does not extend to all harmonic mappings.

Mobile navigation services with augmented reality

In this study, we combine augmented reality (AR) with the technique of assisted global positioning system to construct a guiding system of AR and design the guiding graphs metaphorically, so that the system interface operation is used more intuitively. We further investigate the availability of the system, and present an empirical study to statistically show that the guiding system of AR significantly outperforms that of plane map in terms of the finishing time of mission and correctness. Finally, according to the results of questionnaire of the system availability, we induct six essential factors influencing the guiding system availability of AR, namely guiding service usability factor, user esthetics of design factor, guiding service technique factor, guiding service creativity factor, guiding service entertainment factor, and guiding service practicality factor. The results of the study could be extended to other related studies. In terms of task completion time and accuracy rate, AR navigation is obviously better than the two plane map navigation modes. The users can find the direction of the destination within 7 s on average, and the accuracy rate is as high as 97.73%. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A technique of constructing planar harmonic mappings and their properties

The analytic part of a planar harmonic mapping plays a vital role in shaping its geometric properties. For a normalized analytic function $f$ defined in the unit disk, define an operator $\Phi[f](z) = f(z) + \overline{f(z)-z}$. In this paper, necessary and sufficient conditions on $f$ are determined for the harmonic function $\Phi[f]$ to be univalent and convex in one direction. Similar results are obtained for $\Phi[f]$ to be starlike and convex in the unit disk. This results in the coefficient estimates, growth results and convolution properties of $\Phi[f]$. In addition, various radii constants associated with $\Phi[f]$ have been computed.

Geological and geomorphological evidence for the southwestern extension of the East Anatolian Fault Zone, Turkey

The left lateral strike slip East Anatolian Fault Zone (EAFZ) is the main structural link between the North Anatolian Fault Zone (NAFZ) in north and subduction in the Mediterranean Sea and the transform Dead Sea Fault Zone (DSFZ) in south. We studied the southwestern continuation of the EAFZ using combined field investigations including geomorphology, geology and paleoseismology. Mapping of offset drainages, lineaments, shutter ridges and fault planes in young geological units suggests existence of active faults between the Mediterranean coast and Türkoğlu where it intersects with the DSFZ. Yumurtalık and Toprakkale faults are the main tectonic structures and detailed examination of geological and geomorphological evidences suggest their Quaternary activity. Paleoseismic trenching on these faults provided evidence for at least two surface rupturing events in the last 9,000 yr. Detailed examination of paleo-valleys of the Ceyhan River suggests that the course of the river migrated due to the activity of the Toprakkale Fault. Obtained geological and geomorphological data indicates that the EAFZ continues across the Amanos Mountains and the slip transfer is mainly accommodated by the Toprakkale and Yumurtalık faults.

A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM II

We study properties of the simply connected sets in the complex plane, which are finite unions of domains convex in the horizontal direction. These considerations allow us to state new univalence criteria for complex-valued local homeomorphisms. In particular, we apply our results to planar harmonic mappings obtaining generalisations of the shear construction theorem due to Clunie and Sheil-Small [‘Harmonic univalent functions’, Ann. Acad. Sci. Fenn. Ser. A. I. Math.9 (1984), 3–25].

Semilinear equations in a plane and quasiconformal mappings

Semilinear equations in a plane and quasiconformal mappings

Nonlinear dynamics of extensible viscoelastic cantilevered pipes conveying pulsatile flow with an end nozzle

Nonlinear dynamics of an extensible cantilevered pipe conveying pulsating flow is considered in this paper. The fluid flow fluctuates harmonically and exhausts via a nozzle attached to the end of the pipe. Taking into account the extensibility assumption, the coupled nonlinear lateral–longitudinal equations of motion are derived using Hamilton's principle and discretized via Galerkin's method. The adaptive time step Adams algorithm is applied to extract the time response, and then the bifurcation, power spectral density and phase plane maps are plotted for some case studies. Effects of some geometrical parameters such as flow mass, pulsating flow frequency, gravity, nozzle mass and nozzle aspect ratio parameters are studied on the dynamics of such system and the validity of extensibility assumption is investigated and some conclusions are drawn.

Planar mappings of subexponentially integrable distortion: integrability of distortion of inverses

We establish the optimal regularity for the distortion of inverses of mappings of finite distortion with logarithm-iterated style subexponentially integrable distortion, which generalizes the Theorem 1. of [J. Gill, Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 1, 197--207].

Building the 3D Geological Model of Wall Rock of Salt Caverns Based on Integration Method of Multi-source data

In order to analyse the geological characteristics of salt rock and stability of salt caverns, rough three-dimensional (3D) models of salt rock stratum and the 3D models of salt caverns on study areas are built by 3D GIS spatial modeling technique. During implementing, multi-source data, such as basic geographic data, DEM, geological plane map, geological section map, engineering geological data, and sonar data are used. In this study, the 3D spatial analyzing and calculation methods, such as 3D GIS intersection detection method in three-dimensional space, Boolean operations between three-dimensional space entities, three-dimensional space grid discretization, are used to build 3D models on wall rock of salt caverns. Our methods can provide effective calculation models for numerical simulation and analysis of the creep characteristics of wall rock in salt caverns.