scholarly journals Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto–Sivashinsky SPDEs in One-to-Three Dimensions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 73
Author(s):  
Wensheng Wang ◽  
Dazhong Wang
Keyword(s):  
White Noise ◽  
Limit Theorems ◽  
Three Dimensional ◽  
Space Time ◽  
Asymptotic Distributions ◽  
Three Dimensions ◽  
Bifractional Brownian Motion ◽  
Spatio Temporal ◽  
The Relationship ◽  
Time Type

We study the realized power variations for the fourth order linearized Kuramoto–Sivashinsky (LKS) SPDEs and their gradient, driven by the space–time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. This class was introduced-with Brownian-time-type kernel formulations by Allouba in a series of articles starting in 2006. He proved the existence, uniqueness, and sharp spatio-temporal Hölder regularity for the above class of equations in d=1,2,3. We use the relationship between LKS-SPDEs and the Houdré–Villaa bifractional Brownian motion (BBM), yielding temporal central limit theorems for LKS-SPDEs and their gradient. We use the underlying explicit kernels and spectral/harmonic analysis to prove our results. On one hand, this work builds on the recent works on the delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space–time white noise. On the other hand, it builds on and complements Allouba’s earlier works on the LKS-SPDEs and their gradient.

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

Pattern Characterization in Acceleration Vector Fields Developed in Complex Beam Structures Subject to an Excitation Protocol by Impulsive Forces

2012 ◽  
Author(s):  
Ioannis T. Georgiou
Keyword(s):  
Vector Fields ◽  
Three Dimensional ◽  
Normal Modes ◽  
Space Time ◽  
Time Modulation ◽  
Model Free ◽  
Certification Procedure ◽  
Acceleration Vector ◽  
Spatio Temporal ◽  
Multi Body

Presented are interesting results concerning aspects of the space-time characteristics of coherence patterns of ensembles of impulsive coupled acceleration signals developed in the complex domain of a physical multi-body flexible structure. A modal hammer is used to systematically pulse-interrogate the structure whereas a state of the art piezoelectric tri-axial accelerometer is used to collect at a point time series samples of coupled dynamics. We find the remarkable fact that collocated ensembles of signals of the acceleration vector field are underlain by strong spatio-temporal coherence which is robust under random experimental error introduced in the impulsive force protocol of interrogation. Coherence is characterized-identified optimally in terms of Proper Orthogonal Decomposition (POD) modes. The POD-identified space-time coherence structures, or patterns, feature an unparalleled classical modal-like characterization of coherence of collocated multi-dimensional information. The identified dominant POD spatio-temporal patterns have the space-time modulation characteristics of classical normal modes of vibration of three-dimensional coupled structural dynamics. Exploiting in full the transient dynamics and being model free, this test and evaluation modal-like identification technique can lead to a reliable certification procedure of multi-body flexible structural systems in critical applications.

scholarly journals Simulating rhizodeposition patterns around growing and exuding root systems

2021 ◽  
Author(s):  
Magdalena Landl ◽  
Adrian Haupenthal ◽  
Daniel Leitner ◽  
Eva Kroener ◽  
Doris Vetterlein ◽  
...  
Keyword(s):  
Root Architecture ◽  
Three Dimensional ◽  
Temporal Distribution ◽  
Root Systems ◽  
Distribution Patterns ◽  
Three Dimensions ◽  
Root Branching ◽  
Architecture Model ◽  
Spatio Temporal ◽  
Model Approach

1AbstractIn this study, we developed a novel model approach to compute the spatio-temporal distribution patterns of rhizodeposits around growing root systems in three dimensions. This model approach allows us for the first time to study the evolution of rhizodeposition patterns around complex three-dimensional root systems. Root systems were generated using the root architecture model CPlantBox. The concentration of rhizodeposits at a given location in the soil domain was computed analytically. To simulate the spread of rhizodeposits in the soil, we considered rhizodeposit release from the roots, rhizodeposit diffusion into the soil, rhizodeposit sorption to soil particles, and rhizodeposit degradation by microorganisms. To demonstrate the capabilities of our new model approach, we performed simulations for the two example rhizodeposits mucilage and cit-rate and the example root system Vicia faba. The rhizodeposition model was parameterized using values from the literature. Our simulations showed that the rhizosphere soil volume with rhizodeposit concentrations above a defined threshold value (i.e., the rhizodeposit hotspot volume), exhibited a maximum at intermediate root growth rates. Root branching allowed the rhizospheres of individual roots to overlap, resulting in a greater volume of rhizodeposit hotspots. This was particularly important in the case of citrate, where overlap of rhizodeposition zones accounted for more than half of the total rhizodeposit hotspot volumes. Coupling a root architecture model with a rhizodeposition model allowed us to get a better understanding of the influence of root architecture as well as rhizodeposit properties on the evolution of the spatio-temporal distribution patterns of rhizodeposits around growing root systems.

scholarly journals The Visualization Representation of Space-Time-Path in The Space-Time-Cube

2021 ◽  
Vol 906 (1) ◽  
pp. 012030
Author(s):  
Bingbing Song ◽  
Yanlin Wang ◽  
Fang Li
Keyword(s):  
Three Dimensional ◽  
Temporal Changes ◽  
Space Time ◽  
Temporal Data ◽  
Processing Technologies ◽  
Spatial Object ◽  
Time Path ◽  
Visual Clutter ◽  
Spatio Temporal ◽  
The Impact

Abstract Map is a traditional visualization tool to represent distribution and interaction of spatial objects or spatial phenomenon. However, with the continuous development of acquisition and processing technologies for spatio-temporal data, traditional map can hardly meet the visualization requirement for this type of data. In other words, the dynamic information about spatial object or phenomenon cannot be expressed fully by traditional map. The Space-Time-Cube (STC), as a three-dimensional visualization environment, whose base represents the two-dimensional geographical space and whose height represents the temporal dimension, can simultaneously represent the spatial distribution as well as the temporal changes of spatio-temporal data. For some spatial object or phenomenon, its moving trajectory can be visualized in STC as a Space-Time-Path (STP), by which the speed and state of motion can be clearly reflected. Noticeably, the problem of visual clutter about STP is inevitably due to the complexity of three-dimensional visualization. In order to reduce the impact of visual clutter, this paper discusses different aspects about visualization representation of STP in the STC. The multiple scales representation and the multiple views display can promote interactive experience of users, and the application of different visual variables can help to represent different kinds of attribute information of STP. With the visualization of STP, spatio-temporal changes and attributive characters of spatial object or phenomenon can be represented and analysed.

EXPLORING THE RELATIONSHIP BETWEEN PERCEIVED SERVICE QUALITY AND SPORT INVOLVEMENT

2021 ◽  
pp. 41-42
Author(s):  
Anastasiadis A ◽  
Ntovoli A
Keyword(s):  
Service Quality ◽  
Sport Participation ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Three Dimensional Model ◽  
Policy Makers ◽  
Perceived Service Quality ◽  
Sport Policy ◽  
Sport Facilities ◽  
The Relationship

The purpose of this study was to test the relationship between sport service quality and sport involvement. The data were collected from 500 individuals, users of sport facilities, in the city of Thessaloniki, Greece. Items from the SERVQUAL model were used to measure sport service quality. The three-dimensional model of leisure involvement was used to measure sport involvement (Centrality, Attraction and Self-expression). The results of the study revealed statistically signicant correlations between service quality and two of the three dimensions of sport involvement: centrality and self-expression, supporting the important role of service quality in developing sport policy. These results propose that policy makers should invest on building service quality in sport services and facilities, since this will increase sport participation levels and help citizens adopt a more active life-style.

scholarly journals Spectral Analysis In Three Dimensions: The Examination Of Economic Interdependence Between New York, London, Tokyo, And The Pacific Basin Equity Marketing Indices

2011 ◽  
Vol 12 (3) ◽  
pp. 72 ◽  
Author(s):  
Shih-Mo Lin ◽  
Karen Craft Denning ◽  
K. Victor Chow
Keyword(s):  
New York ◽  
Spectral Analysis ◽  
Statistical Power ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Partial Coherence ◽  
Three Dimensions ◽  
Pacific Basin ◽  
The Pacific ◽  
The Relationship

This paper analyzes the use of three dimensional spectral analyses. We highlight the power of this technique by examining the economic interrelationships between Pacific Basin countries, Tokyo, New York and London equity markets. To the best of our knowledge, no research in financial economics has ever employed the spectral technique with greater than two dimensions. Our use of three way spectral analysis, or partial coherence measures, allows us to ferret out the influence of correlated variables, in this case, major world markets (New York, London, Tokyo) before examining the relationship among the variables of primary interest, the Pacific Basin markets. WE hold constant the influence of New York, London, and Tokyo before examining the relationship among Pacific Basin Newly Industrialized countries equity indices to illustrate our methodology. Simulation techniques enable us to document the statistical power of our technique.

scholarly journals Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wensheng Wang ◽  
Xiaoying Chang ◽  
Wang Liao
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Harmonic Analysis ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Colored Noise ◽  
Asymptotic Distributions ◽  
Heat Equations ◽  
Stochastic Heat Equations

Let u α , d = u α , d t , x ,   t ∈ 0 , T , x ∈ ℝ d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process u α , d , in time, having infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.

scholarly journals “TIME FOR WISDOM” – THE RELATIONSHIP BETWEEN WISDOM AND THE TIME PERSPECTIVE

2020 ◽  
Vol 1 (1) ◽  
pp. 107-121
Keyword(s):  
Time Perspective ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Short Version ◽  
Temporal Perspective ◽  
Cognitive Dimension ◽  
Temporal Profile ◽  
Balanced Time Perspective ◽  
Polish Adaptation ◽  
The Relationship

Analysing the relationships between wisdom and time is increasingly becoming an important and interesting issue. The purpose of the study is empirical verification of the relationship between wisdom and the five categories of the temporal perspective: the positive past (PP), negative past (NP), hedonistic present (HP), fatalistic present (FP) and the future (F). It has been assumed that wisdom will positively correlate with the combination of three dimensions considered the balanced time perspective (past-positive, present-hedonistic, and future) and negatively correlated with the temporal profile considered less functional (past-negative and present-fatalistic perspective). The study has been conducted on a group of 279 Polish respondents, including 67% women, aged 16-28 (M=19.13; SD=3.01). The group has been composed of secondary school pupils and students. Two research tools were used: The Three-Dimensional Wisdom Scale (3D-WS) by Ardelt (2003), in Polish adaptation by Steuden, Brudek and Izebski (2006) and the Zimbardo Time Perspective Inventory (ZTPI-short version), adapted by Cybis, Rowiński and Przepiórka (2012). On the basis of the obtained results, it can be assumed that: 1) participants of the study characterised by general wisdom and its cognitive dimension do not focus on the FP and NP; 2) in case of the reflexive dimension of wisdom, the predictive function is performed by the NP, FP and, to a lesser extent, the PP; 3) the only predictors of the affective dimension of wisdom have turned out to be the FP and the F. The obtained results seem to have the theoretical and empirical justification. Individuals with lower scores on wisdom have expressed aversion to past events and have been convinced that they have no control over the present, and that what is happening is a result of capricious fate. Significant correlations of wisdom concern the negative temporal profile, both in the general dimension of wisdom and in relation to its individual dimensions.

scholarly journals Pemahaman Konsep Siswa pada Materi Bangun Datar Terhadap Hasil Belajar Dimensi Tiga

2018 ◽  
Vol 2 (2) ◽  
pp. 132
Author(s):  
Malik Ibrahim
Keyword(s):  
Learning Outcomes ◽  
Three Dimensional ◽  
Positive Influence ◽  
Three Dimensions ◽  
Ex Post ◽  
Ex Post Facto ◽  
Third Dimension ◽  
Level Of Understanding ◽  
The Impact ◽  
The Relationship

Abstrak: Penelitian ini bertujuan untuk mengetahui seberapa besar pengaruh pemahaman konsep siswa pada materi bangun datar terhadap hasil belajar dimensi tiga kelas X MA. Hidayatul Muhsinin Labulia. Penelitian ini menggunakan pendekatan  kuantitatif jenis Ex Post Facto desain hubungan kausalitas yaitu hubungan yang bersifat sebab akibat. Penelitian ini menggunakan penelitian populasi yang jumlah keseluruhannya adalah 109 siswa terdiri dari kelas XA, XB dan XC.         Hasil penelitian menunjukkan pengaruh pemahaman konsep bangun datar cukup berpengaruh positif terhadap hasil belajar dimensi tiga. Hal ini terlihat pada hasil penelitian dengan melakukan pemberian tes kepada 109 siswa. Hubungan antara pemahaman konsep bangun datar dan hasil belajar dimensi tiga sebesar 0,668 atau 66,8%, ini berarti korelasi antara pemahaman konsep bangun datar dan hasil belajar dimensi tiga adalah cukup, sesuai dengan kriteria yang telah ada. Adapun pengaruh antara pemahaman konsep bangun datar dan hasil belajar dimensi tiga  sebesar 0,447 atau 44,7%. Sedangkan persamaan regresi antara pemahaman konsep bangun datar dan hasil belajar dimensi tiga adalah Y = 8,831 + 0,934 X, ini menjelasakan bahwa keterkaitan antara pemahaman konsep bangun datar dengan hasil belajar dimensi tiga bersifat searah (positif) atau dengan kata lain bahwa, jika tingkat pemahman konsep bangun datar tinggi maka akan mengakibatkan hasil belajar dimensi tiga tinggi pula, dan demikian pula sebaliknya. Berdasarkan penjelasan tersebut dapat disimpulkan bahwa terdapat pengaruh positif pemahaman konsep bangun datar terhadap hasil belajar dimensi tiga.Abstract:  This research aims to find out how much impact the students' conceptual understanding of the material is flat on the learning outcomes of the three dimensions of class X MA. Hidayatul Muhsinin Labulia. This study uses a quantitative approach to the type of Ex Post Facto design causality relationship that is causal relationships. This study uses a population research whose total number is 109 students consisting of classes XA, XB and XC. The results of the study showed that the impact of understanding the flat wake concept was quite a positive effect on the learning outcomes of three dimensions. This can be seen in the results of the study by giving tests to 109 students. The relationship between understanding the concept of flat wake and three dimensional learning outcomes is 0.668 or 66.8%, this means that the correlation between understanding the concept of flat wake and three dimensional learning outcomes is sufficient, according to existing criteria. The influence between the understanding of the concept of flat wake and the third dimension of learning outcomes is 0.447 or 44.7%. While the regression equation between understanding the concept of flat wake and three dimensional learning outcomes is Y = 8.831 + 0.934 X, this explains that the relationship between understanding the concept of flat wake with learning outcomes of three dimensions is unidirectional (positive) or in other words that, if the level of understanding concept wake up high then it will result in high three dimensional learning outcomes too, and vice versa. Based on these explanations, it can be concluded that there is a positive influence on understanding the concept of flat building on the results of three dimensional learning.

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