Bose-Einstein-type statistics, order statistics and planar random motions with three directions

2004 ◽  
Vol 36 (3) ◽  
pp. 937-970 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher
Keyword(s):  
Partial Differential Equations ◽  
Order Statistics ◽  
Constant Velocity ◽  
Uniform Motion ◽  
Change Of Direction ◽  
Telegraph Process ◽  
Cyclic Motion ◽  
Different Types ◽  
Random Motions ◽  
Bose Einstein

In this paper we study different types of planar random motions (performed with constant velocity) with three directions, defined by the vectors dj = (cos(2πj/3), sin(2πj/3)) for j = 0, 1, 2, changing at Poisson-paced times. We examine the cyclic motion (where the change of direction is deterministic), the completely uniform motion (where at each Poisson event each direction can be taken with probability ) and the symmetrically deviating case (where the particle can choose all directions except that taken before the Poisson event). For each of the above random motions we derive the explicit distribution of the position of the particle, by using an approach based on order statistics. We prove that the densities obtained are solutions of the partial differential equations governing the processes. We are also able to give the explicit distributions on the boundary and, for the case of the symmetrically deviating motion, we can write it as the distribution of a telegraph process. For the symmetrically deviating motion we use a generalization of the Bose-Einstein statistics in order to determine the distribution of the triple (N0, N1, N2) (conditional on N(t) = k, with N0 + N1 + N2 = N(t) + 1, where N(t) is the number of Poisson events in [0, t]), where Nj denotes the number of times the direction dj (j = 0, 1, 2) is taken. Possible extensions to four directions or more are briefly considered.

Bose-Einstein-type statistics, order statistics and planar random motions with three directions

2004 ◽  
Vol 36 (03) ◽  
pp. 937-970 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher
Keyword(s):  
Partial Differential Equations ◽  
Order Statistics ◽  
Constant Velocity ◽  
Uniform Motion ◽  
Change Of Direction ◽  
Telegraph Process ◽  
Cyclic Motion ◽  
Different Types ◽  
Random Motions ◽  
Bose Einstein

In this paper we study different types of planar random motions (performed with constant velocity) with three directions, defined by the vectorsdj= (cos(2πj/3), sin(2πj/3)) forj= 0, 1, 2, changing at Poisson-paced times. We examine the cyclic motion (where the change of direction is deterministic), the completely uniform motion (where at each Poisson event each direction can be taken with probability) and the symmetrically deviating case (where the particle can choose all directions except that taken before the Poisson event). For each of the above random motions we derive the explicit distribution of the position of the particle, by using an approach based on order statistics. We prove that the densities obtained are solutions of the partial differential equations governing the processes. We are also able to give the explicit distributions on the boundary and, for the case of the symmetrically deviating motion, we can write it as the distribution of a telegraph process. For the symmetrically deviating motion we use a generalization of the Bose-Einstein statistics in order to determine the distribution of the triple (N0,N1,N2) (conditional onN(t) =k, withN0+N1+N2=N(t) + 1, whereN(t) is the number of Poisson events in [0,t]), whereNjdenotes the number of times the directiondj(j= 0, 1, 2) is taken. Possible extensions to four directions or more are briefly considered.

Motion estimation in vehicular environments based on Bayesian dynamic networks

2021 ◽  
pp. 1-12
Author(s):  
Lauro Reyes-Cocoletzi ◽  
Ivan Olmos-Pineda ◽  
J. Arturo Olvera-Lopez
Keyword(s):  
Real World ◽  
Dynamic Networks ◽  
Ground Truth ◽  
Change Of Direction ◽  
Prediction Rate ◽  
Different Types ◽  
Novel Method ◽  
Comparison Of The Results ◽  
Multiple Obstacles ◽  
Real Traffic

The cornerstone to achieve the development of autonomous ground driving with the lowest possible risk of collision in real traffic environments is the movement estimation obstacle. Predicting trajectories of multiple obstacles in dynamic traffic scenarios is a major challenge, especially when different types of obstacles such as vehicles and pedestrians are involved. According to the issues mentioned, in this work a novel method based on Bayesian dynamic networks is proposed to infer the paths of interest objects (IO). Environmental information is obtained through stereo video, the direction vectors of multiple obstacles are computed and the trajectories with the highest probability of occurrence and the possibility of collision are highlighted. The proposed approach was evaluated using test environments considering different road layouts and multiple obstacles in real-world traffic scenarios. A comparison of the results obtained against the ground truth of the paths taken by each detected IO is performed. According to experimental results, the proposed method obtains a prediction rate of 75% for the change of direction taking into consideration the risk of collision. The importance of the proposal is that it does not obviate the risk of collision in contrast with related work.

scholarly journals Stability of observations of partial differential equations under uncertain perturbations

2017 ◽  
Vol 24 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Martin Lazar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Wave Operator ◽  
System Dynamic ◽  
Schrödinger Equations ◽  
Partial Differential ◽  
Main System ◽  
Different Types ◽  
The Stability ◽  
Observability Estimates

We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalises recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on microlocal defect tools, in particular on standard H-measures when the main system dynamic is governed by the wave operator, and parabolic H-measures in the case of the Schrödinger operator.

scholarly journals Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. M. Mohie EL-Din ◽  
M. M. Amein ◽  
Nahed S. A. Ali ◽  
M. S. Mohamed
Keyword(s):  
Order Statistics ◽  
Linear Transformation ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
The Past ◽  
Different Types ◽  
Past Entropy ◽  
Past Life ◽  
Family Based ◽  
Generalized Order

For a system, which is observed at timet, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.

Some considerations about third-order statistics for different types of random signals

2014 ◽  
Author(s):  
Cristian Ghita ◽  
Teofil-Cristian Oroian ◽  
Razvan-Doru Raicu ◽  
Lucian Anton ◽  
Ioana Suciu
Keyword(s):  
Order Statistics ◽  
Third Order ◽  
Different Types ◽  
Random Signals

Uniform progressing wave solutions of the wave equation

1971 ◽  
Vol 70 (3) ◽  
pp. 455-465
Author(s):  
Erich Zauderer
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Standard Form ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Wave Solutions ◽  
Different Types ◽  
Uniform Expansions

The solution of problems involving the propagation of discontinuities and other singularities for hyperbolic partial differential equations by means of progressing wave expansions is discussed in the book by Courant(l). He also refers to the work of Hadamard, Friedlander, Ludwig and others on this subject. More recently, Ludwig (2), Lewis(3) and others have considered 'uniform' progressing wave expansions for various problems. These expansions are valid in regions where the standard expansions are not suitable and they can be re-expanded in the standard form outside these regions. Examples of such regions are given by envelopes of bicharacteristic curves or, equivalently, caustics and by shadow boundaries such as occur in diffraction problems. In each of these regions, which we term 'transition regions' different types of uniform expansions are required.

scholarly journals Phase Structure of Bose - Einstein Condensate in Ultra - Cold Bose Gases

2015 ◽  
Vol 24 (4) ◽  
pp. 343
Author(s):  
Tran Huu Phat ◽  
Le Viet Hoa ◽  
Dang Thi Minh Hue
Keyword(s):  
Phase Structure ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Double Bubble ◽  
Bose Gases ◽  
Goldstone Theorem ◽  
Bose Einstein Condensate ◽  
Different Types ◽  
Higher Temperature ◽  
Bose Einstein

The Bose - Einstein condensation of ultra - cold Bose gases is studied by means of the Cornwall - Jackiw - Tomboulis effective potential approach in the improved double - bubble approximation which preserves the Goldstone theorem. The phase structure of Bose - Einstein condensate associating with two different types of phase transition is systematically investigated. Its main feature is that the symmetry which was broken at zero temperature gets restore at higher temperature.

scholarly journals A Novel Homotopy Perturbation Algorithm Using Laplace Transform for Conformable Partial Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Sajad Iqbal ◽  
Mohammed K. A. Kaabar ◽  
Francisco Martínez
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Laplace Transform ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Different Types

In this article, the approximate analytical solutions of four different types of conformable partial differential equations are investigated. First, the conformable Laplace transform homotopy perturbation method is reformulated. Then, the approximate analytical solution of four types of conformable partial differential equations is presented via the proposed technique. To check the accuracy of the proposed technique, the numerical and exact solutions are compared with each other. From this comparison, we conclude that the proposed technique is very efficient and easy to apply to various types of conformable partial differential equations.

scholarly journals Strength, Jumping and Change of Direction Speed Asymmetries in Soccer, Basketball and Tennis Players

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1664
Author(s):  
Nejc Šarabon ◽  
Darjan Smajla ◽  
Nicola A. Maffiuletti ◽  
Chris Bishop
Keyword(s):  
Soccer Players ◽  
Knee Extensors ◽  
Tennis Players ◽  
Change Of Direction ◽  
Force Development ◽  
Counter Movement Jump ◽  
Different Types ◽  
Different Populations ◽  
And Training ◽  
Knee Flexors

Despite growing research in the field of inter-limb asymmetries (ILAs), little is known about the variation of ILAs in different populations of athletes. The purpose of this study was to compare ILAs among young basketball, soccer and tennis players. ILAs were assessed in three different types of tests (strength, jumping and change of direction (CoD) speed), each including different tasks: (1) bilateral and unilateral counter movement jump, (2) isometric strength of knee extensors (KE) and knee flexors (KF), and (3) 90° and 180° CoD. Generally, the absolute metrics showed strong reliability and revealed significant differences (p < 0.05) among the three groups in KE maximal torque, KE and KF rate of force development and in both CoD tests. For jumping ILAs, power and force impulse metrics exhibited significant between-limb differences between groups, compared to jump height. For strength and CoD speed ILAs, only KF maximal torque and 180° CoD exhibited significant differences between groups. Greater KF strength ILAs in soccer players and counter-movement jump ILAs in tennis players are most probably the result of sport-specific movement patterns and training routines. Sport practitioners should be aware of the differences in ILAs among sports and address training programs accordingly.

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