scholarly journals Boundary Harnack principle for the absolute value of a one-dimensional subordinate Brownian motion killed at 0

2016 ◽  
Vol 21 (0) ◽  
Author(s):  
Vanja Wagner
Keyword(s):  
Brownian Motion ◽  
Boundary Harnack Principle ◽  
One Dimensional ◽  
Absolute Value ◽  
Subordinate Brownian Motion ◽  
The Absolute

The Level-Crossing Problem: First-Passage, Escape and Extremes

2014 ◽  
Vol 13 (04) ◽  
pp. 1430001 ◽  
Author(s):  
Jaume Masoliver
Keyword(s):  
Brownian Motion ◽  
Diffusion Processes ◽  
Extreme Values ◽  
Level Crossing ◽  
First Passage ◽  
One Dimensional ◽  
Absolute Value ◽  
Dimensional Diffusion

We review the level-crossing problem which includes the first-passage and escape problems as well as the theory of extreme values (the maximum, the minimum, the maximum absolute value and the range or span). We set the definitions and general results and apply them to one-dimensional diffusion processes with explicit results for the Brownian motion and the Ornstein–Uhlenbeck (OU) process.

scholarly journals The Saddle Point Method for the Integral of the Absolute Value of the Brownian Motion

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Leonid Tolmatz
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Saddle Point ◽  
Point Method ◽  
Saddle Point Method ◽  
Tail Asymptotics ◽  
Absolute Value ◽  
Exact Tail Asymptotics ◽  
International Audience ◽  
The Absolute

International audience The distribution function of the integral of the absolute value of the Brownian motion was expressed by L.Takács in the form of various series. In the present paper we determine the exact tail asymptotics of this distribution function. The proposed method is applicable to a variety of other Wiener functionals as well.

scholarly journals THE MINIMIZATION OF MOMENTS AND REACTIVE FORCES IN GRILLAGES WITH A GENETIC ALGORITHM

2011 ◽  
Vol 3 (2) ◽  
pp. 56-63
Author(s):  
Rimantas Belevičius ◽  
Darius Mačiūnas ◽  
Dmitrij Šešok
Keyword(s):  
Finite Element ◽  
Bending Moment ◽  
Design Parameters ◽  
Finite Element Program ◽  
One Dimensional ◽  
Absolute Value ◽  
Element Program ◽  
The Absolute ◽  
The One ◽  
The Given

The aim of the article is to report a technology for the optimization of grillage-type foundations seeking for the least possible reactive forces in the piles for a given number of piles and in the absolute value of the bending moments when connecting beams of the grillage. Mathematically, this seems to be the global optimization problem possessing a large number of local minima points. Both goals can be achieved choosing appropriate pile positions under connecting beams; however, these two problems contradict to each other and lead to diff erent schemes for pile placement. Therefore, we suggest using a compromise objective function (to be minimized) that consists of the largest reactive force arising in all piles and that occurring in the absolute value of the bending moment when connecting beams, both with the given weights. Bending moments are calculated at three points of each beam. The design parameters of the problem are positions of the piles. The feasible space of design parameters is determined by two constraints. First, during the optimization process, piles can move only along connecting beams. Therefore, the two-dimensional grillage is “unfolded” to the one-dimensional construct, and supports are allowed to range through this space freely. Second, the minimum allowable distance between two adjacent piles is introduced due to the specific capacities of a pile driver. Also, due to some considerations into the scheme of pile placement, the designer sometimes may introduce immovable supports (usually at the corners of the grillage) that do not participate in the optimization process and always retain their positions. However, such supports hinder to achieve a global solution to a problem and are not treated in this paper. The initial data for the problem are as follows: a geometrical scheme of the grillage, the given number of piles, a cross-section and material data on connecting beams, the minimum possible distance between adjacent supports and loading data given in the form of concentrated loads or trapezoidal distributed loadings. The results of the solution are the required positions of piles. This solution can serve as a pilot project for more detailed design. The entire optimization problem is solved in two steps. First, the grillage is transformed into the one-dimensional construct and the optimizer decides about a routine solution (i.e. the positions of piles in this construct). Second, backward transformation returns pile positions into the two-dimensional grillage and the “black-box” finite element program returns the corresponding objective function value. On the basis of this value, the optimizer predicts new positions of piles etc. The finite element program idealizes connecting beams as beam elements and piles – as mesh nodes of the finite element with a given boundary conditions in the form of vertical and rotational stiff ness. Since the problem may have several tens of design parameters, the only choice for optimization algorithms is using stochastic optimization algorithms. In our case, we use the original elitist real-number genetic algorithm and launch the program sufficient number of times in order to exclude large scattering of results. Three numerical examples are presented for the optimization of 10-pile grillage: when optimizing purely the largest reactive force, purely the largest in the absolute value of the bending moment and both parameters with equal weights.

From Algebra to Calculus—a Tonka® Toy Does the Trick

1993 ◽  
Vol 86 (4) ◽  
pp. 282-287
Author(s):  
Victoria A. Borlaug
Keyword(s):  
Constant Velocity ◽  
Average Velocity ◽  
Graphical Representation ◽  
Instantaneous Velocity ◽  
One Dimensional ◽  
Absolute Value ◽  
Zero Values ◽  
The Absolute ◽  
Definition Of ◽  
Classroom Presentation

This classroom presentation is designed to introduce and interpret the graphical representation of a Tonka® toy truck's forward and backward motion. It can be used to illustrate an application of slope in an algebra class or to introduce the derivative in a calculus class. In the presentation, the teacher moves the Tonka® truck up and down on the chalkboard using chalk to record the motion, asks students questions about the motion, and encourages discussion. The class is asked to pretend that the toy truck has a speedometer. Unlike speedometers in real trucks, this toy speedometer has negative values to represent backward motion, in addmon to its usual positive and zero values. (Speed is the absolute value of velocity. In this situation, the speedometer might better be renamed “velocity-ometer,” but that term would introduce vocabulary unfamiliar to the student.) The presentation leads students to develop a graphical representation of the truck's one-dimensional motion, creates graphs representing constant velocity, leads students to a definition of average velocity, and introduces the concept of instantaneous velocity.

Optical soliton in a one-dimensional array of a metal nanoparticle-microcavity complex (2021 Commun. Theor. Phys. 73 115105)

2021 ◽  
Author(s):  
Ning Ji ◽  
Tao Shui ◽  
Yilou Liu ◽  
Wangrui Zhang ◽  
Xiumei Chen ◽  
...  
Keyword(s):  
Production Process ◽  
Optical Soliton ◽  
Metal Nanoparticle ◽  
Correct Version ◽  
One Dimensional ◽  
Absolute Value ◽  
Dimensional Array ◽  
Theor Phys ◽  
The Absolute ◽  
Wrong Place

Abstract During the production process an error was introduced into equation (14). The absolute value symbol was moved to the wrong place. Here, we give the correct version of equation (14) ：

Becoming One Self: A Critical Retrieval of 'Choice Biography'

2007 ◽  
Vol 1 (3) ◽  
pp. 272-293 ◽  
Author(s):  
Frits de Lange
Keyword(s):  
Life Course ◽  
Self Management ◽  
Modern Life ◽  
One Dimensional ◽  
Absolute Value ◽  
Life Planning ◽  
Balanced Approach ◽  
The Absolute ◽  
And Control

AbstractThe modern life course is described as a 'choice biography.' Rationality and control, and life planning and self-management are central notions. Instead of rejecting the notion categorically, this article opts for a more balanced approach. The Protestant tradition shares central characteristics with choice biography, as Calvin, Edwards, and Bunyan show. However, there are dissimilarities as well. Fundamental in 'choice biography' is its lack of transcendence. Modern individualism threatens to collapse into one-dimensional secularism and egoism. In retrieving Kierkegaard's legacy, the notion 'choice biography' might undergo a critical re-appraisal. In his philosophy, we find both the absolute value of the individual's choices, and a plea for transcendence.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

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