scholarly journals Robust Pairwise n-Person Stochastic Duel Game

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 825
Author(s):  
Song-Kyoo (Amang) Kim
Keyword(s):  
Stochastic Game ◽  
Time Dependent ◽  
Game Model ◽  
Extended Version ◽  
Explicit Formulas ◽  
Practical Applications

This paper introduces an extended version of a stochastic game under the antagonistic duel-type setup. The most flexible multiple person duel game is analytically solved. Moreover, the explicit formulas are solved to determine the time-dependent duel game model using the first exceed theory in multiple game stages. Unlike conventional stochastic duel games, multiple battlefields are firstly introduced and each battlefield becomes a shooting ground of pairwise players in a multiperson game. Each player selects different targets in different game stages. An analogue of this new theory was designed to find the best shooting time within multiple battlefields. This model is fully mathematically explained and is the basis with which to apply a stochastic duel-type game in various practical applications.

scholarly journals Antagonistic One-To-N Stochastic Duel Game

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1114 ◽  
Author(s):  
Song-Kyoo (Amang) Kim
Keyword(s):  
Real World ◽  
Payoff Function ◽  
Marketing Strategies ◽  
Time Dependent ◽  
Random Time ◽  
Game Model ◽  
Explicit Formulas ◽  
Entry Timing ◽  
The One ◽  
Person Game

This paper is dealing with a multiple person game model under the antagonistic duel type setup. The unique multiple person duel game with the one-shooting-to-kill-all condition is analytically solved and the explicit formulas are obtained to determine the time dependent duel game model by using the first exceed theory. The model could be directly applied into real-world situations and an analogue of the theory in the paper is designed for solving the best shooting time for hitting all other players at once which optimizes the payoff function under random time conditions. It also mathematically explains to build the marketing strategies for the entry timing for both blue and red ocean markets.

Random Forces Resulting From Internal Two-Phase Flow on Bends and Tees

2006 ◽  
Author(s):  
E. de Langre ◽  
J. L. Riverin ◽  
M. J. Pettigrew
Keyword(s):  
Two Phase Flow ◽  
Experimental Results ◽  
Time Dependent ◽  
Phase Flow ◽  
Water Mixture ◽  
Dimensionless Form ◽  
Two Phase ◽  
Practical Applications ◽  
Random Forces

The time dependent forces resulting from a two-phase air-water mixture flowing in an elbow and a tee are measured. Their magnitudes as well as their spectral contents are analyzed. Comparison is made with previous experimental results on similar systems. For practical applications a dimensionless form is proposed to relate the characteristics of these forces to the parameters defining the flow and the geometry of the piping.

scholarly journals Learning Bounds of ERM Principle for Sequences of Time-Dependent Samples

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Mingchen Yao ◽  
Chao Zhang ◽  
Wei Wu
Keyword(s):  
Time Dependent ◽  
Dependent Data ◽  
Empirical Risk Minimization ◽  
Risk Minimization ◽  
Practical Applications ◽  
Empirical Risk ◽  
Learning Tasks ◽  
Generalization Bound ◽  
Erm Principle ◽  
Dependent Samples

Many generalization results in learning theory are established under the assumption that samples are independent and identically distributed (i.i.d.). However, numerous learning tasks in practical applications involve the time-dependent data. In this paper, we propose a theoretical framework to analyze the generalization performance of the empirical risk minimization (ERM) principle for sequences of time-dependent samples (TDS). In particular, we first present the generalization bound of ERM principle for TDS. By introducing some auxiliary quantities, we also give a further analysis of the generalization properties and the asymptotical behaviors of ERM principle for TDS.

A New Method for Completely Force Balancing Simple Linkages

1969 ◽  
Vol 91 (1) ◽  
pp. 21-26 ◽  
Author(s):  
R. S. Berkof ◽  
G. G. Lowen
Keyword(s):  
Center Of Mass ◽  
Time Dependent ◽  
New Method ◽  
Practical Applications ◽  
Mass Distributions ◽  
Linearly Independent ◽  
Planar Linkages

A new method, herein referred to as the “Method of Linearly Independent Vectors,” is shown to permit the complete force balancing of certain planar linkages. This method consists of writing the equation describing the position of the total mechanism center of mass in such a way that the coefficients of the time-dependent terms may be set equal to zero. In this way, the total center of mass can be made stationary, and the shaking force vanishes. Derivations as well as practical applications are shown for four-bar and six-bar linkages with arbitrary link mass distributions.

Corrected Diffusion Model of Chloride in Concrete and its Engineering Application

2011 ◽  
Vol 189-193 ◽  
pp. 1886-1891
Author(s):  
Peng Fei Xue ◽  
Da Ling Mao
Keyword(s):  
Service Life ◽  
Diffusion Model ◽  
Life Prediction ◽  
Engineering Application ◽  
Time Dependent ◽  
Chloride Diffusion ◽  
Chloride Diffusion Coefficient ◽  
Practical Applications ◽  
Environment Variable ◽  
Stochastic Characteristic

A multi-factor diffusion model of chloride in concrete was formulated, in which the hypothesis of Fick’s Law were corrected through parameter definition. The values of the parameters in the model were given for practical applications according to pilot calculation and analysis of mass data. By using this diffusion model, three calculation methods of concrete structure service life were further deduced, it includes definite value method, probability performance based method and time-dependent reliability based method. The service life prediction for the approach bridge of Huang-pu Bridge was carried on by using various prediction approaches mentioned above. The results showed that: time-dependent reliability based method can consider randomness of chloride diffusion coefficient and the depth of concrete covering layer, and the stochastic characteristic of environment variable can be easily taken into account too. By adjusting the target reliability, the prediction results are consistent with those of the other two methods.

TIME-DEPENDENT WIGNER DISTRIBUTION FUNCTION EMPLOYED IN SQUEEZED SCHRÖDINGER CAT STATES: |Ψ(t)〉 = N-1/2(|β〉+eiϕ|-β〉)

2009 ◽  
Vol 23 (25) ◽  
pp. 5049-5066
Author(s):  
JEONG RYEOL CHOI ◽  
KYU HWANG YEON
Keyword(s):  
Distribution Function ◽  
Harmonic Oscillator ◽  
Wigner Distribution ◽  
Time Dependent ◽  
Squeezed States ◽  
Wigner Distribution Function ◽  
Practical Applications ◽  
Schrödinger Cat ◽  
Cat States ◽  
Theory Of Invariants

The Wigner distribution function (WDF) for the time-dependent quadratic Hamiltonian system is investigated in the squeezed Schrödinger cat states with the use of Lewis–Riesenfeld theory of invariants. The nonclassical aspects of the system produced by superposition of two distinct squeezed states are analyzed with emphasis on their application into special systems beyond simple harmonic oscillator. An application of our development to the measurement of quantum state by reconstructing the WDF via Autler–Townes spectroscopy is addressed. In addition, we considered particular models such as Cadirola–Kanai oscillator, frequency stable damped harmonic oscillator, and harmonic oscillator with time-variable frequency as practical applications with the object of promoting the understanding of nonclassical effects associated with the WDF.

DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS

2006 ◽  
Vol 21 (06) ◽  
pp. 1359-1377 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Wave Function ◽  
Darboux Transformation ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Darboux Transformations ◽  
Explicit Formulas ◽  
The Difference ◽  
Dependent Mass ◽  
Position Dependent Mass

The formalism of Darboux transformations is established for time-dependent Schrödinger equations with an effective (position-dependent) mass. Explicit formulas are obtained for the transformed wave function and the difference between the original and the transformed potential. It is shown that for a noneffective mass our Darboux transformation reduces correctly to the well-known Darboux transformation.

Sign in / Sign up

Export Citation Format

Share Document