scholarly journals Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map

2012 ◽  
Vol 2012 (7) ◽  
Author(s):  
Paolo Aschieri ◽  
Leonardo Castellani
Keyword(s):  
Second Order ◽  
Order Expansion ◽  
Noncommutative Gravity

PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS

2021 ◽  
pp. 1-19
Author(s):  
XUHUI WANG ◽  
SHENG-JHIH WU ◽  
XINGYE YUE
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Option Price ◽  
Second Order ◽  
Approximation Formula ◽  
Stochastic Volatility Models ◽  
Regular Perturbation ◽  
Volatility Models ◽  
Order Expansion ◽  
High Level

Abstract We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.

Second Order Perturbation Analysis of a Forced Nonlinear Mathieu Equation

2012 ◽  
Author(s):  
Venkatanarayanan Ramakrishnan ◽  
Brian F. Feeny
Keyword(s):  
Perturbation Analysis ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Mathieu Equation ◽  
Second Order ◽  
Order Perturbation ◽  
Cubic Nonlinearity ◽  
First Order ◽  
Order Expansion ◽  
Direct Forcing

The present study deals with the response of a forced nonlinear Mathieu equation. The equation considered has parametric excitation at the same frequency as direct forcing and also has cubic nonlinearity and damping. A second-order perturbation analysis using the method of multiple scales unfolds numerous resonance cases and system behavior that were not uncovered using first-order expansions. All resonance cases are analyzed. We numerically plot the frequency response of the system. The existence of a superharmonic resonance at one third the natural frequency was uncovered analytically for linear system. (This had been seen previously in numerical simulations but was not captured in the first-order expansion.) The effect of different parameters on the response of the system previously investigated are revisited.

Applicability of second-order expansion in s13 to explore δCP in small and medium baseline ν experiments

2016 ◽  
Vol 31 (09) ◽  
pp. 1650037
Author(s):  
Mandip Singh
Keyword(s):  
Series Expansion ◽  
Second Order ◽  
Mixing Angle ◽  
First Order ◽  
Long Baseline ◽  
Order Expansion ◽  
Matrix Formula ◽  
Small Baseline ◽  
Reactor Mixing ◽  
Baseline Experiment

The series expansion of neutrino evolution matrix “[Formula: see text]”, up to first-order in small reactor mixing angle [Formula: see text] is very useful formalism to study experiments quantitatively. The formalism has been used especially to investigate CP-violating phase [Formula: see text]. In order to perform a broad investigation for the possible measurement of [Formula: see text] phase, we will study small baseline experiments: Chooz [Formula: see text], T2K [Formula: see text] and ESS [Formula: see text], medium baseline experiment: NO[Formula: see text]A [Formula: see text] and long baseline experiment: LBNE [Formula: see text].

An Analytic Formulation of PMD-Induced Pulse Distortion

2015 ◽  
Vol 36 (4) ◽  
Author(s):  
Witold Bardyszewski ◽  
Michael Reimer ◽  
David Yevick
Keyword(s):  
Pulse Shape ◽  
Error Probability ◽  
Input Pulse ◽  
Polarization Mode Dispersion ◽  
Second Order ◽  
Mode Dispersion ◽  
Pulse Distortion ◽  
Order Expansion ◽  
Analytic Expression

AbstractWe systematically analyze the pulse distortion resulting from polarization mode dispersion (PMD) by deriving an analytic expression for the characteristic function of the system bit error probability (BEP) density in terms of the lowest-order moments of the Fourier transformed input pulse shape. We determine the range of validity of our technique, which implements a second-order expansion of the Jones matrix, by comparing our results for chirped and unchirped input pulses with direct numerical simulations. Our method may be easily applied to analyze the role of the first- and second-order PMD in the interference between adjacent pulses.

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