## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (202.070 recursos)

Abstract and Applied Analysis

1. #### First Passage Time of a Markov Chain That Converges to Bessel Process

Kounta, Moussa
We investigate the probability of the first hitting time of some discrete Markov chain that converges weakly to the Bessel process. Both the probability that the chain will hit a given boundary before the other and the average number of transitions are computed explicitly. Furthermore, we show that the quantities that we obtained tend (with the Euclidian metric) to the corresponding ones for the Bessel process.

2. #### Contractibility of Fixed Point Sets of Mean-Type Mappings

Iampiboonvatana, S.; Chaoha, P.
We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.

3. #### Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems

Chen, Xiaoxing; Hu, Manfeng
Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.

4. #### Approximation Properties of $q$ -Bernoulli Polynomials

We study the $q$ -analogue of Euler-Maclaurin formula and by introducing a new $q$ -operator we drive to this form. Moreover, approximation properties of $q$ -Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of $q$ -Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory.

5. #### Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”

Latrous, C.; Memou, A.

6. #### Corrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”

Latrous, C.; Memou, A.

7. #### On the Output Controllability of Positive Discrete Linear Delay Systems

Naim, Mouhcine; Lahmidi, Fouad; Namir, Abdelwahed; Rachik, Mostafa
Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.

8. #### On the Output Controllability of Positive Discrete Linear Delay Systems

Naim, Mouhcine; Lahmidi, Fouad; Namir, Abdelwahed; Rachik, Mostafa
Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.

9. #### Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function

Yun, Beong In
We introduce a generalized sigmoidal transformation ${w}_{m}(r;x)$ on a given interval $[a,b]$ with a threshold at $x=r\in (a,b)$ . Using ${w}_{m}(r;x)$ , we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by...

10. #### Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function

Yun, Beong In
We introduce a generalized sigmoidal transformation ${w}_{m}(r;x)$ on a given interval $[a,b]$ with a threshold at $x=r\in (a,b)$ . Using ${w}_{m}(r;x)$ , we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by...

11. #### Corrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems”

Asfaw, Teffera M.

12. #### Corrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems”

Asfaw, Teffera M.

13. #### Applications of the $g$ -Drazin Inverse to the Heat Equation and a Delay Differential Equation

Abdeljabbar, Alrazi; Tran, Trung Dinh
We consider applications of the $g$ -Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space.

14. #### Applications of the $g$ -Drazin Inverse to the Heat Equation and a Delay Differential Equation

Abdeljabbar, Alrazi; Tran, Trung Dinh
We consider applications of the $g$ -Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space.

15. #### The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

Gómez-Valle, L.; Habibilashkary, Z.; Martínez-Rodríguez, J.
In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we...

16. #### The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

Gómez-Valle, L.; Habibilashkary, Z.; Martínez-Rodríguez, J.
In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we...

17. #### The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

Gómez-Valle, L.; Habibilashkary, Z.; Martínez-Rodríguez, J.
In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we...

18. #### Three Different Methods for New Soliton Solutions of the Generalized NLS Equation

Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions; then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the RKL model, the generalized derivative NLS equation. The solitary wave solutions and trigonometric function solutions are obtained. The obtained solutions are very useful in the nonlinear pulse propagation through optical fibers.