## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Abstract and Applied Analysis

1. #### 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...

2. #### 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.

3. #### On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity

Malek, Stéphane
We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter $\mathrm{ϵ}$ . The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in $\mathbb{C}$ . We construct a family of sectorial meromorphic solutions obtained as a small perturbation in $\mathrm{ϵ}$ of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in $\mathrm{ϵ}$ as Gevrey asymptotic expansion of some order depending on...

4. #### On Singular Solutions to PDEs with Turning Point Involving a Quadratic Nonlinearity

Malek, Stéphane
We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter $\mathrm{ϵ}$ . The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in $\mathbb{C}$ . We construct a family of sectorial meromorphic solutions obtained as a small perturbation in $\mathrm{ϵ}$ of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in $\mathrm{ϵ}$ as Gevrey asymptotic...

5. #### A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem

Asfaw, Teffera M.
Let $X$ be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space ${X}^{*}$ . Let $T:X\supseteq D(T)\to {\mathrm{2}}^{{X}^{*}}$ be maximal monotone, $S:X\to {\mathrm{2}}^{{X}^{*}}$ be bounded and of type $({S}_{+}),$ and $C:D(C)\to {X}^{*}$ be compact with $D(T)\subseteq D(C)$ such that $C$ lies in ${\mathrm{\Gamma }}_{\sigma }^{\tau }$ (i.e., there exist $\sigma \ge \mathrm{0}$ and $\tau \ge \mathrm{0}$ such that $‖Cx‖\le \tau ‖x‖+\sigma$ for all $x\in D(C)$ ). A new topological degree theory is developed for operators of the type $T+S+C$ . The theory is essential because no degree theory and/or existence result is available to address solvability of...

6. #### A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem

Asfaw, Teffera M.
Let $X$ be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space ${X}^{⁎}$ . Let $T:X\supseteq D(T)\to {\mathrm{2}}^{{X}^{⁎}}$ be maximal monotone, $S:X\to {\mathrm{2}}^{{X}^{⁎}}$ be bounded and of type $({S}_{+}),$ and $C:D(C)\to {X}^{⁎}$ be compact with $D(T)\subseteq D(C)$ such that $C$ lies in ${\mathrm{\Gamma }}_{\sigma }^{\tau }$ (i.e., there exist $\sigma \ge \mathrm{0}$ and $\tau \ge \mathrm{0}$ such that $‖Cx‖\le \tau ‖x‖+\sigma$ for all $x\in D(C)$ ). A new topological degree theory is developed for operators of the type $T+S+C$ . The theory is essential because no degree theory and/or existence result is available to...

7. #### Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

Hadžiabdić, V.; Kulenović, M. R. S.; Pilav, E.
We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$ , ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$ , $n=\mathrm{0,1},\dots$ , where the parameters ${A}_{\mathrm{1}}$ , ${A}_{\mathrm{2}}$ , ${B}_{\mathrm{1}}$ , ${B}_{\mathrm{2}}$ , ${C}_{\mathrm{1}}$ , and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.

8. #### Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

Hadžiabdić, V.; Kulenović, M. R. S.; Pilav, E.
We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$ , ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$ , $n=\mathrm{0,1},\dots$ , where the parameters ${A}_{\mathrm{1}}$ , ${A}_{\mathrm{2}}$ , ${B}_{\mathrm{1}}$ , ${B}_{\mathrm{2}}$ , ${C}_{\mathrm{1}}$ , and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.

9. #### Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

Hadžiabdić, V.; Kulenović, M. R. S.; Pilav, E.
We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$ , ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$ , $n=\mathrm{0,1},\dots$ , where the parameters ${A}_{\mathrm{1}}$ , ${A}_{\mathrm{2}}$ , ${B}_{\mathrm{1}}$ , ${B}_{\mathrm{2}}$ , ${C}_{\mathrm{1}}$ , and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.

10. #### On Weighted Montgomery Identity for $k$ Points and Its Associates on Time Scales

Nwaeze, Eze R.; Tameru, Ana M.
The purpose of this paper is to establish a weighted Montgomery identity for $k$ points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

11. #### On Weighted Montgomery Identity for $k$ Points and Its Associates on Time Scales

Nwaeze, Eze R.; Tameru, Ana M.
The purpose of this paper is to establish a weighted Montgomery identity for $k$ points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

12. #### On Weighted Montgomery Identity for $k$ Points and Its Associates on Time Scales

Nwaeze, Eze R.; Tameru, Ana M.
The purpose of this paper is to establish a weighted Montgomery identity for $k$ points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

13. #### The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials

Baxhaku, Behar; Berisha, Artan
We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given.

14. #### The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials

Baxhaku, Behar; Berisha, Artan
We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given.

15. #### The Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper Type Polynomials

Baxhaku, Behar; Berisha, Artan
We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given.

16. #### Generalized Hölder’s and Minkowski’s Inequalities for Jackson’s $q$ -Integral and Some Applications to the Incomplete $q$ -Gamma Function

Nantomah, Kwara
We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s $q$ -integral. As applications, we derive some inequalities involving the incomplete $q$ -Gamma function.

17. #### Generalized Hölder’s and Minkowski’s Inequalities for Jackson’s $q$ -Integral and Some Applications to the Incomplete $q$ -Gamma Function

Nantomah, Kwara
We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s $q$ -integral. As applications, we derive some inequalities involving the incomplete $q$ -Gamma function.

18. #### Generalized Hölder’s and Minkowski’s Inequalities for Jackson’s $q$ -Integral and Some Applications to the Incomplete $q$ -Gamma Function

Nantomah, Kwara
We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s $q$ -integral. As applications, we derive some inequalities involving the incomplete $q$ -Gamma function.

19. #### Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

Hwang, Jin-soo
We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.

20. #### Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

Hwang, Jin-soo
We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.

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