scholarly journals A Spectral Collocation Technique for Riesz Fractional Chen-Lee-Liu Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
M. A. Abdelkawy ◽  
S. A. Alyami
Keyword(s):  
Schrodinger Equation ◽  
Optical Solitons ◽  
Numerical Results ◽  
Spatial Variable ◽  
The Other ◽  
Current Paper ◽  
Spectral Accuracy ◽  
Spectral Collocation ◽  
Collocation Technique ◽  
Temporal Variable

This paper discusses the study of optical solitons that are modeled by Riesz fractional Chen-Lee-Liu model, one of the versions of the famous nonlinear Schrödinger equation. This model is solved by the assistance of consecutive spectral collocation technique with two independent approaches. The first is the approach of the spatial variable, while the other is the approach of the temporal variable. It is concluded that the method of the current paper is far more efficient and credible for the proposed problem. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

Focus Position for Stripping Remnant

2020 ◽  
Vol 7 (2) ◽  
pp. 221
Author(s):  
Mohammad Ali Al Zahrani ◽  
Khulud Helal Al Thagafi
Keyword(s):  
The Other ◽  
Current Paper ◽  
Focus Position ◽  
Focus Movement ◽  
The One ◽  
Syntactic Properties ◽  
Pf Deletion ◽  
Minimalist Framework

The current paper examines the syntactic properties of HA stripping: a type of ellipsis. Within the Minimalist framework, the paper adopts the PF-Deletion approach to show that stripping in HA is derived firstly by the movement of the remnant constituent from TP to Focus Position (FP), and, secondly, by the deletion of the TP. These two operations are licensed by the Ellipsis feature (E) located in the focus head F°. Thus, on the one hand, the paper contributes to the existing body of literature supporting the hotly-debated issues on the movement of the stripping remnants, and on the other, enriches the very minimal HA studies on ellipsis. The findings show that HA stripped constituents must move to Spec, FP, before the TP- deletion process. Two pieces of evidence in support of the focus movement to FP spring from Island sensitivity and p-stranding facts in HA.

scholarly journals Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 761
Author(s):  
Călin-Ioan Gheorghiu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Error Estimation ◽  
Schrodinger Equation ◽  
Error Control ◽  
High Order ◽  
Order Of Approximation ◽  
Schrödinger Equations ◽  
Spectral Collocation ◽  
Integration Interval

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

Optical solitons for weakly nonlocal Schrödinger equation with parabolic law nonlinearity and external potential

Optik ◽  
2021 ◽  
Vol 230 ◽  
pp. 166281
Author(s):  
Lanre Akinyemi ◽  
Mehmet Şenol ◽  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Optical Solitons ◽  
External Potential ◽  
Parabolic Law ◽  
Parabolic Law Nonlinearity

Behavioral flexibility in Belief-Desire- Intention (BDI) architectures

2020 ◽  
Vol 16 (4) ◽  
pp. 343-377
Author(s):  
Adel Saadi ◽  
Ramdane Maamri ◽  
Zaidi Sahnoun
Keyword(s):  
Critical Review ◽  
Practical Reasoning ◽  
Behavioral Flexibility ◽  
The Other ◽  
Current Paper ◽  
Simple Experiment ◽  
Bdi Agents ◽  
Popular Approach ◽  
Other Hand

The Belief-Desire-Intention (BDI) model is a popular approach to design flexible agents. The key ingredient of BDI model, that contributed to concretize behavioral flexibility, is the inclusion of the practical reasoning. On the other hand, researchers signaled some missing flexibility’s ingredient, in BDI model, essentially the lack of learning. Therefore, an extensive research was conducted in order to extend BDI agents with learning. Although this latter body of research is important, the key contribution of BDI model, i.e., practical reasoning, did not receive a sufficient attention. For instance, for performance reasons, some of the concepts included in the BDI model are neglected by BDI architectures. Neglecting these concepts was criticized by some researchers, as the ability of the agent to reason will be limited, which eventually leads to a more or less flexible reasoning, depending on the concepts explicitly included. The current paper aims to stimulate the researchers to re-explore the concretization of practical reasoning in BDI architectures. Concretely, this paper aims to stimulate a critical review of BDI architectures regarding the flexibility, inherent from the practical reasoning, in the context of single agents, situated in an environment which is not associated with uncertainty. Based on this review, we sketch a new orientation and some suggested improvements for the design of BDI agents. Finally, a simple experiment on a specific case study is carried out to evaluate some suggested improvements, namely the contribution of the agent’s “well-informedness” in the enhancement of the behavioral flexibility.

Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

Distinctions in procedural meaning

2019 ◽  
Vol 11 (1) ◽  
pp. 79-108 ◽  
Author(s):  
Valandis Bardzokas
Keyword(s):  
The Other ◽  
Current Paper ◽  
Modern Greek ◽  
Careful Exploration

Abstract The current paper aims to investigate the distinctions in meaning between two prototypical markers of contrast in Modern Greek, i.e. alla and ma, from a relevance-theoretic viewpoint. At first sight, the two markers seem freely interchangeable across contexts, creating the impression that they basically share the same meaning. However, a more careful exploration of the contextual occurrences of these markers unravels their finely grained distinctions in meaning. This type of exploration requires a detailed categorization of the types of context that license or preclude the application of the markers at hand. In this sense, specific contexts highlight aspects of interpretation that motivate the use of one of the markers but not the other. Specifically, as it turns out, while the use of alla is chiefly associated with contexts of procedural elimination, in standard relevance-theoretic terms, the use of ma is justified in relation to expressing the speaker’s attitude of surprise to a contextual assumption constructed by the hearer, in addition to effecting procedural elimination. In this sense, ma proves to encode a dual constraint on the implicitly communicated content of an utterance, explained univocally in procedural terms.

scholarly journals Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 138
Author(s):  
Alyaa A. Al-Qarni ◽  
Huda O. Bakodah ◽  
Aisha A. Alshaery ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Numerical Results ◽  
Decomposition Algorithm ◽  
Adomian Decomposition ◽  
High Level ◽  
Do So

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.

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