scholarly journals Fractional isospectral and non-isospectral AKNS hierarchies and their analytic methods for N-fractal solutions with Mittag-Leffler functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bo Xu ◽  
Yufeng Zhang ◽  
Sheng Zhang
Keyword(s):  
Spectral Problem ◽  
Fractional Order ◽  
Point Of View ◽  
Adjoint Equations ◽  
Scattering Data ◽  
Bilinear Method ◽  
Soliton Equation ◽  
Scattering Transform ◽  
First Time ◽  
Hirota Bilinear

AbstractAblowitz–Kaup–Newell–Segur (AKNS) linear spectral problem gives birth to many important nonlinear mathematical physics equations including nonlocal ones. This paper derives two fractional order AKNS hierarchies which have not been reported in the literature by equipping the AKNS spectral problem and its adjoint equations with local fractional order partial derivative for the first time. One is the space-time fractional order isospectral AKNS (stfisAKNS) hierarchy, three reductions of which generate the fractional order local and nonlocal nonlinear Schrödinger (flnNLS) and modified Kortweg–de Vries (fmKdV) hierarchies as well as reverse-t NLS (frtNLS) hierarchy, and the other is the time-fractional order non-isospectral AKNS (tfnisAKNS) hierarchy. By transforming the stfisAKNS hierarchy into two fractional bilinear forms and reconstructing the potentials from fractional scattering data corresponding to the tfnisAKNS hierarchy, three pairs of uniform formulas of novel N-fractal solutions with Mittag-Leffler functions are obtained through the Hirota bilinear method (HBM) and the inverse scattering transform (IST). Restricted to the Cantor set, some obtained continuous everywhere but nondifferentiable one- and two-fractal solutions are shown by figures directly. More meaningfully, the problems worth exploring of constructing N-fractal solutions of soliton equation hierarchies by HBM and IST are solved, taking stfisAKNS and tfnisAKNS hierarchies as examples, from the point of view of local fractional order derivatives. Furthermore, this paper shows that HBM and IST can be used to construct some N-fractal solutions of other soliton equation hierarchies.

Riemann–Hilbert problem for the generalized modified Korteweg–de Vries equation with N distinct arbitrary-order poles

2021 ◽  
pp. 2150232
Author(s):  
Xin Wu ◽  
Shou-Fu Tian
Keyword(s):  
Hilbert Problem ◽  
Asymptotic Properties ◽  
Scattering Data ◽  
Direct Scattering ◽  
Scattering Transform ◽  
De Vries ◽  
Jost Functions ◽  
Special Solutions ◽  
First Time ◽  
Riemann Hilbert Problem

In this work, the generalized modified Korteweg–de Vries (gmKdV) equation is constructed by the first time and is solved by the Riemann–Hilbert method with the zero boundary condition. In the direct scattering transform, the analytical and asymptotic properties related to the Jost functions and the scattering matrix are given. On the basis of the above results, the appropriate Riemann–Hilbert problem (RHP) is constructed. By solving the RHP, we obtain the exact solution of the gmKdV equation in the case of no reflection potential when the scattering data [Formula: see text] has simple poles and higher-order poles. Furthermore, the three special solutions under different zero points are given and the phenomenon of their spread is described, respectively.

Thanato-Laboratorien. Theorien von Tod und Sterben und Elias Canettis Buch gegen den Tod

2020 ◽  
Vol 4 (1) ◽  
pp. 67-86
Author(s):  
Elisabeth Heyne
Keyword(s):  
Human Life ◽  
Death And Dying ◽  
Point Of View ◽  
Visual Images ◽  
Elias Canetti ◽  
History Of ◽  
Series Of Experiments ◽  
First Time ◽  
Textual Form ◽  
Or History

AbstractAlthough visual culture of the 21th century increasingly focuses on representation of death and dying, contemporary discourses still lack a language of death adequate to the event shown by pictures and visual images from an outside point of view. Following this observation, this article suggests a re-reading of 20th century author Elias Canetti. His lifelong notes have been edited and published posthumously for the first time in 2014. Thanks to this edition Canetti's short texts and aphorisms can be focused as a textual laboratory in which he tries to model a language of death on experimental practices of natural sciences. The miniature series of experiments address the problem of death, not representable in discourses of cultural studies, system theory or history of knowledge, and in doing so, Canetti creates liminal texts at the margins of western concepts of (human) life, science and established textual form.

A Nabatean port on the Red Sea: note on the pottery finds from al-Qusayr (al-Wajh, Saudi Arabia)

2020 ◽  
Author(s):  
Caroline Durand
Keyword(s):  
Saudi Arabia ◽  
19Th Century ◽  
Red Sea ◽  
Point Of View ◽  
The Other ◽  
Trade Routes ◽  
Other Hand ◽  
Roman Egypt ◽  
Pottery Sherds ◽  
First Time

Al-Qusayr is located 40 km south of modern al-Wajh, roughly 7 km from the eastern Red Sea shore. This site is known since the mid-19th century, when the explorer R. Burton described it for the first time, in particular the remains of a monumental building so-called al-Qasr. In March 2016, a new survey of the site was undertaken by the al-‘Ula–al-Wajh Survey Project. This survey focused not only on al-Qasr but also on the surrounding site corresponding to the ancient settlement. A surface collection of pottery sherds revealed a striking combination of Mediterranean and Egyptian imports on one hand, and of Nabataean productions on the other hand. This material is particularly homogeneous on the chronological point of view, suggesting a rather limited occupation period for the site. Attesting contacts between Mediterranean merchants, Roman Egypt and the Nabataean kingdom, these new data allow a complete reassessment of the importance of this locality in the Red Sea trade routes during antiquity.

Ground state molecular parameters of phosphine, PH3, from the simultaneous analysis of the high-resolution infrared, microwave and submillimeterwave spectra

1985 ◽  
Vol 50 (11) ◽  
pp. 2480-2492 ◽  
Author(s):  
Soňa Přádná ◽  
Dušan Papoušek ◽  
Jyrki Kauppinen ◽  
Sergei P. Belov ◽  
Andrei F. Krupnov ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Ground State ◽  
Unitary Transformation ◽  
Point Of View ◽  
Acoustic Detection ◽  
Molecular Parameters ◽  
Microwave Spectrometer ◽  
Fourier Transform Spectra ◽  
First Time

Fourier transform spectra of the ν2 band of PH3 have been remeasured with 0.0045 cm-1 resolution. Ground state combination differences from these data have been fitted simultaneously with the microwave and submillimeterwave data to determine the ground state spectroscopical parameters of PH3 including the parameters of the Δk = ± 3n interactions. The correlation between the latter parameters has been discussed from the point of view of the existence of two equivalent effective rotational operators which are related by a unitary transformation. The ΔJ = 0, +1, ΔK = 0 (A1 ↔ A2, E ↔ E) rotational transitions in the ν2 and ν4 states have been measured for the first time by using a microwave spectrometer and a radiofrequency spectrometer with acoustic detection.

scholarly journals An exceptionally preserved conulariid from Ordovician erratics of Northern European Lowlands

PalZ ◽  
2021 ◽  
Author(s):  
Consuelo Sendino ◽  
Martin M. Bochmann
Keyword(s):  
Internal Structure ◽  
Late Pleistocene ◽  
Point Of View ◽  
Three Dimensions ◽  
Northern European ◽  
Current Location ◽  
Transport Direction ◽  
First Time ◽  
Erratic Boulder

AbstractA conulariid preserved in three dimensions from Ordovician fluvioglacial erratics of the Northern European Lowlands (North German Plain) is described under open nomenclature. It is assigned to the genus Conularia with similarities to Baltoscandian conulariids. The lithology of the erratic boulder and fauna contained in it provide important information on the origin and transport direction of the sediment preserved in a kame from the Saalian glaciation. This paper deals with the site of origin of the boulder in Baltoscandia analysing the comprised palaeofauna, from a palaeostratigraphic and palaeogeographic point of view, from its deposition in Ordovician times until its arrival at its current location in the Late Pleistocene. It also reveals for the first time the internal structure of the conulariid aperture.

scholarly journals Approximate analytical fractional view of convection–diffusion equations

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 897-905
Author(s):  
Hassan Khan ◽  
Saima Mustafa ◽  
Izaz Ali ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Variational Iteration Method ◽  
Absolute Error ◽  
Form Solution ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Suggested Technique ◽  
First Time ◽  
Modified Variational Iteration Method

Abstract In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection–diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.

Information-based decoding of the coupling among human brain activity and movement paths

2021 ◽  
pp. 1-10
Author(s):  
Shahul Mujib Kamal ◽  
Norazryana Mat Dawi ◽  
Hamidreza Namazi
Keyword(s):  
Brain Activity ◽  
Point Of View ◽  
Physiological Signals ◽  
Human Walking ◽  
Eeg Signals ◽  
Rehabilitation Science ◽  
Information Contents ◽  
First Time ◽  
The Brain ◽  
Brain Reaction

BACKGROUND: Walking like many other actions of a human is controlled by the brain through the nervous system. In fact, if a problem occurs in our brain, we cannot walk correctly. Therefore, the analysis of the coupling of brain activity and walking is very important especially in rehabilitation science. The complexity of movement paths is one of the factors that affect human walking. For instance, if we walk on a path that is more complex, our brain activity increases to adjust our movements. OBJECTIVE: This study for the first time analyzed the coupling of walking paths and brain reaction from the information point of view. METHODS: We analyzed the Shannon entropy for electroencephalography (EEG) signals versus the walking paths in order to relate their information contents. RESULTS: According to the results, walking on a path that contains more information causes more information in EEG signals. A strong correlation (p= 0.9999) was observed between the information contents of EEG signals and walking paths. Our method of analysis can also be used to investigate the relation among other physiological signals of a human and walking paths, which has great benefits in rehabilitation science.

scholarly journals New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gui-qiong Xu
Keyword(s):  
Field Equation ◽  
Standing Wave ◽  
Higgs Field ◽  
Jacobi Elliptic Function ◽  
Bilinear Method ◽  
Wave Solutions ◽  
New Type ◽  
Function Expression ◽  
Parameter Values ◽  
Hirota Bilinear

Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation. The Jacobi elliptic function expression and long wave limits of the periodic solutions are also presented. By selecting appropriate parameter values, we analyze the interaction properties of periodic-periodic waves and periodic-solitary waves by some figures.

“Satisfied with the Ruins of Berlin”: The German Capital’s Image in Soviet Graphics of 1945

2021 ◽  
Vol 17 (6) ◽  
pp. 564-575
Author(s):  
Irina I. Rutsinskaya
Keyword(s):  
Visual Art ◽  
Visual Image ◽  
Point Of View ◽  
The Public ◽  
Historical Justice ◽  
Public Consciousness ◽  
Post War ◽  
The One ◽  
First Time ◽  
The City

An artist who finds themselves in the last days of a war in the enemy’s defeated capital may not just fix its objects dispassionately. Many factors influence the selection and depicturing manner of the objects. One of the factors is satisfaction from the accomplished retribution, awareness of the historical justice triumph. Researchers think such reactions are inevitable. The article offers to consider from this point of view the drawings created by Soviet artists in Berlin in the spring and summer of 1945. Such an analysis of the German capital’s visual image is conducted for the first time. It shows that the above reactions were not the only ones. The graphics of the first post-war days no less clearly and consistently express other feelings and intentions of their authors: the desire to accurately document and fix the image of the city and some of its structures in history, the happiness from the silence of peace, and the simple interest in the monuments of European art.The article examines Berlin scenes as evidences of the transition from front-line graphics focused on the visual recording of the war traces to peacetime graphics; from documentary — to artistry; from the worldview of a person at war — to the one of a person who lived to victory. In this approach, it has been important to consider the graphic images of Berlin in unity with the diary and memoir texts belonging to both artists and ordinary soldiers who participated in the storming of Berlin. The combination of verbal and visual sources helps to present the German capital’s image that existed in the public consciousness, as well as the specificity of its representation by means of visual art.

Lump solutions to a generalized Kadomtsev–Petviashvili–Ito equation

2021 ◽  
pp. 2150437
Author(s):  
Liyuan Ding ◽  
Wen-Xiu Ma ◽  
Yehui Huang
Keyword(s):  
Symbolic Computation ◽  
Three Dimensional ◽  
Order Derivative ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Dynamical Behaviors ◽  
Contour Plots ◽  
Hirota Bilinear ◽  
Ito Equation

A (2+1)-dimensional generalized Kadomtsev–Petviashvili–Ito equation is introduced. Upon adding some second-order derivative terms, its various lump solutions are explicitly constructed by utilizing the Hirota bilinear method and calculated through the symbolic computation system Maple. Furthermore, two specific lump solutions are obtained with particular choices of the parameters and their dynamical behaviors are analyzed through three-dimensional plots and contour plots.

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