Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

Hierarchy of Lax Integrable Lattice Equations, Darboux Transformation and Conservation Laws

A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy.

BACKLUND TRANSFORMATION, NONLINEAR SUPERPOSITION FORMULAE AND INFINITE CONSERVED LAWS OF BENJAMIN EQUATION

Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.

THE TRANSFORMATION LAW AND TRACE FORMULA ON THETA SERIES UNDER SIEGEL MODULAR GROUP

The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.

Gentrification Within the Law of Transformation of Areas at Disaster Risks in Turkey Sulukule,Istanbul Example

With coming in force of The Law of Transformation of Areas at Disaster Risks numbered 16.5.2012/6306 by Ministry of Environment and Urbanization,the concept of urban transformation has entered to our life in Turkey.Gentrification as one of the forms of urban transformation brought the existence of liberated zones produced by neo-liberal mentality.Sulukule area(Neslisah Sultan settlement)which is subject to research is counted among“the areas to be renewed and to be put under preservation”by numbered 2006/10299 decision of Council of Ministers.Due to the shortage of lands in the city,it is observed especially in 1980s that the families in high-income group have preferred to live in horizontally expending villa towns far from the center.While these residential areas are deepening the distance from the center in time,the pressure of housing demand of middle-income people and rent circles who are not planning to leave the city center caused to have an eye on these areas which are residential areas of mostly low-income people and appeared in certain regions as they are established without infrastructure and healthy conditions.With this law,the transformation has started in the areas such as Fikirtepe,Dolapdere,Esenler,and Banks of Halic(Golden Horn)where structural life is completed,and floor area ratio has been raised to 4.0 from 2.07.Vertical housing is stimulated by adding the street between the parcels to the blocks,it has been tried to prevent the victimization of local people to unearned income.There are some quarters that,under the name of gentrification,Romany citizens who passed to permanent settlement from nomadic culture at the Ottoman era,and who are engaged in activities such as handicraft,adornments,shoe making,weaving beside the show business at Fatih Sulukule district are convicted to lodge in the houses built in suburban if they have title deed,and in jerry-built tents if they don’t have deed.Chamber of Architects,Chamber of City Planners Istanbul Branch and Roma Culture Development and Solidarity Association filed“nullity suit”and“stay of execution”.Despite the continuing judicial process,the demolition started in 2009,and starting the constructing the villas in 2010 breaking the resistance of Romany citizens,the area was victimized to rent.

A novel image encryption scheme based on Keplers third law and random Hadamard transform

In this paper, a novel image encryption scheme based on Keplers third law and random Hadamard transform is proposed to ensure the security of a digital image. First, a set of Kepler periodic sequences is generated to permutate image data, which is characteristic of the plain-image and the Keplers third law. Then, a random Hadamard matrix is constructed by combining the standard Hadamard matrix with the hyper-Chen chaotic system, which is used to further scramble the image coefficients when the image is transformed through random Hadamard transform. In the end, the permuted image presents interweaving diffusion based on two special matrices, which are constructed by Kepler periodic sequence and chaos system. The experimental results and performance analysis show that the proposed encrypted scheme is highly sensitive to the plain-image and external keys, and has a high security and speed, which are very suitable for secure real-time communication of image data.

An Improved Robust Model Predictive Control Approach to Systems with Linear Fractional Transformation Perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.

Riccati-type Bcklund transformations of nonisospectral and generalized variable-coefficient KdV equations

We extend the method of constructing Bgcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg-de Vries （KdV） equations as examples, their Backlund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Es- pecially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.

Watermarking Scheme Based on Wavelet Transformation and Visual Cryptography

Based on the principles of the visual cryptography and the law of large numbers, the unexpanded shares are generated during the processes of embedding and verifying the hidden watermark. The watermark embedding is done in the frequency domain, which can be decoded by the human visual system （HVS） without the necessity of any complicated computation and the help of the original image. Experimental results indicated that our method had a good robustness on darkening, lightening, blurring, sharpening, noise, distorting, jitter, joint photographic experts group （JPEG） compression, and crop attacks.

From Translation to Linear and Linear Canonical Transformations

In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂x) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.

Scaling Transformation for Nonlocal Interactions

In the light of their relationships with renormalization, in this paper we associate the scaling transformation with nonlocal interactions. On one hand, the association leads us to interpret the nonlocality with locally symmetric method. On the other hand, we find that the nonlocal interaction between hadrons could be test ground for scaling transformation if ascribing the running effects in renormalization to scaling transformation. The nonlocal interaction Lagrangian turns out to vary under scaling transformation, analogous to running cases in renormalization. And the total Lagrangian becomes scale invariant only under some extreme conditions. The conservation law of this extreme Lagrangian is discussed and a contribution named scalum appears to the spin angular momentum. Finally a mechanism is designed to test the scaling effect on nonlocal interaction.

Optimization Parameter of Transformation of Parallel Translation for Ship Pitch Simulation

The transformation of parallel translation can improve the smoothness of discrete series sometimes. In this paper, for ship pitch, a method to modify the system error is proposed via the transformation of parallel translation, which can give the optimize parameters using the Method of Minimum Squares. The series in the method can fit white exponential law better, and then be applied in GM (1,1) very well. The numerical experiments imply that the method is practical, which make the ship pitch system model more accurate than GM ( 1,1 ).

Non-Perturbative Guiding Center and Stochastic Gyrocenter Transformations:Gyro-Phase Is the Kaluza-Klein 5^(th) Dimension also for Reconciling General Relativity with Quantum Mechanics

The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model. Electrodynamics becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson’s approach. The gyrocenter law of motion is the Schrödinger equation.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

人工智能生成内容的著作权客体性思考——兼论作品判定的独创性标准选择

以基于转换器的生成式预训练模型(GPT)为代表的高阶人工智能凭借其强大的智能型内容生成机制,使得内容产品生产中的技术占比不断上升,人的直接投入占比相对下降,传统著作权法作品的独创性要求、权利人本原则等基本理论受到冲击。面对人工智能生成内容(AIGC)可作品性问题,基于自然人智力投入的创造性本质理论和闭合性作品概念显得力不从心。在过程视角下(主观标准),人工智能内容生成过程符合人类创作的思维特征;在结果视角下(客观标准),人工智能生成内容具有著作权作品的外观形式和信息消费功能,符合著作权作品的本质属性。如果人为割裂人工智能生成内容与著作权作品在产生过程和实质作用上的同质关系,强行区分人工智能生成内容和自然人创作作品的法律性质,则有悖著作权法因应技术发展调整信息消费品利益的制度旨趣,最终将导致著作权法律秩序的混乱。

网络刑法的发展回溯与理论供源

传统刑法体系遭遇网络犯罪形态后频现应答疲态,预防性立法由此显身,开启由网络犯罪策动刑法转型的号角,但网络刑法的理论根基尚不稳。网络刑法的演进是网络社会发展与网络犯罪迸发共同作用下真实的渐显;网络空间社会思维是网络刑法的建构基石,衍生丰富的刑法学意义。网络安全秩序价值的相对优位与网络自由的并重、网络安全法益的统领地位与刑法任务变更、预防性理念的内在觉醒与审慎运行,是网络刑法的根基之本,框定网络刑法的发展脉络。刑法知识迁移是渐进的,网络犯罪、网络归责、网络制裁堪当生成网络刑法知识范畴的参照性“母版”,未来可创设网络刑法典以实现知识结构的创造性立法固化。

新质生产力的知识产权法保障研究

发展新质生产力是应对社会主要矛盾变化和国际竞争的需要。新质生产力以创新为主导,对劳动者和生产资料提出了新要求。基于生产力决定生产关系、生产关系反作用于生产力的原理,知识产权法作为国际通行的调整科技、文化成果市场权益的法律,能够通过权利保护机制、创新激励机制、利益平衡机制以及市场导向机制,促进、引导新质生产力的发展。基于社会第一性、法律第二性的原理,技术发展引发社会现实的变化,对知识产权法带来新的挑战,知识产权法需从制度理念、制度设计等方面作出改进,以为新质生产力发展提供更适宜的制度保障。

人工智能背景下法学专业教学与研究的数字转型

法学专业教学与研究需要与新兴数字技术融合,实现数字转型。根据相关研究成果,分析法学专业教学与研究数字转型的构成,并以其数字化实践作为研究对象,分析数字转型的要素和准备度,探索人工智能背景下法学专业教学与研究数字转型的实践问题,尝试建构更完善的数字转型新模式。

《大明律》对成宗时期朝鲜的影响

朝鲜从成宗初年开始,适用法律偏离《大明律》的做法遭到了挑战,多种法律并存的状况发生变化,《大明律》成为定罪量刑的基本准则。随着《大明律》地位的提升,君主不可随意变通《大明律》的观念逐渐形成,《大明律》甚至成了抵制君主不正确决定的根据。由半岛特定的国情与风俗所决定,君主虽仍时或会推动朝廷对《大明律》的一些条款进行变通,但已相当节制。为了进一步提升《大明律》的地位与权威,朝廷还积极以《大明律》移风易俗,这是以法律形塑社会,乃《大明律》在半岛发挥的重要功能。

一维热传导方程推导及定解条件小结

以均匀且各向同性的细棒为例,用两种方法推导细棒在传热过程中温度所满足的偏微分方程,且对一些常见的定解条件进行总结说明.