Adaptive Video Dual Domain Watermarking Scheme Based on PHT Moment and Optimized Spread Transform Dither Modulation

To address the challenges of video copyright protection and ensure the perfect recovery of original video,we propose a dual-domain watermarking scheme for digital video,inspired by Robust Reversible Watermarking(RRW)technology used in digital images.Our approach introduces a parameter optimization strategy that incre-mentally adjusts scheme parameters through attack simulation fitting,allowing for adaptive tuning of experimental parameters.In this scheme,the low-frequency Polar Harmonic Transform(PHT)moment is utilized as the embedding domain for robust watermarking,enhancing stability against simulation attacks while implementing the parameter optimization strategy.Through extensive attack simulations across various digital videos,we identify the optimal low-frequency PHT moment using adaptive normalization.Subsequently,the embedding parameters for robust watermarking are adaptively adjusted to maximize robustness.To address computational efficiency and practical requirements,the unnormalized high-frequency PHT moment is selected as the embedding domain for reversible watermarking.We optimize the traditional single-stage extended transform dithering modulation(STDM)to facilitate multi-stage embedding in the dual-domain watermarking process.In practice,the video embedded with a robust watermark serves as the candidate video.This candidate video undergoes simulation according to the parameter optimization strategy to balance robustness and embedding capacity,with adaptive determination of embedding strength.The reversible watermarking is formed by combining errors and other information,utilizing recursive coding technology to ensure reversibility without attacks.Comprehensive analyses of multiple performance indicators demonstrate that our scheme exhibits strong robustness against Common Signal Processing(CSP)and Geometric Deformation(GD)attacks,outperforming other advanced video watermarking algorithms under similar conditions of invisibility,reversibility,and embedding capacity.This underscores the effectiveness and feasibility of our attack simulation fitting strategy.

The Report of Homological Algebra

The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.

A Class of Simple Modules for Electrical Lie Algebra of Type D_(5)

The simple modules for electrical Lie algebra of type D5 were investigated.The sufficient and necessary criteria of the simple Z-graded highest weight modules were established by means of determining the singular vectors of the Verma modules.The simple highest weight module is isomorphic to either that for the symplectic Lie algebra sp4 or Verma module.

Generalized super-Virsoro algebras and their Verma modules

For any additive subgroup M of a field F and α∈F such that 2α∈M ,there are two classes of generalized super-Virasoro algebras denoted by SVir [M,α] and SVir [M,α] by Su and Zhao. The latter is in fact a trivial extension of the former. In this paper,based on the discussion on isomorphisms,the Verma modules of Svir [ M,α] are studied,and the irreducibility of these modules are obtained.

CHAIN CONDITIONS FOR C＊-ALGEBRAS COMING FROM HILBERT C＊-MODULES

In this paper we define and study chain conditions for Hilbert C＊-modules through their C＊-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C＊-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C＊-algebra with a faithful conditional expectation.

Two Dimensional Indecomposable Modules over Infinite Dimensional Hereditary Path Algebras

Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.

The Structure Theorem for Module Coalgebras

This paper,mainly gives the structure theorem for module coalgebras by a kind of new method,and deletes the condition that the antipode S of the Hopf algebra H is bijective.

On the Decomposition of Hopf Module Coalgebra

In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.

Simple Bounded Weight Modules for the Vector Field Lie Algebras of Infinite Rank

In this paper,we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of in nite rank.It turns out that any such modules are intermediate series modules.This result is very di erent from the vector eld Lie algebra Wd of nite rank.

On the Structure of the B-cocleft Module Coalgebra

In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.

Imaginary Whittaker Modules of the Twisted Affine Nappi-Witten Lie Algebra <img src="http://admin.scirp.org/Editer/attached/image/Edit_fc740d60-7009-4d6f-939a-ac2a113f1539.bmp"alt=""/>

The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.

QED-Lie Algebra and Their &pound;-Modules in Superconductivity

It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) ?andO(3,1) , based in admissible representations of U(1) , and SU(n)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of ￡-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.

新一代通用视频编码标准H.266/VVC:现状与发展

相比于上一代标准,新一代通用视频编码标准(H.266/VVC)在同等质量下能够节省大约50%的码率,且适用于多种多样的视频应用场景。论文从H.266/VVC的关键技术出发,对标准的现状、实现和应用发展进行深入探讨。H.266/VVC沿用既往标准中的双层码流体系和混合编码框架,针对帧内预测、帧间预测、变换、量化、环路滤波等所有主要编码模块进行了技术革新,并为屏幕内容视频等应用提供了高效的专用编码工具。H.266/VVC标准目前已处于实用化阶段,官方参考软件VTM和开源编解码器VVenC/VVdeC是目前最具代表性的软件编解码实现。对H.266/VVC的性能分析可以看出:H.266/VVC针对高分辨率视频取得的编码增益更为突出;主要编码工具对性能的贡献通常以复杂度为代价,但也有部分编码工具在提升编码性能的同时可降低整体编码复杂度。H.266/VVC的硬件实现面临诸多挑战,发展明显滞后于软件实现,现有研究主要集中在对具体编码模块的硬件加速方面。H.266/VVC标准发布之后,下一代视频编码标准的发展目前仍围绕混合编码框架进行探索,聚焦在两大方向:超越VVC的增强压缩关注更为先进的、非神经网络的编码工具,基于神经网络的视频编码则探索采用神经网络的编码工具。除此之外,部分或完全跳出现有混合编码框架的端到端视频编码也在飞速发展,未来视频编码标准与神经网络结合成为趋势,但面临着计算资源依赖和稳定结构两方面的考验。

Injective Envelopes of a Hilbert C~*Module

As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .

Crossed modules of Lie color algebras

The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.

Induced Modules of Restricted Lie Superalgebras

In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.

相间短路故障条件下级联H桥光伏逆变器的有功功率回流抑制策略

针对现有零序电压补偿策略无法有效抑制级联H桥光伏并网逆变器在电网不对称故障期间存在有功功率回流的问题,定量分析现有零序电压补偿策略的局限性,提出一种正负序最大最小值谐波零序电压注入控制策略,该策略能有效缩小过调制区域,扩大级联H桥型光伏并网逆变器在相间短路故障条件下的运行范围。实验结果验证了所提出控制策略的有效性和可行性。

Module Structures on U(ε^(-))for the Euclidean Algebra

We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie algebra.Sufficient and necessary conditions for the simplicity of these modules are given.From these modules we construct modules which are infinitely generated when restricted to the maximal toral subalgebra.

Derivations of the Schrodinger Algebra on Restricted Simple Modules

Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ) of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.