Action recognition using a hierarchy of feature groups

To improve the recognition performance of video human actions,an approach that models the video actions in a hierarchical way is proposed. This hierarchical model summarizes the action contents with different spatio-temporal domains according to the properties of human body movement.First,the temporal gradient combined with the constraint of coherent motion pattern is utilized to extract stable and dense motion features that are viewed as point features,then the mean-shift clustering algorithm with the adaptive scale kernel is used to label these features.After pooling the features with the same label to generate part-based representation,the visual word responses within one large scale volume are collected as video object representation.On the benchmark KTH（Kungliga Tekniska H？gskolan）and UCF （University of Central Florida）-sports action datasets,the experimental results show that the proposed method enhances the representative and discriminative power of action features, and improves recognition rates.Compared with other related literature,the proposed method obtains superior performance.

Construction of new bornological quantum groups based on Galois objects

Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.

FUNDAMENTAL GROUPS OF CLOSED POSITIVELY CURVED MANIFOLDS WITH ALMOST DISCRETE ABELIAN GROUP ACTIONS

Let M be a closed n-manifold of positive sectional curvature. Assume that M admits an effective isometrical T1× Zpk-action with p prime. The main result of the article n＋1 for n 〉 5, then there exists a positive constant p（n）, is that ifk=lforn=3or k〉 n＋1/4 for n≥5,then there exists a positive constant p（n）,depending only on n, such that π1 （M） is cyclic if p ≥ p（n）.

Lattice of Finite Group Actions on Prism Manifolds

The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.

The p.q.-Baer Property of Skew Group Rings under Finite Group Action

In this paper, Let R is a ring, G be a finite group of ring automorphisms of R. R*G denote the skew group ring of R under G. We investigate the right p.q.-Baer property of skew group rings under finite group action, Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R, then 1) R*G is p.q.-Baer if and only if R is G-p.q.-Baer;2) if R is p.q.-Baer, then R*G is p.q.-Baer.

The p.q.-Baer Property of Fixed Rings under Finite Group Action

A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. For a ring R, let G be a finite group of ring automorphisms of R. We denote the fixed ring of R under G by RG. In this work, we investigated the right p.q.-Baer property of fixed rings under finite group action. Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R. Then we show that: 1) If R is G-p.q.-Baer, then RG is p.q.-Baer;2) If R is p.q.-Baer, then RG are p.q.-Baer.

Chemospecific and Regioselective Ethereal Methyl-Oxygen Bond Cleavage Behavior of Aroylated Dimethoxynaphthalenes by Combined Action of AlCl₃and Aroyl Group

AlCl3-mediated cleavage of ethereal methyl–oxygen bond in aroylated 2,7-dimethoxynaphthalene compounds proceeds chemospecifically and regioselectively. The ethereal bond at the β(2)-position of 1-monoaroylated 2,7-dimethoxynaphthalene is cleaved readily and predominantly against the β(7)-position, whereas scission of β-ethereal bonds of 1,8-diaroylated 2,7-dimethoxynaphthalene hardly undergoes like the non-aroylated mother frame compound of 2,7-dimethoxynaphthalene.

Group Structure of Stabilizer of 2×2 Matrix under Similarity Action

This paper determines the group structure of stabilizer of 2×2 matrix under similarity action over arbitrary field. Then, the cardinal number of any orbit is calculated over finite field.

ON DENSITY OF SMOOTH ELEMENTS FOR AN ACTION OF AN AMENABLE GROUP

The aim of this paper is to prove the problem 2.2.2 in Bratteli's paper, It is proved that the problem is true for amenable group action.

Lie Groups Actions on Non Orientable <i>n</i>-Dimensional Complex Manifolds

Analytic atlases on can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-Möbius transformations in complex coordinates Abelian groups are constructed making this manifold a Lie group. Actions of Lie groups on differentiable manifolds are well known and serve different purposes. We have introduced in previous works actions of Lie groups on non orientable Klein surfaces. The purpose of this work is to extend those studies to non orientable n-dimensional complex manifolds. Such manifolds are obtained by factorizing with the two elements group of a fixed point free antianalytic involution of . Involutions h(z) of this kind are obtained linearly by composing special Möbius transformations of the planes with the mapping . A convenient partition of is performed which helps defining an internal operation on and finally actions of the previously defined Lie groups on the non orientable manifold are displayed.

CHAOTIC GROUP ACTIONS

It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F ,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.

Differential Representations of SO(4) Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.

Properties of Suborbits of the Dihedral Group D_nActing on Ordered Subsets

A group action on a set is a process of developing an algebraic structure through a relation defined by the permutations in the group and the elements of the set. The process suppresses most of the group properties, emphasizing the permutation aspect, so that the algebraic structure has a wider application among other algebras. Such structures not only reveal connections between different areas in Mathematics but also make use of results in one area to suggest conjectures and also prove results in a related area. The structure (G, X) is a transitive permutation group G acting on the set X. Investigations on the properties associated with various groups acting on various sets have formed a subject of recent study. A lot of investigations have been done on the action of the symmetric group Sn on various sets, with regard to rank, suborbits and subdegrees. However, the action of the dihedral group has not been thoroughly worked on. This study aims at investigating the properties of suborbits of the dihedral group Dn acting on ordered subsets of ?X={1,2,...,N}. The action of Dn on X[r], the set of all ordered r-element subsets of X, has been shown to be transitive if and only if n = 3. The number of self-paired suborbits of Dn acting on X[r] has been determined, amongst other properties. Some of the results have been used to determine graphical properties of associated suborbital graphs, which also reflect some group theoretic properties. It has also been proved that when G = Dn acts on ordered adjacent vertices of G, the number of self-paired suborbits is n + 1 if n is odd and n + 2 if n is even. The study has also revealed a conjecture that gives a formula for computing the self-paired suborbits of the action of Dn on its ordered adjacent vertices. Pro-perties of suborbits are significant as they form a link between group theory and graph theory.

THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.

Group Action on Fuzzy Modules

In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.

The Orbital Graph of Primitive Group with Socle A7 ×A7

In this paper, we mainly study the orbital graphs of primitive groups with the socle A7 x A7 which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7, then we discuss the stabilizer of two points in A7. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.

Personalized Action Rules for Side Effects Object Grouping

There have been multiple techniques to discover action-rules, but the problem of triggering those rules was left exclusively to domain knowledge and domain experts. When meta-actions are applied on objects to trigger a specific rule, they might as well trigger transitions outside of the target action rule scope. Those additional transitions are called side effects, which could be positive or negative. Negative side effects could be devastating in some domains such as healthcare. In this paper, we strive to reduce those negative side effects by extracting personalized action rules. We proposed three object-grouping schemes with regards to same negative side effects to extract personalized action rules for each object group. We also studied the tinnitus handicap inventory data to apply and compare the three grouping schemes.

A Contribution to the DLF-Theory: On Singularities of the SU(2,2)-Action in U(1,1)

Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.

Asymmetric Key Cryptosystem for Image Encryption by Elliptic Curve over Galois Field GF(2^(n))

Protecting the integrity and secrecy of digital data transmitted through the internet is a growing problem.In this paper,we introduce an asymmetric key algorithm for specifically processing images with larger bit values.To overcome the separate flaws of elliptic curve cryptography(ECC)and the Hill cipher(HC),we present an approach to picture encryption by combining these two encryption approaches.In addition,to strengthen our scheme,the group laws are defined over the rational points of a given elliptic curve(EC)over a Galois field(GF).The exclusive-or(XOR)function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key matrix.By integrating the inverse function on the pixels of the image,we have improved system security and have a wider key space.Furthermore,through comprehensive analysis of the proposed scheme with different available analyses and standard attacks,it is confirmed that our proposed scheme provides improved speed,security,and efficiency.

环F_2+uF_2的Galois扩张上的迹码

环F2+uF2是介于环Z4与域F4之间的一种四元素环,因此分享了环Z4与域F4的一些好的性质,此环上的编码理论研究成为一个新的热点。该文给出了环F2+uF2的Galois扩张的相关理论,指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群;定义了Galois扩环上的迹码的概念及子环子码的概念,证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。