Rights Act Research Articles

Dichotomy theorem for topological semigroup actions

Dichotomy theorem for topological semigroup actions

Bowen's equations for packing BS dimension of subsets for free semigroup actions

We introduce and study the relations between the packing BS dimension of an arbitrary subset and topological pressure for free semigroup actions. We show that the packing BS dimension is the unique root of the topological pressure function for semigroup actions. Also, we establish a variational principle between the packing BS dimension and the measure-theoretic BS dimension for an arbitrary non-invariant compact set of an action S .

Variational Principles for BS Dimension of Subsets for Free Semigroup Actions

Variational Principles for BS Dimension of Subsets for Free Semigroup Actions

Correlation Entropy of Free Semigroup Actions

Correlation Entropy of Free Semigroup Actions

On the Dimension of Limit Sets on ℙ(ℝ3) via Stationary Measures: Variational Principles and Applications

Abstract This paper investigates the (semi)group action of $\textrm{SL}_{n}({\mathbb R})$ on ${\mathbb P}({\mathbb R}^{n})$, a primary example of non-conformal, non-linear, and non-strictly contracting action. We establish variational principles of the affinity exponent for two main examples: the Borel Anosov representations and the Rauzy gasket. In [ 32], they obtain a dimension formula for the stationary measures on ${\mathbb P}({\mathbb R}^{3})$. Combined with our result, it allows us to study the Hausdorff dimension of limit sets of Anosov representations in $\textrm{SL}_{3}({\mathbb R})$ and the Rauzy gasket. It yields the equality between the Hausdorff dimensions and the affinity exponents in both settings, generalizing the classical Patterson–Sullivan formula. In the appendix, we improve the numerical lower bound of the Hausdorff dimension of Rauzy gasket to $1.5$.

Rees short exact sequences and preenvelopes

Abstract In this paper, we consider some properties of commutative diagrams of Rees short exact sequences, and we also investigate the sufficient and necessary condition under which the induced sequences by functors − ⊗ M for the left S-act M. The main conclusions extend some known results. Further, we investigate preenvelopes and precovers in the category 𝓔 S of Rees short exact sequences of right S-acts.

Ultrafine Aramid Nanofiber-Assisted Large-Area Dense Stacking of MXene Films for Electromagnetic Interference Shielding and Multisource Thermal Conversion.

Polymers are often used as adhesives to improve the mechanical properties of flexible electromagnetic interference (EMI) shielding layered films, but the introduction of these insulating adhesives inevitably reduces the EMI performance. Herein, ultrafine aramid nanofibers (UANF) with a diameter of only 2.44 nm were used as the binder to effectively infiltrate and minimize the insulating gaps in MXene films, for balancing the EMI shielding and mechanical properties. Combining the evaporation-induced scalable assembly assisted by blade coating, flexible large-scale MXene/UANF films with highly aligned and compact MXene stacking are successfully fabricated. Compared with the conventional ANF with a larger diameter of 7.05 nm, the UANF-reinforced MXene film exhibits a "brick-mortar" structure with higher orientation and compacter stacking MXene nanosheets, thus showing the higher mechanical properties, electrical conductivity, and EMI shielding performance. By optimizing MXene content, the MXene/UANF film can achieve the optimal tensile strength of 156.9 MPa, a toughness of 2.9 MJ m-3, satisfactory EMI shielding effectiveness (EMI SE) of 40.7 dB, and specific EMI SE (SSE/t) of 22782.4 dB cm2/g). Moreover, the composite film exhibits multisource thermal conversion functions including Joule heating and photothermal conversion. Therefore, the multifunctional MXene/UANF EMI shielding film with flexibility, foldability, and robust mechanical properties shows the practical potential in complex application environments.

Topological entropy of i.i.d. case and free semigroup actions

In this paper, firstly we give a new condition to prove that classical topological entropy is equal to Pesin topological entropy in i.i.d. case. After that, we generalize the concepts of topological entropy of free semigroup actions and study the relationship between the entropies of i.i.d. case and the entropies of free semigroup actions. Finally, for any non-empty subset A⊆Σm+, we introduce the concepts of entropies of any subset A actions and give an analogue of Befutov's formula (the Theorem 1 in [6]) under any subset A actions, which is a supplement of [7].

Jujube-cake inspired lightweight and flexible MXene/liquid metal/bacterial cellulose electromagnetic interference shielding film with excellent Joule heating and thermal conductivity

The modern 5G communication electronics and systems require lightweight and flexible films that have superior electromagnetic interference (EMI) shielding performance as well as high thermal conductivity. This work reports a facile “one-pot” synthesis strategy to create EMI shielding films with a structure inspired by “jujube cake”. The two-dimensional Ti3C2Tx MXene nanosheets were combined with one-dimensional bacterial cellulose (BC) to form a mechanically entangled supporting framework resembling the structure of a “sponge cake”, wherein zero-dimensional liquid metal (LM) droplets like “jujubes” were ingeniously introduced. A series of multifunctional Ti3C2Tx/LM/BC (TLB) EMI shielding films with highly efficient conductive networks and complete thermal conductivity pathways were prepared through a simple, eco-friendly and highly scalable fabrication process involving vacuum-assisted filtration and hot pressing. Such ultrathin (18 μm) and lightweight (0.63 g cm−3) TLB composite film demonstrates an outstanding specific SE (SSE/t) of 21695.8 dB cm2 g−1. Meanwhile, it exhibits a remarkable in-plane thermal conductivity of 10.44 W m−1 K−1 and exceptional Joule heat performance from room temperature to 95 °C at 3.0 V in seconds. These attractive properties and scalable fabrication of TLB composite film showcase its potential in the realm of flexible electronics, particularly for applications pertaining to EMI shielding protection, electromagnetic compatibility and thermal management.

Shadowable Points of Free Semigroup Actions

Shadowable Points of Free Semigroup Actions

A PVDF/MWCNTs/GO@MWCNTs/AgNWs bilayer structured composite film with ultra‐high EMI shielding and conductivity performance

AbstractElectromagnetic interference (EMI) shielding materials with easy processing, high electrical conductivity, and excellent absorption loss are urgently needed in aerospace, military stealth and portable electronic devices. In this study, a polyvinylidene fluoride/multi‐walled carbon nanotubes (PVDF/MWCNTs)‐3 wt% composite film prepared by simple solution mixing and polyethylene terephthalate (PET) nonwoven scraping method was used as the substrate, and the PVDF/MWCNTs/graphene oxide@multi‐walled carbon nanotubes (PVDF/MWCNTs/GO@MWCNTs) and PVDF/MWCNTs/GO@MWCNTs/silver nanowires (PVDF/MWCNTs/GO@MWCNTs/AgNWs) bilayer composite films were prepared by vacuum‐assisted filtration (VAF). When the amount of GO@MWCNTs was 20 mL, the conductivity of PVDF/MWCNTs/GO@MWCNTs film is 3.5 × 101 S m−1, the total EMI shielding effectiveness (EMI SET) was 15.5 dB and the EMI absorption efficiency (EMI SEA) was 10.7 dB, the specific EMI SE (SSE/T) was 539.5 dB/ dB/(cm−2 g). When the amount of AgNWs was 25 mL, the conductivity of PVDF/MWCNTs/GO@MWCNTs/AgNWs film with 0.47 mm thickness was 1.6 × 104 S m−1, the EMI SET was 69.1 dB, the EMI SEA was 61.1 dB, and the SSE/T was 2320.0 dB cm2 g−1. The results show that the absorption was played a dominant role in the EMI shielding mechanism of obtained films. The addition of GO@MWCNTs/AgNWs increases the electrical conductivity and EMI shielding performance of the film more than the addition of GO@MWCNTs. This is mainly because GO， MWCNTs and AgNWs formed a novel three‐dimensional conductive network structure inside the composite film due to their hydrogen bonding and van der Waals forces, which increases the carrier channels and promotes the interaction between the internal microcurrents and the electromagnetic waves, achieving the purpose of attenuating the electromagnetic waves. The obtained PVDF/MWCNTs/GO@MWCNTs/AgNWs film has good potential in EMI shielding in aerospace, military and electronic intelligence applications.Highlights Well‐dispersed and highly conductive GO@MWCNTs were prepared by hydrothermal synthesis. AgNWs with good conductivity and high aspect ratio were prepared. PVDF‐based bilayer composite films with novel 3D conductive network were prepared. The synergistic EMI shielding mechanism of the film is discussed.

Metric Mean Dimension of Free Semigroup Actions for Non-Compact Sets

Metric Mean Dimension of Free Semigroup Actions for Non-Compact Sets

Topological actions of Temperley–Lieb monoids and representation stability

In this paper, we consider the Temperley–Lieb algebras [Formula: see text] at [Formula: see text]. Since [Formula: see text], we can consider the multiplicative monoid structure and ask how this monoid acts on topological spaces. Given a monoid action on a topological space, we get an algebra action on each homology group. The main theorem of this paper explicitly deduces the representation structure of the homology groups in terms of a natural filtration associated with our [Formula: see text]-space. As a corollary of this result, we are able to study stability phenomena. There is a natural way to define representation stability in the context of [Formula: see text], and the presence of filtrations enables us to define a notion of topological stability. We are able to deduce that a filtration-stable sequence of [Formula: see text]-spaces results in representation-stable sequence of homology groups. This can be thought of as the analogue of the statement that the homology of configuration spaces forms a finitely generated FI-module.

Global regularity and decay behavior for Leray equations with critical-dissipation and its application to self-similar solutions

In this paper, we show the global regularity and the optimal decay of weak solutions to the generalized Leray problem with critical dissipation. Our approach hinges on the maximal smoothing effect, L p L^{p} -type elliptic regularity of linearization, and the action of the heat semigroup generated by the fractional powers of Laplace operator on distributions with Fourier transforms supported in an annulus. As a by-product, we construct a self-similar solution to the three-dimensional incompressible Navier-Stokes equations. Most notably, we prove the global regularity and the optimal decay without the need for additional requirements found in existing literatures.

Human Rights with Focus on Gender, Race, and Religion: A Comparative Study Between Jordanian Legislation and International Human Rights Acts

This study sheds light on the role of Jordanian legislation in implementing human rights. It focuses on the development of Jordanian laws to adjust with the current advice to help put an end to discrimination within its society. In addition to discussing the atrocities people of minorities suffer from because of their race, sex, and religion, this research focuses on the root issues that lead to discrimination. This research also focuses on the psyche behind discriminatory acts to further establish what could cause these gaps between the population of people in our current time. It includes the different treaties and laws that punish crimes fueled by hate towards those who are considered different and introduces the possible solutions to assist in eliminating this problem.

Wold decomposition and C*-envelopes of self-similar semigroup actions on graphs

We study the Wold decomposition for representations of a self-similar semigroup P action on a directed graph E. We then apply this decomposition to the case where P=N to study the C*-envelope of the associated universal non-selfadjoint operator algebra AN,E by carefully constructing explicit non-trivial dilations for non-boundary representations. In particular, it is shown that the C*-envelope of AN,E coincides with the self-similar graph C*-algebra OZ,E.

Substantive Equality and the Possibilities of the Queensland Human Rights Act 2019

The passage of the Human Rights Act 2019 (Qld) (‘HRA 2019’) was a significant achievement, particularly in a state often known for its parochial conservatism and disinterest in, if not outright rejection of, human rights. The HRA 2019 is substantially based upon the human rights Acts in place in Victoria and the Australian Capital Territory. However, there are some small, but potentially important differences between the HRA 2019 and the corresponding state and territory equivalents. In this article, I focus on one of these differences: the definition of discrimination contained in the HRA 2019. Unlike the Charter of Human Rights and Responsibilities Act 2006 (Vic) the definition of discrimination in the HRA 2019 is not tied to the definition or grounds of discrimination in the state discrimination legislation. This small but important distinction could feasibly allow courts to define discrimination and the broader notion of equality in a more substantive manner, covering a wider variety of actions and conduct, and apply that wider definition to a broader range of attributes (commonly understood as ‘grounds’). The purpose of this article is to consider the possibilities and potential challenges confronting Queensland courts in broadening the definition of discrimination in the context of HRA 2019. I argue that, though a substantive interpretation of discrimination and equality is challenging and requires a degree of ‘creativity’ on the part of judges, it is a challenge worth undertaking.

Coverings of Graphoids: Existence Theorem and Decomposition Theorems

A graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. Naturally, as it appears, this definition displays unusual behaviour since the projection of the corresponding underlying graphs is not necessarily a graph covering. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid and combinatorially in terms of voltage assignments on arcs. In the present paper, the existence theorem is formulated and proved in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. Further, the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings are studied in detail. It is shown that with mild adjustments in the formulation, all the analogous theorems that hold in the context of graphs are still valid in this wider setting.

Specification and Shadowing Properties of Free Semigroup Actions

Specification and Shadowing Properties of Free Semigroup Actions

A polynomial analogue of Berggren’s theorem on Pythagorean triples

Say that ( x , y , z ) (x, y, z) is a positive primitive integral Pythagorean triple if x , y , z x, y, z are positive integers without common factors satisfying x 2 + y 2 = z 2 x^2 + y^2 = z^2 . An old theorem of Berggren gives three integral invertible linear transformations whose semi-group actions on ( 3 , 4 , 5 ) (3, 4, 5) and ( 4 , 3 , 5 ) (4, 3, 5) generate all positive primitive Pythagorean triples in a unique manner. We establish an analogue of Berggren’s theorem in the context of a one-variable polynomial ring over a field of characteristic ≠ 2 \neq 2 . As its corollaries, we obtain some structure theorems regarding the orthogonal group with respect to the Pythagorean quadratic form over the polynomial ring.