Space Translation Research Articles

Second order Killing tensors related to symmetric spaces

We discuss the pairs of quadratic integrals of motion belonging to the n-dimensional space of independent integrals of motion in involution, that provide integrability of the corresponding Hamiltonian equations of motion by quadratures. In contrast to the Eisenhart theory, additional integrals of motion are polynomials of the fourth, sixth and other orders in momenta. The main focus is on the second-order Killing tensors corresponding to quadratic integrals of motion and relating to the special combinations of rotations and translations in Euclidean space.

An Introduction to Noncommutative Physics

Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics in a range of areas, including classical physics, condensed matter systems, statistical mechanics, and quantum mechanics, and we present some important examples of noncommutative algebras, including the classical Poisson brackets, the Heisenberg algebra, Lie and Clifford algebras, the Dirac algebra, and the Snyder and Nambu algebras. Potential applications of noncommutative structures in high-energy physics and gravitational theory are also discussed. In particular, we review the formalism of noncommutative quantum mechanics based on the Seiberg–Witten map and propose a parameterization scheme to associate the noncommutative parameters with the Planck length and the cosmological constant. We show that noncommutativity gives rise to an effective gauge field, in the Schrödinger and Pauli equations. This term breaks translation and rotational symmetries in the noncommutative phase space, generating intrinsic quantum fluctuations of the velocity and acceleration, even for free particles. This review is intended as an introduction to noncommutative phenomenology for physicists, as well as a basic introduction to the mathematical formalisms underlying these effects.

Towards Spatially Disentangled Manipulation of Face Images With Pre-Trained StyleGANs

Generative Adversarial Networks with style-based generators could successfully synthesize realistic images from input latent code. Moreover, recent studies have revealed that interpretable translations of generated images could be obtained by linearly traversing in the latent space. However, in most existing latent spaces, linear interpolation often leads to ‘spatially entangled modification’ in the manipulation result, which is undesirable in many real-world applications where local editing is required. To solve this problem, we propose to manipulate the latent code in the ‘style space’ and analyze its advantage in achieving spatial disentanglement. Furthermore, we point out the weakness of simply interpolating in the style space and propose ‘Style Intervention’, a lightweight optimization-based algorithm, to further improve the visual fidelity of manipulation results. The performance of our method is verified with the task of attribute editing on high-resolution face images. Both qualitative and quantitative results demonstrate the advantage of image translation in the style space and the effectiveness of our method on both real and synthetic images.

Sonographic Measurement of Condylar Translation, Joint space and Mouth Opening in Healthy and Subjects with Temporomandibular Joint Disorders

Objectives: A sonographic approach can be used to quantify joint movement, muscle thickness, and available joint space. This study aimed to compare the amount of mouth opening, joint articular distance, and both anterior and inferior translation of the mandibular condyle between healthy participants and individuals with temporomandibular joint (TMJ) disorders. Methods: A cross-sectional study design was used with 52 participants (control: 26 healthy and TMJ: 26 symptomatic individuals) recruited using convenience sampling. The joint space distance and the anterior and inferior condylar translation on both sides were evaluated using sonography during maximum mouth opening and closing. Mouth opening was measured with a graduated ruler. Reliability was performed on a subgroup (n=10) with an interval of 3-7 days. Results: The reliability was good to excellent (ICC=0.57-0.94). The highest reliability was related to the joint space distance. The mean values for mouth opening were 43.1 and 35.3mm, respectively for healthy and TMJ patients. The anterior condylar translation was 7.14-7.57mm, inferior condylar translation was 2.35-2.66mm, and the joint space distance was 49.4-0.44mm. No significant differences were found between the left and right sides in either group. The mouth opening and joint space values were significantly higher in the healthy group while the rate of anterior transition movement was higher but not significant. Furthermore, there was a significant negative relationship between pain, mouth opening, and joint distance. Discussion: Sonography can be considered an accurate tool for the assessment of joint space and condylar translation in individuals with symptomatic TMJ disorders.

Plane and linear blow-up and source

Nonrelativistic equations of continuum mechanics are invariant with respect to space translations and Galilean translations. These symmetries form the 6-parameter group. The 3-dimensional subgroup of the general type containing the Galilean subgroup produces invariant solutions with the blow-up and the instantaneous source. The subgroup generating the solutions with the plane and linear blow-up and source or with both singularities together is considered. Gas particles move along a straight line for the invariant solutions and along plane curvilinear trajectories for the partially invariant solutions with special state equations. The classification of the state equations for these solutions with constant entropy is obtained. Simple solutions for the polytropic gas and the specific gas are found.

Electron and neutrino scattering off the deuteron in a relativistic framework

We build a relativistic model to perform calculations of exclusive, semi-exclusive and inclusive unpolarized cross sections and various polarization observables in electron and neutrino scattering experiments with deuteron targets. The strong interaction dynamics is defined by an explicit dynamical unitary representation of the Poincar\'e group, where representations of space translations and rotations in the interacting and non-interacting representations are the same. The Argonne V18 potential is used to construct a relativistic nucleon-nucleon interaction reproducing the experimental deuteron binding energy and nucleon-nucleon scattering observables. Our formalism does not include the pion production channel and neglects two-body contributions in the electromagnetic as well as in the weak nuclear current operator. We show that it is applicable to processes at kinematics, where the internal two-nucleon energy remains below the pion production threshold but the magnitude of the three-momentum transfer extends at least to several GeV.

Group Analysis of Equal-Width Equation

We study a third-order nonlinear equal width equation, which has been used for simulation of a one-dimensional wave propagation in a non-linear medium with dispersion process, by symmetry analysis. First, Lie point symmetries are obtained and used to reduce reduce the equal width equation thereby constructing exact solutions. Traveling waves are constructed using of a linear combination of space and time translation symmetries. We have used the multiplier technique to compute conservation laws.

GROUP ANALYSIS OF A NONLINEAR HEAT-LIKE EQUATION

We study a nonlinear heat like equation from a lie symmetry stand point. Heat equation have been employed to study ow of current, information and propagation of heat. The Lie group approach is used on the system to obtain symmetry reductions and the reduced systems studied for exact solutions. Solitary waves have been constructed by use of a linear span of time and space translation symmetries. We also compute conservation laws using multiplier approach and by a conservation theorem due to Ibragimov.

La traducción en la enseñanza virtual de las lenguas gabonesas

Translation in The E-learning of Gabonese Languages
 The definitions that revolve around language are as plural as the functions that are assigned to it. For some people, it is an instrument of communication. Other people see it as an instrument for analysing the world, as a personal and social identification. Considering the evolution of societies, the preponderant place of language in any development process is more and more indisputable. Gabon, a sub-Saharan African country, is multilingual. This multilingualism is characterised by a double linguistic heritage. On the one hand, it is made up of some fifty endogenous languages, also known as local languages. On the other hand, it is made up of a foreign language: French, a language received from colonial education and established throughout the country as the language of education, administration and official communication since its independence on 17 August 1960.
 However, the work of many Gabonese sociolinguists presents some worrying results. The sociolinguistic context in Gabon is today characterised by a proven glottophagy, as the French language has opacified the endogenous languages. This language of the colonising country is thus positioned like a dinosaur that swallows all the others with which it shares the Gabonese national territory. Numerous sociolinguists, Gabonese linguists and language teachers are tirelessly calling on the high authorities and the Gabonese population about the situation in Gabon. The promotion of these local Gabonese languages in training and education is the first solution, alongside intra-ethnic communication within the family unit. But today, the inaction of the public authorities regarding the introduction of these languages in the curricula has led to the creation of several virtual platforms dedicated to the teaching-learning of Gabonese local languages and cultures. These are taught by staff with a variety of profiles. In other words, the teaching of Gabonese endogeneity through virtual channels would no longer be the specific work of pedagogues or other actors in the world of education and the field of languages, but it becomes the business of any willing person. Looking at these virtual teaching-learning spaces, we can see that different courses are given through different didactic activities, such as translation. In this study, we focus on pedagogical translation in a virtual educational space. In other words, this article presents a qualitative analysis, in an exploratory approach, of the place and manifestation of translation in this process of teaching endogenous Gabonese knowledge through, specifically, the Langue 241 web page and its Facebook platform. 
 Translation is a pedagogical discipline whose contours are guided by interpretative and comparative theory. It is on the curriculum in formal and institutional foreign language classes through the tandem in french thème and version. We will examine here how it operates in this virtual setting in order to better appreciate the teachers and the courses offered by means of screenshots taken on mobile phones. In order to carry out this study, we interpret the reasons for the courses, the profile of the webmaster and analyse the programme offered and the results expected through it. In addition, we take a critical look at the translation activities carried out in order to better understand the transfer processes, the items studied and above all the learning context. As this is a translation aimed at the teaching-learning of Gabonese languages, i.e. African languages with a tone, a look is also taken at the transcriptions that are made and the alphabet used for this purpose.
 The results of the various analyses carried out make it possible to see whether the theme and version courses given are of a didactic relevance that truly enables users to learn their local Gabonese languages well, both orally and in writing.

A 4-DoF Parallel Robot With a Built-in Gripper for Waste Sorting

This article presents a new robot concept dedicated to fast and energy-efficient waste sorting applications. This parallel robot can provide at the same time the three translations in space (3-DoF) and the opening/closing of a built-in gripper (1 additional DoF). The movement of the clamp is enabled thanks to a configurable platform at the end of the parallel structure. This platform is composed of a two-gear train gripper which is directly controlled by the 4 actuators attached to the base of the manipulator. The inverse kinematic as well as the differential models have been developed. A first prototype has been realized to validate this new parallel architecture for pick-and-toss tasks.

A Group Approach to Exact Solutions and Conservation laws of Burger’s Equation

A classical Burger’s equation is studied by symmetry analysis. The Lie point symmetries con- structed are applied in symmetry reductions and the resulting reduced systems investigated for exact group-invariant solutions. We also construct solitons using symmetry span of space and time translations. Finally, we prove that Burgers equation is a conservation law by the multiplier technique.

Bearing-Based Distributed Formation Control of Unmanned Aerial Vehicle Swarm by Quaternion-Based Attitude Synchronization in Three-Dimensional Space

Most of the recent research on distributed formation control of unmanned aerial vehicle (UAV) swarms is founded on position, distance, and displacement-based approaches; however, a very promising approach, i.e., bearing-based formation control, is still in its infancy and needs extensive research effort. In formation control problems of UAVs, Euler angles are mostly used for orientation calculation, but Euler angles are susceptible to singularities, limiting their use in practical applications. This paper proposed an effective method for time-varying velocity and orientation leader agents for distributed bearing-based formation control of quadcopter UAVs in three-dimensional space. It combines bearing-based formation control and quaternion-based attitude control using undirected graph topology between agents without the knowledge of global position and orientation. The performance validation of the control scheme was done with numerical simulations, which depicted that UAV formation achieved the desired geometric pattern, translation, scaling, and rotation in 3D space dynamically.

Crystal gravity

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".

On the primitivity of the AES-128 key-schedule

The key-scheduling algorithm in the AES is the component responsible for selecting from the master key the sequence of round keys to be xor-ed to the partially encrypted state at each iteration. We consider here the group [Formula: see text] generated by the action of the AES-128 key-scheduling operation, and we prove that the smallest group containing [Formula: see text] and all the translations of the message space is primitive. As a consequence, we obtain that no linear partition of the message space can be invariant under its action.

Resource Recommendation Based on Industrial Knowledge Graph in Low-Resource Conditions

Resource recommendation is extremely challenging under low-resource conditions because representation learning models require sufficient triplets for their training, and the presence of massive long-tail resources leads to data sparsity and cold-start problems. In this paper, an industrial knowledge graph is developed to integrate resources for manufacturing enterprises, and we further formulate long-tail recommendations as a few-shot relational learning problem of learning-to-recommend resources with few interactions under low-resource conditions. First, an industrial knowledge graph is constructed based on the predesigned resource schema. Second, we conduct schema-based reasoning on the schema to heuristically complete the knowledge graph. At last, we propose a multi-head attention-based meta relational learning model with schema-based reasoning to recommend long-tail resources under low-resource conditions. With the IN-Train setting, 5-shot experimental results on the NELL-One and Wiki-One datasets achieve average improvements of 28.8 and 13.3% respectively, compared with MetaR. Empirically, the attention mechanism with relation space translation learns the most important relations for fast convergence. The proposed graph-based platform specifies how to recommend resources using the industrial knowledge graph under low-resource conditions.

Orbital stability of a sum of solitons and breathers of the modified Korteweg–de Vries equation

In this article, we prove that a sum of solitons and breathers of the modified Korteweg–de Vries equation (mKdV) is orbitally stable. The orbital stability is shown in H 2. More precisely, we will show that if a solution of mKdV is close enough to a sum of solitons and breathers with distinct velocities at t = 0 in the H 2 sense, then it stays close to this sum of solitons and breathers for any time t ⩾ 0 in the H 2 sense, up to space translations for solitons or space and phase translations for breathers, provided the condition that the considered solitons and breathers are sufficiently decoupled from each other and that the velocities of the considered breathers are all positive, except possibly one. The constants that appear in this stability result do not depend on translation parameters. From this, we deduce the orbital stability of any multi-breather of mKdV, provided the condition that the velocities of the considered breathers are all positive, except possibly one (the condition about the decoupling of the considered solitons and breathers between each other is not required in this setting). The constants that appear in this stability result depend on translation parameters of the considered solitons and breathers.

GA-MKB:A Multi-kernel Boosting Learning Method based on Normalized Kernel Target Alignment and Kernel Difference

Concentrates on the problem that the traditional kernel target alignment(KTA) is not invariance under data translation in the feature space, a cosine matrix alignment method is proposed for kernel selection, which is called normalized kernel target alignment(NKTA). On the basis of normalized kernel target alignment and kernel difference, we propose a new multi-kernel boosting. Firstly, the value of NKTA is taken as the election rarget of the kernel function in each iteration of algorithm, which leads to a selective kernel fusion. Secondly, the kernel difference measure is used to construct the combination coefficient to increase the diversity of weak classifiers, and then improve the generalization performance of integrated strong classifiers. Finally, among the 6 data sets, the GA-MKB performed better than MKBoost-D1 under the accuracy of classification, and can improve the generalization performance of the integrated classifier compared with MKBoost-D2.

Translation in momentum space and minimal length

We show that in the presence of the Snyder algebra the notion of translation in momentum space is modified to a formula similar to the relativistic addition of velocities. These results confirm the strict connection between Snyder algebra and the Lorentz group.

Distributed Energy Storage Cluster Control Method for DC Microgrid Considering Flexibility

As the core support, when we develop some new energies, the energy storage industry and energy storage technology cover both the power supply, grid and the user side, residential side, and socialized functional store of the energy facilities. If we can implement the storage of energy by the distributed unit, we can save the time and space translation of energy in function and has the characteristics of flexible layout and installation at the equipment level. It is important to promote the production and consumption of renewable energy and improve the operational reliability of alternating current or direct current AC/DC hybrid power grids. It is a virtual form and develops a tendency for energy storage resources in the power grid in the future. However, as an emerging technology and resource, the use of distributed energy storage still has problems such as low efficiency, high idle rate, and single functional scenarios. Distributed energy storage systems can be used almost everywhere around the system of power, have broad application prospects and huge application potential, and will become more and more significant for the power grid in the near future. In general, the distributed energy storage system now is at a primary level of engineering application, and deep study about it still exists various key technologies which needed to lay the foundation for its popularization and application. In this paper, by constructing a microgrid experimental system containing a variety of distributed energy storage systems, research is carried out around the modeling, control, efficiency analysis, and energy management of distributed energy storage systems.

On local extension of the group of parallel translations in three-dimensional space

On local extension of the group of parallel translations in three-dimensional space