Transformation Laws Research Articles

Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics

We study the use of methods based on the real symplectic groups Sp(2n,R) in the analysis of the Arthurs-Kelly model of proposed simultaneous measurements of position and momentum in quantum mechanics. Consistent with the fact that such measurements are in fact not possible, with arbitrary precision, we show that the observable consequences of the Arthurs-Kelly interaction term are contained in the symplectic transformation law connecting the system plus apparatus variance matrices at an initial and a final time. The individual variance matrices are made up of averages and spreads or uncertainties for single hermitian observables one at a time, which are quantum mechanically well defined. The consequences of the multimode symplectic covariant Uncertainty Principle in the Arthurs-Kelly context are examined.

Nonstandard Action of Diffeomorphisms and Gravity’s Anti-Newtonian Limit

A tensor calculus adapted to the Anti-Newtonian limit of Einstein gravity is developed. The limit is defined in terms of a global conformal rescaling of the spatial metric. This enhances spacelike distances compared to timelike ones and in the limit effectively squeezes the lightcones to lines. Conventional tensors admit an analogous Anti-Newtonian limit, which however transforms according to a non-standard realization of the spacetime Diffeomorphism group. In addition to the type of the tensor the transformation law depends on, a set of integer-valued weights is needed to ensure the existence of a nontrivial limit. Examples are limiting counterparts of the metric, Einstein, and Riemann tensors. An adapted purely temporal notion of parallel transport is presented. By introducing a generalized Ehresmann connection and an associated orthonormal frame compatible with an invertible Carroll metric, the weight-dependent transformation laws can be mapped into a universal one that can be read off from the index structure. Utilizing this ‘decoupling map’ and a realization of the generalized Ehresmann connection in terms of scalar field, the limiting gravity theory can be endowed with an intrinsic Levi–Civita type notion of spatio-temporal parallel transport.

Study advances of microwave processing technology in traditional Chinese medicine

The iterative innovation of processing technology is one of the important tasks in studies on processing of traditional Chinese medicine(TCM). It is also the prerequisite for modern, refined, automatic and intelligent manufacturing of TCM pieces. Microwave processing is a new fire processing technique developed in the recent 30 years, with a unique thermodynamic form, and energy transfer and transformation laws. Moreover, it owns the advantages of a high processing efficiency, good product properties and low production energy consumption, with great application prospects. This paper introduced the study overview of microwave expansion technology in the food industry, reviewed the origin of microwave processing technology of TCM, and expounded the basic concept, principle and main purpose of microwave processing technology used in TCM. Then, the impacts of drug factors and microwave factors on the microwave processing effect were summarized, the industrial equipment that could be used for microwave processing was listed, and the impacts of microwave heating on starch, polysaccharide, protein and other components in Chinese herbal medicines were analyzed. Furthermore, the study advance of microwave processing of 14 herbs was investigated, including Aconiti Lateralis Radix Praeparaia, Galli Gigerii Endothelium Corneum and Asini Corii Colla; and the appearance and components of herbs processed by traditional processing method and microwave processing method were compared, so as to reveal the opportunities and challenges of microwave processing technology in the industrial transformation. We hoped that the systematic study of microwave processing technology could provide new ideas and techniques for the high-quality and high-level development of the TCM pieces industry in the new era, and promote its inheritance, innovation and transformation.

Development of Defining Equations for the Mathematical Theory of Concrete Corrosion Processes

The fundamental difference of the developed defining equations is that they consider the dual system of porosity and kinetic laws of physical and chemical transformations to describe individual stages of corrosion processes. The dual porosity system comprises through capillaries (pores) of the longitudinal direction and adjacent capillaries of the transverse direction. During the reagent mass transfer in through capillaries (pores) there takes place their transfer to transverse ones, in which we can observe the neutralization (dissolution) reaction of chemically active substances in solid phase with the formation of the moving boundaries. The binding and release rate in case of leaching are determined from the respective boundary value problems and are similar in structure. In defining equations, all parameters are reduced to two generalized ones. Their values for forecasting the technical condition of operating structures are to be determined on the basis of concentration distribution of the aggressive component in concrete layer depth in the above-specified structures.

Kinetics and Energetics of High-Temperature Pyrolysis of Highly Filled Elastomers

Based on an analysis and generalization of the results of theoretical and experimental studies of the basic laws of physicochemical transformations that occur in highly filled elastomers upon heating, a differential mathematical model of the kinetics and energy of the pyrolysis process of these materials is formulated. A distinctive feature of the model is the inclusion of changes in the composition of the material during heating to high temperatures, as well as the influence of the heating rate on the process parameters. The results of numerical studies are in satisfactory agreement with experimental data.

Local Weakening Laws and Energy Transformation of Roadway Surrounding Rock with Structural Planes

Coal resources are major energy resources for consumption in China. As the exploration of coal resources gradually turns to deep mining, the problem of supporting roadways in rock with structural planes under high ground stress is becoming increasingly significant. This research takes a support project of surrounding rock with structural planes in the Bai Yang Ling Coal Mine as the research object. To better support roadways in areas with local structural planes, this study conducts a methodological analysis, laboratory tests and field investigations to comprehensively explore the mechanical properties of areas with structural planes around roadways and to determine the influence of the structural planes on the weakening of local areas of roadway surrounding rock and the energy transformation laws during this surrounding rock weakening. Based on the Mohr-Coulomb failure principle, the influence of structural planes on the overall stability of rock samples is methodologically analysed, and failure criteria are determined. Through a loading test, the impact of areas between structural planes on the weakening of the strength and stiffness and the stress-strain relationship of rock samples is investigated under the influence of both internal and external factors, and the energy transformation process of rock samples weakened by structural planes is analysed. A concept for controlling local weakening of the roadway system is proposed, and measures for controlling the weakening of the structural planes around roadways are verified through field tests. The test results show that the strength, stiffness and stability of rock samples are controlled by areas of local weakening formed by structural planes rather than by traditional single-point failure; the location and shape of the weakening areas change with the change in the internal and external factors acting on the rock samples; the dislocation and failure of samples under the influence of the structural planes directly increase energy dissipation and reduce the elastic energy reserve; the closer the dip angle of the structural plane is to 60°, the more sensitive the strength, stiffness and stability of rock samples in the areas weakened by structural planes, and the worse the stability of the roadway surrounding rock; additionally, for structural plane dip angles ranging from 45° to 60°, increasing confining pressure may be the best way to restrain the weakening of the strength and stiffness of rock.

Importance of Ssurface water background values for objectively assessing water quality in a unique basin

Ignoring differences in surface water background values of different basins is a prominent shortcoming in water resource assessment and management systems in China. This study described the impact of this shortcoming on the results of water quality assessments by analysing water quality and the intensity of anthropogenic activities in 10 water resource basins in China. In particular, the Songhuajiang River Basin had a relatively undegraded natural environment with minimal anthropogenic activity. However, water quality assessment results showed the lowest water quality, and this basin is the most seriously affected by background values. The Huma River source water reserve was selected to conduct research of background value identification, concentration characteristics, migration and transformation laws, and output mechanism characteristics to enable the acknowledgment of the severe background value problem. Most data collected in basins with minimal anthropogenic pollution failed to meet Chinese water quality standard requirements, and high background values mainly resulted from litter leachate and soil erosion by rainfall or snowmelt runoff. A revised water quality assessment method was proposed in view of the particularity and heterogeneity of background values in the Songhuajiang River Basin. This study therefore clarified the negative impact of background values on water quality assessments, so that these values can be properly considered in Chinese water quality assessment and management systems.

Combined laser variosystems paraxial design for longitudinal movement of a Gaussian beam waist.

Optical variosystems that form the required diameter of the Gaussian beam waist and perform its smooth longitudinal movement with a constant diameter for laser technologies, processing materials, moving microobjects, etc., are considered. A combined method based on a movable tunable-focus lens for changing the optical characteristics of laser variosystems is proposed. The features and fundamental differences between the laws of transformation of Gaussian beams by optical systems of different structures for the dimensional synthesis of laser variosystems are discussed. Based on these laws and the theory of laser optics, a method for the dimensional synthesis of one- and two-component laser variosystems is developed, an algorithm for their automated synthesis, and an example of calculation are given.

Mathcal{N} -extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

In this work we present the ultra-relativistic mathcal{N} -extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under mathcal{N} -extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to mathcal{N} = ( mathcal{N} , 0), with mathcal{N} even, and to mathcal{N} = (p, q), with p, q > 0. The mathcal{N} -extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of mathfrak{osp} (2|2) ⊗ mathfrak{sp} (2), to mathfrak{osp} (2|1) ⊗ mathfrak{osp} (2, 1), to an mathfrak{so}left(mathcal{N}right) extension of mathfrak{osp} (2| mathcal{N} ) ⊗ mathfrak{sp} (2), and to the direct sum of an mathfrak{so} (p) ⊕ mathfrak{so} (q) algebra and mathfrak{osp} (2|p) ⊗ mathfrak{osp} (2, q), respectively. We also analyze the flat limit (ℓ → ∞, being ℓ the length parameter) of the aforementioned mathcal{N} -extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic mathcal{N} -extended (flat) Chern-Simons supergravity theories invariant under mathcal{N} -extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.

Strategic Updating of Internet Plus Considering Digital Transformation

Since the Internet Plus initiative was proposed five years ago, innovations associated with the new-generation information technology have accelerated and digital transformation of the economy and society has exhibited many new features. These necessitate the construction of a new system and exploration of new paths for the transformation, and measures currently taken under the Internet Plus initiative need to be evolved and upgraded. This study follows the objective laws of technological industry transformation and is based on the theoretical paradigm of technology economics. It analyzes the new trend and research frontiers of digital transformation at the technology, application, and policy levels. The study reveals that the current technology system and technological capabilities of digital transformation have gradually improved, a new blueprint for the transformation has emerged, and the integration of information technology with the real economy has entered a new stage. However, the digital transformation framework system needs to be reconstructed, the key elements of transformation needs to be strengthened, and key breakthroughs need to be achieved. To this end, in the follow-up policy design of the Internet Plus initiative and during the formulation of the 14th Five-Year Plan, China should focus on exploring the potentials of digital elements, promote the construction of the digital transformation ecology, establish transformation and innovation networks, and upgrade the policy support system for the Internet Plus initiative, thereby promoting the digital transformation of economy and society to a higher level.

О ПРОБЛЕМЕ «ПЕРЕНАСЕЛЕНИЯ» ПЛАНЕТЫ

The article is devoted to the study of overpopulation problems in the context of the laws of evolutionary development and revolutionary transformations. The features of local and planetary overpopulation are revealed. The influence on overpopulation of the phenomenon of acceleration of social evolution in the last two centuries is being studied. The key provisions of political economy and sociology regarding the highest stage of development and population problems are considered. Statistical data are presented.

A Deep Learning Based Method for Detecting of Wear on the Current Collector Strips’ Surfaces of the Pantograph in Railways

In pantographs, current collector strips transmit the electrical energy they receive from the catenary to the locomotive and provide the necessary power for the locomotive's movement. In order for the current collector strips to transmit electricity to the locomotive in a healthy way, their surface must be smooth. Wear on the surface of the current collector strips reduces conductivity and can create arcs, endangering the health and safety of the pantograph and catenary system. In this paper, a Convolutional Neural Network (CNN) architecture is developed to detect wear on the current collector strips. Images obtained from pantographs used on railways were created with a clean and improved data set using Hough Transform and Power Law Transform. The created dataset contains 909 pantograph images. This dataset was trained and tested with both the developed CNN architecture and classic deep learning architectures (ResNet50, VGG16). The experimental results show that the developed CNN architecture's training results and test results are more successful than classical architectures.

On the Numerical Prediction of Process-Dependent Properties of Current High-Performance Materials with Material Model *MAT_254 in LS-DYNA

Over the last years, the forecast quality in production and especially (cold) forming simulations has reached a high level at least for standard materials. It has become state-of-the-art to take the results of these process simulations into account e.g. for crashworthiness analyses. For most of the currently used high-performance materials, however, the manufacturing processes do not only result in plastic deformation and thinning of the parts. There usually is a thermal component to these processes, which significantly influences the microstructure of the material and results in a spatial distribution of material properties within the final part. In order to predict the later behavior of the part with the same quality as for standard materials and standard processes, the virtual process chain has to be closed and material models have to be used that are able to simulate the microstructure evolution during the process. The press-hardening of the manganese-boron steel grade 22MnB5 is, for example, a standard in automotive industry. For this material FEM software for process simulation tools like LS-DYNA were extended in the past to take the microstructure evolution into account. The implemented material models are tailored for this certain alloy and process. To ensure the usability of the simulation tool the material models were generalized. In LS-DYNA, material model *MAT_GENERALIZED_PHASECHANGE (*MAT_254) has been devised to serve this purpose. Core of the model is a phase evolution table that takes into account up to 24 individual phases and consequently defines up to 552 possible phase transformations, not all of which have to be defined. The appropriate transformation law for each of the phase changes can be chosen from a list of generic phase change mechanisms. Due to its relatively flexible input structure and generality of the implementation, the model has been successfully used for different processes such as press-hardening, welding, additive manufacturing, and heat treatment, and for different materials, such as ultra-high strength steels, aluminum 6xxx alloys and titanium. This contribution will introduce the material formulation in detail and show the recent extensions based on the microstructure evolution of titanium.

Frame-indifference of cross products, rotations, and the permutation tensor

ABSTRACT Under improper transformations, the traditional transformation laws for cross products, the permutation tensor, and rotations are incorrect. For a cross product, using a counter-example the left-hand rule is proved wrong. The unique rule for a cross product is the right-hand rule. Coordinate systems have handedness, while a cross product is frame-indifference. Since the permutation tensor is defined as a triple product including a cross product, the law for the permutation tensor is false. For a rotation, its pseudovector representation is incorrect, because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.

Transformation laws for generalized Dedekind sums associated to Fuchsian groups

We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups $\Gamma_0(N)$, and the non-congruence arithmetic groups $\Gamma_0(N)^+$.

Unimodular Matrix with Layered Compound Structure and Its Transformation Theory

Unimodular compound structural matrix and the transformation theory are studied. Conceptually, unimodular compound structural matrix is a matrix set with layered compound structure constructed by taking some special original matrix as element and structure mode, thus having some basic properties such as unimodular, orthogonality and symmetry. Theoretically, the transformation theory of unimodular matrix have been established, using which the natural exponential matrix function of real variable and unimodular matrix can be solved efficiently; and when it is applied to the transformation of vector variable, the transformation law of variables and the invariants related to the matrix symmetry have obtained general conclusions. The results of this study are the extension of Pauli matrix, Dirac algebra and Euler equation, thus have potential applications in mathematics and physics: mathematically, which can be used as compound special matrixes to describe the compound special unitary group, to construct the algebraic structure of layered linear space, and to analytically calculate the exponential function of unimodular matrix; physically, which can be used to describe the new symmetry of intrinsic space, to express the recombination of basic particle structures, and to analysis the correlation transformation of physical mechanism.

Curve counting on elliptic Calabi–Yau threefolds via derived categories

We prove the elliptic transformation law of Jacobi forms for the generating series of Pandharipande–Thomas invariants of an elliptic Calabi–Yau threefold over a reduced class in the base. This proves part of a conjecture by Huang, Katz, and Klemm. For the proof we construct an involution of the derived category and use wall-crossing methods. We express the generating series of PT invariants in terms of low genus Gromov–Witten invariants and universal Jacobi forms. As applications we prove new formulas and recover several known formulas for the PT invariants of \mathrm{K3} \times E , abelian 3-folds, and the STU-model. We prove that the generating series of curve counting invariants for \mathrm{K3} \times E with respect to a primitive class on the \mathrm{K3} is a quasi-Jacobi form of weight –10 . This provides strong evidence for the Igusa cusp form conjecture.

Структурний стан чорнозему за довгострокової постагрогенної трансформації

The purpose. To determine the main laws of transformation and regulatory parameters of the structural state change of chernozems of the forest-steppe zone in conditions of long-term post-agrogenic transformation according to the results of dry sieving of soil samples and statistical analysis of the data using the method of principal components, factor and non-parametric analysis. Methods. Laboratory analytical, experimental field, statistical. Results. The performed statistical processing of results of the analysis of dry sieving of the structure of chernozems in the long-term post-agrogenic state demonstrates the promise of using factor, cluster and non-parametric analysis methods. An important role in the restoration of the structure of chernozems is played by a combination of structural units 3.0–0.5 mm in size, with which the additional density in the humus horizon is inversely proportional, and with the humus content, it is directly proportional. The carried out clustering indicates that the content of the presented chernozems in the state of virgin soil and long-term deposits is the separated and not similar state of soil objects. But there is a general pattern of formation of a set of structural units of 3.0-0.5 mm similar to chernozems in the state of virgin soil, which content exceeds 40-50% of the content of parts in the agronomically valuable interval. Conclusions. After withdrawal from agricultural circulation, chernozems of agrocenoses enter into a complex process of self-healing, which goes in the direction of the virgin zone type. During post-agrogenic evolution, the accumulation of total humus occurs and the structural organization of the arable layer is gradually restored. In the first 20-25 years, there is a noticeable increase in the share of macroaggregates, including agronomically valuable ones, and the corresponding decrease in the number of microaggregates, which indicates an improvement in agronomic properties of shifted chernozems. In accordance with the number of agronomically valuable aggregates, all chernozems of the represented fallow series are characterized as excellent, and the dynamics of the growth of the structural coefficient increases with age towards virgin soil.

Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes

We consider the numerical approximation of the Shallow Water Equations (SWEs) in spherical geometry for oceanographic applications. To provide enhanced resolution of moving fronts present in the flow we consider adaptive discrete approximations on moving triangulations of the sphere. To this end, we re-state all Arbitrary Lagrangian Eulerian (ALE) transport formulas, as well as the volume transformation laws, for a 2D manifold. Using these results, we write the set of ALE-SWEs on the sphere. We then propose a Residual Distribution discrete approximation of the governing equations. Classical properties as the DGCL and the C-property (well balancedness) are reformulated in this more general context. An adaptive mesh movement strategy is proposed. The discrete framework obtained is thoroughly tested on standard benchmarks in large scale oceanography to prove their potential as well as the advantage brought by the adaptive mesh movement.

Semi-Analytical Solution of Magnetic Force and Torque for a Novel Magnetically Levitated Actuator in Rotary Table

This article proposes a fast and accurate semi-analytical calculation method of magnetic force and torque in the magnetically levitated rotary table. Benefited from the high computation efficiency and accuracy, the solution is suitable for the optimization and real-time control of the magnetically levitated system. Different with the existing harmonic method for modeling the magnetic field produced by the circular magnet array in the rotary table, the gaps in circular permanent magnet array are taken into account for the force and torque computation in this article. With the obtained magnetic flux density distribution, the magnetic force and torque can be acquired via the coordinate transformation and Lorenz integral law. Then, the numerical integral method is used to calculate the exact results of complex Lorentz integrals. Finally, the effectiveness and accuracy of the semi-analytical solution are verified by a boundary element software named Radia. Compared with the existing solutions, the new semi-analytical method is more accurate and suitable for the magnetically levitated actuator in the rotary table.