Four-dimensional Representation Research Articles

A new order parameter model for the improper ferroelastic phase transitions in KMnF3 single crystal.

This paper proposes a new order parameter model which satisfactorily explains complicated symmetry changes, the temperature-pressure (T-P) phase diagram and elastic anomalies observed experimentally with the improper ferroelastic phase transitions in multiferroic KMnF3 single crystal. First, it is shown that the order parameter model is transformed according to the four-dimensional reducible representation of the wavevector star channel group. Second, based on the order parameter model and the singularity theory, the sixth-order structurally stable Landau potential model is constructed. Finally, the theoretical T-P phase diagram is plotted and the elastic anomalies possible for each of the phase transitions are discussed.

Light Field Neural Rendering.

Classical light field rendering for novel view synthesis can accurately reproduce view-dependent effects such as reflection, refraction, and translucency, but requires a dense view sampling of the scene. Methods based on geometric reconstruction need only sparse views, but cannot accurately model non-Lambertian effects. We introduce a model that combines the strengths and mitigates the limitations of these two directions. By operating on a four-dimensional representation of the light field, our model learns to represent view-dependent effects accurately. By enforcing geometric constraints during training and inference, the scene geometry is implicitly learned from a sparse set of views. Concretely, we introduce a two-stage transformer-based model that first aggregates features along epipolar lines, then aggregates features along reference views to produce the color of a target ray. Additionally, we propose modifications that allow the model to generalize to scenes without any fine-tuning. Our model outperforms the state-of-the-art on multiple forward-facing and 360 ° datasets, with larger margins on scenes with severe view-dependent variations. Code and results can be found at https://light-field-neural-rendering.github.io/.

Understanding relativistic time: Exploring the concepts of spacetime and time dilation

Relativistic time deals with concepts as spacetime and time dilation. I will try to explain this as clearly as possible. To explain the concept of spacetime is not at all impossible, although it is four-dimensional. But that means that we define it using four numbers. If we describe us through age, weight, height, and IQ, that would be a four-dimensional representation of us.

Video images compression method based on floating positional coding with an unequal codograms length

The subject of research in the article are the video images compression and encryption processes during the critically important objects managing process. The goal is to develop a method for compressing video images based on floating positional coding with an uneven codegrams length to simultaneously ensure information reliability and confidentiality during its transmission with a given time delay. Objectives: analyzing existing approaches to ensuring the video images confidentiality; development a method for compressing video images based on floating positional coding with an uneven codegrams length; evaluate the developed method effectiveness. The methods used are: digital image processing methods, digital image compression methods, image encryption and scrambling methods, structural-combinatorial coding methods, statistical analysis methods. The following results are obtained. The technology of floating encoding of an uneven sequence of blocks is proposed. Code values are formed from elements of different video image blocks. For this, a scheme for linearizing an image point coordinates from its four-dimensional representation on a plane into a one-dimensional element coordinate in a vector has been developed. The four-dimensional element coordinate on the plane describes the image block coordinates and the coordinates of the element in this block. Code values are formed under conditions of control their binary representation's length. At the same time, coding is implemented for an indeterminate number of video image elements. The number of elements depends on the length of the code word. Accordingly, codegrams with an indeterminate length are formed. Their length depends on the service data values, generated during the encoding process. Service data acts as a key element. Conclusions. The one-stage polyadic image encoding method in a differentiated basis has been further improved. The developed encoding method provides image compression without information quality loss. The original images volume compression provides by 3–20 % better compared to the TIFF data presentation format and by 4–15 % compared to the PNG format. The overhead amount is less than 2.5 % of the entire codestream size.

A typology of secondary research in Applied Linguistics

Abstract Secondary research is burgeoning in the field of Applied Linguistics, taking the form of both narrative literature review and especially more systematic research synthesis. Clearly purposed and methodologically sound secondary research contributes to the field because it provides useful and reliable summaries in a given domain, facilitates research dialogues between sub-fields, and reduces redundancies in the published literature. It is important to understand that secondary research is an umbrella term that includes numerous types of literature review. In this commentary, we present a typology of 13 types of well-established and emergent types of secondary research in Applied Linguistics. Employing a four-dimensional analytical framework, focus, review process, structure, and representation of text of the 13 types of secondary research are discussed, supported by examples. This article ends with recommendations for conducting secondary research and calls for further inquiry into field-specific methodology of secondary research.

Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane.

Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.

Space-variant Shack-Hartmann wavefront sensing based on affine transformation estimation.

The space-variant wavefront reconstruction problem inherently exists in deep tissue imaging. In this paper, we propose a framework of Shack-Hartmann wavefront space-variant sensing with extended source illumination. The space-variant wavefront is modeled as a four-dimensional function where two dimensions are in the spatial domain and two are in the Fourier domain with priors that both gently vary. Here, the affine transformation is used to characterize the wavefront space-variant function. Correspondingly, the zonal and modal methods are both escalated to adapt to four-dimensional representation and reconstruction. Experiments and simulations show double to quadruple improvements in space-variant wavefront reconstruction accuracy compared to the conventional space-invariant correlation method.

Linear and non-linear relationships among the dimensions representing the cognitive structure of emotion

ABSTRACT While dimensional models play a key role in emotion psychology, no consensus has been reached about their number and nature. The current study sheds a new light on this central issue by examining linear and non-linear relationships among the dimensions in the cognitive emotion structure. The meaning of 80 emotion terms was evaluated on 68 features representing appraisals, action tendencies, bodily reactions, expressions, and subjective experiences by 213 English-speaking US, 156 French-speaking Swiss, and 194 Indonesian-speaking Indonesian students. In a two-dimensional valence and arousal representation, neither linear nor non-linear relationships were observed. In a four-dimensional valence, power, arousal, and novelty representation, both linear (e.g. a positive relationship between valence and power) and non-linear (e.g. a strong positive correlation between valence and power found only for positively valenced emotion terms) relationships were observed. Joy- and sadness-related emotion terms where about as well represented by the two- than by the four-dimensional representation. However, especially anger- and surprise-related terms were only adequately represented by the four-dimensional representation. These findings were generalisable across the three languages. Even though a two-dimensional structure fits the data well in general, four dimensions are needed to sufficiently represent the cognitive structure of the whole gamut of human emotions.

Political skill in higher military staff: Measurement properties and latent profile analysis.

Social effectiveness, including political skill, reflects individuals' ways of handling interpersonal processes at work. Most research has used a variable-oriented approach to investigate associations between political skill and key organizational factors, including performance, in civil settings. Thus, little is known of whether political skill transfers to a military context and whether there are specific profiles of political skill. Combining variable-oriented and person-oriented approaches, this study used self-reports from two samples of military student officers to: (1) investigate measurement properties of the 18-item political skill inventory; (2) explore whether it is possible to identify different profiles of political skill; and (3) investigate whether such profiles differ in demographics, personality, and job performance. Exploratory (sample 1: n = 185) and confirmatory (sample 2: n = 183) factor analyses supported a four-dimensional representation of political skill including networking ability, apparent sincerity, social astuteness, and interpersonal influence. Latent profile analysis (samples 1 and 2: N = 368) identified four distinct combinations of these dimensions, namely: (1) weak political skill; (2) weak political skill with strong sincerity; (3) moderate political skill; and (4) strong political skill. Importantly, profiles differed consistently in networking ability. Subsequent comparisons suggested potentially important differences in demographics, personality, and job performance. Despite needing additional research of how profiles of political skill develop over time, these findings may have practical implications for recruitment and training in organizational settings where social effectiveness is important.

Isogenies of certain K3 surfaces of rank 18

We construct geometric isogenies between three types of two-parameter families of K3 surfaces of Picard rank 18. One is the family of Kummer surfaces associated with Jacobians of genus-two curves admitting an elliptic involution, another is the family of Kummer surfaces associated with the product of two non-isogeneous elliptic curves, and the third is the twisted Legendre pencil. The isogenies imply the existence of algebraic correspondences between these K3 surfaces and prove that the associated four-dimensional Galois representations are isomorphic. We also apply our result to several subfamilies of Picard rank 19. The result generalizes work of van Geemen and Top.

Multivariate Index for Ranking

In previous work, severe weather outbreaks have been classified either as major tornado outbreaks or as primarily nontornadic outbreaks, but the large majority of such events are of a mixed character. This study proposes a reproducible method for ranking all types of severe weather outbreaks from the period 1960-2006. Numerous nonmeteorological artifacts exist in the severe weather reports archived during this period, and many of the variables used to formulate the multivariate indices had to be detrended to reduce the effect of secular trends. The resulting outbreak rankings indicate that the methodology presented herein is able to distinguish the most significant severe weather outbreaks from intermediate outbreak days and days with a large amount of geographic scatter in the severe reports. The rankings of the most severe outbreaks and those outbreak days with a large degree of spatial scatter exhibit only limited variability when the selection of parameters and their weights are modified, but a relatively high degree of volatility is noted with the intermediate cases. This result suggests there is relatively little difference in the severity of these intermediate events. However, the particular modes of severe weather in these events can be quite different. A k-means cluster analysis of the outbreak days, using a four-dimensional representation of the multivariate indices developed, indicates that outbreak days can be separated into five groups: major tornado, wind-dominated, hail-dominated, multi-modal, and days with considerable spatial scatter of the severe reports.

Microprocessor-Based Current Protection Based on a Four-Dimensional Representation of Operating Parameters

Microprocessor-Based Current Protection Based on a Four-Dimensional Representation of Operating Parameters

Three-Dimensional Dirac Phonons with Inversion Symmetry.

Dirac semimetals associated with bulk Dirac fermions are well known in topological electronic systems. In sharp contrast, three-dimensional (3D) Dirac phonons in crystalline solids are still unavailable. Here we perform symmetry arguments and first-principles calculations to systematically investigate 3D Dirac phonons in all space groups with inversion symmetry. The results show that there are two categories of 3D Dirac phonons depending on their protection mechanisms and positions in momentum space. The first category originates from the four-dimensional irreducible representations at the high symmetry points. The second category arises from the phonon branch inversion, and the symmetry guarantees Dirac points to be located along the high symmetry lines. Furthermore, we reveal that nonsymmorphic symmetries and the combination of inversion and time-reversal symmetries play essential roles in the emergence of 3D Dirac phonons. Our work not only offers a comprehensive understanding of 3D Dirac phonons but also provides significant guidance for exploring Dirac bosons in both phononic and photonic systems.

Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: Relativistic analogies and lattice theory

We show that the general low-energy Bogoliubov-de Genness Hamiltonian in a multiband superconductor with broken time reversal and preserved inversion symmetry is a generator of real four-dimensional representation of $SO(4)$. In the particular representation such an effective Hamiltonian is a purely imaginary matrix, and it is proportional to the antisymmetric tensor of a fictitious electromagnetic field which one can define in the momentum space. The quantum time evolution of the low-energy quasiparticle state becomes this way closely related to the classical relativistic motion of a charged particle in the presence of the Lorentz force that would be derived from such an electromagnetic field configuration. The condition for the emergence of a Bogoliubov-Fermi surface can then be understood as orthogonality of the fictitious electric and magnetic fields, which would allow zero Lorentz force. The corresponding zero-energy eigenstates are identified as the physical timelike and the unphysical spacelike solutions of the Lorentz force equation. We study the looming instability of the inversion-symmetric Bogoliubov-Fermi surface in presence of electron-electron interaction by formulating a concrete interacting model on the Lieb lattice that features the requisite $SO(4)$ kinetic energy term together with nearest-neighbor two-body repulsion. The latter is shown to favor dynamical breaking of the inversion symmetry. The inversion symmetry in our lattice model indeed becomes spontaneously broken at zero temperature at infinitesimal repulsion, with the original Bogoliubov-Fermi surface deformed and reduced in size. General features of this symmetry breaking phenomenon are discussed and a comparison with other works in literature is presented.

Anyon Networks from Geometric Models of Matter

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

ПОВЫШЕНИЕ ЭНЕРГОЭФФЕКТИВНОСТИ ПРОИЗВОДСТВА ЗА СЧЕТ ПРИМЕНЕНИЯ СИЛОВЫХ ФИЛЬТРОВ ВЫСШИХ ГАРМОНИК

Актуальность. В настоящее время все большее количество технологических процессов и производств в нефтегазовой отрасли реализуется на базе высокопроизводительного оборудования с полупроводниковыми преобразователями электрической энергии, в число которых, например, входят частотно-регулируемые электроприводы переменного тока или бесперебойные источники питания, которые относятся к классу нелинейных нагрузок и могут вызывать большое количество негативных явлений в работе распределительных сетей, включающих в себя несимметрию фазных напряжений и токов, резонансные процессы, тепловые потери в нейтральном проводе, перегрев двигателей и трансформаторов и т. д. Для улучшения электромагнитной совместимости различного рода электроприемников в составе промышленных систем электроснабжения довольно часто используют пассивные конденсаторные батареи для коррекции коэффициента мощности, которые малоэффективны в случае нелинейных процессов. Кроме этого, данный тип компенсационных устройств продолжает потреблять реактивную энергию при отсутствии каких-либо нагрузок и не удовлетворяет современным требованиям в области энергосбережения. Описанные выше недостатки в работе трехфазных систем переменного тока требуют разработки новых схемотехнических решений, методов анализа энергетических процессов и синтеза алгоритмов силовой фильтрации, позволяющих обеспечить нормированные показатели качества электрической энергии в распределительных сетях низкого и среднего классов напряжения вне зависимости от конкретного вида электрических цепей нагрузки. Цель исследования заключается в комплексном анализе существующих технических решений, направленных на повышение электромагнитной совместимости распределительных сетей, а также в описании основных ограничений в работе силовых фильтрокомпенсирующих устройств применительно к промышленным объектам минерально-сырьевого комплекса; в разработке базовых структур активных силовых фильтров с пониженными требованиями по производительности, объему памяти и быстродействию программно-аппаратной части системы управления, практическое применение которых обеспечивает нормированное качество электрической энергии при изменении режимов работы технологического оборудования или конфигурации питающей линии. Объекты: автономные или децентрализованные электроэнергетические системы переменного тока с преобразовательными устройствами силовой электроники и частотно-регулируемыми электроприводами, а также элементами силовой цепи с нелинейными характеристиками, например, реакторами или трансформаторами с насыщенными сердечниками, в которых присутствуют значительные искажения в мгновенной форме трехфазных сигналов; пассивные и активные силовые фильтры высших гармоник. Методы: некоммутативная алгебра кватернионов; четырехмерное гиперкомплексное пространство; методы спектрального анализа и разложения в ряд Фурье. Результат: краткий обзор различных подходов и технических средств к повышению качества электрической энергии в системах электроснабжения промышленных объектов минерально-сырьевого сектора, а также системы управления,рамках которых достигается синусоидальный закон изменения во времени сетевых токов с нулевым или опережающим/отстающим угловым сдвигом при одновременном соблюдении условия симметрии по мгновенным значениям.

Quantitative representation of perception and evaluation method for service quality in university library under 4-D space

PurposeThe purpose of this paper is to evaluate the service quality of university library more accurately and dynamically and improve the service efficiency of library. The paper realizes quantified representation of library service quality and overcomes the shortcoming of the traditional library evaluation system, which does not consider reader’s identity and cannot be evaluated separately. In addition, according to the function configuration of each department of library, a relation between library evaluation parameter and its organization structure is built. According to the evaluation results and the chain of relations, some suggestions for improving library service can be put forward; thus, it can improve the quality of library service and management efficiency.Design/methodology/approachIn this paper, a four-dimensional (4-D) representation method is put forward to express four kinds of parameters, namely, the category of participants, the number of people evaluated, the rating level and the weight of parameters, which is expressed by chromaticity and a three-dimensional column coordinate space. Considering the existing evaluation methods such as LibQUAL+TM, the content of evaluation parameters, the grade of evaluation parameters and the weight of evaluation parameters are modified. Using the volume and the equivalent number of people under this evaluation system, the evaluation grade can be quantified and the total results can be evaluated quantitatively.FindingsThe evaluation model proposed in this paper is a 4-D system that is based on content parameters to evaluate the number of participants, score segments, evaluation content weights and reader information. It gives full consideration to the good advice of many scholars and combines the actual operation of domestic libraries. The situation effectively integrates successful experience abroad. Both the undergraduate and teacher sampling evaluation results and their analysis in this paper show the accuracy and credibility of the method.Originality/valueAlthough the satisfaction index model has a good effect in foreign countries, taking into account that readers of university libraries in China are different from those in foreign countries in the evaluation methods of the tutorial, professional multi-level evaluation will produce greater errors in practical applications. The traditional four-level method based on Chinese education evaluation (excellent, good, pass and fail) has reached consensus among teachers and students in practical application, and it is easy to achieve consistency. Therefore, this paper also adopts four-level evaluation, that is, very satisfied, satisfied, generally satisfied and very dissatisfied. The embedded application will be able to perform dynamic evaluation and thus can be used in China. The evaluation of service quality in university libraries provides an effective new method.

Representations of optical fibre communications in three‐ and four‐dimensional spaces

The authors study some electromagnetic field representations with a focus on optical communications, light polarisation and phase. Well-known three- and four-dimensional representations are compared with each other and with new ones that are presented and analysed from an analytical point of view. A symmetry emerges in the relationships between the various representations, showing that they are closely related formulas. In fact, different representations point out different characteristics or domains of the same phenomenon. This study results in a more accurate description of the electromagnetic field and especially in its capacity to carry information for telecommunications purposes. From a technological point of view, the partial orthogonality of the described spaces suggests the possibility of exploiting simultaneously more than one representation in order to carry more information or the possibility of using these representations as a natural codifying system with the aim of increasing reliability or confidentiality of communications.

Energy and momentum operator substitution method derived from Schrödinger equation for light and matter waves

In this paper, the energy and momentum operator substitution method derived from the Schrödinger equation is used to list all possible light and matter wave equations, among which the first light wave equation and relativistic approximation equation are proposed for the first time. We expect that we will have some practical application value. The negative sign pairing of energy and momentum operators are important characteristics of this paper. Then the Klein–Gordon equation and Dirac equation are introduced. The process of deriving relativistic energy–momentum relationship by undetermined coefficient method and establishing Dirac equation are mainly introduced. Dirac’s idea of treating negative energy in relativity into positrons is also discussed. Finally, the four-dimensional space-time representation of relativistic wave equation is introduced, which is usually the main representation of quantum electrodynamics and quantum field theory.

Spatially-Decomposed Free Energy of Solvation Based on the Endpoint Density-Functional Method.

A spatially resolved version of the density-functional method for solvation thermodynamics is presented by extending the free-energy functional previously established in the one-dimensional, energy representation and formulating a new expression in a mixed four-dimensional representation (three dimensions for position and one dimension for energy). The space was further divided into a set of discrete regions with respect to the relative position of a solvent molecule from the solute, and the spatially decomposed energetics of solvation were analyzed for small molecules with a methyl, amine, or hydroxyl group and alanine dipeptide in solvent water. It was observed that the density of the solvation free energy is weakly dependent on the solute site in the excluded-volume region and is distinctively favorable in the first shells of the solute atoms that can readily form hydrogen bonds with water. The solvent-reorganization term reduces faster with the separation from the solute than the direct interaction between the solute and solvent, and the latter governs the energetics in the second shell and outer regions. The sum of the contributions to the free energy from the excluded volume and first shell was found to deviate significantly from the total sum over all the regions, implying that the solvation free energy is not spatially localized near the solute in a quantitative sense. Still, a local description was shown to be valid as confirmed by the correlation of the total value of free energy with the corresponding value obtained by integrating the free-energy density to the second shell. The theoretical framework developed in the present work to spatially decompose the solvation free energy can thus be useful to identify stabilizing or destabilizing regions of solvent proximate to a solute and to analyze the role that the displacement of interfacial water plays in the thermodynamics of molecular association.