Duality Principle Research Articles

Regularization-Theory-Based Fast Torque Tracking Method for Interior Permanent Magnet Synchronous Machines

With the rapid growth of interior permanent magnet synchronous machines in electric vehicle applications, there is a need to generate torque tracking look-up tables, that can both track the torque command and implement maximum torque per ampere (MTPA)/maximum torque per volt (MTPV). So far, most torque tracking methods require a large amount of test points, giving rise to long test time and workloads. This paper proposes a fast torque tracking MTPA/MTPV look-up table generating method to improve the efficiency. The proposed method is based on a machine learning regularization theory, using a L1/L2 regularization to establish a data-driven torque tracking model. Then a Lagrange dual principle is introduced to solve the unknown parameters, so that the look-up tables of optimal d-q axis currents are yielded by a global optimization solver. Experimental results show that the proposed method can generate the look-up tables with the same accuracy as classical methods, but requires less test points and testing time. As a result, the testing work loads are reduced, as the time cost is only 10-15% of the classical methods.

On duality principles and related convex dual formulations suitable for local and global non-convex variational optimization

Abstract This article develops duality principles, a related convex dual formulation and primal dual formulations suitable for the local and global optimization of non convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg–Landau type equation. Other applications include primal dual variational formulations for a Burger’s type equation and a Navier–Stokes system. We emphasize the novelty here is that the first dual variational formulation developed is convex for a primal formulation which is originally non-convex. Finally, we also highlight the primal dual variational formulations presented have a large region of convexity around any of their critical points.

Belief Propagation Optimization for Lossy Compression Based on Gaussian Source

In the Internet of Things, sensor nodes collect environmental information and utilize lossy compression for saving storage space. To achieve this objective, high-efficiency compression of the continuous source should be studied. Different from existing schemes, lossy source coding is implemented based on the duality principle in this work. Referring to the duality principle between the lossy source coding and the channel decoding, the belief propagation (BP) algorithm is introduced to realize lossy compression based on a Gaussian source. In the BP algorithm, the log-likelihood ratios (LLRs) are iterated, and their iteration paths follow the connecting relation between the check nodes and the variable nodes in the protograph low-density parity-check (P-LDPC) code. During LLR iterations, the trapping set is the main factor that influences compression performance. We propose the optimized BP algorithms to weaken the impact of trapping sets. The simulation results indicate that the optimized BP algorithms obtain better distortion–rate performance.

Characterizations of pointwise multipliers of Besov spaces in endpoint cases with an application to the duality principle

Let p,q∈(0,∞], s∈R, and M(Bp,qs(Rn)) denote the pointwise multiplier space of the Besov space Bp,qs(Rn). In this article, the authors first establish the characterizations of both M(B1,∞s(Rn)) with s∈R∖{0} and M(B∞,1s(Rn)) with s∈(−∞,0]. Then, as an application, the authors give a corrected proof of the well-known duality principle for pointwise multiplier spaces of Besov spaces, namely the formulaM(Bp,qs(Rn))=M(Bp′,q′−s(Rn)), where p,q∈[1,∞], s∈R, and 1/a+1/a′=1 for any a∈[1,∞], and, moreover, the authors also show that this duality principle is sharp in some sense. The proofs of all these results essentially depend on the duality theorem of Besov spaces themselves, some elaborate estimates of paraproducts as well as the relation between M(Bp,qs(Rn)) and the auxiliary multiplier space M(B˜p,qs(Rn)), where B˜p,qs(Rn) denotes the completion of the Schwartz function space S(Rn) in Bp,qs(Rn).

Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator DzαSN,Sϑz and derive conditions on the normalized analytic function f that lead to sandwich-type subordination in combination with an appropriate fractional differential operator.

Minimum realization for controllability/observability of switched linear systems

In this work, we address the minimum realization problem for controllability of both continuous-time switched linear systems and reversible discrete-time switched linear systems. For both classes of n-dimensional switched linear systems, we show that n(n+1)2−1 switches are the tight upper bound for controllability switching realization. The minimum realization problem for observability is also addressed by means of the duality principle.

Rights to the Result of Intellectual Activity of Artificial Intelligence in Terms of the Dualism of Intellectual Law

This article reveals the author's view on the issues arising in the field of intellectual property rights in connection with the development of artificial intelligence systems. The topic of the research is touched upon due to the fact that the modern technological renewal in the modern world is so large-scale that many scientists are inclined not only to historical changes, but also to anthropological ones: technology becomes dominant in an inextricable connection with the human operator. In the modern Russian legislation there is no institutional fixation of norms of law regulating the relations connected with creation and use of results of artificial intelligence. In the global legal field the recognition of artificial intelligence as the author of the invention has been an open question for a long time. The article considers different points of view on the definition of artificial intelligence, including foreign sources. The author argues about the applicability of the concept of "inventor" in relation to artificial intelligence. The author's position in relation to the results of artificial intelligence is presented on the basis of the principle of intellectual property duality, where the main idea is the separation of non-property and property rights to the results of artificial intelligence. Methods of analysis, synthesis, modeling, comparative-legal were used. In the end conclusions are made about the recognition of authorship on the result of artificial intelligence, based on the creative contribution to its creation and work, the emergence and transfer of exclusive rights.

Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians

We construct explicit complex-valued p-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace–Beltrami and the so-called conformality operator. A known duality principle implies that these p-harmonic functions and harmonic morphisms also induce such solutions on the Riemannian symmetric non-compact dual spaces.

Excitation of Surface Waves With On-Demand Polarization at Self-Complementary Metasurface

Surface electromagnetic waves are the main carriers of the highly localized in-plane signal in planar antennas and photonic devices. However, the polarization degree of freedom is generally absent for surface waves as far as it is still a challenge to excite the surface waves with a necessary polarization state. In this letter, for the first time, we propose a method to excite the surface waves of arbitrary polarization using the self-complementary metasurfaces obeying Babinet's duality principle. Namely, we demonstrate the excitation of surface waves with i) linear horizontal and vertical, ii) linear diagonal, iii) right- and left-handed circular, and iv) elliptical polarizations covering, in principle, a whole Poincaré sphere of polarization states. Finally, we analyze the impact of substrate on the efficiency of polarization-demanded surface waves excitation. The results obtained may find the numerous applications in planar photonic and flat optical polarization devices.

Galois connections and isomorphism of simultaneous ordered relations

In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented. Furthermore, some theorems on order isomorphism and Galois connections are derived.

Three-dimensional Limit Analysis using the Extended-Matsuoka–Nakai yield criterion

This paper investigates the implementation of the Extended-Matsuoka–Nakai yield criterion on a strict Limit Analysis finite element formulation. The current approach is based on a three-field mixed finite element model and the Alternating Direction Method of Multipliers optimization algorithm. With the support of duality principles two variants are derived, the lower bound and the upper bound element. The main novelty of this work is the development of an efficient iterative predictor–corrector scheme, customized for the Extended-Matsuoka–Nakai. This scheme is an indispensable requirement for this formulation. To conclude four numerical examples are presented to assess the effectiveness and efficiency of the numerical tool.

The Development of the Duality Model of Village Government Based on Local Wisdom Tri Hita Karana in Bali Province 1979 to 2019

The Decentralization and Regional Autonomy Policy issued by the Central Government and the Bali Regional Regulation on Pakraman/Indigenous Villages significantly affects the relationship between the two villages, which is currently a concern that leads to dualism and rivalry. In this regard, Balinese local wisdom, Tri Hita Karana, is urgently laying the foundation for harmonious relationship governance for the two village government systems. A descriptive approach is used in this study. The research was carried out in the Province of Bali. This study uses a purposive sampling technique to determine the research subjects. Collecting data using observation methods, document recording methods, and interview methods. The research was carried out using qualitative methods. The first stage consists of gathering primary and secondary data. The second step is to select a theory to study the data. The third stage is to analyze and interpret the selected data. The fourth stage involves writing and constructing research findings. The findings demonstrated the evolution of the duality model of village government from 1979 to 2019. The Duality Model of Village Government Period I. Overall, the Duality Model of Village Government Period I from 1979 to 1998 can be concluded, with the applicable regulations being Law No. 6 of 1986 concerning the Position, Function, and Role of Traditional Villages as Units of Customary Law Communities in Bali. Duality in Functional Relations and leading government administration between the Traditional Village and the Tri Hita Karana Local Wisdom-Based Service Village has been running well. Village Government Duality Model Period II. Overall, it can be concluded that the Village Government Duality Model Period II in the period 1999 to 2013 with the applicable Regional Regulation No. 3 of 2001 concerning Desa Pakraman and Regional Regulation No. 3 of 2003 concerning Amendments to the Regional Regulation of the Province of Bali No. 3 of 2001 concerning Pakraman Village are the regulations. Duality in Functional Relations and leading government administration between the Traditional Village and the Tri Hita Karana Local Wisdom-Based Service Village has been running well. Village Government Duality Model Period III. Overall, it can be concluded that the Village Government Duality Model Period III in the period 2014 to 2019 with the applicable Law No. 23 of 2014 on Regional Government, Law No. 6 of 2014 on Villages, and Regional Regulation No. 4 of 2019 on Traditional Villages in Bali are the regulations. Duality in Functional Relations and leading government administration between Traditional Villages and Tri Hita Karana Local Wisdom-Based Service Villages can still run well. The success of indigenous peoples in overcoming the intervention of various external forces is evident in Bali. The principle of duality, the basis of religious teachings, has succeeded in maintaining the coexistence of the Dinas village and the traditional village/ pekraman that live in harmony. It is recognized that it is in the Customary Village unit or Pekramansocial solidarity and social order can be enforced, two things that the Balinese people need to optimize the benefits of government and development that will be more prosperous.

Dual-mode hyperbolicity, supercanalization, and leakage in self-complementary metasurfaces

Abstract Anisotropic Self-Complementary Metasurfaces (SC-MTSs) are structures constituted by an alternation of complementary inductive and capacitive strips, which are “self-dual” according to Babinet’s duality principle. They support the propagation of two orthogonally polarized surface-wave modes with the same phase velocity along the principal directions (i.e., along the strips and normal to them). The isofrequency dispersion curves of these modes are hyperbolas, and therefore, these MTSs fall in the category of hyperbolic MTSs. It is shown here that the hyperbolic dispersion curves may degenerate in same cases into almost straight lines, which implies that the velocity of energy transport is constantly directed along the same direction for any possible phasing orthogonal to the strips. In this circumstance, the SC-MTS can be conveniently used to design dual-polarized leaky-wave antennas by modulating the impedances of the complementary strips.

A note on Kakeya sets of horizontal and SL(2)$SL(2)$ lines

AbstractWe consider unions of lines in . These are lines of the form where . We show that if is a Kakeya set of lines, then the union has Hausdorff dimension 3. This answers a question of Wang and Zahl. The lines can be identified with horizontal lines in the first Heisenberg group, and we obtain the main result as a corollary of a more general statement concerning unions of horizontal lines. This statement is established via a point‐line duality principle between horizontal and conical lines in , combined with recent work on restricted families of projections to planes, due to Gan, Guo, Guth, Harris, Maldague and Wang. Our result also has a corollary for Nikodym sets associated with horizontal lines, which answers a special case of a question of Kim.

Formation of the Adaptive Management System for the Economic Security of Enterprises in the COVID-19 Context

The relevance of this scientific research is justified by the increased attention that the economic community pays to economic security, for the development of microeconomic systems in modern conditions of uncertainty, caused by global challenges, as a result of the COVID-19 pandemic. The purpose of the study is to identify the principles of the formation of an adaptive management system of economic security of enterprises in the conditions of the COVID-19 pandemic. The authors founded the methodological basis for the formation of the adaptive management system of the economic security of companies, based on the identification of the systemic approach and specific principles of compliance, duality and feedback, as well as the functions of adaptive management. The conducted research makes possible to generalize that the formation of a system of adaptive management of the economic security of enterprises in the COVID-19 conditions is a special type of management activity, which involves the use of a wide range of measures and tools for making effective management decisions, which are characterized by timeliness, flexibility, creativity and innovation.

On p-adic tight wavelet frames

We propose a simple method to constructing step mask and corresponding step wavelet functions that generate tight wavelet frames on the field Qp of p-adic numbers. To construct this mask we use three new ideas. First, we consider only an additive group of the field Qp. Second, to construct the mask we use a special tree. Thirdly, we do not use the principle of unitary extension, we use Pontryagin's principle of duality instead. Using this method, we obtain all step refinable functions.

Self-Complementary Hyperbolic Metasurface Antennas

Anisotropic Self-Complementary Metasurfaces (SCM) are structures constituted by a “self-dual” (according to Babinet’s duality principle) alternance of inductive and capacitive complementary strips. They support orthogonally polarized surface-wave modes with the same phase velocity in the principal direction of propagation. The isofrequency dispersion curves of these modes are hyperbolas, and therefore these metasurfaces (MTSs) fall in the category of hyperbolic MTSs. It is shown here that the hyperbolas may degenerate in same cases into almost straight lines, which implies that the velocity of energy transport is constantly directed along the complementary strips at any frequency and for any possible phasing orthogonal to the strips. In this circumstance, the SCM can be conveniently used to design dual-polarized leaky-wave antennas by modulating the impedances of the complementary strips. Each strip behaves as a channel, which can be independently fed with the desired phase and amplitude. We demonstrate here that these antennas exhibit a strong decoupling between both co-polar and cross-polar channels, even when the distance between strips is electrically small. This increases the performance of the antenna, especially in azimuthal beam scanning. A prototype at 2.6 GHz has been constructed and successfully measured confirming the theoretical conjectures.

R-linguistics. The Principle of Linguistic Duality

Introduction. R-linguistics uses the axiomatic method in its approach to modeling the world and language [1]. Axioms define the categories of language, their properties and ways of formation. On this basis, when processing the accumulated data in the form of relations, it is possible to form systems of categories and determine the verbs connecting these categories. A reasonable question arises: if categories (to be such) must satisfy certain axioms, does this requirement apply to verbs as well? The purpose of this article is to deal with this issue.Methodology and sources. The results of the previous parts of the series are used as research tools. The axioms and methods of verb categorization formulated earlier are used to develop the necessary mathematical representations of the verb axiomatics.Results and discussion. The article introduces the axiom for the verbs of the language (the axiom of the verbal cross) and shows that this axiom is related to the categorization axiom (the correctness axiom). Although this connection is not identical, it becomes such with the additional use of the axiom of extensiveness. This relationship made it possible to formulate the fundamental principle of linguistics – the principle of duality.Conclusion. The axiomatics of verbs and categories of a language turns out to be connected, and one determines the other, so that by and large it does not matter which of them is the source of the model of the world and the appearance of language. This unity is formulated as the principle of duality in linguistics. The manifestations of the principle of duality in the language are diverse, but this article focuses on the discussion of the appearance in the language of verbs-processes and adverbs. This transition is considered, starting with obtaining the initial data about the world, to the emergence of ideas about processes and adverbs as a feature system of verbs.

Implementation of the Principle of Dualism in Intellectual Property Law on the Example of the Copyright Contract

The relevance of the conducted research is due to the presence of a number of factual contradictions between the position of the courts in considering the issues of exclusive rights to works created during the execution under the contract of copyright with the rules of law contained in the civil legislation of the Russian Federation. The proposed issues are examined from the point of view of copyright and civil law, legal acts of foreign countries, judicial practice of the Russian Federation and foreign courts. The analysis of examples from judicial practice is given as a substantiation of legislative consolidation of the principle. This article reveals the author's view of the principle of duality of intellectual property law as an independent principle of a sub-branch of civil law and its implementation in the contract of copyright. Principles of law are defined by the author as its guiding principles that define the rules of law in the system of legal regulation, its content and direction. The purpose of the study is determined by the title and content of the work: the essential characteristics of the principle of duality of intellectual property rights, including the implementation of contractual relations in the performance of the author's order are considered. The totality of general scientific, special legal methods of knowledge is used: thanks to the analysis and synthesis the approaches to the proposed topic are generalized and conclusions are made. The principle of duality of intellectual property is considered as a fundamental idea of law, neglecting the account of which entails a violation of rights and freedoms and has legal consequences. Recommendations on the legislative consolidation of the mandatory written form of the copyright contract and the contract of alienation of exclusive rights in its continuation are given.

Empirical Validation of “G-D’s Physics’” “UNCIARE Critical Prediction” Discards “Dark-Matter” as “Superfluous”!

Despite numerous experimental efforts to “detect” the presence of “Dark-Matter” (DM) over the past two decade (assumed to comprise up to 95% of all the mass in the universe), no direct experimental evidence of DM has been found to date. But, without the existence of “dark-matter” the accelerated rate of the universe’s expansion cannot be explained? Fortunately, a new alternative “G-D’s Physics” (previously termed: the “Computational Unified Field Theory”) was discovered that offers an alternative explanation for the accelerated expansion of the universe – while discarding “dark-matter” as “superfluous” (i.e., non-existent”). Based on direct empirical validation of two unique “Critical Predictions” of the “G-D’s Physics”, as more valid than the corresponding predictions of both General Relativity Theory (GRT) and Quantum Mechanics (QM) the” G-D’s Physics” is accepted as the new satisfactory Physics Paradigm for 21st century Theoretical Physics; Specifically, empirical validation of the “G-D’s Physics” “Universe’s Non-Continuous Increase in its Accelerated Rate of Expansion (UNCIARE) “Critical Prediction” as evidenced by the “Astronomical-Cosmological Gap in the Universe’s Accelerated Rate of Expansion” (ACGUARE) negates the possibility of the existence of “dark-matter”. The (purely hypothetical) existence of DM is further negated based on the G-D’s Physics “Computational Duality Principle” Theoretical Postulate, which points at the G-D’s Physics singular higher-ordered “Universal Computational Principle” (UCP) that simultaneously computes every exhaustive spatial pixel in the universe at the incredible rate of “c2/h” = 1.36-50 (sec’)! The new G-D’s Physics Paradigm is also shown to resolve the apparent “theoretical inconsistency” between GRT & QM and completely unify between the four basic physical features of “space”,” time”, “energy” & “mass”, based on a newly discovered “Universal Computational Formula” (UCP).