Duality Principle Research Articles

Circuit Theoretic Considerations of LED Driving: Voltage-Source Versus Current-Source Driving

Light-emitting diodes (LEDs) are solid-state devices with specific $v$ – $i$ characteristics. In this paper, we study the basic requirement of the driving circuits and discuss the proper approach to drive LEDs in view of their characteristics. We compare voltage source driving and current source driving, and discuss their relative advantages and constraints. We specifically introduce the use of circuit duality principle for developing new current-source-mode (CSM) drivers that are less known but are theoretically more versatile compared to their conventional voltage-source-mode counterparts. The study highlights the effects of the choice of driving circuits in terms of the number and size of circuit components used, duty cycle variation, sensitivity of control, nonlinearity and control complexity of LED drivers. We propose a CSM single-inductor multiple-output (SIMO) converter, which demonstrates the advantage of having inductorless and easily controlled current-source drivers, and present a comparison of the CSM SIMO converter with the existing SIMO converters. We further illustrate that a high-voltage-step-down ratio can be naturally achieved by the CSM high-voltage-step-down converter without the use of transformers. This paper presents a systematic and comparative exposition of the circuit theory of driving LEDs, with experimental evidence supporting the major conclusions.

Generalized Circuit Model for Eddy Current Effects in Multi-Winding Transformers

This paper presents a novel circuit model for eddy-current effects for multi-winding transformers. It presents the theoretical framework to model eddy currents applicable to layer or disk windings with n-layers for two-dimensional (2-D) transformer arrangements. The new white-box model is physical, dual, and leakage reversible. Additionally, it does not have mutually coupled elements or negative inductors. The paper presents a complete circuit for transformer windings (including capacitances) and core. The model accurately predicts the variation of resistance (dc component, skin, and proximity effects) and leakage inductance of windings from dc to hundreds of kilohertz. Being derived from the principle of duality, the circuit elements can be physically related one-to-one to the distribution of flux and current in the winding geometry. A practical winding discretization, based on field penetration depth for the given frequency, allows estimating the parameters using very simple formulae requiring only geometrical information and properties of materials. Model verification is done using finite element simulations. It is shown that the circuit model matches very well with 2-D FEM simulations. The circuit can be easily implemented in any circuit simulation software like EMTP-RV, PSCAD, ATP, etc., by simply dragging and dropping elements.

A Power Exchange Strategy for Multiple Areas with Hydro Power and Flexible Loads

Areas with hydro power may purchase extra power from the outside power market during dry seasons, which will cause a deviation between the actual and expected power purchase amount due to the inaccurate judgment of the market situation. Because of the uncertainty of price fluctuations, the risk of purchasing power in the real-time market to eliminate this deviation is very high. This paper proposes an innovative trade mode, where the power exchange strategy between multiple areas is adopted through forming an alliance, i.e., one area can use the controllable elements within others, and constructing a monthly and post day-ahead two phase optimization model. The objective function of the monthly stochastic robust optimization considers the power purchase cost to determine the controllable elements dispatch dates for every area in the alliance. Thus, areas can make reasonable dispatch schedules for controllable elements to avoid the resource waste that means more controllable elements are prepared before post day-ahead optimization but less are used after post day-ahead optimization. While the post day-ahead optimization model determines the internal controllable elements dispatch and power exchange amount after the day-ahead market clearing process, users’ satisfaction and dispatch schedule changes for energy storage device are also considered. In order to solve the proposed two phase model, the dual principle and linearization methods are used to convert them into mixed-integer linear programming problems that can be effectively solved by the Cplex solver. The study case verifies the power deviation cost decreases with the power exchange strategy and the important role of energy storage devices.

Impact of a single distance phase retrieval algorithm on spatial resolution in X-ray inline phase sensitive imaging.

A single-projection based phase retrieval method based on the phase attenuation duality principle (PAD) was used to compare the spatial resolution of the acquired phase sensitive and PAD processed phase retrieved images. An inline phase sensitive prototype was used to acquire the phase sensitive images. The prototype incorporates a micro-focus x-ray source and a flat panel detector with a 50 μm pixel pitch. A phantom composed of a 2 cm thick 50-50 adipose-glandular mimicking slab sandwiched with a 0.82 cm thick slanted PMMA sharp edge was used. Phase sensitive image of the phantom was acquired at 120 kV, 3.35 mAs with a 16 μm tube focal spot size under a geometric magnification (M) of 2.5. The PAD based method was applied to the acquired phase sensitive image for the retrieval of phase values. With necessary data processing, modulation transfer function (MTF) curves were determined for the estimation and comparison of the spatial resolution. The PAD processed phase retrieved values of the phantom were in good agreement with the theoretically calculated values. Phase sensitive images showed higher spatial resolution at all spatial frequencies compared to the phase retrieved images. It was noted that the high-frequency signal components in the retrieved image were suppressed that resulted in lower MTF values. When compared to the phase sensitive image, the cutoff resolution (10% MTF) for phase retrieved image dropped 32% from 15.6 lp/mm (32μm) to 10.6 lp/mm (47μm). The resolution offered by this phase sensitive prototype is radiographically enough to detect breast cancer.

ПРОБЛЕМА СУЩЕСТВОВАНИЯ И ПРИНЦИП ДОПОЛНИТЕЛЬНОСТИ ФИЛОСОФСКИХ КАТЕГОРИЙ

The paper introduces a new principle called the principle of duality of philosophical categories by example of the four pairs of concepts: perception/accepting, recognition/support, believing/supposition, thing/would. This principle consists in the following: certain philosophical categories cannot be correctly considered with-out a parallel study of dual categories. We also consider the problem of the relation between the notions of being and existence and the connection between categories related to existence and three dimensions of time.

Robust Performance and Observer Based Control for Periodic Discrete-Time Uncertain Systems

This paper presents an approach for the synthesis of observer-based controllers for discrete-time periodic linear systems. The H2 performance criterion has been employed to design both the observer and the controller. For the periodic observer design, two conditions in the form of Linear Matrix Inequalities (LMIs) are proposed, which stem from the Lyapunov Theory applied over the dynamics of the estimation error. The LMI condition obtained for the periodic state-feedback controller results from the application of the duality principle over the periodic system, under the assumption that only the estimated states are available to be used in the state-feedback compensation. Numerical experiments illustrate the potential of the proposed observer-based control technique.

CONSISTENCY OF THE DEFINITION OF THE MAGNETIC MOMENT WITH THE PRINCIPLE OF PERMUTATIONAL DUALITY

A representation of the principle of permutation duality of Maxwell's equations, which differs from the traditional representation by symmetry with respect to direct and inverse permutations of electrical and magnetic quantities and ease of use, is proposed. A generalized solution of the corresponding symmetric system of Maxwell's equations is constructed. The definition of the magnetic moment of arbitrarily distributed in the environment of closed currents is given, consistent with the newly formulated principle of permutation duality.

Of the matrics of the equilibrium of the rod formation system based on the principle the duality of the problems of structures mechanics

The formation of the equilibrium matrix of the core system in the matrix form is based on the use of the mechanical model of the system obtained by its discretization. The topological structure of the model is set using the graph and the accompanying incidence matrix. The matrix transformation of the vector of nodal displacements in combination with the extended incidence matrix allows determining the absolute elongations and distortions of each finite element. The composition of only two matrices (matrix of incidence and lengths of elements) and the skew vector leads to a geometric matrix characterizing the dependence of concentrated bending deformations in the calculated cross sections of the core system from the nodal displacements for a given load. Based on the duality principle, by transposing the geometric matrix, the equilibrium equation of the core system is derived in matrix form.

Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials

Abstract To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism with values in \mathbb{Q}[X] . We deduce from the interacting bialgebras an algebraic proof of the duality principle, a generalization and a new proof of a result on B-series due to Whright and Zhao, using a monoid of characters on quasi-posets, and a generalization of Faulhaber’s formula. We also give non-commutative versions of these results, where polynomials are replaced by packed words. We obtain, in particular, a non-commutative duality principle.

Hardy–Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis

Estimates of the norms of spaces associated to weighted first-order Sobolev spaces with various weight functions and summation parameters are established. As the main technical tool, boundedness criteria for the Hardy–Steklov integral operator with variable limits of integration in Lebesgue spaces on the real axis are used.

Coherence and information conservation and their applications in Mach-Zehnder interferometer

Coherence and complementarity are two important themes in quantum mechanics, which have been widely and thoroughly investigated. Recently, with the rapid development of quantum information theory, various measures have been introduced for quantitatively studying the coherence and complementarity. However, most of these studies are independent of each other in that they focus on only one theme, for example, the wave-particle duality and Heisenberg uncertainty principle are usually regarded as manifestation of Bohr’s complementary principle, while coherence is a quantum feature closely related to quantum superposition. During the past few years, there has been a flurry of research interest in the study of quantum coherence from the quantum resource-theoretic point of view. In this paper, we establish two information conservation relations and employ them to characterize complementarity and quantum coherence. As an illustration of the main results, we discuss these two themes in the Mach-Zehnder interferometer. Our study reveals that these two quantum themes are closely related to each other. Our main results are listed as follows. Firstly, we establish two information conservation relations, one is based on " Bures distance versus fidelity” and the other based on " symmetry versus asymmetry”. Then we employ these information conservation relations to investigate coherence and complementarity. Specifically, we provide an explanation of the " Bures distance versus fidelity” trade-off relation from the information conservation perspective, establish the link between the information conservation relation and wave-particle duality, and derive the famous Englert inequality concerning " fringe visibility versus path distinguishability” from the information conservation relation. Furthermore, in the general framework of state-channel interaction, we derive " symmetry versus asymmetry” trade-off relation and explain it as an information conservation relation, reveal its intrinsic relations with coherence and complementarity. Lastly, we demonstrate that the two information conservation relations are closely interrelated, and we also discuss the coherence, decoherence and complementarity in the Mach-Zehnder interferometer, explicitly, we reveal that the Bures distance can be regarded as a lower bound of the asymmetry of state-channel interaction while fidelity is an upper bound of the symmetry of state-channel interaction. We expect that our information conservation relation can provide a unified framework for the study of coherence and complementarity.

Методическая модель обучения иноязычному профессиональному общению студентов направления подготовки «Агроинженерия» на основе интегрированного предметно-языкового обучения

Methodical model is a set of interconnected components that form a single system aimed at achieving a common goal – the formation of foreign language communicative competence among students in the “Agricultural Engineering” programme based on content and language integrated learning. The teaching system is built on the basis of system, competency-based, per-sonal-activity, communicative-cognitive approaches, as well as content and language integrated learning. These approaches are implemented in practice using a number of didactic and methodical principles. We describe in detail the methodical principles of content and language integrated learning: principle 4 “C”, the principle of cognition, the principle of unity of thought and speech activity, the principle of integration of a foreign language and subject content, the principle of gradual complication of content, the principle of duality of reliance on native and foreign lan-guages, the principle of optimality, the principle of knowledge personalization, the principle of in-teractivity and the principle of language adaptation. Content and language integrated learning of students is carried out on the basis of the following teaching methods: interactive, communicative, information-reproductive, productive, tandem-method, vocational teaching and control methods. The content of teaching based on content and language integrated modeling reflects the profile specifics of training specialists in the framework of a particular specialty. Learning tools are a set of tools of a teacher for the purpose of development, teaching and upbringing. We present and de-scribe in detail all the components of the methodical model.

Optimal Continuous/Impulsive LQ Control With Quadratic Constraints

In this paper, the optimal continuous/impulsive linear quadratic (LQ) control problem with quadratic constraints is thoroughly solved for the first time. The main contributions of this paper can be stated as in the following. First, the maximum principle is developed by using the variational method. Then, by using the Lagrange duality principle, the optimal continuous/impulsive control can thus be obtained via decoupling the forward and backward differential/difference equation (FBSDE). Finally, the optimal parameter can be calculated by using the gradient-type optimization algorithm.

Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality.

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that outperforms general purpose numerical solvers by a large margin and compares favourably to current state-of-the-art. Further, our approach is able to handle the large problem instances commonly occurring in structure from motion settings and it is trivially parallelizable. Experiments are presented for a number of different instances of both synthetic and real-world data.

Risk-based Reserve Coordinative Unit Commitment for a Large-scale Wind-storage System

The increasingly high integration of wind power into power systems will further increase the power uncertainty and make it difficult to calculate the requirement of the reserve. In this article, a risk-based reserve optimization approach is proposed to quantitatively evaluate the reserve requirement of a large-scale wind-storage system. Conditional value-at risk (CVaR) is adapted to calculate the risk reserve managing the uncertainty of wind generation; this risk reserve achieves the optimal risk without sacrificing system reliability. An energy storage system (ESS) is employed to undertake the role of reserve transfer (RT) by cooperating with wind generation and conventional thermal units in the decision-making of unit commitment (UC); their cooperation and coordination can be achieved by building a bilevel optimization model with a day-ahead risk-constrained unit commitment model and a real-time risk reserve adjustment model. By using the duality principle and the big-M method, the formulations are converted into a mixed integer linear programing problem (MILP) that is solved using a column and constraint generation algorithm (C&CG). The model is tested on the six-bus system and the IEEE 118-bus system. The simulation results show that the ESS can transfer the reserve capacity of the thermal generator and improve the ability to accommodate the uncertainty of wind power generation, thereby demonstrating the effectiveness of the proposed methodology.

Sawyer's duality principle for grand Lebesgue spaces

AbstractThe aim of this paper is to extend Sawyer's duality principle from the cone of decreasing functions of the Lebesgue space to the cone of decreasing functions of the grand Lebesgue space and to prove the boundedness of classical Hardy operators in the grand Lebesgue spaces.

The quantum physics of emergency management

This paper takes information from human behaviour, social connection and quantum physics to describe emergency management phenomena. Emergency management is analysed as part of a complex adaptive system where the interconnections between people, technology and resources work together to create order from chaos. The world of quantum physics has multiple lessons for emergency planners. Events are intrinsically random, and as such it is impossible to have all the information that is necessary to create a complete picture of the world around. Combining this idea with the principles of uncertainty, duality and entanglement, this paper provides specific lessons from quantum physics as well as the actions emergency managers may take to respond effectively to the changing environment.

A new class of costs for optimal transport planning

We study a class of optimal transport planning problems where the reference cost involves a non-linear functionG(x, p) representing the transport cost between the Dirac measureδxand a target probabilityp. This allows to consider interesting models which favour multi-valued transport maps in contrast with the classical linear case ($G(x,p)=\int c(x,y)dp$) where finding single-valued optimal transport is a key issue. We present an existence result and a general duality principle which apply to many examples. Moreover, under a suitable subadditivity condition, we derive a Kantorovich–Rubinstein version of the dual problem allowing to show existence in some regular cases. We also consider the well studied case of Martingale transport and present some new perspectives for the existence of dual solutions in connection with Γ-convergence theory.

Formalizing Constructive Projective Geometry in Agda

We present a formalization of Projective Geometry in the proof assistant and programming language Agda. We formalize a recent development in constructive Projective Geometry which has been shown appropriate to cover most traditional topics in the area applying only constructively valid methods. The equivalence with other well-known constructive axiomatic systems for projective geometry is proved and formalized.The implementation covers a basic fragment of intuitionistic synthetic Projective Plane Geometry including the axioms, principle of duality, Fano and Desargues properties and harmonic conjugates.We focus in an illustrative example of implementation of a complex and large proof which appears partially and vaguely described in the literature; namely the uniqueness of the harmonic conjugate.The most important details of our implementation are described and we show how to take advantage of several interesting properties of Agda such as modules, dependent record types, implicit arguments and instances which result very helpful to reduce the typical verbosity of formal proofs.

Method of singular integral equations in diffraction by semiinfinite grating: E -polarization case

Diffraction of the E-polarized electromagnetic wave by a semiinfinite strip grating is considered. The scattered field is represented as a superposition of the field induced by the currents on the strips of an infinite periodic grating and the field induced by the correction current excited due to end of the grating. A singular integral equation with additional conditions for correction current density is obtained. A solution for the infinite periodic grating in the E-polarization case is obtained from the corresponding solution for the H-polarization case using the duality principle. Numerical results for the current density and far fields distribution are represented.