A large group of closed plane curves may be classified as roulettes, including epicycloids, hypocycloids, and related epitrochoids and hypotrochoids. The equation for the roulette in complex polar form shows that any roulette may be described by the vector sum of two vectors of specified constant magnitudes rotating with constant angular velocities. Methods for plotting, and for electronic display of roulettes are described. An equation is derived for a roulette approximation for an N-sided regular polygon. In particular, an application to two-dimensional potential theory is described and illustrated by consideration of the roulette approximation for a square as an equipotential curve, with derivation of equations for equipotential curves in the field surrounding the square. General equations are derived for given closed plane curves with points whose x and y coordinates may separately be expanded in Fourier series as functions of the polar angle, assuming these expansions are valid. It is shown that, in general, a closed plane curve may be considered as being described by an infinite sum of vectors, each rotating in a circle. Simplifying effects of symmetry about a polar axis and/or about the origin are discussed, and methods for harmonic analysis of a given closed plane curve with aid of an electronic calculator are described. 相似文献
A sequence of metrics {DN} is said to be additive and matched to a discrete memoryless channel (DMC) if DN is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum DN-distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 (2). 相似文献
The problem of designing quantizers for use in decision-making systems is considered. Applying the theory of local tests, general criteria are derived for the optimal selection of quantizer parameters for the large-sample-size case. These criteria agree with previously established results based on optimization in terms of distance measures and are shown also to lead to that quantizer-decision system which is most efficient asymptotically. To illustrate the design procedure, several applications to signal detection are discussed. 相似文献
Higher-order statistics (HOS) are well known for their robustness to additive Gaussian noise and ability to preserve phase. HOS estimates, on the other hand, have been criticized for high complexity and the need for long data in order to maintain small variance. Since rank reduction offers a general principle for reduction of estimator variance and complexity, we consider the problem of designing low-rank estimators for HOS. We propose three methods for choosing the transformation matrix that reduces the mean-square error (MSE) associated with the low-rank HOS estimates. We also demonstrate the advantages of using low-rank third-order moment estimates for blind system estimation. Results indicate that the full rank MSE corresponding to some data length N can be attained by a low-rank estimator corresponding to a length significantly smaller than N. 相似文献
Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (dc = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free-energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: follows governed by the Gaussian fixed point at shorter distances and enters a plateau at larger distances whose height decays as with a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables, including the two-point correlation, the magnetic fluctuations at zero and nonzero Fourier modes and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems. 相似文献
In this paper, we design two distributed output consensus controllers for heterogeneous linear systems based on internal model principle and then study the quantization effect on the controllers when uniform quantizers are used in the communication channels. The first controller considers the general situation when the internal model state matrix of the system may be unstable and the communication graphs are strongly connected directed graphs. We prove that the bound of the consensus error is proportional to the quantizer parameter with a coefficient related to the size of the network and the property of the communication graphs. The second controller considers the situation when the internal model state matrix is neutrally stable and the communication graphs are undirected connected graphs. In this case, we derive a better bound of the consensus error which is proportional to the quantizer parameter and the coefficient is unrelated to the size of the network when the linear systems are homogeneous. Simulation examples are provided to illustrate the theoretical results. 相似文献
A self-organization algorithm for image compression and the associated VLSI architecture are presented. A frequency upper-threshold is effectively used in the centroid learning method. Performances of the self-organization networks and traditional nonself-organization algorithms for vector quantization are compared. This new algorithm is quite efficient and can achieve near-optimal results. A trainable VLSI neuroprocessor based upon this new self-organization network has been developed for high-speed and high-ratio image compression applications. This neural-based vector quantization design includes a fully parallel vector quantizer and a pipelined codebook generator which obtains a time complexity O (1) for each quantization vector. A 5 × 5-dimensional vector quantizer prototype chip has been designed and fabricated. It contains 64 inner-product neural units and an extendable winner-take-all block. This mixed-signal chip occupies a compact silicon area of 4.6 × 6.8 mm2 in a 2.0-μm scalable CMOS technology. It provides a computing capability as high as 3.33 billion connections per second. It can achieve a speedup factor of 110 compared with a SUN-4/75 workstation for a compression ratio of 33. Real-time adaptive VQ on industrial 1024 × 1024 pixel images is feasible using multiple neuroprocessor chips. An industrial-level design to achieve 104 billion connections per second for the 1024-codevector vector quantizer can be fabricated in a 125 mm2 chip through a 1 μm CMOS technology. 相似文献
This work is devoted to the study of symmetric control systems. It establishes a relation between internal symmetry and external one for a linear invariant control system having n real simple poles. The symmetric stabilization problem is studied using a symmetric feedback gain such that the output control stabilizes the closed-loop system. A necessary and sufficient condition is given to solve this stabilization problem for a symmetric control system (A,B,C) and a generalized symmetric control system (E,A,B,C). 相似文献
This paper mainly concerns N-step off-line suboptimal predictive controller design for discrete nonhomogeneous Markov jump systems, in which the Markov chains are time-varying transition probabilities matrix modeled as a polytope. The design procedure is divided into N-step, more precisely, the first is to design the Nth step when the changes of Euclidean form of mode-dependent feedback law between the Nth and the (N+1)th asymptotically stable mode-dependent ellipsoids are less than the given accuracy. Then the N th asymptotically stable mode-dependent invariant ellipsoid is defined. In the previous (N−1) steps, an off-line mode-dependent predictive controller is designed to drive the state to this small area including the origin. Compared with on-line MPC algorithm, the computation time is dramatically reduced while the dynamic performance of controller is comparable. One numerical example is presented to illustrate the validity of the developed results. 相似文献
Fixed point properties of the binomial function are developed. It is shown that for any 1 < L < N, TLNhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability pFAand an initial detection probability pD, then TLN(pFA) < pFAand TLN(pD) > pDif, and only if, pFA < p? < pD. When this condition is satisfied, as N → ∞, TLN(pFA) → 0 and TLN(pD → 1. 相似文献
For a general quantum network system with a non-zero Hamiltonian H composed of n identical m-level quantum subsystems, any symmetric consensus state in the interaction picture exactly corresponds to an orbit in the Schrödinger picture, which is called the H-orbit of the symmetric consensus state. By using the interaction picture transformation and the tool of the LaSalle invariance principle, this paper analyzes the orbit consensus of this quantum network and designs the corresponding swapping operators such that the system converges to the H-orbit of the target symmetric consensus state that exists in the interaction picture. In particular, we prove the convergence of the quantum network to the H-orbit when the quantum interaction graph is connected and the system Hamiltonian is permutation invariant. The orbit consensuses of a four-qubit network system and a quantum network of three identical three-level subsystems are achieved numerically, which verifies the correctness of our theoretical results and the effectiveness of the designed swapping operators. 相似文献
The nonlinear buckling and postbuckling behavior of rectangular plates in symmetric and antisymmetric modes is re-examined, in the context of Bifurcation and Catastrophe Theories, using a two-degrees-of-freedom model, which has been adopted for the same purpose in the pioneer literature. At first the perfect system is dealt with in detail, symbolically utilizing the exact as well as the approximate equilibrium equations, the latter being products of a universal unfolding of the original total potential energy function. Conditions for the existence of remote secondary bifurcations are fully assessed and the stability of critical states is determined, revealing sudden qualitative changes in the postbuckling response of the perfect system, which have been also reported for the actual continuous structural system—the rectangular plate—using the von Kárman equations. Thereafter, the imperfection sensitivity is dealt with, introducing symmetric as well as asymmetric imperfections, considered as individual or consecutive perturbations of the perfect system. It is found that symmetry breaking bifurcations give birth to complicated cusp singularities, which may lead to unexpected jumps from one to two-mode remote postbuckling behavior. Finally, considering the general case of random imperfections, higher order two-mode singularities are revealed, mainly of the double-cusp catastrophe type, which have been also discovered in the postbuckling response of rectangular plates, a fact validating the choice of the foregoing nonlinear simulation. 相似文献
This paper is concerned with the problem of designing an observer-based quantized feedback controller for the continuous-time switched linear systems, in which the transmission of switching signal is subject to unbounded delays and packet loss. To deal with the unbounded switching delays, we design a constant to determine that the switching signal received by controller is ignored or not. Based on that, if the signal is timestamped, the controller’s mode is uniquely determined. Moreover, we adjust the quantizer parameters in real time depending on the actual transmission situations to ensure the unsaturation of quantizer and thus the boundness of quantization error. Within this setup, we derive a maximum allowable packet loss rate ensuring the mean square stability of the closed-loop switched systems. An illustrative example is given to show the usefulness of the proposed framework for the quantized stabilization of some classes of switched systems. 相似文献
N-containing organic compounds are of vital importance to lives. Practical synthesis of valuable N-containing organic compounds directly from dinitrogen (N2), not through ammonia (NH3), is a holy-grail in chemistry and chemical industry. An essential step for this transformation is the functionalization of the activated N2 units/ligands to generate N−C bonds. Pioneering works of transition metal-mediated direct conversion of N2 into organic compounds via N−C bond formation at metal-dinitrogen [N2-M] complexes have generated diversified coordination modes and laid the foundation of understanding for the N−C bond formation mechanism. This review summarizes those major achievements and is organized by the coordination modes of the [N2-M] complexes (end-on, side-on, end-on-side-on, etc.) that are involved in the N−C bond formation steps, and each part is arranged in terms of reaction types (N-alkylation, N-acylation, cycloaddition, insertion, etc.) between [N2-M] complexes and carbon-based substrates. Additionally, earlier works on one-pot synthesis of organic compounds from N2 via ill-defined intermediates are also briefed. Although almost all of the syntheses of N-containing organic compounds via direct transformation of N2 so far in the literature are realized in homogeneous stoichiometric thermochemical reaction systems and are discussed here in detail, the sporadically reported syntheses involving photochemical, electrochemical, heterogeneous thermo-catalytic reactions, if any, are also mentioned. This review aims to provide readers with an in-depth understanding of the state-of-the-art and perspectives of future research particularly in direct catalytic and efficient conversion of N2 into N-containing organic compounds under mild conditions, and to stimulate more research efforts to tackle this long-standing and grand scientific challenge. 相似文献
We present numerical simulations of DNA-chip hybridization, both in the “static” and “dynamical” cases. In the static case, transport of free targets is limited by molecular diffusion; in the dynamical case, an efficient mixing is achieved by chaotic advection, with a periodic protocol using pumps in a rectangular chamber. This protocol has been shown to achieve rapid and homogeneous mixing. We suppose in our model that all free targets are identical; the chip has different spots on which the probes are fixed, also all identical, and complementary to the targets. The reaction model is an infinite sink potential of width dh, i.e., a target is captured as soon as it comes close enough to a probe, at a distance lower than dh. Our results prove that mixing with chaotic advection enables much more rapid hybridization than the static case. We show and explain why the potential width dh does not play an important role in the final results, and we discuss the role of molecular diffusion. We also recover realistic reaction rates in the static case. 相似文献
An investigation has been made of the development of the solarized latent image with p-amino-phenol, pyrogallol and hydroquinone developer without potassium bromide, and with a series of hydroquinone developers containing potassium bromide from 0.002N to 0.269N solution. These developers represent a series with different reduction potentials. The investigation was restricted to a pure silver bromide emulsion.It was shown by the application of the Bravais-Pearson method of determination of the correlation coefficient that A. H. Nietz' straight line proportionality between density and the logarithm of the potassium bromide concentration holds in general for normal exposures, but that in extreme cases of exposure and development, deviations from the straight line proportionality are detectable. This proportionality holds only in a limited way for the solarization region. At the threshold of the first reversal of the solarization there is no correlation at all.The criterion that a family of curves has, or has not, a tie-point was investigated by the determination of the correlation coefficient between density and gamma. It was shown that the tie-point of the solarization curves moves toward the origin of the distance/log E axes with increasing content of potassium bromide in the developer. 相似文献
In this paper, we consider leader–follower decentralized optimal control for a hexarotor group with one leader and large population followers. Our hexarotor is modeled based on the quaternion framework to resolve singularity of the rotation matrix represented by Euler angles, and has 6-DoF due to six tilted propellers, which allows to control its translation and attitude simultaneously. In our problem setup, the leader hexarotor is coupled with the follower hexarotors through the followers’ average behavior (mean field), and the followers are coupled with each other through their average behavior and the leader’s arbitrary control. By using the mean field Stackelberg game framework, we obtain a set of decentralized optimal controls for the leader and N follower hexarotors when N is arbitrarily large, where each control is a function of its local information. We show that the corresponding decentralized optimal controls constitute an ϵ-Stackelberg equilibrium for the leader and N followers, where ϵ → 0 as N → ∞. Through simulations with two different operating scenarios, we show that the leader–follower hexarotors follow their desired position and attitude references, and the followers are controlled by the leader while effectively tracking their approximated average behavior. Furthermore, we show the nonsingularity and 6-DoF control performance of the leader–follower hexarotor group due to the novel modeling technique of the hexarotor presented in the paper. 相似文献
