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1.
Polar coordinates quantization of the bivariate Gaussian and other cir- cularly symmetric sources has already been investigated. The schemes quantize the polar coordinates representation of the random variables independently in an attempt to reduce the mean square error below that of an analogous rectangular coordinates quantizer. It has been shown for the Gaussian case that the polar quantizer outperforms the rectangular quantizer when the number of levels N is large, while for small N, the rectangular form is often better than the polar form. This paper is an investigation of the optimality of polar quantizers with the subsequent development of optimal circularly symmetric quantizers (labelled Dirichlet polar quantizers). 相似文献
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Martin J. Bastiaans 《Journal of The Franklin Institute》2011,348(9):2670-2673
It is shown that the recently introduced T-class of time-frequency distributions is a subclass of the S-method distributions. From the generalization of the S-method distribution by rotating it in the time-frequency plane, a similar generalization of the T-class distribution follows readily. The generalized T-class distribution is then applicable to signals that behave chirp like, with their instantaneous frequency slowly varying around the slope of the chirp; this slope needs no longer be zero, as is the case for the original T-class distribution, but may take an arbitrary value. 相似文献
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数控车床是机械制造系统中一种具有高效率、高精度与高柔性的自动化机床。可以有效解决复杂、精密、小批多变零件的加工问题。而对于轴类零件上一些高精度的非圆曲线,如椭圆、双曲线、正弦线、余弦线、抛物线等构成的回转体表面,通常采用直线逼近法来加工,本文结合自己多年的实习操作经验,现以华中世纪星HNC-21T系统数控车床为例,对加工正弦曲线的宏程序的编程方法进行探讨。 相似文献
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Edith L. Morgan 《Journal of The Franklin Institute》1947,243(4):309-322
Using the theory of the logarithmic potential and the methods of intersecting circles and radii, plots are obtained for the lines of flow and equipotentials for eight cases of two sources, two sinks, or a source and a sink of varying strengths. A detailed analysis of the equilibrium equipotentials is included. The problem of three unit sources placed at the vertices of an equilateral triangle is investigated; and the general expression of the equilibrium equipotential for n similar unit sources (or sinks) placed at the vertices of a regular n-sided polygon is developed. 相似文献
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Document clustering is an important tool for document collection organization and browsing. In real applications, some limited knowledge about cluster membership of a small number of documents is often available, such as some pairs of documents belonging to the same cluster. This kind of prior knowledge can be served as constraints for the clustering process. We integrate the constraints into the trace formulation of the sum of square Euclidean distance function of K-means. Then,the combined criterion function is transformed into trace maximization, which is further optimized by eigen-decomposition. Our experimental evaluation shows that the proposed semi-supervised clustering method can achieve better performance, compared to three existing methods. 相似文献
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Dragan Antić Bratislav Danković Saša Nikolić Marko Milojković Zoran Jovanović 《Journal of The Franklin Institute》2012,349(1):323-336
In this paper, we define a class of almost orthogonal rational functions of Legendre type in a new manner. Relations of these functions with classical exponentional functions orthogonal over interval (0, ∞), as well as classical polynomials orthogonal over (0, 1) are explained. Defining relations of these functions can be used for designing almost orthogonal filters. These filters are generators of orthogonal signals and can be successfully applied in finding the best signal approximation in the sense of the mean square error. The filters orthogonal property enables building of physical (in this case electrical) models of dynamical systems (the sources of signals to be approximated) either with less components for the same model accuracy or higher accuracy for the same number of components than the other known models. New filters represent further improvement of previously designed filters, by the same authors, in the sense of simplicity, higher accuracy, lesser approximation time and even a possibility to approximate signals generated by systems with built-in imperfections. Series of experiments were performed to analyze the dependence of approximation accuracy and the number of filters sections. 相似文献
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Wm. Bender 《Journal of The Franklin Institute》1933,216(2):157-182
In the Introduction the several branches of Physics are classified according to the sensory experience whereby the coincidence is recorded, thereby orienting the term “visual coincidence.” The rôle of the clock mechanism in dynamical formulation is briefly discussed.In Part I, an array of Michelson rotating mirror clocks, giving a postulated light-velocity effect, is used as a background for an empirical criterion for the synchronization of clocks.In Part II, the empirical criterion for synchronization in question is formulated in such a way as to disclose the existence of an absolute kinematic quantum, capable of macroscopic test, contingent on the light-velocity effect postulated in Part I.In Part III, the galilean spacetime scale is introduced as a kinematic “crystal” lattice whose gauge is the absolute kinematic quantum discussed in Part II. The question is raised whether in problems involving the ordering of sharp steady light images concentrated in lines or points, the images themselves may not form a three coördinate galilean or non-galilean spacetime lattice of synchronized clock-points, and are not more immediately described this way than by reference to the amorphous galilean or non-galilean four-coördinate reference systems. It is suggested that the quantum problem insofar as it treats of spectroscopic and crystallographic electromagnetic image patterns may be treated through an establishment of transformation equations between observed coincidences of a spacetime scale, as such, and the same observed coincidences referred to a uniform length scale. 相似文献
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H.B. Maris 《Journal of The Franklin Institute》1947,244(1):27-62
The equations of equilibrium in a stress field as given by Lamé are compared with those given by Cauchy. The (P ? Q and P ? R) terms of the Lamé equations identified by the new words detend and double detend are invariant for any point in a stress field. The principal stresses are defined as real stress components. The terms of the Cauchy equations are considered as imaginary force components. Real and imaginary stress and force components are differentiated by the differences between ray vectors, as for example a force which has only one real value and direction, and diffuse vectors, as for example a gradient, which has a real value in any direction. Shear is differentiated from detend value by its variation with the direction in which it is taken. Shear is found to be an imaginary component of force parallel to a plane.The photoelastic equidetend (isochromatic) and isoclinic maps of a plane stress field define, for any point, a gradient triangle with the three maximum gradients, Δ(P ? Q) ΔP and Δ ? Q, for its sides. Five quantities, the detend (P ? Q), the ratio of the detend to its gradient (r4), the ratio (r3) of the isoclinic normal ds3 to the stress axis direction change along its length dα, the direction of the equidetend normal (θ) and the orientation of an isoclinic line (ω) with reference to a principal stress direction, determine each gradient triangle. Five equations which define elements of the gradient triangle in terms of the five measurable quantities, are developed. Definition of the triangle can be complete with two of the five measurable quantities or two of the five equations omitted. Graphic integration of principal stress changes along any line in a stress field can be made by plotting the line straight and measuring the area swept out by the normal projections, along the line, of the sides of the gradient triangle, after it has been rotated through 90 degrees.Properties of the gradient triangle are used to solve several symmetrical stress problems and to integrate along two lines through a stress field. 相似文献
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Guillermo Oaxaca-Adams Raúl Villafuerte-Segura Baltazar Aguirre-Hernández 《Journal of The Franklin Institute》2021,358(9):4671-4686
In this paper an explicit numerical procedure is proposed to determine the non-fragility of parameters of controllers used to stabilize a class of time delay systems. The proposed procedure finds the largest possible circle inscribed in a stability subregion delimited by a simple closed curve in the plane of the controller parameters. The center of this circle is declared to be the controller’s least fragile parameters. The obtained theoretical results are applied and compared with some of the most relevant examples found in the literature. This illustrates that the proposed procedure improves previous results found in the literature so far. 相似文献
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《Journal of The Franklin Institute》1986,321(6):337-350
In the first part of the paper, a systematic procedure for constructing high-order magic squares as an extension of the lower-order basic magic squares is developed and demonstrated. For a 2N x 2N magic square, one can start with a basic N x N magic square, say, N = 3,4,5 or 7,11,13. Using small 2 x 2 squares, like (1,2,3,4) or (5,6,7,8), to fill the elements of the basic N x N magic square according to the ordering of the magic square, one develops the 2N x 2N magic square automatically. For a 3N x 3N magic square, one can choose another basic N x N magic square, say, the 4 x 4 magic square. Then, inserting 3 x 3 small squares in the 16 empty spaces according to the ordering of the 4 x 4 magic square, one develops the 12 x 12 magic square. There may be small adjustments in the numbering of (1,2,3,4) in the 2 x 2 small square, or of (1,2,3,4,5,6,7,8,9) in the 3 x 3 small square to form the proper 2N x 2N or 3N x 3N magic squares. In most cases, the correct results are obtained without adjustments. For N = 4, 4N x 4N produces the 16 x 16 magic square. For N = 5 or 7, using 2 x 2 small squares produces 10 x 10 or 14 x 14 magic squares. Part II of the paper gives a review of other known procedures for constructing odd and even order magic squares with illustrative examples for 4 x 4, 5 x 5, 7 x 7, 10 x 10, 11 x 11, 13 x 13, 15 x 15, 17 x 17, 19 x 19 and 20 x 20 magic squares. One 18 x 18 magic square is given in Part I. In the Appendix, the G and H squares, given by Moschopulus of Constantinople nearly five centuries ago, are discussed concerning symmetrical and pandiagonal squares. It is shown that H can be modified to form H1 which is both symmetrical and pandiagonal. 相似文献
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C.A. Morrison 《Journal of The Franklin Institute》1947,243(1):55-61
A system of numerical specification of the sensitometric curves of photographic papers is described. Comparison of original curves and their reproductions, made by a new curve duplicator from specifications, shows that the system is satisfactory for production control. 相似文献
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John Stensby 《Journal of The Franklin Institute》2005,342(2):149-159
A quadrature lock detector is incorporated in almost all coherent radio communication receivers. This commonly-used receiver subsystem is comprised of a quadrature phase detector that drives a low-pass filter, the output of which is subjected to a user-specified threshold to make a lock/unlock decision. Signal acquisition and phase lock are declared if an above threshold condition is observed. Unfortunately, this method of lock detection may yield a positive lock indication when the receiver is false locked; i.e., a classical quadrature lock detector may generate a false-positive lock indication. This tendency to produce an incorrect lock indication can be reduced significantly by using the new lock detector algorithm that is described here. Compared to the classical quadrature lock detector, the new lock detector is better able to differentiate between true phase lock and anomalous false lock. The classical quadrature lock detector is a simple, first-order approximation of the new lock detector algorithm. That is, the new lock detector algorithm consists of a classical quadrature detector that is augmented by a correction term. 相似文献
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W.F.G. Swann 《Journal of The Franklin Institute》1934,218(2):173-241
Using the velocity analyzer of Zartman with improved technique the combined velocity spectrum of Bi atoms and Bi2 molecules was obtained at 827°, 851°, 875°, 899°, 922°, 947° C. From the spectral distribution curves the relative abundance of Bi atoms and Bi2 molecules in the beams at the above temperatures could be determined to 1 per cent. The vapor pressure curve of Bi was obtained experimentally by the method of effusion and the values so obtained were combined with the degree of dissociation of the vapor as computed from the beams to give the heat of dissociation. The heat of dissociation was computed from the data, assuming the pressure to be given by the temperature of the crucible Tc. In calculating the heat of dissociation, the equilibrium temperature was taken as that of the slit chamber Ts which was 24° above Tc. The results of these calculations plotted with log10Kp as ordinates against give a straight line whose slope yields the value of the heat of dissociation as 77,100±1200 calories. The curves for the distribution of velocities observed and computed on the assumption of a given ratio of Bi atoms to Bi2 molecules in the beam were compared in an attempt to test the law of distribution of velocities. On the high velocity side agreement in two curves was obtained within the limits of experimental accuracy. On the low velocity side important deviations were noted of such a sort that the observed curves below a velocity , (α is the most probable velocity) gave more molecules than the theory demanded. Other deviations were observed on some of the runs taken with a fourth slit in which a deficiency of molecules was observed between velocities of .75α and . This deviation was probably due to a warping of the fourth slit carriage due to heat. The nature of the variation at velocities less than indicated the presence of molecules of greater mass than Bi2 in the beam and at the lower temperatures a distinct peak corresponding to Bi8 molecules was observed which were present to less than 2 per cent. The vapor pressure curve for Bi was determined by least square reduction of the observed points to be given by between 1100° and 1220° abs. It lies very close to the extrapolated curve given in the International Critical Tables. 相似文献
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Ioannis M. Besieris 《Journal of The Franklin Institute》1973,296(4):249-258
A technique first suggested by Knop (1) has been used to invert exactly a special contour integral arising in the study of space-time evolution of pulsed plane electro- magnetic signals in the presence of a class of generalized conducting media. The final expressions are given in terms of Lommel functions of two imaginary variables. These findings have been applied to the examination of plane transient wave propagation in uniformly moving conducting media, and materials described by a dissipative Klein-Gordon equation. 相似文献
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Mapping of curves from the physical to the hodograph plane, when the Jacobian vanishes along a curve is discussed in detail here. A certain quadratic expression occuring in the equations has been identified as the important factor in the transformation. The nature of the transformation depends on whether the roots are complex or real distinct and so on. A geometrical representation of the referred quadratic expression is also presented, resulting in a better understanding of the transformation technique. 相似文献
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J.M. Lowerre 《Journal of The Franklin Institute》1977,303(6):517-526
For the linear statistical model y = Xb + e, X of full column rank estimates of b of the form (C + X′X)+X′y are studied, where C commutes with X′X and Q+ is the Moore-Penrose inverse of Q. Such estimators may have smaller mean square error, component by component than does the least squares estimator. It is shown that this class of estimators is equivalent to two apparently different classes considered by other authors. It is also shown that there is no C such that (C + X′X)+X′Y = My, in which My has the smallest mean square error, component by component. Two criteria, other than tmse, are suggested for selecting C. Each leads to an estimator independent of the unknown b and σ2. Subsequently, comparisons are made between estimators in which the C matrices are functions of a parameter k. Finally, it is shown for the no intercept model that standardizing, using a biased estimate for the transformed parameter vector, and retransforming to the original units yields an estimator with larger tmse than the least squares estimator. 相似文献