The usual use of fractals involves self-similar geometrical objects to fill a space, where the self-similar iterations may continue ad infinitum. This is the first paper to propose the use of self-similar mechanical objects that fill an alloted space, while achieving an invariance property as the self-similar iterations continue (e.g. invariant strength). Moreover, for compressive loads, this paper shows how to achieve minimal mass and invariant strength from self-similar structures. The topology optimization procedure uses self-similar iteration until minimal mass is achieved, and this problem is completely solved, with global optimal solutions given in closed form. The optimal topology remains independent of the magnitude of the load. Mass is minimized subject to yield and/or buckling constraints. Formulas are also given to optimize the complexity of the structure, and the optimal complexity turns out to be finite. That is, a continuum is never the optimal structural for a compressive load under any constraints on the physical dimension (diameter). After each additional self-similar iteration, the number of bars and strings increase, but, for a certain choice of unit topology shown, the total mass of bars and strings decreases. For certain structures, the string mass monotonically increases with iteration, while the bar mass monotonically reduces, leading to minimal total mass in a finite number of iterations, and hence a finite optimal complexity for the structure. The number of iterations required to achieve minimal mass is given explicitly in closed form by a formula relating the chosen unit geometry and the material properties. It runs out that the optimal structures produced by our theory fall in the category of structures we call tensegrity. Hence our self-similar algorithms can generate tensegrity fractals. 相似文献
Montgomery multiplication of two elements a and b of a finite field Fq is defined as abr-1 where r is a fixed field element in . In this paper we define Montgomery multiplication of elements a(x) and b(x) in a polynomial ring modulo the ideal generated by a reducible polynomial f(x). We then show that Montgomery multiplication over a field represented by a polynomial ring modulo an irreducible pentanomial can be performed more efficiently in terms of time delay by embedding the field in a quotient of a polynomial ring modulo a reducible trinomial. The trinomial has a degree that is slightly higher than that of the pentanomial, thereby increasing the number of gates in the multiplier by a small amount. 相似文献
In this paper, a method for the design of 2-D analog and recursive digital filters is presented. Starting from a structure in the analog domain, suitable even or odd parts of two-variable Hurwitz polynomials are generated. This enables 2-variable very strictly Hurwitz polynomials (VSHP) to be obtained,2 thus avoiding non-essential singularities of the second kind. Thus it will ensure a stable 2-D recursive digital filter obtained by the use of bilinear transformations. Examples are given to illustrate the method. 相似文献
The computational complexity of the numerical simulation of fractional chaotic system and its synchronization control is O(N2) compared with O(N) for integer chaotic system, where N is step number and O is the computational complexity. In this paper, we propose optimizing methods to solve fractional chaotic systems, including equal-weight memory principle, improved equal-weight memory principle, chaotic combination and fractional chaotic precomputing operator. Numerical examples show that the combination of these algorithms can simulate fractional chaotic system and synchronize the fractional master and slave systems accurately. The presented algorithms for simulation and synchronization of fractional chaotic system are up to 1.82 and 1.75 times faster than the original implementation respectively. 相似文献
Charmonium is a bound state of a charmed quark and a charmed antiquark, and a charmoniumlike state is a resonant structure that contains a charmed quark and antiquark pair but has properties that are incompatible with a conventional charmonium state. While operating at center-of-mass energies from 2 to 5 GeV, the BESIII experiment can access a wide mass range of charmonium and charmoniumlike states, and has contributed significantly in this field. We review BESIII results involving conventional charmonium states, including the first observation of the M1 transition ψ(2S) → γηc(2S) and the discovery of the ψ2(3823) state; and report on studies of charmoniumlike states, including the discoveries of the Zc(3900) and Zc(4020) tetraquark candidates, the resolution of the fine structure of the Y(4260) state, the discovery of the new production process e+e− → γX(3872) and the uncovering of strong evidence for the commonality among the X(3872), Y(4260) and Zc(3900) states. The prospects for further research at BESIII and proposed future facilities are also presented. 相似文献
Studies of two-element-kind ladder networks are well known in the classical literature, among them, the most celebrated ones are due to Cauer. Driving point immittance function synthesis by using continued fractions to obtain the series and shunt arm L-C element values is a standard and routine work. The idea of introducing a class of more general networks, the inhomogeneous ladder networks, was first developed by Lee and Brown, and subsequently the synthesis techniques of such a network were established.In this paper, new results are found such as: (1) the Iff. conditions of the existence of an inhomogeneous ladder network by a given chain matrix of the network satisfying: (a) determinant of the chain matrix is 1; (b) the zeros of A(s) and z?1B(s) or A(s) and y?1C(s) alternate with respect to [z(s)y(s), k] with an appropriate leading set of zeros of A(s); (c) the poles of A(s) and z?1B(s) or A(s) and y?1C(s) are the poles of z(s)y(s) of multiplicity of n and n?1, where n the number of sections of ladder networks; (2) the Iff. condition for the inhomogeneous ladder network to be optimal is that it be antimetrical, whereas for the extended class of inhomogeneous ladder networks it is symmetrical, where an optimal inhomogeneous ladder network is defined as the corresponding network with the minimum sum of immittance levels in the series and shunt arms; (3) algorithms of synthesis procedures were developed as the by-products of the Theorems. 相似文献
Magnetic loss in remanent state ferrites1 has generally been described through the artifice of a magnetic loss tangent (tanδm = μ″?μ′). This characterization is not directly relatable to intrinsic material parameters. The results presented in this paper indicate that magnetic loss in the remanent state can be related to intrinsic material parameters by describing the ferrite mathematically by a complex “average” permeability tensor. The “average” permeability includes the effects of magnetocrystalline anistropy, remanent magnetization, linewidth and an average demagnetizing field appropriate to the distribution of magnetic domains. Experimental examples are given showing that excellent agreement is obtained between theoretically predicted and measured losses. 相似文献
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
This paper investigates a stability problem for linear systems with time-varying delays. By constructing suitable augmented Lyapunov–Krasovskii functionals, improved stability criteria under various conditions of time-varying delays are derived within the framework of linear matrix inequalities (LMIs). Moreover, to reduce the computational burden caused by the non-convex term including h2(t), how to deal with it is applied by estimating it to the convex term including h(t). Finally, three illustrative examples are given to show the effectiveness of the proposed criteria. 相似文献
In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?ci/?t = Di?2ci+Qi(c), where the enumerator index i runs 1 to n, ci = ci(x, t) denotes the concentration or density of the ith participating molecular or biological species, Di is the diffusivity constant for the ith species and Qi(c), an algebraic function of the n-tuple c = (c1,\3., cn), expresses the local rate of production of the ith species due to chemical reactions or biological interactions. 相似文献
In this article, we provide a complete detection analysis, in its exact form, of what is known as moderately fluctuating radar targets when the background environment contains a number of interfering targets along with the target under test. The illumination of this class of radar targets by a coherent pulse train, return a train of correlated pulses with a correlation coefficient in the range 0<ρ<1 (intermediate between SWII and SWI models). Since the adaptive detection is one of the desirable features for modern radar receivers, it becomes of importance to adaptively detect this class of targets. The attractive class of adaptive detectors is that based on order-statistics (OS) technique. The more advanced version of the OS algorithm, known as the generalized trimmed-mean (GTM) scheme, is chosen here to carry out this task. It implements trimmed averaging of a weighted ordered range samples. This processor is analyzed for the case where the radar receiver incorporates a postdetection integrator amongst its contents and where the operating environment is multitarget. The primary and the secondary interfering targets are assumed to be fluctuating in accordance with partially correlated χ2 fluctuation model. SWI and SWII well-known models represent the cases where the signal is completely correlated and completely decorrelated, respectively, from pulse to pulse. It is shown that the processor performance improves, for weak SNR of the primary target, as the correlation coefficient ρs increases and this occurs either in the absence or in the presence of spurious targets. For strong SNR, on the other hand, the processor performance degrades as ρs increases and the SWI and SWII models enclose the correlated target case and this behavior is common for all GTM based schemes. 相似文献
In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with two deviating arguments of the form
Let χm+1=T(χm) or even χm+1=T(χm,χm?1, …, χm?q), m=1,2,3 … be an iteration method for solving the nonlinear problem F(χ)=0, where F(χ) and its derivatives possess all of the properties required by T(χm). Then if it can be established that for the problem at hand ∥F(χm+1)∥?βm∥F(χm)∥, ? m > M0 (M0<∞) and 0?βm<1 , definitions are established and theorems proven concerning convergence, uniqueness and bounds on the error after ‘m’ successive iterations of a new approach to convergence properties T(χm). These charateristics are referred to as “alternate” (local, global) convergence properties and none of the proofs given are restricted to any specific type of method such as, e.g. contraction mapping types. Application of results obtained are illustrated using Newton's method as well as the general concept of Newton-like methods. 相似文献
An algorithm for constructing a black box model of the sinusoidal input/steady-state response behavior of nonlinear time-invariant systems over a set of frequencies and amplitudes is presented. It is assumed that the steady-state response is periodic of the same fundamental frequency as the excitation, and that the Fourier coefficients are continuous functions of amplitude and square-integrable functions of frequency. The algorithm converges, in a mean-square sense, to an exact representation of the first N harmonics of the steady-state response minus its d.c. component. The model constructed by the algorithm admits a relatively simple physical realization characterized by 2NM+1 linear dynamic elements, and N(2M+1)+1 nonlinear static elements. The underlying mathematical structure of the model is an orthogonal series expansion relative to time whose coefficients are themselves truncated orthogonal expansions relative to frequency. Here M, the number of harmonics used for frequency interpolation, is determined by the algorithm. Of the N(2M+1)+1 memoryless nonlinearities which characterize the model, N of these are specified ahead of time (Tchebysheff polynomials), and 2NM+1 are parameters which mold the representation to the specific system being modeled. Each of these functions of a single variable can be obtained in a pointwise manner directly from steady-state measurements. The algorithm was implemented on a digital computer, and forced versions of the classic equations of van der Pol and Duffing were run as examples. An additional analytic example of a frequency multiplier of prescribed bandwidth was also presented. 相似文献
The usual model for (Poissonian) linear birth-death processes is extended to multiple birth-death processes with fractional birth probabilities in the form λi(Δt)α+o((Δt)α, 0<α<1. The probability generating function for the time dependent population size is provided by a fractional partial differential equation. The solution of the latter is obtained and comparison with the usual model is made. The probability of ultimate extinction is obtained. One considers the special case of fractional Poissonian processes with individual arrivals only, and then one outlines basic results for continuous processes defined by fractional Poissonian noises. The key is the Taylor’s series of fractional order f(x+h)=Eα(hαDxα)f(x), where Eα(·) is the Mittag-Leffler function, and Dxα is the modified Riemann-Liouville fractional derivative, as previously introduced by the author. 相似文献
A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m1 and m2 = m−m1 zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m1=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method. 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
The supramolecular chemistry of nanoclusters is a flourishing area of nano-research; however, the controllable assembly of cluster nano-building blocks in different arrays remains challenging. In this work, we report the hierarchical structural complexity of atomically precise nanoclusters in micrometric linear chains (1D array), grid networks (2D array) and superstructures (3D array). In the crystal lattice, the Ag29(SSR)12(PPh3)4 nanoclusters can be viewed as unassembled cluster dots (Ag29–0D). In the presence of Cs+ cations, the Ag29(SSR)12 nano-building blocks are selectively assembled into distinct arrays with different oxygen-carrying solvent molecules―Cs@Ag29(SSR)12(DMF)x as 1D linear chains (Ag29–1D), Cs@Ag29(SSR)12(NMP)x as 2D grid networks (Ag29–2D), and Cs@Ag29(SSR)12(TMS)x as 3D superstructures (Ag29–3D). Such self-assemblies of these Ag29(SSR)12 units have not only been observed in their crystalline state, but also in their amorphous state. Due to the diverse surface structures and crystalline packing modes, these Ag29-based assemblies manifest distinguishable optical absorptions and emissions in both solutions and crystallized films. Furthermore, the surface areas of the nanocluster crystals are evaluated, the maximum value of which occurs when the cluster nano-building blocks are assembled into 2D arrays (i.e. Ag29–2D). Overall, this work presents an exciting example of the hierarchical assembly of atomically precise nanoclusters by simply controlling the adsorbed molecules on the cluster surface. 相似文献
