Length Approaches Infinity Research Articles

A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes

It is known that both the optimal exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are based on a given reference value $\delta$, which, for the CUSUM chart, is the magnitude of a shift in the mean to be detected quickly. In this paper a generalized EWMA control chart (GEWMA) which does not depend on $\delta$ is proposed for detecting the mean shift. We compare theoretically the GEWMA control chart with the optimal EWMA, CUSUM and the generalized likelihood ratio (GLR) control charts. The results of the comparison in which the in-control average run length approaches infinity show that the GEWMA control chart is better than the optimal EWMA control chart in detecting a mean shift of any size and is also better than the CUSUM control chart in detecting the mean shift which is not in the interval $(0.7842\delta ,1.3798\delta )$. Moreover, the GLR control chart has the best performance in detecting mean shift among the four control charts except when detecting a particular mean shift $\delta,$ when the in-control average run length approaches infinity.

Tubular Adhesive Joints Under Axial Load

In this paper a general study on tubular adhesive joint under axial load is presented. We focus our attention on both static and dynamic behavior of the joint, including shear and normal stresses and strains in the adhesive layer, joint optimization, failure load for brittle crack propagation, and crack detection based on free vibrations. First, we have considered the shear and normal stresses and strains in the adhesive layer to propose an optimization to uniform axial strength (UAS) and to reduce the stress peaks in the bond. The stress analysis confirms that the maximum shear stresses are attained at the ends of the adhesive and that the peak of maximum shear stress is reached at the end of the stiffer tube and does not tend to zero as the adhesive length approaches infinity. A fracture energy criterion to predict brittle crack propagation for conventional and optimized joint is presented. The stability of brittle crack propagation and the strength of the joint, as well as the ductile-brittle failure transition, are analyzed. A detection method to predict crack severity, based on joint dynamic behavior, is also proposed. The crack detection is achieved through the determination of the axial natural frequencies of the joint as a function of the crack length, by determining the roots of a determinantal equation.

Construction of fast recovery codes using a new optimal importance sampling method

We introduce the problem of constructing good fast recovery convolutional codes. When the constraint lengths of the candidate codes are long (say more than 12), it is too computationally complex to perform the code search task. Fortunately, we can transform the code construction problem to a problem related to a transient Markov system. We then develop an optimal importance sampling (IS) method to fulfil the tasks. In this article, we also prove several propositions for optimal IS. For instance, we show analytically that the optimal IS method is unique. We prove that the optimal IS method must converge to the standard Monte Carlo (MC) simulation method when the sample path length approaches infinity. This finding shows that it is not the size of the state space of the Markov system, but the sample path length, that limits the efficiency of the IS method. Based on insights from the optimal IS method, a suboptimal IS method is then proposed to search for long fast recovery codes. The suboptimal method can achieve a substantial speedup gain. After that, several numerical results are presented to study the efficiency of the IS methods and to justify the code search procedures. Finally, we give the code search results and the application of these codes.

Tubular bonded joint under torsion: Theoretical analysis and optimization for uniform torsional strength

The paper analyses the problem of torsion in an adhesive bonded tubular joint. The constitutive, equilibrium and compatibility equations were used to obtain the stress field in the adhesive. The analysis confirms that the maximum stresses are attained at the ends of the adhesive and that the peak of maximum stress is reached at the end of the stiffer tube and does not tend to zero as the adhesive length approaches infinity. A special type of tubular joint can be produced by modifying the joint profile, thus ensuring that the stress field in the adhesive is constant and thereby optimizing the tubular joint for uniform torsional strength. This result is of considerable practical utility and makes it possible to produce adhesive bonded joints which are both lighter and stronger under torsion. Finally, some suggestions for the joint design are presented.

Fractal relations. Modelling fractals and analogy with Feigenbaum's period-doubling diagram

The equivalence relation, l, defined previously on Kekulé spaces of benzenoid hydrocarbons (S. El-Basil, J. Chem. Soc., Faraday Trans., 89 (1993) 909; J. Mol. Struct. (Theochem), 288 (1993) 67; J. Math Chem., 14 (1993) 305) is used to map Kekulé spaces of benzenoid systems onto various stages of deterministic fractals including the Cantor set, the Sierpinski triangle, the Sierpinski carpet, the Koch curve and the box fractal as well as certain stages of cellular automata. Furthermore, the Kekulé spaces of quasicrystalline benzenoids (defined by S. El-Basil in J. Chem. Soc., Faraday Trans., 89 (1993) 909) exhibit a period-doubling pattern which manifests itself through a full analogy with Feigenbaum's scaling theorem (M. Feigenbaum, J. Stat. Phys., 19 (1978) 25) including a bifurcation universality constant, a control parameter (of the logistic equation) and cycle-sizes (which can only be integral powers of two). It was found that in certain instances l is also a “ percolation” process where larger clustering (of the Kekulé space) occurs (D. Stauffer, Introduction to Percolation Theory, Taylor and Francis, London, 1985). Cases in which l percolates the Kekulé space correspond to benzenoid systems which are energetically more stable than those in which the resulting clusters are too small to allow percolation of the space by l. A fractal-like scale factor, s, is defined as the limit of the ratio of Clar counts to Kekulé counts in a given homologous series of benzenoid hydrocarbons as the molecule's length approaches infinity. This limit shows that with quasicrystalline benzenoids (branched and/or unbranched), the extent of data reduction using Clar structures is maximum (i.e. s = 0) and hence the use of such structures as a quantum-mechanical basis set in the method of Herndon and Hosoya (W.C. Herndon and H. Hosoya, Tetrahedron, 40 (1984) 3987) is most suited for this class of benzenoid systems. The linear acenes, however, lead to a value of s = 1 and hence, as the size of the molecule gets larger, the computational scheme of Herndon and Hosoya becomes progressively less efficient. This scale factor has certain arithmetical properties which are in harmony with the ultraviolet spectra of the corresponding benzenoid systems.

Information approach to estimating the accuracy of analog electronic devices and its application

A method is proposed for estimating the accuracy of analog devices which is based on an entropy approach. The loss of information by an analog device is sought as the limit of the information loss of an analog-to-digital device as its word length approaches infinity. Applications of the method are considered for an angle-parameter-number converter and for a measuring system.

Optimal mean squared error analysis of the harmonic gradient estimators

This paper presents a mean squared error analysis of the harmonic gradient estimators for steady-state discrete-event simulation outputs. Optimal mean squared errors for the harmonic gradient estimators are shown to converge to zero as the simulation run length approaches infinity at the same rate as the optimal mean squared errors for the symmetric (two-sided) finite-difference gradient estimator. Implications of this result are discussed.

Parallelization of Bresenham's line and circle algorithms

Parallel algorithm for line and circle drawing that are based on J.E. Bresenham's line and circle algorithms (see Commun. ACM, vol.20, no.2, p.100-6 (1977)) are presented. The new algorithms are applicable on raster scan CRTs, incremental pen plotters, and certain types of printers. The line algorithm approaches a perfect speedup of P as the line length approaches infinity, and the circle algorithm approaches a speedup greater than 0.9P as the circle radius approaches infinity. It is assumed that the algorithm are run in a multiple-instruction-multiple-data (MIMD) environment, that the raster memory is shared, and that the processors are dedicated and assigned to the task (of line or circle drawing).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized model for the diffusion-limited aggregation and Eden models of cluster growth.

The diffusion-limited aggregation (DLA) model of cluster growth and aggregation has been extended to include both a finite and variable diffusion length for the particle's random walk. The new model generates a variety of different structures similar in geometry to the DLA model; however, they lack the fractal scaling indices normally expected from the DLA model. It is postulated that the DLA and Eden models of cluster growth are both limiting cases of the finite-diffusion-length model where the diffusion length approaches infinity and zero, respectively.

VIBRATION MODES CHARACTERIZED BY RAYLEIGH WAVES PROPAGATING IN AN ELASTIC LAYER ON A RIGID BASE

Due to fact the that Rayleigh waves are attributed to a kind of natural vibration of a surface layer, their nature can be understood by vibration experiments using a shaking table or by vibration mode analysis of a layer of finite length. This has been confirmed experimentally, analytically and numerically. In the limiting case, where the wave length approaches infinity, the wave motion is found to be reduced to shear vibration and longitudinal vibration of the layer.

The relation between maximum likelihood estimation of structured covariance matrices and periodograms

A generalized Burg technique has been developed recently by Burg, Luenberger, and Wegner for maximum likelihood estimation of structured covariance matrices. In this correspondence, the unique solution for the positive definite estimate over a class of nonnegative definite, symmetric matrices with known eigenvectors is presented. This solution coincides with the Karhunen-Loeve expansion, and for the class of circulant matrices can be interpreted in terms of periodograms. For stationary processes and infinitely large sample size, it is shown that the sequence of optimal covariance matrices among the class of circulant matrices is asymptotically equivalent to the sequence of true covariance matrices as the observation length approaches infinity.

Classical excitation energies for a finite-length sine-Gordon system

We present simple analytic expressions for the classical energies of previously obtained nonlinear-standing-wave and single-soliton solutions to the sine-Gordon equation for a finite-length system with fixed- and free-boundary conditions. Plots of these energies are presented for several system lengths and the energy expressions are shown to reduce to those appropriate to familiar solutions in the infinite system as the length approaches infinity.

Hydrophobic solvation of nonspherical solutes

The theory of hydrophobic effects presented by Pratt and Chandler is generalized to include nonpolar solutes which are distinctly aspherical. The theory is used to study the solvation of simple aspherical hydrocarbon solutes in liquid water. The radial solvation of each component of diatomiclike solutes is studied as a function of their separation, or bond length. From these results it is found that when the bond length is large enough that one water molecule can fit between the apolar pair, the radial solvation of each is the same as that when the bond length approaches infinity. The solvation of the various sites of the homologous series methane, ethane, propane, and n-butane is also studied, and effects of the geometrical structure of the solutes on their solvation is discussed.

A new universal coding scheme for the binary memoryless source

A coding scheme for the binary memoryless source is presented. The scheme is an extension of a scheme discovered by Lynch and Davisson and developed by Schalkwijk, and is based upon the Schalkwijk algorithm for the Lynch-Davisson (LD) code. The new coding scheme is shown to be asymptotically optimal as the block length approaches infinity, regardless of the source statistics. Although the LD scheme is minimax-universal, it is not optimal for low source entropies and finite block lengths. Run length coding is shown to be closer to optimal for low source entropies, and the new scheme is shown to be practically equivalent to run length coding in this range.

Power Reflection from a Lossy One-Dimensional Random Medium

We consider the problem of an electromagnetic plane wave normally incident upon a slab of material whose constitutive parameters are subjected to lossy random perturbations. A transmission line model is adopted, wherein the four distributed parameters are assumed to be strongly mixing random functions of distance along the line. We study the reflection of energy at the input in the diffusion limit, an asymptotic limit involving weak random perturbations and long transmission lines. In the presence of dissipation, the probability density function for the modulus of the reflection coefficient approaches a nontrivial limit as the line length approaches infinity. We compute the mean and fluctuations of the voltage and power reflection coefficients with respect to this limiting density as a function of the dissipation.

Natural Heat Convection in a Vertical Circular Tube

Pure natural heat convection fields in the entrance region of a heated vertical circular tube, in which the temperature and velocity profiles were developing simultaneously, were solved by a numerical method of finite difference. And then the characteristics of heat transfer were obtained. The analysis presented here was based on the assumption that the inlet velocity profile is uniform. It was verified analytically and numerically that, for the case of uniform wall temperature, the inlet velocity U1 has an asymptotic value 1/8 as the tube length approaches infinity. As for the case of uniform heat flux at the wall, U1 is directly proportional to √(L/p)r over the range L>Le, where Le is the entrance length. The relationship between the dimensionless pipe length L and dimensionless suction velocity U1 was also obtained, using Pr=0.72, for both the wall conditios. In the case that the pipe length is semi-infinite and the wall temperature is uniform, a relationship between Pr and thermal, as well as hydrodynamic, entrance length was obtained for Pr=0.01, 0.1, 0.72, 1.0, 10 and 100, and some interesting irregularities of developing velocity profiles were also observed except for the case Pr=1.0.