Minimizing the span of d-walks to compute optimum frequency assignments

In this paper we deal with the Minimum Span Frequency Assignment Problem (MSFAP), that is the problem of assigning a limited set of radio frequencies to the base stations of a radio network so as the bandwidth occupancy is minimized and the overall interference is not too large. We present a new integer linear formulation for MSFAP in the multidemand case, which is the basis of an exact algorithm to compute both lower and upper bounds for MSFAP. Frequency assignments are represented as walks (sequence of nodes) in a graph. We look for a walk of minimum span, where the span of a walk is defined as the cost of a maximum cost subwalk (subsequence). The new approach is able to find optimum solutions over a large set of classical benchmarks. Received: July 10, 2000 / Accepted: July 6, 2001?Published online October 26, 2001     

Experimental design for estimating the optimum point in a response surface

The problem of optimal experimental design for response optimization is considered. The optimal point (control)x ^* of a response surface is to be determined by estimating the response parameters from measurements performed at design pointsx ⁱ,i=1,...,N. Classical sequential approaches for choosing thex ⁱ's are recalled. A loss function related to the issue of response optimization is used to define control-oriented design criteria. The design policies differ depending on whether least-squares or minimum risk estimation is used to estimate. Connections between various criteria suggested in the literature are exhibited. Special attention is given to quadratic model responses. Most approaches presented assume that the response is correctly described by a given parametric function over the region of interest. Possible deterministic departures from this function raise the problem of model robustness, and the literature on the subject is briefly surveyed.     

Modeling of coupling mechanisms and frequency separation in double disk resonators

We present modeling expressions for the coupling mechanisms in vertically stacked disk resonators. Using lumped modeling techniques, analytic expressions for coupling mechanisms in a stack of two disks are derived. The modeling results are compared to those of high-fidelity finite element analyses and show that the analytic expressions derived can be used to predict frequency separation between radial extensional modes. The established model is useful for gaining insight into parameter sensitivity when designing a stacked double disk resonator.     

影响城市地价最优因素组合的选择及权重确定

笔者在城市土地定级估价综合模型[1] 的基础上 ,应用最优回归自变量集的选择方法[2 ] ,得到了影响城市地价最优因素组合的选择方法及权重的确定方法 ,并将其实际应用于山西省古交市的地产评估 ,结果表明 ,该方法比现行方法节省经费且使评估结果更符合实际。     

Decentralized optimum load frequency control of interconnected power systems

A new approach for designing a linear regulator for the problem of load frequency control (LFC) of interconnected power systems is developed. The control is specified to be of proportional-plus-integral (P-I) form and is only a function of the measurable states. The LFC problem is formulated as a parameter optimization problem.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

A conic relaxation model for searching for the global optimum of network data envelopment analysis

Network data envelopment analysis (DEA) models the internal structures of decision-making units (DMUs). Unlike the standard DEA model, multiplier-based network DEA models are often highly non-linear and cannot be converted into linear programs. As such, obtaining a non-linear network DEA's global optimal solution is a challenge because it corresponds to a nonconvex optimization problem. In this paper, we introduce a conic relaxation model that searches for the global optimum to the general multiplier-based network DEA model. We reformulate the general network DEA models and relax the new models into second order cone programming (SOCP) problems. In comparison with linear relaxation models, which is potentially applicable to general network DEA structures, the conic relaxation model guarantees applicability in general network DEA, since McCormick envelopes involved are ensured to be finite. Furthermore, the conic relaxation model avoids unnecessary linear relaxations of some nonlinear constraints. It generates, in a more convenient manner, feasible approximations and tighter upper bounds on the global optimal overall efficiency. Compared with a line-parameter search method that has been applied to solve non-linear network DEA models, the conic relaxation model keeps track of the distances between the optimal overall efficiency and its approximations. As a result, it is able to determine whether a qualified approximation has been achieved or not, with the help of a branch and bound algorithm. Hence, our proposed approach can substantially reduce the computations involved.     

Short-range potential and a model of operator extension theory for resonators with semitransparent boundary

On the basis of operator extension theory, a model of the quantum point is constructed as a resonator with semitransparent boundary. It is proved that the model operator is the limit (in the resolvent sense) of short-range Hamiltonians. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 703–711, May, 1999.     

An intercausal cancellation model for Bayesian-network engineering

When constructing Bayesian networks with domain experts, network engineers often use the noisy-OR model, and causal interaction models more generally, to alleviate the burden of probability elicitation: the use of such a model serves to reduce the number of probabilities to be elicited on the one hand, and on the other hand forestalls experts having to give assessments for probabilities with compound conditions which they feel are hard to envision. Recently, we have shown that ill-considered use of the noisy-OR model specifically can substantially decrease a network's performance, especially in domains in which causal mechanisms include cancellation effects. Motivated by this observation, we designed a new causal interaction model, with the same engineering advantages as the noisy-OR model, to describe such effects. We detail properties of our intercausal cancellation model, and compare it against existing causal interaction models. We further illustrate the application of our model in the real-world domain of pharmacology.     

A linear programming model for an optimum admissions policy in education

This work is a kind of feasibility study mixed with optimization techniques to decide upon the possibility of achieving a certain manpower structure together with a complete removal of illiteracy after a certain planning period. Changing the manpower structure is achieved by controlling the proportions of students who enter the different channels of formal education. The removal of illeteracy is achieved by accepting more and more students into the compulsory stage. It will be found that there is more than one option for achieving these objectives through the many control paths available.It is not easy to fulfil these two aims; the obstacles are the non-availability of teachers as well as the universal budget constraint. This will result in a limited number of feasible opportunity paths to choose from.In this paper the solution to the above problem is given. First the feasibility problem is dealt with by examining the possibility of changing the manpower structure after a certain planning period and subject to the above constraints. Once this is found possible, the optimal path regarding the admission of the students to the compulsory stage is given for the quickest removal of illiteracy.     

A stochastic model of nanowire growth by molecular beam epitaxy

In this paper, a stochastic model of nanowire growth by molecular beam epitaxy based on probability mechanisms of surface diffusion, mutual shading, rescattering of adatoms, and survival probability is proposed. A direct simulation algorithm based on this model is constructed. A comprehensive study of kinetics of the growth of a family of nanowires initially distributed at a height from about tens of nanometers to about several thousand nanometers is carried out. The time range corresponds to an experimental growth of nanowires of up to 3–4 hours. The following statement is formulated and confirmed numerically: under certain conditions, which can be implemented in real experiments, the height distribution of nanowires narrows with time, that is, in the ensemble of nanowires their heights become aligned with time. For this, the initial radii distribution of the nanowires must be narrow and the density of the nanowires on the substrate must not be very high.     

A delay-time model for repairable machinery: maximum likelihood estimation of optimum inspection intervals

A delay-time model is presented for a complex repairable systemin which defects arise according to a nonhomogeneous Poissonprocess. The focus of this paper is not on the resulting probabilisticmodel itself, but on the estimation of the model parametersand their errors from records of failure times and number ofdefects found at inspections of a machine which has been operatedfor some time under some (usually suboptimal) inspection regime.The likelihood function of the observed failure and inspectiondata is derived, and a general approach for estimating the optimuminspection interval is discussed. An example relating to themaintenance of medical equipment is used to illustrate the techniquesdescribed in the paper.     

Admissible frequency domain response functions of dielectrics

Few empirical formulae produced to represent the complex dielectric constant in the frequency domain are discussed here from the view point of the possibility of their representation in the time domain. Because a generic function of the frequency does not necessarily admit an inverse Fourier transform, it is not always possible to obtain the corresponding time domain representation of the constant defined in the time frequency. With the use of the fractional derivatives, we introduce a tentative model of the dielectric constant including a linear term, the complex dielectric constant with its loss, and the loss of the direct current electrical conductivity. With appropriate values of the parameters, the system reproduces in the frequency domain the K. Cole and R. Cole model, without the contribution of the loss of the direct current electrical conductivity, which is studied by an autonomous constitutive equation. Copyright © 2014 John Wiley & Sons, Ltd.     

Vibrational frequency distribution for nonconservative model of double-walled carbon nanotube

The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of dynamical boundary conditions at the right end. We also present the four-branch vibrational spectrum of the system. All the results are purely analytical; they will be complemented by numerical simulations in a forthcoming work.     

On the theory of cylindrical resonators

This paper contains an introduction to the methods of operator-valued functions for solving some non-linear eigenvalue problems of the electrodynamics of guided waves. One simple example of the problem of fundamental frequencies for the rectangular-slot resonator is considered that gives an opportunity to follow all the steps and features of this technique.     

Recommendations for the optimum design of pultruded frameworks

Conclusions For the optimum choice of pultruded beam members in frameworks there is a need to have a greater understanding of framework behavior under load. Research on the lateral-torsional buckling of a symmetric I-section has shown how much the resistance may be affected by the loading position and the support boundary conditions. By changing the warping at the connections from free, as assumed in the USA design manual, to fixed, as may be achieved with practical connection designs it is shown that there is a potential doubling in the buckling resistance. In addition, practical connections have some initial stiffness and moment resistance, thus the connections behave in a semirigid manner. This connection behavior makes inappropriate the present procedure for choosing beam sections on the basis of limiting deflection for a simply supported member. It is proposed that research be conducted to establish the potential of semirigid design, as now being used with structural steelwork. Results from such research should provide the first stage in the process for the optimum design of frameworks.Published in Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 675–682, September–October, 1993.     

Selecting the Number of Knots for Penalized Splines

Penalized splines, or P-splines, are regression splines fit by least-squares with a roughness penalty.P-splines have much in common with smoothing splines, but the type of penalty used with a P-spline is somewhat more general than for a smoothing spline. Also, the number and location of the knots of a P-spline is not fixed as with a smoothing spline. Generally, the knots of a P-spline are at fixed quantiles of the independent variable and the only tuning parameters to choose are the number of knots and the penalty parameter. In this article, the effects of the number of knots on the performance of P-splines are studied. Two algorithms are proposed for the automatic selection of the number of knots. The myopic algorithm stops when no improvement in the generalized cross-validation statistic (GCV) is noticed with the last increase in the number of knots. The full search examines all candidates in a fixed sequence of possible numbers of knots and chooses the candidate that minimizes GCV.The myopic algorithm works well in many cases but can stop prematurely. The full-search algorithm worked well in all examples examined. A Demmler–Reinsch type diagonalization for computing univariate and additive P-splines is described. The Demmler–Reinsch basis is not effective for smoothing splines because smoothing splines have too many knots. For P-splines, however, the Demmler–Reinsch basis is very useful for super-fast generalized cross-validation.     

响应变量删失情况下线性模型的FIC模型选择和模型平均

本文给出了响应变量随机右删失情况下线性模型的FIC (focused information criterion) 模型选择方法和光滑FIC 模型平均估计方法, 证明了兴趣参数的FIC 模型选择估计和光滑FIC 模型平均估计的渐近正态性, 通过随机模拟研究了估计的有限样本性质, 模拟结果显示, 从均方误差和一定置信水平置信区间的经验覆盖概率看, 兴趣参数的光滑FIC 模型平均估计均优于FIC, AIC (Akaikeinformation criterion) 和BIC (Bayesian information citerion) 等模型选择估计; 而FIC 模型选择估计与AIC 和BIC 等模型选择估计相比, 也表现出了一定的优越性. 通过分析原发性胆汁性肝硬化数据集, 说明了本文方法在实际问题中的应用.     

Mathematical model and optimum design approach of sinusoidal pressure wave generator for downhole drilling tool

Mud pulse generators have been widely used for the real-time transmission of valuable directional and formation data from downholes with depths of thousands of meters. There have been numerous studies on the design of mud pulse generators in which the pressure waves were typically nonsinusoidal. Sinusoidal waves provide improved long-distance data transmission and signal noise suppression compared with nonsinusoidal waves. Although sinusoidal pressure wave generators have been studied in the published literature, the influence of the risks of clogging on the design of the generator for producing sinusoidal pressure waves has rarely been considered. To generate sinusoidal pressure waves and to reduce the risks of clogging, a mathematical model for the design of a sinusoidal pressure wave generator is developed in this paper. The effects of the axial and radial clearances between the rotor and stator on the design of the generator are considered in the model. An optimum design method for the generator is provided by combining the developed model and a computational fluid dynamics analysis. Finally, an experimental platform was built and experiments at frequencies 2 Hz and 10 Hz were conducted to validate the design result. The simulation and experimental results show that the optimized pressure waves closely approximate sine waves. Therefore, the developed mathematical model and optimization approach can be used to design a sinusoidal pressure wave generator.     

Algebraic substructuring (AS) for eigenvalue and frequency response calculations

Eigenvalue and frequency response calculations are ubiquitous in scientific modeling and engineering analysis. Algebraic substructuring (AS) method is a powerful numerical technique for solving extremely large scale problems. We developed a unified framework and AS code that can solve both problems efficiently. Furthermore, we addressed some of the open problems in this field, including resolving arbitrary eigenmodes, performing high frequency response analysis, accuracy and performance. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)