Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

The personalization of security selection: An application of fuzzy set theory

We apply the theory of fuzzy subsets to the multiple objective decision problem of stock selection. We allow our objectives to have varying degrees of importance. We discuss various criteria used in selecting stocks. We indicate some procedures for subjectively evaluating the membership functions associated with these criteria.     

Attenuation and depolarization of millimeter waves due to incoherent scattering in tropical rainfall

The radiative transfer equation has been applied to investigate the effects of multiple scattering on communication at the millimeter wavelength in tropical rain. Horizontal linearly polarized incident waves are assumed. The scattering characteristics are calculated using the Mie theory at frequencies of 16, 34.8, 82, 140 and and at rainfall rates of 12.5, 50 and . Some results of the directional patterns of the incoherent intensities at various points in the rain medium are presented. The frequency dependence of the propagation distance, attenuation coefficient and the variation of incoherent specific intensities in tropical rainfall are investigated. The incoherent power at the receiver relative to the coherent power, which is important in assessing the quality of signal in the receiver, is also investigated. It is observed that the maximum incoherent copolarized received power is about in tropical rainfall at rainfall rate. Also the difference between the copolarized incoherent power in tropical and temperate rainfall is about at frequencies higher than , and about for the cross-polarized incoherent power components. It may therefore be safely said that multiple scattering may not result in serious degradation of the coherent wave component even in the most intense tropical precipitation. It also appears that it is independent of regional rainfall climatology.     

Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations

This paper considers a like-queue production system in which server vacations and breakdowns are possible. The decision-maker can turn a single server on at any arrival epoch or off at any service completion. We model the system by an M^[x]/M/1 queueing system with N policy. The server can be turned off and takes a vacation with exponential random length whenever the system is empty. If the number of units waiting in the system at any vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N units in the system, he immediately starts to serve the waiting units. It is assumed that the server breaks down according to a Poisson process and the repair time has an exponential distribution. We derive the distribution of the system size through the probability generating function. We further study the steady-state behavior of the system size distribution at random (stationary) point of time as well as the queue size distribution at departure point of time. Other system characteristics are obtained by means of the grand process and the renewal process. Finally, the expected cost per unit time is considered to determine the optimal operating policy at a minimum cost. The sensitivity analysis is also presented through numerical experiments.     

Twin solutions to singular boundary value problems

In this paper we establish the existence of two nonnegative solutions to singular and singular focal boundary value problems. Our nonlinearity may be singular at , and/or .

     

Multiple access interference cancellation in Manchester-coded synchronous optical PPM-CDMA network

A new interference cancellation technique for direct-detection optical code- division multiple-access (OCDMA) network employing pulse-position modulation (PPM) is proposed in this paper. The multiple access interference (MAI) estimation is achieved by pre-reserving one of optical spreading code sequences at the receiver based on the correlation property of padded modified prime codes (PMPC). The estimated interference is then cancelled out after photo-detection process. Additionally, the transmitted signal is Manchester-coded to further improve the system performance. Based on this proposed interference canceller in a shot-noise limited regime, we have obtained an expression for the upper bound of the bit-error probability (BEP) taking into account effects of both MAI and shot-noise. This BEP is compared with that of a PPM-OCDMA without cancellation. Finally, the receiver structure of the proposed optical network unit (ONU) is fairly simple to compare with the conventional cancellation schemes.     

Multiple nano-TiO2 layers to prevent dye/nano-TiO2 from photodegradation under a UV-exposure environment

A device of multiple nano-TiO₂ layers was proposed and fabricated to prevent a dye/nano-TiO₂ region from serious photo-degradation. In this device, the top of the dye/TiO₂ region was designed to be coated using sol-gel nano-TiO₂ thin films to shield UV irradiation from the photo-degradation effect. The sol-gel TiO₂ was prepared in a low temperature (75 °C) and verified as nano-sized particles and an anatase crystalline structure. Different devices of the multi-layer samples fabricated using different compositions of nano-TiO₂ were produced and exposed for UV irradiation tests. Results show that the presence of the sol-gel TiO₂ films coated on top of the dye/TiO₂ region can significantly alleviate the dye photo-degradation under UV irradiation. This multi-layer device can effectively improve the photo-stability of the dye/TiO₂ region in a UV-exposure environment.     

Measuring spatial coherence by using a mask with multiple apertures

A simple method to measure the complex degree of spatial coherence of a partially coherent quasi-monochromatic light field is presented. The Fourier spectrum of the far-field interferogram generated by a mask with multiple apertures (small circular holes) is analyzed in terms of classes of aperture pairs. A class of aperture pairs is defined as the set of aperture pairs with the same separation vector. The height of the peaks in the magnitude spectrum determines the modulus of the complex degree of spatial coherence and the corresponding value in the phase spectrum determines the phase of the complex degree of spatial coherence. The method is illustrated with experimental results.     

Multivariate Normal Slice Sampling

By introducing auxiliary variables, the traditional Markov chain Monte Carlo method can be improved in certain cases by implementing a “slice sampler.” In the current literature, this sampling technique is used to sample from multivariate distributions with both single and multiple auxiliary variables. When the latter is employed, it generally updates one component at a time.

In this article, we propose two variations of a new multivariate normal slice sampling method that uses multiple auxiliary variables to perform multivariate updating. These methods are flexible enough to allow for truncation to a rectangular region and/or exclusion of any n-dimensional hyper-quadrant. We present results of our methods and existing state-of-the-art slice samplers by comparing efficiency and accuracy. We find that we can generate approximately iid samples at a rate that is more efficient than other methods that update all dimensions at once. Supplemental materials are available online.     

Weighted Influence Non-linear Gauge System (WINGS) – An analysis method for the systems of interrelated components

The WINGS method has been derived from DEMATEL and can be widely used as a structural model for analysis of intertwined factors and causal relations between them. Its novelty comes from an idea of including in one mathematical mechanism both strength (importance) and influence of the system components. In particular, WINGS can be applied as the MCDA method for evaluating alternatives when interrelations between criteria cannot be neglected. For the problem with independent criteria, WINGS reproduces the additive aggregation of preferences, a classical method in MCDA.