THE SUM OF FINITE MOVING AVERAGE PROCESSES

Abstract. It is well known that the sum of moving average processes is itself a moving average process. Existing theory does not provide formulae relating the innovations in the sum process to those in the component processes when some zeros of the autocovari-ance function of the sum process are on the unit circle. This gap is filled here by first showing that these zeros are necessarily shared by the component processes. Conditions for the innovations in the sum process to be current are given. Throughout the paper contemporary innovations in the component processes are allowed to be correlated, replacing the usual assumption that they are uncorrelated.     

Note of the estimation of the Θ temperature and Ψ parameter from the critical temperature data

Summary Critical values of the polymer volume fraction _2,c and the interaction parameter _c have been computed for the case that the equation for the chemical potential of solvent contains terms _{c 2} ³ and _{c 2} ⁴ in addition to ₂ ² . For 0 _c 1/3, the limits for infinite chain length are _2,c = 0 and _c = 0.5. Quite different results are obtained for _c > 1/3, _2,c being finite and _c lower than 1/2. Conclusions for the estimation of the temperature and the entropy-of-dilution parameter are discussed.     

The participation of block copolymers in the increase in the number of tie molecules

Three-block copolymers polyamide-block-polyX-block-polyamide (where X is styrene, ethylene-co-1-butene, and others) are able to improve substantially the toughness of poly(ϵ-caprolactam). Outer blocks of these copolymers are able to take part in folding lamellae of semi-crystalline polyamide, inner blocks are not. They operate as a spacer, meaning that the end blocks of copolymers capable of folding become parts of different lamellae, or that the unfoldable part of a block copolymer is pushed out of a folding lamella with a certain probability of the remaining outer block taking part in folding another lamella. This increases the number of tie-molecules.     

TEM Investigations of Fine Niobium Precipitates in HSLA Steel

Commercially produced 0.03 % C, 0.08 % Nb, 0.01 % Ti high strength low alloyed (HSLA) steel in the form of 20 mm thick plates was investigated. The steel was thermomechanically processed and the mechanical properties of the steel were evaluated by tensile testing. Using analytical and high resolution transmission electron microscopy the distribution, morphology, composition, crystal structure and particle size of niobium and titanium carbonitrides were observed and identified in these steels. The distribution of the precipitates was found to be nearly random, with occasional occurrence of precipitation free zones. Complex agglomerates with a cubic TiN seed crystal overgrown by a cubic NbC particle were the most commonly observed precipitates. Further TEM analysis in the accelerated cooled and tempered specimens in 1/4 plate thickness did not reveal any evidence that additional precipitation in the ferrite occurred. Precipitation in ferrite was only detected after subsequent cold deformation and tempering of the same samples. By a combination of EFTEM, STEM, HRTEM in addition to EDX spectroscopy, a large population of strain induced NbC precipitates with fcc crystal structure ranging in size down to 2 nm were identified in the ferrite matrix.     

The Coulomb potential and the paradoxes of PT symmetrization

In a parallel to the standard quantum version of the Coulomb/Kepler problem, an alternative Coulomb/Kepler quantum model is formulated and solved. The new model is shown to exhibit not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties. The paper is made self-contained by explaining the underlying innovative quantization strategy that assigns an entirely new role to symmetries.     

SWSNL: Semantic Web Search Using Natural Language

As modern search engines are approaching the ability to deal with queries expressed in natural language, full support of natural language interfaces seems to be the next step in the development of future systems. The vision is that of users being able to tell a computer what they would like to find, using any number of sentences and as many details as requested. In this article we describe our effort to move towards this future using currently available technology. The Semantic Web framework was chosen as the best means to achieve this goal. We present our approach to building a complete Semantic Web Search Using Natural Language (SWSNL) system. We cover the complete process which includes preprocessing, semantic analysis, semantic interpretation, and executing a SPARQL query to retrieve the results. We perform an end-to-end evaluation on a domain dealing with accommodation options. The domain data come from an existing accommodation portal and we use a corpus of queries obtained by a Facebook campaign. In our paper we work with written texts in the Czech language. In addition to that, the Natural Language Understanding (NLU) module is evaluated on another domain (public transportation) and language (English). We expect that our findings will be valuable for the research community as they are strongly related to issues found in real-world scenarios. We struggled with inconsistencies in the actual Web data, with the performance of the Semantic Web engines on a decently sized knowledge base, and others.     

Estimation of the effective conjugation length of oligo-p-phenylenes from specific refractive index increments of solutions

Summary An unusually strong molecular weight dependence of the specific refractive index increment which has been reported for solutions of oligomers (M < 10³) of p-2-methyl phenylene is attributed to the exaltation of polarizability of phenylene units. The saturation length is estimated to be l _s≅ 6 phenylene units. Received: 3 November 1997/Revised version: 20 April 1998/Accepted: 22 April 1998     

Optical characterization of diamond-like carbon thin films non-uniform in thickness using spectroscopic reflectometry

Two formulae expressing the reflectance of non-uniform thin films are presented. The first of them corresponds to the arbitrary shapes of this non-uniformity and illuminated light spot under the assumption that this non-uniformity is sufficiently slight. The second formula corresponds to the wedge-shaped non-uniformity of arbitrary magnitude within the circular light spot. It is shown that both the formulae are suitable for the successful optical characterization of non-uniform diamond-like carbon (DLC) thin films in contrast to the usually used reflectance formula for the uniform thin films. Within the optical characterization the values of the standard deviation of non-uniformity is determined together with the correct values of the mean thickness and material parameters corresponding to the dispersion model based on the parametrization of the density of electronic states. On the basis of the material parameters determined the correct spectral dependences of the optical constants of the DLC films studied are calculated.