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.     

Volatile compounds from interdigital gland of male white-tailed deer (Odocoileus virginianus)

Interdigital secretions were collected from eight male white-tailed deer of various ages. Analysis of volatiles was performed by gas chromatography-mass spectrometry with a modified headspace technique. Forty-six volatile compounds were found including alkanes, arenes, aldehydes, ketones, aliphatic acids, esters, pyrroles, furans, and sulfur compounds. Eleven occurred in higher concentrations (P0.10) in dominant (3.5-year-old) than in subordinate (1.5-year-old) animals. Dominant males typically have higher serum testosterone levels, and fatty acids and esters fluctuate with sebum production, which is under hormonal control. Therefore, these compounds may reflect testosterone levels and act as chemical signals indicating the presence of a dominant male. Interdigital volatiles also may act as generalized scent trail markers.     

Obstacles reconstruction from partial boundary measurements based on the topological derivative concept

In this work a new method for obstacles reconstruction from partial boundary measurements is proposed. For a given boundary excitation, we want to determine the quantity, locations and sizes of a number of holes embedded within a geometrical domain, from partial boundary measurements related to such an excitation. The resulting inverse problem is written in the form of an ill-posed and over-determined boundary value problem. The idea therefore is to rewrite it as an optimization problem where a shape functional measuring the misfit between the boundary measurement and the solution to an auxiliary boundary value problem is minimized with respect to a set of ball-shaped holes. The topological derivative concept is used for solving the associated topology optimization problem, leading to a second-order reconstruction algorithm. The resulting algorithm is non-iterative – and thus very robust with respect to noisy data – and also free of initial guess. Finally, some numerical results are presented in order to demonstrate the effectiveness of the proposed reconstruction algorithm.     

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.     

Comparison of Urinary Scents of Two Related Mouse Species, <Emphasis Type="Italic">Mus spicilegus</Emphasis> and <Emphasis Type="Italic">Mus domesticus</Emphasis>

Whereas the house mouse (Mus domesticus) has been studied extensively in terms of physiology/behavior and pheromonal attributes, the evolutionarily related mound-building mouse (Mus spicilegus) has received attention only recently due to its divergent behavioral traits related to olfaction. To date, no chemical studies on urinary volatile compounds have been performed on M. spicilegus. The rationale for our investigations was to determine if there are differences in urinary volatiles of intact and castrated M. spicilegus males and to explore further whether this species could utilize the same or structurally similar pheromones as the male house mouse, M. domesticus. The use of capillary gas chromatography/mass spectrometry (GC-MS) together with sorptive stir bar extraction sampling enabled quantitative comparisons between the intact and castrated M. spicilegus urinary profiles. Additionally, through GC-MS and atomic emission (sulfur-selective) detection, we identified qualitative molecular differences between intact M. spicilegus and M. domesticus. A series of volatile and odoriferous lactones and the presence of coumarin were the unique features of M. spicilegus, as was the notable absence of 2-sec-butyl-4,5-dihydrothiazole (a prominent M. domesticus male pheromone) and other sulfur-containing compounds. Castration of M. spicilegus males eliminated several substances, including δ-hexalactone and γ-octalactone, and substantially decreased additional compounds, suggesting their possible role in chemical communication. Some other M. domesticus pheromone components were also found in M. spicilegus urine. These comparative chemical analyses support the notion of metabolic similarities as well as the uniqueness of some volatiles for M. spicilegus, which may have a distinct physiological function in reproduction and behavior.