The analog of the Kanazawa-Gordon formula for cylindrical resonators

In this paper, a formula relating the shift in the resonant frequency of a shear piezoceramic cylindrical resonator to the viscosity of a Newtonian liquid that loads the resonator surface was established. This formula is analogous to the classical Kanazawa-Gordon formula that describes the change in the resonant frequency of a shear planar resonator loaded with a Newtonian liquid. To this end, the author applied the perturbation method to analyze the behavior of the piezoceramic cylindrical resonators vibrating in a shear mode and loaded with a viscous liquid. The shift in resonant frequency obtained using the perturbation method (mechanical model) was compared to an exact value of the shift in resonant frequency obtained from the complete electromechanical model (admittance diagrams) that describes shear vibrations of a piezoceramic cylindrical resonator loaded with a viscous liquid. Good conformity between the two types of results obtained can prove the correctness of the analytical formulas established in this paper. The results of this work can be applied for the design and construction of viscosity sensors.     

Organotin compounds in the liver tissue of marine mammals from the Polish coast of the Baltic Sea

Butyltins (BTs) and phenyltins (PhTs) were determined in the livers of marine mammals found by-caught or stranded along the Polish coast of the Baltic Sea. During the investigation an original analytical method was developed. Butyltin compounds were detected in all the liver samples, whereas phenyltins were not detected in any of the samples. The total concentrations of BTs ranged from 43.9 to 7698 ng(Sn) x g(-1) dry weight. Age-related trends to accumulate BTs in immature porpoises were found. At the same time there were no male-female differences in BTs concentrations observed. No statistically significant spatial distribution differences were found between the locations corresponding to the open Baltic Sea waters and inside the Gulf of Gdańsk, which is characterized by high maritime activity. In comparison to butyltin levels in marine mammals from other geographic regions, the samples analyzed indicate a significant degree of tributyltin pollution along the Polish coast of the Baltic Sea. On the basis of a literature review, higher BT levels are usually found in waters close to highly industrialized areas, such as Japan, Hong Kong, and the United States.     

Importance and reduction of the sidewall-induced band-broadening effect in pressure-driven microfabricated columns

The influence of the detailed design of the sidewall region upon the over-all band-broadening in microfabricated packed-bed or collocated monolithic support structure (COMOSS) columns has been investigated using computational fluid dynamics (CFD) simulation techniques. It is shown that, under unretained solute conditions, very small structural variations of the order of only 5% of the particle diameter can give rise to a 4-fold increase of the band-broadening. A comprehensive study has been made to quantify this effect as a function of the fluid velocity, the particle diameter, the channel widths, and of course, the sidewall region design. Because the sidewall effect can be fully attributed to a mismatch between the flow rates in the column center and in the sidewall region, it is fortunately also quite straightforward to avoid it. A very simple design, yielding band-broadening values identical to that of a hypothetical sidewall-less column for all possible values of the flow velocity, the particle diameter, or the channel width is proposed.     

Evidence Theory and VPRS model

The Rough Set Theory (RST) was proposed by Pawlak [4] as a new mathematical approach to deal with uncertain knowledge in expert systems. In 1991 Ziarko [11] proposed the Variable Precision Rough Set Model (VPRSM) as a certain extension of the rough set theory. VPRSM approach makes it possible to use a certain level of misclassification.The aim of this paper is to introduce belief and plausibility functions defined by the β-approximation regions. On the basis of the β-approximation regions, the β-basic probability assignment is defined and the Dempster's combination rule for product of two decision tables is constructed. This entire approach is illustrated by examples.     

Strategic capital budgeting: asset replacement under market uncertainty

In this paper the impact of product market uncertainty on the optimal replacement timing of a production facility is studied. The existing production facility can be replaced by a technologically more advanced and thus more cost-effective one. We take into account strategic interactions among the firms competing in the product market by analyzing the problem in a duopolistic setting. We calculate the value of each firm and show that i) a preemptive (simultaneous) replacement occurs when the associated sunk cost is low (high), ii) despite the preemption effect uncertainty always raises the expected time to replace, and iii) the relationship between the probability of optimal replacement within a given time interval and uncertainty is decreasing for long time intervals and humped for short time intervals. Furthermore it is shown that result ii) carries over to the case where firms have to decide about starting production rather than about replacing existing facilities. Correspondence to: Grzegorz PawlinaThis research was undertaken with support from the European Union's Phare ACE Programme 1997. The content of the publication is the sole responsibility of the authors and in no way represents the views of the Commission or its services. The authors would like to thank Kuno Huisman, Enrico Pennings, two anonymous referees, and participants of the Advances in Game Theory Conference in Hilvarenbeek, EFMA 2002 in London, and the Workshop on Recent Topics in Real Options Valuation in Krems for helpful comments.G. Pawlina     

Dynamical diseases of brain systems: different routes to epileptic seizures

In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the system's attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the system's parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the system's response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed.     

Determination of the shear impedance of viscoelastic liquids using cylindrical piezoceramic resonators

In this paper, a new method for determining the rheological parameters of viscoelastic liquids is presented. To this end, we used the perturbation method applied to shear vibrations of cylindrical piezoceramic resonators. The resonator was viscoelastically loaded on the outer cylindrical surface. Due to this loading, the resonant frequency and quality factor of the resonator changed. According to the perturbation method, the change in the complex resonant frequency /spl Delta/~/spl omega/ = /spl Delta/w/sup re/ + j/spl Delta//spl omega//sup im/ is directly proportional to the specific acoustic impedance for cylindrical waves Zc of a viscoelastic liquid surrounding the resonator, i.e., /spl Delta/~w /spl sim/ jZ/sub c/, where j = (-1)/sup 1/2/. Hence, the measurement of the real and imaginary parts of the complex resonant frequency determines the real part, R/sub c/, and imaginary part, X/sub c/, of the complex acoustic impedance for cylindrical waves Z/sub c/ of an investigated liquid. Further-more, the specific impedance Z/sub L/ for plane waves was related to the specific impedance Z/sub c/ for cylindrical waves. Using theoretical formulas established and the results of the experiments performed, the shear storage modulus /spl mu/ and the viscosity /spl eta/ for various liquids (e.g., epoxy resins) were determined. Moreover, the authors derived for cylindrical resonators a formula that relates the shift in resonant frequency to the viscosity of the liquid. This formula is analogous to the Kanazawa-Gordon formula that was derived for planar resonators and Newtonian liquids.     

Membrane Systems with Marked Membranes

Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness.     

Tiny Signals from the Human Brain: Acquisition and Processing of Biomagnetic Fields in Magnetoencephalography

Low-temperature superconductivity plays an important role in some specific biomedical applications, and, in particular, in non-invasive imaging methods of human brain activity. Superconducting magnets are indispensable for functional magnetic resonance imaging (fMRI) which allows functional imaging of the brain with high spatial but poor temporal resolution. Superconducting quantum interference devices (SQUIDs) are the most sensitive magnetic field detectors. Up to a few hundreds of SQUIDs are nowdays used in modern whole-head magnetoencephalography (MEG) systems. They allow tracking brain activation with a superior temporal resolution of milliseconds, which is a quintessential condition for the monitoring of brain dynamics and the understanding of information processing in the human brain. We introduce the prerequisites of MEG data acquisition and briefly review two established methods of biomagnetic signal processing: The concept of signal averaging, and the subsequent source identification as a solution of the biomagnetic inverse problem. Beside these standard techniques, we discuss advanced methods for signal processing in MEG, which take into account the frequency content of the recorded signal. We briefly refer to the prospects of Fourier analysis and wavelet transform in MEG data analysis, and suggest matching pursuit as a promising tool for signal decomposition and reconstruction with high resolution in time-frequency plane.     

Comments on ?On Hamiltonian Cycles as Optimal p-Cycles?

For original paper by D.A. Schupke see ibid., vol.9, no 4, p.360-2, April 2005. It is shown that in the above letter by Schupke corollaries related to a necessary condition on the network to ensure that a set of Hamiltonian p-cycles is able to reach the theoretical logical redundancy bound are wrongly calculated