Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Ordinary differential equations with impulse action are considered at fixed moments of time when finite limits points are admitted to the set of moments of the shocks. The topological structure of this set is clarified: it must be resolvable, in particular nowhere dense in R.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 378–383, March, 1990.     

Finding numerical solution of linear partial differential equations of first order with real coefficients

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order

Effects of osmotic manipulation of intracellular hydration of HeLa S-3 cells on their proton NMR relaxation times

Pellets of HeLa from suspension cultured cells in isotonic medium (300 mosmolar) were introduced into a Bruker CXP100 NMR spectrophotometer at 80 mHz within 5 min of the start of centrifugation. T1 and T2 times were measured within a total elapsed time of 20-25 min at 80 mHz and 37 degrees C, and averaged 1430 msec and 120 msec, respectively. Extrapolation to zero extracellular space gave a corrected T1 of 1370 msec. For cells collected after 10 min in hypotonic medium (down to 30 mosmolar) increased proton density correlated well with increased cell water content, but relaxation times did not rise in proportion to that predicted for the entry of "bulk" water (T1 of 4700 msec), except when swelling approached lysis point. Cells partially dehydrated by 10 min in hypertonic medium of up to 1500 mosmolar have also been analyzed, but once again the shortening of T1 was not proportional to the loss of "free" (bulk phase) water. At the upper limit of hypertonic treatment, lacunae or vacuoles of a watery nature separated within the cytomatrix, preventing maximum dehydration. The relationship of cell water to T1 is complex over the whole range of tonicity that HeLa S-3 cells tolerate. The data indicate, however, that hypotonically induced water probably has an average T1 time considerably lower than bulk phase water. In contrast, raising the total extracellular volume with medium had precisely the predicted effect on T1 time, further strengthening the case that water taken up by cell acquires a shorter T1 time. Cells adapting to hypotonic conditions oscillated in size and water content over 2-3 hr before returning to near their initial volume. Under these circumstances, T1 oscillated in the same way but with a reduced amplitude, consistent with the above findings.     

Water 1H spin-lattice relaxation as a fingerprint of porous media

The 1H spin-lattice relaxation curves of water in samples of natural porous media can be thought of as "fingerprints" of the porous samples. Also the whole of traditional petrophysical properties (permeability, irreducible water saturation, etc.) can be thought of as "fingerprints" of the porous samples. The characteristics of the pore space determine on one hand the relaxation curve shape, and on the other the petrophysical properties. The understanding of this correspondence can contribute to a better definition of the concept of the architecture of a porous medium. At this purpose we have obtained 1H spin-lattice relaxation curves from a collection of standard sandstone cores of known petrophysical properties and characterized by the same surface properties. The results corroborate the idea that the structure of relaxation curves contains information on the distance scale and on the architecture of the pore space, even if it is difficult to extract it without ambiguities. Different methods of curve fitting were performed and compared with the aim of getting the maximum information from the relaxation curves. Several aspects of this kind of investigation indicate the analogies between 1H response of water confined in porous media and in biological tissues.     

Electronic surface states on Pd(110): Theory and comparison with experiment

A relativistic Green function formalism has been applied to calculate layer-projected densities of states on Pd(110). In particular, we obtained unoccupied surface states and their dispersion relations along two directions in the surface Brillouin zone. Good agreement with recent inverse photoemission data is reached by using an energy-dependent dynamical surface potential barrier, which is based on a simple electron-plasmon interaction model, instead of a static surface barrier.     

Erbium:YAG (2.94 mum) laser effects on dental tissues

Past trials with soft and calcified tissues have demonstrated that long pulse train (2.5 mus) Er:YAG (2.94 mum) laser may be used to ablate tooth structure of human teeth. Determination of physical and thermal damage to surrounding tissue during removal of enamel and dentin is a primary objective of this study. Extracted human teeth with thermal probes imbedded in the pulp chambers were submitted to cavity preparation using an Erbium YAG laser with water mist. Wavelength selection as well as use of a water mist during the procedure resulted in efficient tissue removal without significant surrounding damage. Ground sections and SEM sections of teeth showed little or no melting or ash formation in adjacent dentin and enamel and no visible change in the pulp chamber. The surfaces produced by laser ablation were rough and irregular with craters and grooves. Average temperature change in the pulp chamber monitored during tooth preparation was 2.2 degrees Centigrade. These findings suggest that constantly available water aids vaporization and microexplosions, increasing the efficiency of tooth structure removal, and aids in cooling of the tooth structures. The long pulse Er:YAG (2.94 mum) laser may be an effective method for tooth reduction applications when used with a water mist.     

Positron annihilation studies on the electronic structure of Pd−Ag−H system

Angular Correlation of Annihilation Radiation (ACAR) is shown to be useful to examine the electronic structure of -phase Pd_1–y Ag _y H _x system. Hydrogen absorption by Pd_1–y Ag _y alloys results in the increase of both nearly free andd-localized electron numbers in compliance with the KKR-CPA calculation outcomes. The investigation of -phase systems, PdH _x hydrides as well as Pd_1–y Ag _y H _x materials, failed because of a high concentration of lattice defects.     

Approximation of functions of several variables by trigonometric polynomials with given number of harmonics,and estimates of ε-entropy

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A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels

In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X⁺ = {c∈L¹: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X⁺. The proof is based on weak L¹ compactness methods applied to suitably chosen approximating equations.