Darbe nagrinėjamas dvimatis atstatymo procesas. Gaunami jo integralinių lygčių ir laplaso transformacijų pavidalai, bei jų asimptotikos. / In graduate research a two-dimentional renewal process. The integral differential equation of renewal function, its Laplase transform and asymptotic's was found.

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Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with four boundaries. A Type I walk starts at integer-valued coordinates (h; k), where0 < h < m and 0 < k < n. On each step, the process moves one unit either up, down, left, or right with positive probabilities pu, pd, pl, pr, respectively, where pu + pd + pl + pr = 1. The process stops when it hits a boundary. A Type II walk is similar to a Type I walk except that on each step, the walk moves diagonally, either left and upward, left and downward, right and downward, or right and upward with positive probabilities plu, pld, prd, pru, respectively. We mainly answer two questions on these two types of two-dimensional random walks: (1) What is the probability of hitting one boundary before the others from an initial starting point? (2) What is the average number of steps needed to hit a boundary? To do so, we introduce a Markov Chains method and a System of Equations method. We then apply the obtained results to a boundary problem involving two independent one-dimensional random walks and answer various questions that arise. Finally, we develop a conjecture to calculate the probability of a two-sided downward-drifting Type II walk with even-valued starting coordinates hitting the x-axis before the y-axis, and we test the result with Mathematica simulations

Interferons comprise a class of structurally related proteins which exert several regulatory effects in responsive cells. These effects include the establishment of an antiviral state, the inhibition of cellular proliferation and the alteration of different immune reactions. In particular, the IFN:s rapidly augment the lytic activity of the natural killer (NK) cells. In the present thesis, some of the functional and molecular mechanisms by which IFN:s act on NK cells and other leucocytes are studied. A good correlation is found between the ability of different tumor cell lines to induce IFN production among peripheral blood lymphocytes and their sensitivity to NK cell cytotoxicity, indicating that IFN might regulate the activity of NK cells through a positive feed-back mechanism. When studying the interaction between the NK cells and two target cell lines it is demonstrated that the two cell lines are not recognized by the same receptors. The augmentation of NK cell cytotoxicity by IFN is shown to involve both alteration of receptor structures on the NK cell and enhancement of steps in their lytic machinery. The effects of IFN on the synthesis of individual proteins is then studied by two-dimensional electrophoresis. It is demonstrated that IFN-a and IFN-ß within 1.5 hours induce the synthesis of nine proteins (Mf80, 75, 62, 58, 53, 38, 36, 33 and 30 kD) in human lymphocytes. Tne induction is dependent on a rapid de novo RNA synthesis, which is initiated less than 30 minutes after the addition of IFN. The expression of the nine proteins is well correlated to the development of augmented NK cell cytotoxicity. Four of the proteins (Mr 80, 62, 38 and 33 kD) are found to be expressed in a panel of ten hematopoetic and two anchorage-dependent cell lines, whereas the remaining proteins seem to be expressed in leucocytes only. IFN induce the synthesis of the same proteins in both purified large granular lymphocytes (responsible for the main NK cell activity in man), T cells and monocytes, demonstrating that the augmentation of NK cell activity does not involve the formation of unique 1NK-cel11 specific proteins. Rather, the augmentation of the lytic activity of both NK cells, cytotoxic T cells and monocytes seem to involve common stages in their lytic mechanisms. In contrast to IFN-a and IFN-ß, IFN-y, does not induce any detectable proteins in either NK cells or T cells. This lack of effect of IFN-y on the protein synthesis is not a general phenomenon, since the effects of IFN-a and IFN-y are similar 1n a glioma cell line. These results demonstrate that there exists at least one pathway to augment the NK cell cytotoxicity which does not involve the increased synthesis of the nine IFN-a/IFN-ß inducible proteins and indicates that either these proteins are mainly involved in other effects of IFN, or that the augmentation by IFN-a/IFN-ß and IFN-y involve different pathways. When the effects of IFN-a on the synthesis of membrane-associated proteins is studied, it is demonstrated that only the 80 kD IFN-a inducible protein is associated with the cell membrane. In addition, IFN-a seems to induce three additional, me mb rane-as so ci a ted proteins (Mr 94, 76 and 66 kD) which are not detected in whole cell lysates. / <p>Diss. (sammanfattning) Umeå : Umeå universitet, 1985, härtill 5 uppsatser.</p> / digitalisering@umu

Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

The physical properties within the two-dimensional flow produced by the reflection of a plane shock of intermediate strength at a wedge, have been determined by analysis of the particle trajectories. The particle trajectories were obtained by high speed photography of smoke tracers within the flow. Trajectories were determined for different initial positions of the tracers relative to the wedge. The conservation of mass equation was used to determine the density at points within the flow. A knowledge of the shock configurations within the flow, together with the Rankins-Hugoniot equation, was used to determine the pressure immediately behind the incident and reflected shocks. The isentropic equation of state was used to determine the pressure after the passage of the reflected shock. The pressure determined in this manner agreed, within the limits of experimental error, with that obtained using a piezo-electric transducer. The temperature, velocity of sound, and particle velocity at points within the flow were also determined. / Graduate / 0605