Showing papers by "Technion – Israel Institute of Technology published in 1969"

On the optimal filtering of diffusion processes

Abstract: Let x(t) be a diffusion process satisfying a stochastic differential equation and let the observed process y(t) be related to x(t) by dy(t) = g(x(t)) + dw(t) where w(t) is a Brownian motion. The problem considered is that of finding the conditional probability of x(t) conditioned on the observed path y(s), 0≦s≦t. Results on the Radon-Nikodym derivative of measures induced by diffusions processes are applied to derive equations which determine the required conditional probabilities.

Some lower bounds on signal parameter estimation

Abstract: New bounds are presented for the maximum accuracy with which parameters of signals imbedded in white noise can be estimated. The bounds are derived by comparing the estimation problem with related optimal detection problems. They are, with few exceptions, independent of the bias and include explicitly the dependence on the a priori interval. The new results are compared with previously known results.

Time‐minimizing transportation problems

Abstract: A method is given for finding those solutions of a transportation problem which minimize the total time necessary for transporting goods from the suppliers to the consumers. Several extensions of the model are presented.

Determination of Reinforcement Unbonding of Composites by a Vibration Technique

Abstract: An experimental technique was developed to determine the condi tions for the onset of reinforcement unbonding in composite materials. The technique is based upon the continuous measurement of the d...

Prediction of Swelling Pressure of Clays

Abstract: The mathematical formulation of the swelling pressure of pure clay was verified experimentally by Bolt (1956). However, in naturally occurring clays a statistical model is preferable, with chemico-physical properties such as specific surface area or particle spacing represented by simple indicative parameters. This study was carried out with basic theoretical concepts in mind. An attempt was made to relate the parameters. Good statistical correlation was found to exist between swelling pressure and a combined function of initial dry density, moisture content, and liquid limit. Bolt's mathematical formulation was used to derive an expression relating the compression index to the liquid limit.

Riemann-Stieltjes approximations of stochastic integrals

Abstract: We consider the space C[0, 1] together with its Borel σ-algebra A and a Wiener measure P. Let Ω denote a point in C[0, 1] and let x(Ω, t) denote the coordinate process. Then, {x(Ω, t), te[0, 1]} is a Wiener process, and stochastic integrals of the form $$\int\limits_0^1 \varphi {\text{ }}(\omega ,t)dx(\omega ,t)$$ can be defined for a suitable class of ϕ. In this paper we consider a sequence of Stieltjes integrals of the form $$I_n = \int\limits_0^1 \varphi {\text{ }}(\omega ^n (\omega ),t)dx(\omega ^n (\omega ),t)$$ where {Ω n (Ω)} is a sequence of polygonal approximations to co. Conditions are found which ensure the quadratic-mean convergence of {I n }, and the limit is expressed as the sum of the stochastic integral $$\int\limits_0^1 \varphi {\text{ }}(\omega ,t)dx(\omega ,t)$$ and a “correction term”.

Electrical Breakdown in Solids

Abstract: Publisher Summary This chapter focuses on theory of thermal breakdown and continues with theory and experimental description of breakdown first in semiconductors and then in insulators. Thermal breakdown voltages on the application of pulses are larger than the steady state breakdown voltages. Information on the basic breakdown properties of many substances is imperfect and relatively few insulators have been investigated in detail. An average temperature of the breakdown events during vaporization was obtained in metal oxide semiconductor (MOS) samples by photographing the spectrum of discharges and comparing the intensities of spectral lines. The calculation of the breakdown strength by impact ionization requires the solution of the Boltzmann equation, considering the effects of applied field, phonon, and interelectronic collisions, ionizations, and recombinations on the free electron distribution function. The statistical breakdown events observed in the oxides may also be explained by the development of critical size avalanches, if it is assumed that this depends on particular transport and trapping properties of the holes and on field emission at the cathode.

Algorithms for Stochastic Games with Geometrical Interpretation

Abstract: The paper presents a new approach, based on analysis and geometrical interpretation, to the solution of Markov stochastic games. The proposed algorithm, using iterations in policy space, turns out to be a Newton-Raphson type procedure. Several numerical examples are given, covering the terminating and non-terminating cases respectively and illustrating the advantages of the proposed algorithm compared with other known algorithms. Special attention is given to Howard's sequential decision problem with discrete and continuous policy spaces.

Alteration of Nuclear Distribution in B-Mutant Strains of Schizophyllum Commune

Abstract: Sexual morphogenesis in Schizophyllum commune , a higher basidiomycete, is controlled by two incompatibility factors, A and B . A key event, the migration of nuclei from each mate throughout the mycelium of the other, is controlled by the B factor and occurs in A = B ≠ matings. The distribution of nuclei in the resulting heterokaryon is irregular, and anucleate, uninucleate, binucleate and multinucleate cells are found. A similar distribution of nuclei is found in homokaryons carrying a mutation in the B factor. Because of their developmental history, strains that carry a mutated B factor offer a relatively simple system for the study of the events associated with nuclear migration. Growth of mutant- B germlings occurs in three stages: (I) most cells are binucleate; (II) most cells are uninucleate; (III) cells contain varied numbers of nuclei. The ratio of nuclei; cells remains constant during the transition from stage II to stage III. Changes in nuclear distribution result from movement of the nuclei from cell to cell, and the movement is associated with the disruption of the dolipore septum. The mutant- B system appears to offer an opportunity for the biochemical resolution of the events related to nuclear migration.

Line Width Determination in the 9.4-μ and 10.4-μ, Bands of CO 2 Using a CO 2 Laser

Abstract: A CO2 laser was used to measure the ratio of line strength to line width for a great number of rotational lines in the 9.4–μ and 10.4–μ bands of CO2. The laser used for this purpose incorporated a grating, which allowed the tuning of the laser to about 100 different rotation lines. By assuming a given value of the line strength of the line P(20) in each of the two bands studied, the line width was calculated up to a rotational quantum number J = 40. These results are compared with other values recently reported in the literature.

Ion Fractionation by Foam

Abstract: Ionic charge and size of the species present govern the selectivity of surface adsorption of counterions in foam fractionation processes. A theory based on the Gouy-Chapman model of the diffuse double layer, with the restriction that the closest approach to the surface is determined by the finite size of the hydrated ions, enables one to predict the distribution factor of each species between a solution of mixed electrolytes and a surface layer, and to calculate the selective adsorption coefficient between two ions. Good agreement was found between the theoretical prediction and experimental data.

Do Faster-than-Light Group Velocities imply Violation of Causality?

Abstract: >DISCUSSION of the properties of hypothetical systems1–6 in which group velocities exceed the speed of light has considered chiefly whether such systems would violate the axioms of special relativity. In particular they appear at first sight to violate causality.

Regression on a Random Field

Abstract: The use of observations of a random function in space (random field) as independent variables in regression is considered including the numerical aspects. Details are presented for obtaining a numerical approximation to a Karhunen-Loeve expansion when the random function is observed at a large number of points. The procedure involves a two stage modified principal component analysis. The dependent variable is then regressed on the principal components. An example from meteorology is presented. The random field is the 700 mb height surface observed at 505 points over the northern hemisphere. The dependent variable is the temperature at Washington, D. C. A by-product of the analysis is an estimate of the generalized spectrum and covariance function of the random field without assuming symmetry.

A new experimental test of special relativity

Abstract: Although the special theory of relativity is almost generally accepted as a verified theory, existing experiments cannot distinguish it from a number of other rival theories that assume the existence of a preferred frame of reference (ether), and physical Lorentz contractions. It is shown that the Michelson-Morley experiment, performed in a solid transparent medium, is capable of such a distinction. The negative result of this experiment enhances the experimental basis of special relativity.

A Time-Sharing Queue with a Finite Number of Customers

Abstract: A time-sharing queue serving a finite number of customers is described. It is assumed that both the service time and the time elapsing between termination of service and the next arrival of the same customer at the queue (service station) are exponential. The model was studied by Krishnamoorthi and Wood, but their results are not in complete agreement with the results of this paper. In addition, some new results are presented in terms of steady-state expectations.

Rotation boundaries and crystal growth in the hexagonal system

Abstract: A rotating crystal x-ray diffraction technique has been employed for the measurement of rotation boundary angles in natural graphite crystals, and the values obtained have been compared with those predicted by coincidence boundary theory. It is shown that for natural graphite crystals these values do not correlate with theory, while previous measurements for graphite in dendritic form (Oron and Minkoff 1964) were in good agreement with predicted values. The results may be evaluated by considering attachment kinetics at an interface which has, in the case of graphite, the step of a rotation boundary of varying angle. For the dendritic growth form, which may be identified with a maximum in the growth rate, atom attachment occurs at the step of a rotation boundary tending to a maximum in coincidence. The rotation boundary values actually obtained are related to the structure and density of coincidence lattices. For graphite, atoms on the coincidence lattice are shared between the two rotated planes,...

The Crystal Structures at 110 and 300 degrees K of the Equimolar Molecular Compound of Pyrene and Pyromellitic Dianhydride

Abstract: The crystal structures of the 1:1 pyrene-pyromellitic dianhydride molecular compound at 110 and at 300 degrees K have been determined by three-dimensional X-ray diffraction methods (visual intensity measurement, least-squares refinement with isotropic Debye-Waller factors). The component molecules are arranged, plane to plane, in alternating array in mixed stacks. At 110 degrees K the pyrene molecules in the stacks alternate in two different orientations (about 12 degrees apart) with respect to the interleaving pyromellitic dianhydride molecules, which themselves have small displacements of alternating sign off the stack axis. At about 200 degrees K this ordered structure changes to a disordered structure which has been determined at 300 degrees K. The component molecules appear in mean positions, abnormally large Debye-Waller factors indicating disorder. The transformation itself has not yet been studied in detail. Review of the literature suggest that the existence of positional disorder provides an explanation for the widespread reports of high degrees of thermal vibration in crystals of II-molecular compounds. Some structure determinations appear to have been of disordered structures without this having been fully appreciated. Analysis of Debye-Waller factors, electron-density and difference syntheses suggests that different types of disorder are found in pyrene-pyromellitic dianhydride and pyrene-1,3,7,9-tetramethyluric acid (Damiani et al. 1965) on the one hand and in naphthalene-tetracyanoethylene (Williams & Wallwork 1967) and naphthalene-1,2,4,5-tetracyanobenzene (Kumakura, Iwasaki & Saito 1967) on the other. The dimensions found for the planar pyrene molecule at 110 degrees K agree well with those in pyrene itself but are more accurate; the agreement between the present experimental bond lengths and those calculated by the simple valence-bond method is exceptionally good (r.m.s. discrepancy = 0$\cdot $004 angstrom). The dimensions of the pyromellitic dianhydride molecule agree well with previous results but are more accurate; the molecule is slightly twisted into a non-centrosymmetric shape.

Remarks concerning the theoretical explanation of Hund’s rule

Abstract: According to the accepted theoretical explanation ofHund’s rule the electronic interaction energy is smallest in the ground state which is of the highest multiplicity A breakdown of the total energy into one- and two-electron contributions in the case of carbon atom based on self-consistent field calculations and configuration interaction treatment shows that this assumption is not valid According to our results the main differences in the energies of different terms arising from the same electronic configuration are due to differences in the one-electron energies