Linear time geometrical design rule checker based on quadtree representation of VLSI mask layouts

An efficient geometrical design rule checker is proposed, based on operations on quadtrees, which represent VLSI mask layouts. The time complexity of the design rule checker is O(N), where N is the number of polygons in the mask. A pseudoPascal description is provided of all the important algorithms for geometrical design rule verification.

Reflexive Incidence Matrx (RIM) Representation of Petr Nets

Although incidence matrix representation has been used to analyze the Petri net based models of a system, it has the limitation that it does not preserve reflexive properties (i.e., the presence of selfloops) of Petri nets. But in many practical applications self-loops play very important roles. This paper proposes a new representation scheme for general Petri nets. This scheme defines a matrix called "reflexive incidence matrix (RIM) c which is a combination of two matrices, a "base matrix Cb,,, and a "power matrix CP." This scheme preserves the reflexive and other properties of the Petri nets. Through a detailed analysis it is shown that the proposed scheme requires less memory space and less processing time for answering commonly encountered net queries compared to other schemes. Algorithms to generate the RIM from the given net description and to decompose RIM into input and output function matrices are also given. The proposed Petri net representation scheme is very useful to model and analyze the systems having shared resources, chemical processes, network protocols, etc., and to evaluate the performance of asynchronous concurrent systems.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Concepts and Object-Oriented Knowledge Representation

Tutkielma käsittelee nykyisiä kognitiotieteen teorioita käsitteistä ja niiden mallintamista oliokeskeisillä tietämyksen esittämisen menetelmillä. Käsiteteorioista käsitellään klassinen, määritelmäteoria, prototyyppiteoria, duaaliteoriat, uusklassinen teoria, teoria-teoria ja atomistinen teoria. Oliokeskeiset menetelmät ovat viime aikoina jakautuneet kahden tyyppisiin kieliin: oliopohjaisiin ja luokkapohjaisiin. Uudet olio-pohjaiset olio-ohjelmointikielet antavat käsitteiden representointiin mahdollisuuksia, jotka puuttuvat aikaisemmista luokka-pohjaisista kielistä ja myös kehysmenetelmistä. Tutkielma osoittaa, että oliopohjaisten kielten uudet piirteet tarjoavat keinoja, joilla käsitteitä voidaan esittää symbolisessa muodossa paremmin kuin perinteisillä menetelmillä. Niillä pystytään simuloimaan kaikkea mitä luokkapohjaisilla kielillä voidaan, mutta ne pystyvät lisäksi simuloimaan perheyhtäläisyyskäsitteitä ja mahdollistavat olioiden dynaamisen muuttamisen ilman, että siinä rikotaan psykologisen essentialismin periaatetta. Tutkielma osoittaa lisäksi vakavia puutteitta, jotka koskevat koko oliokeskeistä menetelmää. Avainsanat: käsitteet, käsiteteoriat, tekoäly, komputationaalinen psykologia, olio-ohjelmointi, tiedon esittäminen

Freddy Godshaw (Gottschalk) (far left) on Pfingsten (Pentacost) with two unidentified friends who perished in the Holocaust. Portraits Children

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A new formalism for representation of binary thermodynamic data

The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.

Inscription on the Holocaust memorial, Mahnmal am Opernplatz; Hannover, Germany.

Gottschalk family member names engraved on the memorial to the Jews of Hannover who perished in the Holocaust; Elizabeth Gottschalk nee Steinfeld, Henriette Gottschalk nee Rothschild, Jeanette Gottschalk (relationship unknown), and Karl Gottschalk.

Eva Blumenau nee Stern (far left) during a gathering of Holocaust survivors; Moenchengladbach (Rheydt), Germany.

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Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Freddy Godshaw (Gottschalk) (far left) on Pfingsten (Pentacost) with two unidentified friends who perished in the Holocaust. Portraits Children

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Eva Blumenau nee Stern (far left) during a gathering of Holocaust survivors; Moenchengladbach (Rheydt), Germany.

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Before the Holocaust: Letters to Alice (and Edith) 1939-1941.

Collection of transcribed 32 letters with accompanying notes, photographs and family trees. The letters were written by Flora Mattersheim Kleinmann to her daughter Alice Kleinmann Loewenstein and her granddaughter Edith from Vienna between July 1939 and October 1941. Introduced and edited by Ruth Leeds Love (Inge Ruth Loewenstein), Alice Kleinmann Loewenstein's granddaughter; transcripts by Herbert Weber.

From Holocaust to Rebirth Commemorative Medal

Obverse: A fading Star of David imprisoned behind bars, above the bars clear Star of David. Reverse: The emblem of the State of Israel, inscription.