Abstract: A method for characterization of objects has the steps of: a) describing an object with an elliptical self-adjoint eigenvalue problem in order to form an isometrically invariant model; b) determining eigenvalues of the eigenvalue problem; and c) characterizing the object by the eigenvalues.

Abstract: Umbilics of two surfaces are compared and it is determined from this comparison whether the suspect surface is a copy of the original surface based on the comparison. Comparing umbilics includes determining whether locations of the umbilics of the suspect surface match within a specified margin umbilics of the original surface, and determining whether pattern types of umbilics of the suspect surface match pattern types of corresponding umbilics of the original surface. A “weak” test may be performed, in which corresponding points on the two surfaces are compared, wherein the comparison of umbilics is performed if corresponding points of the two surfaces are located within a specified margin of each other. The points may be gridpoints on wireframes, which in turn may be based on lines of curvature of the surfaces. Comparing umbilics is performed if it is determined that each surface has at least one umbilic.

Abstract: Umbilics of two surfaces are compared and it is determined from this comparison whether the suspect surface is a copy of the original surface based on the comparison. Comparing umbilics includes determining whether locations of the umbilics of the suspect surface match within a specified margin umbilics of the original surface, and determining whether pattern types of umbilics of the suspect surface match pattern types of corresponding umbilics of the original surface. A “weak” test may be performed, in which corresponding points on the two surfaces are compared, wherein the comparison of umbilics is performed if corresponding points of the two surfaces are located within a specified margin of each other. The points may be gridpoints on wireframes, which in turn may be based on lines of curvature of the surfaces. Comparing umbilics is performed if it is determined that each surface has at least one umbilic.

Abstract: The invention relates to catalysts containing ruthenium and at least one other metal having an atomic number in the range of from 23 to 82 prepared by (a) mixing a suspension of a ruthenium compound having a specific surface area in the range of from 50 to 300 m2/g with a solution of at least one metal compound in which at least one such metal compound contains a metal different from ruthenium and has an atomic number in the range of from 23 to 82, and (b) treating the mixture of the suspension and the solution with a reducing agent.

Abstract: The invention relates to a process for the preparation of optically active alcohols from optically active carboxylic acids by reducing an optically active carboxylic acid with hydrogen in the presence of a catalyst comprising ruthenium and at least one further metal or transition metal having an atomic number in the range of from 23 to 82.

Abstract: The invention relates to a process for preparing optically active amino alcohols from optically active amino acids by reducing an optically active amino acid with hydrogen in the presence of a ruthenium-containing catalyst and an acid.

Abstract: Cyclopropanecarboxylic acid derivatives are prepared by reacting halogenocyclopropanecarboxylic acid derivatives with metals in the presence of bases and with or without addition of hydrogen in an advantageous manner if the base is added during the reaction. By means of the process according to the invention, good yields and selectivities and a high proportion of cis isomers in the reaction product may be achieved.

Abstract: Unsubstituted or substituted 2-fluoro-pyrimidines can be prepared by reaction of the underlying 2-amino-pyrimidines with diazotization agents, mixtures of HF and H.sub.2 O containing 30-70% by weight of HF, based on the total of HF and H.sub.2 O, serving as reaction medium. The reaction medium can also contain diluents and/or inorganic salts, preferably fluorides.

Abstract: Dimethyl carbonate (DMC) is prepared by continuous gas reaction of carbon monoxide and methyl nitrite a heterogeneous catalyst comprising a platinum at 50.degree. to 170.degree. C. under 1 to 5 bar.

Abstract: Dimethyl carbonate is obtained with a high selectivity and great constancy over time by reacting carbon monoxide with methyl nitrite in a continuous gas phase reaction in the presence of a heterogeneous catalyst prepared by the application to a suitable support of one or more palladium compounds of the formula[Pd(N(R.sup.1, R.sup.2, R.sup.3)).sub.n ]X.sup.1.sub.2 (I) ,wherein R.sup.1, R.sup.2, R.sup.3, X.sup.1 and n are as defined in the disclosure, optionally in combination with one or more promoters from the group consisting of the elements Fe, Co, Ni, V, Nb, Mo, Ta, Ti, Cu and Cr, the rare earths and/or compounds thereof, and/or with one or more promoters from the group consisting of alkali metal and alkaline earth metal halides.

Abstract: Dialkyl carbonates can be prepared by reacting carbon monoxide with alkyl nitrites in a continuous gas phase reaction in the presence of a heterogeneous platinum metal catalyst, the activity of this catalyst being maintained by the addition of small amounts of halogen. The dialkyl carbonates are thus formed with almost quantitative selectivity and no deactivation of the catalyst occurs.

Abstract: Dialkyl carbonates can be prepared by reaction of carbon monoxide with alkyl nitrites in a continuous gas-phase reaction using a platinum metal catalyst on a metal phosphate support and adding hydrogen halide stepwise or continuously during the course of the reaction in almost quantitative selectivity; the corresponding dialkyl oxalates are formed in such small amounts that in most cases they cannot be detected.

Abstract: Dialkyl carbonates can be prepared by the reaction of carbon monoxide with alkyl nitrites in a continuous gas phase reaction, using a platinum group metal catalyst on an alumosilicate zeolite having acidic centers, preferably in the H.sup.+ form, as a support, which catalyst may optionally comprise additional material of a compound of antimony, bismuth, aluminum, copper, vanadium, niobium, tantalum, tin, iron, cobalt, nickel or a mixture of a plurality of these, and hydrogen halide being added in the course of the reaction intermittently or continuously. In this reaction, the dialkyl carbonates are formed with almost quantitative selectivity; the corresponding dialkyl oxalates cannot be detected in most cases.

Abstract: Dialkyl carbonates can be prepared by the reaction of carbon monoxide with alkyl nitrites in a continuous gas phase reaction, using a platinum metal catalyst on an amorphous alumosilicate having a content of 30-80 atom% Al, based on the sum of Al and Si, as a support, which catalyst may optionally comprise additional material of a compound of antimony, bismuth, aluminium, copper, vanadium, niobium, tantalum, tin, iron, cobalt, nickel or a mixture of a plurality of these, and hydrogen halide being added in the course of the reaction intermittently or continuously. In this reaction, the dialkyl carbonates are formed with almost quantitative selectivity; the corresponding dialkyl oxalates cannot be detected in most cases.

Abstract: Dialkyl carbonates can be prepared by reaction of carbon monoxide with alkyl nitrites in a continuous gas phase reaction, in which a platinum metal catalyst of oxidic or hydroxidic compounds of elements from group Vb of the Periodic Table (Mendeleev) as supports and, if desired, addition of an antimony, bismuth, aluminium, copper, vanadium, niobium, tantalum, tin, iron, cobalt, nickel compound or a mixture of a plurality thereof on this catalyst are used, and the hydrogen halide which is discharged from the reactor together with the reaction mixture is batchwise or continuously replaced in the course of the reaction. This results in the formation of dialkyl carbonates in almost quantitative selectivity; the corresponding dialkyl oxalates can, in most cases, not be detected.

Abstract: Dialkyl carbonates can be prepared by reaction of carbon monoxide with alkyl nitrites in continuous gas phase reaction, in which a platinum metal halide catalyst on aluminum oxides, aluminum oxide hydrates or aluminum hydroxides as support and, if desired, an additive comprising an antimony, bismuth, aluminum, copper, vanadium, niobium, tantalum, tin, iron, cobalt, nickel compound or a mixture of a plurality thereof on this catalyst are used and hydrogen halide is replaced during the course of the reaction batchwise or continuously in at least the amount which is discharged from the reactor together with the reaction mixture. This results in the formation of dialkyl carbonates in almost quantitative selectivity, while the corresponding dialkyl oxalates can not in most cases be detected. The abovementioned supports are characterized by a BET surface area of more than 1 m.sup.2 /g.

Abstract: .beta.-Amino-acrylic acid esters of the formula(R.sup.1 R.sup.2)NCH.dbd.CR.sup.3 --COOR.sup.4can be obtained by reaction of .beta.-hydroxy-acrylic acid ester alkali metal salts of the formulaMe.sup..sym. .crclbar. OCH.dbd.CR.sup.3 --COOR.sup.4with ammonium salts of the formula(R.sup.1 R.sup.2) NH.sub.2.sup..sym. .crclbar.according to the general reaction equation(R.sup.1 R.sup.2) NH.sub.2 X+MeOCH.dbd.CR.sup.3 --COOR.sup.4 .fwdarw.(R.sup.1 R.sup.2) NCH.dbd.CR.sup.3 --COOR.sup.4 +MeX.dbd.H.sub.2 OR.sup.1, R.sup.2, R.sup.3, R.sup.4, Me.sup..sym. and X.sup..crclbar. having the meaning indicated in the description and the reaction being carried out in an aprotic organic solvent, in which the reaction components are suspended, as the reaction medium and it being possible to replace a part of the aprotic organic solvent by a protic organic solvent which is miscible with the aprotic solvent to give a homogeneous phase.

Abstract: Acid halides of the formula (R.sup.1, R.sup.2, R.sup.3)C--CO--Hal are obtained by reacting alkyl halides of the formula (R.sup.1, R.sup.2, R.sup.3)C--Hal with carbon monoxide under a pressure of 5 to 1,000 bar and at a temperature of -20.degree. C. to +100.degree. C. in the presence of 0.001 to 0.3 mol of AlCl.sub.3 and/or FeCl.sub.3, if appropriate in the presence of a further Bronsted or Lewis acid, per mol of the alkyl halide. The process is carried out, if desired in the presence of a solvent which is customary for Friedel-Crafts or Friedel-Crafts-related reactions and, if appropriate in the presence of a hydrogen halide. The acid chloride can be isolated from the reaction mixture or further reacted.

Abstract: In the preparation of 3,5-dichloro-.alpha.-methylstyrene by isopropylation of an m/p-dichlorobenzene mixture, isomerization of the resulting alkylation mixture, subsequent side chain bromination of the alkylation mixture and dehydrobromination of the resulting bromination mixture, the improvement which comprises reacting an excess of an m/p-dichlorobenzene mixture which contains at least 50% by weight of m-dichlorobenzene with isopropyl halide, isomerizing the resulting alkylation mixture under pressure in the presence of aluminum chloride until thermodynamic equilibrium has been attained, separating off the isomerized alkylation mixture from the unreacted m/p-dichlorobenzene mixture, and recycling the unreacted mixture for further reaction.

Abstract: Substituted benzaldehydes are prepared by reaction of the substituted benzenes from which they are derived with carbon monoxide and hydrogen chloride in the presence of metal halides, the process being performed in the presence of 0.5 to 10 mols of hydrogen chloride per mol of metal halide at a partial pressure of carbon monoxide from 1 to 100 bars and a temperature from -20.degree. C. to +100.degree. C. and, if desired, in the presence of an inert diluent. The substituted benzaldehyde which contains, as a substituent, alkyl with at least 2 carbon atoms, cycloalkyl or optionally substituted benzyl, is prepared by reacting the appropriately substituted benzene with the additional presence of a benzene which does not contain the substituents mentioned, but which is identical in respect of further substituents which are optionally present with the benzene from which it is derived.