Struktur und Mechanismus bei Fragmentierungsreaktionen 1. Teil. Die stereoisomeren 10-Chlor-decahydro-isochinoline. Fragmentierungsreaktionen, 23. Mitteilung

cis-10-Chloro-N-methyl-decahydro-isoquinoline ( 5 ) and its trans-isomer 6 undergo heterolytic fragmentation in 80% ethanol by different mechanisms. As predictable on stereo-chemical grounds the cis-isomer 5 reacts by the accelerated synchronous mechanism, the trans-isomer 6 , however, by the two-step carbonium ion mechanism. Synchronous fragmentation therefore dominates over the two-step process even when the latter would lead to a relatively stable tertiary carbonium ion. In both cases the more highly substituted and thermochemically more stable olefinic fragment 8 is formed.     

Some Properties and Applications of Simple Orthogonal Matrices

Conditions are found for a general transformation in the planeof two vectors u and v to be orthogonal. The results characterizea rotation in the (u, v)-plane by the angle ø betweenu and v and the angle of rotation. When ø = /2 the Jacobirotation matrix is a special case, but other choices of øare interesting. The rotation that maps a single vector x intoa vector y of the same size, by rotating in the (x, y)-plane,is found and this may be used in much the same way that Householdertransforms are used. If (x₁, y₁) and (x₂, y₂) are pairs of vectorscompatible in size and angle, the orthogonal matrix that rotatesin a suitably chosen plane so that x₁ x₂ and y₁ y₂ is found.This has applications in mapping two columns of a matrix toa simple form, similar to Householder operations on a singlecolumn.     

Specific heat of concentrated kondo systems: (La,Ce)Al2 and CeAl2

We report on specific heat measurements of (La_1–x Ce _x )Al₂ samples, with 1.5 a/ox100 a/o, performed in magnetic fields of up to 5 T between 0.3 and 10 K. In the Ce rich alloys, and especially in CeAl₂, a-type peak of an antiferromagnetic phase transition, and at lower temperatures spin waves and very large electronic contributions are clearly visible. In higher magnetic fields, that is when antiferromagnetic order can be suppressed, the specific heat of the alloys exhibits a broadened Schottky peak. All these phenomena add up tok ln 2, i.e. to the correct entropy change per single Ce³⁺ ion in its ₇ crystal field ground state.We interpret experimental results as an interplay between cooperative magnetism and the single-ion Kondo effect which describes a gradual turning off of one magnetic moment. The broadening of the Schottky peak is directly related to the Kondo temperatureT _K , which we determine with a simple resonance level model.T _K increases by an order of magnitude whenx increases from 1.5 a/o to 100 a/o. This is interpreted as caused by a lattice contraction.A quadraticx dependence of the Néel temperature suggests that (forTT _K ) stable Ce moments can only exist through pair interactions. The very large (and almost field independent) specific heat term linear in temperature with a coefficient=135 mJ/K² mole for CeAl₂ is attributed to the Kondo effect—still present in the antiferromagnetically ordered state. Our evaluation of the experimental data is backed by a molecular field theory for a simplified antiferromagnetic structure combined with the simplest possible Kondo theory.Preliminary results have been presented at the Int. Conf. on Magnetic Alloys and Oxides, Haifa 1977 [Bredl, C.D., Steglich, F.: J. Magnetism and Magnetic Materials, in press]     

Magnetostriction measurement by means of strain modulated ferromagnetic resonance (SMFMR)

A novel method for measuring magnetostriction constants is presented. A strain, periodic in time, applied to the sample, causes a modulation of the ferromagnetic resonance line position. The height of the signal obtained after phase-sensitive detection is proportional to the strain modulation depth. The appropriate magnetostriction constant λ is obtained by comparing the height of the SMFMR signal with that of the FMR line, as recorded by means of magnetic field modulation. Features of the new technique are:

1. high sensitivity: λ_min? 10_?9 forM=100 Oe and linewidth ΔH _d=1 Oe;
2. λ's belonging to distinct precession modes are separately determined;
3. applicable to thin layers for which strain gauge techniques cannot be used;
4. wide temperature range: 1.2 K<T<300 K;
5. uniform stress.

An illustrative example (YIG layer on GGG substrate) is given.     

An Einstein-Gödel universe

The metric for the standard static Einstein model of the universe can be expressed in coordinates for which a congruence of spacelike world lines of the model will be twisting. A method of shifting the twist has been devised by which the twist on spacelike world lines is shifted onto the timelike world lines. The model universe then becomes Gödel's model. A combined Einstein-Gödel model containing a parameter is obtained. Switching from +1 to –1 will effect the shift of twist in the world lines and lead from the Einstein model to the Gödel model.     

Auditory-nerve response from cats raised in a low-noise chamber

A litter of four cats, born and raised in a soundproofed chamber, was studied in an attempt to determine which, if any, features of the auditory-nerve response from routinely available cats might be due to the chronic effects of noise exposure. Two features of routine-normal response were especially suspect in this regard: (1) a "notch" in the distribution of single-unit thresholds centered at characteristic frequencies (CF's) near 3 kHz and (2) a compression of the distribution of rates of spontaneous discharge for units with CF above 10 kHz. A third feature of response in routine animals was the presence of a small number (roughly 10%) of units with virtually no spontaneous discharge and very high thresholds, sometimes 80 dB less sensitive than high-spontaneous units of similar CF. In the data from chamber-raised animals, the high-spontaneous units showed exceptionally low thresholds at all CF regions, however, there were signs of the midfrequency notch in the threshold distribution of at least two of these animals. The compression of the spontaneous rate distribution was not seen in any of the three most sensitive animals. The data suggest that there is a significant amount of "normal pathology" in the high-CF units from routine animals. Low-spontaneous, high-threshold units were present in all four chamber-raised ears with the same characteristics as in routine animals (exceptionally narrow tuning curves and exceptionally low maximum discharge rates) and at roughly the same percentage of the unit sample. A class of units with medium spontaneous rates and intermediate thresholds could also be identified. The possible significance of a classification of auditory-nerve units according to spontaneous rate is discussed.     

The absorption spectrum of the Ag2 molecule

The high dispersion absorption spectrum of the Ag₂ molecule has been photographed in the ～5300–1500-Å region. Observations include the previously reported A ← X, B ← X, C ← X, D ← X, and E ← X transitions and a new H ← X transition which occurs in the vacuum ultraviolet. Extensive spectral blending precluded detailed rotational analyses, but the band structures are consistent with $\text{ΔΩ}\text{= 0}$ and $\text{ΔΩ}\text{≥1}$ for D-X and C-X, respectively. The H state is perturbed and probably predissociated. The following molecular constants (in cm^?1) were obtained from fitting bandhead data to the usual expressions:

     

998.

One massless particle equals two Dirac singletons     

M. Flato  C. Fronsdal 《Letters in Mathematical Physics》1978,2(5):421-426

The remarkable representations of the 3+2 de Sitter group, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di Di, Di Rac, and Rac Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, massless particle may be interpreted as a state of two free singletons — and vice versa. The term massless is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.     

999.

A theorem on asymptotic expansion of Feynman amplitudes     

M. C. Bergère  C. de Calan  A. P. C. Malbouisson 《Communications in Mathematical Physics》1978,62(2):137-158

For any Feynman amplitude, where any subset of invariants and/or squared masses is scaled by a real parameter going to zero or infinity, the existence of an expansion in powers of and ln is proved, and a method is given for determining such an expansion. This is shown quite generally in euclidean metric, whatever the external momenta (exceptional or not) and the internal masses (vanishing or not) may be, and for some simple cases in minkowskian metric, assuming only finiteness of the — eventually renormalized — amplitude before scaling. The method uses what is called Multiple Mellin representation, the validity of which is related to a generalized power-counting theorem.On leave of absence from University of Bahia (Brazil). Fellow of CAPES, Brazil     

1000.

Crystalline titanium dichloride—an active catalyst in ethylene polymerization. II. Polymer structure,polymerization variables,and scope     

C. J. Benning  W. R. Wszolek  F. X. Werber 《Journal of polymer science. Part A, Polymer chemistry》1968,6(4):755-762

Polymerization of ethylene with ball-milled titanium dichloride leads to a completely linear polymer with terminal unsaturation corresponding to approximately one carbon–carbon double bond per molecule. Polymerization rate is first-order in both monomer and catalyst concentration at 140°C. Due to a thermal deactivation of the catalyst, the polymerization rate falls sharply with temperature above 180°C. Propylene and butene-1 will copolymerization with ethylene in this system, propylene more efficiently than butene-1. Evidence for copolymerization of trans-2-butene, but not of the cis-isomer or of isobutene, in trace concentrations is presented. Propylene is homopolymerized to a product low in isotactic content. The significance of the structural and (limited) kinetic data in terms of the mechanism of polymerization are discussed.     

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State	Te	ωc	Xωt
X	0.0	192.0	0.58
B	35 838.6	151.8	0.87
C	37 631.6	171.0	0.84
D	39 014.5	168.2	1.20
E	40 159.9	146.1	1.58
H	58 273.1	165.9	2.46

One massless particle equals two Dirac singletons

The remarkable representations of the 3+2 de Sitter group, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di Di, Di Rac, and Rac Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, massless particle may be interpreted as a state of two free singletons — and vice versa. The term massless is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.     

A theorem on asymptotic expansion of Feynman amplitudes

For any Feynman amplitude, where any subset of invariants and/or squared masses is scaled by a real parameter going to zero or infinity, the existence of an expansion in powers of and ln is proved, and a method is given for determining such an expansion. This is shown quite generally in euclidean metric, whatever the external momenta (exceptional or not) and the internal masses (vanishing or not) may be, and for some simple cases in minkowskian metric, assuming only finiteness of the — eventually renormalized — amplitude before scaling. The method uses what is called Multiple Mellin representation, the validity of which is related to a generalized power-counting theorem.On leave of absence from University of Bahia (Brazil). Fellow of CAPES, Brazil     

Crystalline titanium dichloride—an active catalyst in ethylene polymerization. II. Polymer structure,polymerization variables,and scope

Polymerization of ethylene with ball-milled titanium dichloride leads to a completely linear polymer with terminal unsaturation corresponding to approximately one carbon–carbon double bond per molecule. Polymerization rate is first-order in both monomer and catalyst concentration at 140°C. Due to a thermal deactivation of the catalyst, the polymerization rate falls sharply with temperature above 180°C. Propylene and butene-1 will copolymerization with ethylene in this system, propylene more efficiently than butene-1. Evidence for copolymerization of trans-2-butene, but not of the cis-isomer or of isobutene, in trace concentrations is presented. Propylene is homopolymerized to a product low in isotactic content. The significance of the structural and (limited) kinetic data in terms of the mechanism of polymerization are discussed.