Common tangent space ℝ 1 4 fromU(2) charges

It is discussed how a common space-time can be constructed from a proposed hiddenU(2) world. Schrödinger's idea to obtain discrete eigenvalues by solving the Maxwell equations for the fieldF on compact spaces without boundaries is modified by orthogonality and identification concepts for the potentialsA. Using residue classes with respect to the metric (Clifford algebra), a common spinor space ⁴=RL and a common Minkowski tangent space ₁ ⁴ are bilinearly constructed from tangent spaces ofU(2) individuals [U(2) manifolds with orthogonal potentials]. The space constructed has the following properties. (1) There are algebraic elements for the identification ofU(2) individuals from ₁ ⁴ as spinors and vectorsA. (2) The transfer of the potentials fromU(2) via ⁴ to ₁ ⁴ is linear. (3) The hiddenU(2) content of the left- and right-handed spaces (L, R) is quite different. The potentials on U(2) individuals are transformed into complex wave functions on the spinor space and into 1-formsA on ₁ ⁴ that can be enlarged to gauge potentials. The construction is discussed from an old point of view of Einstein's, starting with the electric charge as the primary concept for quantum theory. The construction of the tangent space ₁ ⁴ does not depend on a preceding introduction of any points (uncertainty). The identity problem of the interpretation of the quantum theory is discussed in some detail. It is indicated how the algebraic, partiallyad hoc constructions can give a rigid frame for further analytical work.     

Limits of the dynamic glass transition zone in an ethylene-vinylacetate copolymer

Previous measurements on an ethylene-vinylacetate copolymer are discussed anew in the framework of new concepts for the glass transition. The response signals (n.m.r., ultrasonics, dielectric polarization, torsion, and specific heat) are presented in a logarithm of frequency-temperature diagram. An arrangement of the response signals across the glass transition zone similar to that in other polymers was found. The absorption maximum temperature of ultrasonics and the temperature where the super-Lorentzian shape distinctively appears in the wl-n.m.r. spectra are located at the high frequency limitb of the glass transition zone corresponding to short-range correlated molecular motions.     

Phasenumwandlung zweiter Art als kritische Erscheinung eines inneren Phasengleichgewichtes

It is demonstrated that the transition in a state with two internal phases is a second order phase transition. The term internal phases means phase-like regions inside the system which are not separated by boundaries in the sense of ordinary phase boundaries, and the dimensions and shape of which as well as their properties as such are object of an equilibrium. In a generalization (quasi phases) a long ranged correlation of alternating or periodical character is considered as a typical element of the low temperature state. Such states can be described thermodynamically with the help of a new pair of variablesQ-η. The transition intoQ-η-T is generally analogous to the critical point of ordinary phase transitions inP-V-T, andη ～(?t)^1/3 andC _p～(?t)^?2/3 with a small constant of proportionality are obtained (t=T-T _u). Using the Pippard-relations in the formV-V _γ=(dT _γ/dP) (S-S _γ) the low temperature behaviour of the entropy and density surface as a function ofP andT near the transition line can be completely described. E.g. the saturation magnetization of a ferromagnetic model is derived proportional to (?t)^1/3. Under the action of a magnetic field the transition will be of first order when the saturation magnetization is achieved, without the outer field being analogous toP orQ. Should only one internal phase differ from the high temperature state we obtain an edge point (x=0 analogous to theμ ₁?x-diagram of solutions) with finite jump inC _p andη～({t). A possible relationship to the BCS- model of the supraconductors is indicated.     

Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses

High-resolution synchrotron-radiation powder diffraction experiments were performed to observe structural changes induced by hydrogen loading in rapidly-quenched Ti-Zr-Ni alloy ribbons with dominant icosahedral character. Lattice expansion effects due to hydrogen storage in Ti-Zr-Ni quasicrystals as well as phonon and phason disorder coefficients are obtained from an analysis of diffraction linewidths. Received: 26 August 1997 / Revised: 8 January 1998 / Accepted: 10 February 1998     

Struik law for enthalpy retardation at the glass transition in poly(n-alkylmethacrylates) measured by DSC aging experiments

Results of calorimetric (DSC) experiments on a series of poly (n-alkylmethcrylates), from methyl to pentyl, after different aging timest _e at different aging temperaturesT _e are presented. The aging behavior is quite different from that in other polymers, for example PS. For all poly(n-alkylmethacrylates) investigated the aging peak temperatureT _max is shifted parallel to the aging temperatureT _e in a large temperature interval below the glass temperature. The results are discussed with respect to shear and entropy response in the splitting region.     

17α-Konfigurierte 20-methylpregnan-derivate

A mixture of 1a+1b (17α), obtained by C-17-epimerization of pregnenolone (1a) was converted into 3a+3b by Wittig-reaction. 3a+3b were acetylated to a mixture of 4a+4b, from which 4b was isolated by cristallization of 3a and following AgNO₃-chromatography of the mother-liquors. Δ²⁰⁽²²⁾ → Δ¹⁷-doublebond-isomerization occurs by hydrogenation (Pd/C) of 3a (17β) to give 5. Hydrogenation (Pt-catalyst) of 4b (17α) leads to 8b, which was converted into the 20-methylpregnane-derivatives 7b, 9b–13b. By comparison with the 17β epimers 1a–4a, 7a–13a a spectroscopic determination of the relative configuration on C-17 of 17-alkylsubstituted steroids was possible.     

Dynamic shear modulus in the splitting region of poly(alkyl methacrylates)

A systematic study of the dynamic shear modulusG ^*=G+G in three poly(alkyl methacrylates) (PEMA, PnPMA, PnBMA) at frequencies between 0.001 and 500 rad/s is presented. As the splitting frequencies _s are low, aging effects can be observed in the splitting region. There is a systematic shift of the splitting frequency _s to lower values with increasing length of the alkyl side group. In PnBMA a separate shear appearance is observed about two frequency decades below the local mode . This is discussed in terms of the concept of minimal cooperativity. Aging effects are: Shift of the maximum loss frequency to lower values, peak sharpening of the relaxation, and intensity changes of and . These effects are discussed in terms of the sequential aging concept. Aging leads to a pronounced bending of the traces upwards from the equilibrium line in the Arrhenius diagram. These non-equilibrium phenomena are promoted by the small slope m=d(log )/dT of the trace in the splitting region.Dedicated to Prof. E. W. Fischer at the occasion of his 65th Birthday Lieber Herr Fischer, die Hallenser Polymerphysiker danken Ihnen aufrichtig für die warmherzige und effektive Förderung der Polymerwissenschaften im Raum Halle-Merseburg.