Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

Unital Groups and General Comparability Property

Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined addition + which is not necessarily commutative and therefore with two complements, left and right. If they satisfy a special kind of the Riesz decomposition property, they are intervals in unital po-groups. The general comparability property in unital po-groups with strong unit (G,u), allows to compare elements of G in some intervals with Boolean ends. Such a po-group is always an -group admitting a state. We prove that every such (G,u) is a subdirect product of linearly ordered unital po-groups.     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

Nuclear magnetic resonance-compatible furnace for high temperature MR imaging and spectroscopy in situ

A high temperature magnetic resonance compatible furnace for real time in situ monitoring of materials, processes, and chemical reactions with magnetic resonance imaging and spectroscopy is described. Design issues are analyzed. Example applications are demonstrated with a time sequence of proton images of the binder burnout in a porous green ceramic cylinder containing polyethylene glycol binder at 200 degrees C, and 7Li images of the molten salt LiCl at 700 degrees C.     

tBuP(NH2)2--a reactive synthon for the synthesis of molecular imidophosphinates of group 13 metals

Reactions of tBuP(NH(2))(2) with Group 13 trialkyls MR(3) (M=Al, Ga, In; R=Me, tBu) were investigated in detail. According to variable-temperature (VT) NMR investigations, the reaction proceeds stepwise with the initial formation of aminophosphane adducts, which subsequently react to give iminophosphorane adducts and finally the heterocyclic metallonitridophosphinates. BP86/TZVPP (DFT) calculations were performed to verify this reaction pathway, to elucidate the influence of the central Group 13 element on the stability of the reaction intermediates and the heterocycles, as well as to assess the thermodynamics of their formation. The relative stability of free and complexed aminophosphane RP(NH(2))(2) and iminophosphorane R(H(2)N)(H)P=NH (adducts) with P(III) and P(V) centers was studied in more detail with DFT and MP2 methods. In addition, the influence of the substituent R was investigated by variation of R from H to Me, tBu, F, and NH(2). In general, the aminophosphane form was found to be favored for the free ligand, however, upon complexation with MR(3) (M=Al, Ga; R=alkyl) both forms are almost equal in energy.     

An Analog for the Frattini Factorization of Finite Groups

Using the classification of finite simple groups, we prove that if H is an insoluble normal subgroup of a finite group G, then H contains a maximal soluble subgroup S such that G=HN_G(S). Thereby Problem 14.62 in the Kourovka Notebook is given a positive solution. As a consequence, it is proved that in every finite group, there exists a subgroup that is simultaneously a -projector and a -injector in the class, , of all soluble groups.     

Constructive Matrix and Orderable Groups

We study into the relationship between constructivizations of an associative commutative ring K with unity and constructivizations of matrix groups GL _n(K) (general), SL _n(K) (special), and UT _n(K) (unitriangular) over K. It is proved that for n 3, a corresponding group is constructible iff so is K. We also look at constructivizations of ordered groups. It turns out that a torsion-free constructible Abelian group is orderly constructible. It is stated that the unitriangular matrix group UT _n(K) over an orderly constructible commutative associative ring K is itself orderly constructible. A similar statement holds also for finitely generated nilpotent groups, and countable free nilpotent groups.