A combinatorial theory of Grünbaum's new regular polyhedra,part I: Grünbaum's new regular polyhedra and their automorphism group

The new regular polyhedra, defined and investigated by Branko Grünbaum in [4], and theirn-dimensional generalizations are classified in terms of their symmetry group.     

On the theorems of Drake and Lenz

A generalization and an improvement of the results of Drake and Lenz on the constructions of projective Hjelmslev planes are obtained. Using this, some new series of invariant pairs including 4 new pairs (t, 2),t 1000, for projective Hjelmslev planes are obtained.     

Graph factorization,general triple systems,and cyclic triple systems

In this self-contained exposition, results are developed concerning one-factorizations of complete graphs, and incidence matrices are used to turn these factorization results into embedding theorems on Steiner triple systems. The result is a constructive graphical proof that a Steiner triple system exists for any order congruent to 1 or 3 modulo 6. A pairing construction is then introduced to show that one can also obtain triple systems which are cyclically generated.     

On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Some bounds for partially balanced block designs

Bounds on eigenvalues of theC-matrix for a partially balanced block (PBB) design are given together with some bounds on the number of blocks. Furthermore, a certain equiblock-sized PBB design is characterized. These results contain, as special cases, the known results for variance-balanced block designs and so on.     

Factorizing multivariate time series operators

Motivated by problems occurring in the empirical identification and modelling of a n-dimensional ARMA time series X(t) we study the possibility of obtaining a factorization (I + a₁B + … + a_pB^p) X(t) = [Π_i=1^p (I ? α_iB)] X(t), where B is the backward shift operator. Using a result in [3] we conclude that as in the univariate case such a factorization always exists, but unlike the univariate case in general the factorization is not unique for given a₁, a₂,…, a_p. In fact the number of possibilities is limited upwards by $\text{(np)!}\text{(n!)}{}^{\mathrm{p}}$, there being cases, however, where this maximum is not reached. Implications for the existence and possible use of transformations which removes nonstationarity (or almost nonstationarity) of X(t) are mentioned.     

Cellularity in polyhedra

A compact subset X of a polyhedron P is cellular in P if there is a pseudoisotropy of P shrinking precisely X to a point. A proper surjection between polyhedra f:P→Q is cellular if each point inverse of f is cellular in P. It is shown that if f:P→Q is a cellular map and either P or Q is a generalized n-manifold, n≠4, then f is approximable by homeomorphisms. Also, if P or Q is an n-manifold with boundary, n≠4, 5, then a cellular map f:P→Q is approximable by homeomorphisms. A cellularity criterion for a special class of cell-like sets in polyhedra is established.     

Time-resolved study of intramolecular charge transfer fluorescence in 1,2,3,4-tetrachloro-11H-isoindolo-[2, 1-a]-benzimidazol-11-one

Fluorescent properties of 1,2,3,4-tetrachloro-11H-isoindolo-[2,1-a]-benzimidazol-11-one (TCIB) in various organic solutions are described. Detailed investigation of the fluorescence from the solutions revealed that it was ascribable to the electronic transition from the lowest singlet excited state of an isolated molecule to its ground state, though the fluorescence spectrum was broad and structureless and the Stokes’ shift was about 1 eV. The absorption peak of TCIB was relatively insensitive to change in solvent polarity, whereas its fluorescence peak shifted to the red with an increase in the polarity. This finding suggests that the dipole moment of the molecule in the ground state is almost zero, and that the excited state has a non-zero dipole moment, which coincides with the predicted semiempirical molecular orbital calculation. Fluorescence quantum efficiency decreased with increase of solvent polarity. The efficiency was reduced by a factor of 39 in going from n-hexane solution to acetonitrile solution. The radiative rate constant also decreased with increase of solvent polarity. However, its reduction was very moderate; the reduction factor was only 2.5 for acetonitrile solution as compared with n-hexane solution. This finding indicates that the emitting state of the title compound is influenced by a solvent-dependent non-radiative mechanism, for which solvent-sensitive intersystem-crossing deactivation is tentatively proposed.     

Almost hermitian structures with parallel torsion

The characteristic connection of an almost hermitian structure is a hermitian connection with totally skew-symmetric torsion. The case of parallel torsion in dimension 6 is of particular interest. In this work, we give a full classification of the algebraic types of the torsion form, and, on the basis of this, undertake a systematic investigation into the possible geometries. Numerous naturally reductive spaces are constructed and classified, and examples on nilmanifolds given.     

Synthesis and Sm/Sm doping effects on photoluminescence properties of Sr4Al14O25

Complete and partial samarium reduction was achieved under strong reducing atmosphere by solid-state and combustion synthesis of Sr_3.96Sm_0.04Al₁₄O₂₅. Dependence of different fluxing agents on the formation of various strontium aluminates was examined. The samples were investigated by X-ray powder diffraction, temperature dependent luminescence decay and photoluminescence measurements. Excitation with UV radiation resulted in sharp and well resolved emission lines of samarium ions. Distinct temperature behavior for Sm²⁺ and Sm³⁺ were detected in the range of 100-500 K. Estimated emission thermal quenching values (TQ_1/2) for divalent samarium were approximately 270 K while for trivalent state around 660 K. Measured luminescence decay values of Sm²⁺ are substantially lower than for Sm³⁺,≈1.7 and ≈2.7 ms, respectively. The spectral feature of Sm²⁺ emission spectrum indicates that dopant occupies low symmetry site in Sr₄Al₁₄O₂₅ compound.