Electronic spectra of cationic forms of meso-tetrapropylporphin in a nanoporous silicate gel matrix

We have studied the fluorescence and fluorescence excitation spectra at 300 K, 77 K, and 4.2 K for silicate gel matrices colored with meso-tetrapropylporphin by impregnation of the matrix with a solution of the pigment. Comparison of the data obtained with the absorption spectra in acidified solutions and analysis of the low-temperature fine-structure vibronic spectra, and also taking into account data obtained earlier for octaethylporphin in a xerogel showed formation of two cationic forms of meso-tetrapropylporphin in the gel matrix: the short-wavelength form has a dicationic structure, while the long-wavelength form has a monocationic structure. We have traced out the correlations of the vibrational structure in the spectra of the dicationic form with data for the porphin dication, and we have drawn a number of conclusions concerning the normal vibrational modes that are active in the vibronic fluorescence and absorption spectra of the studied cationic forms. Using the AM1 semiempirical quantum chemical method, we optimized the geometry of the mesotetrapropylporphin dication: the most stable of the possible conformers is the dication structure with saddleshaped macrocycle nonplanarity. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 453–461, July–August, 2006.     

HF heating of a plasma column at frequencies below the electron cyclotron frequency

Dispersion of waves, excited by the helical structure in a plasma column and the heating of a tail of the electron distribution function is studied at frequencies below the electron plasma and the electron cyclotron frequency.We wish to thank Dr. R.Klíma for valuable discussions and Dr. J.Lacina and Mrs. P.Jaroová for the computational work. We also thank Dr. L.Bárdo, Dr. L.Kryka and Dr. G. L.Khorosanov from Sukhumi Institute, USSR, for their help during different stages of the experiment. We are indebted to Mr. J.Dvoák, Mr. F.Jiránek and Mr. B.usta for their expert technical assistance.     

3D dependence of the dielectric dispersion in a BaTiO3 single crystal

The 3D dependences ?′(log f, T) and tanδ(logf, T) of a perfect BaTiO₃ single crystal grown by the Remeika method have been studied in the ranges f = 1–2 × 10⁷ Hz and T = ?80–130°C. These dependences characterize a transition from the paraelectric phase (121.5°C) as a near-antiferroelectric transition followed by the transition to the tetragonal phase at ～79.5°C. According to a number of signs, the range 121.5–79.5°C corresponds to a metastable phase typical of first-order phase transitions. The unexpected result of this work has been discussed with invoking the hypothesis on the BaTiO₃ structure in the paraelectric phase, according to which it consists of three antiferroelectric states oriented along the crystallographic axes. Using the dielectric properties of BaTiO₃ as an example, the method of direct correct determination of the temperatures of the structural transformations from the anomaly of tanδ(logf, T) has also been demonstrated.     

Short-term reversible changes in the dielectric dispersion of a barium titanate single crystal

An effect of spontaneous fluctuation of the dispersion frequency was detected during investigations of the dielectric dispersion of a BaTiO₃ single crystal while measuring under the electric field only. A decrease in the dispersion frequency by three orders of magnitude and its subsequent return to the previous value was observed. A possible mechanism of this phenomenon is suggested, which involves the dynamics of the screening process.     

Face numbers of generalized balanced Cohen-Macaulay complexes

A common generalization of two theorems on the face numbers of Cohen-Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Bj?rner-Frankl-Stanley (sufficiency) that characterizes all possible face numbers of a-balanced CM complexes, while the second is the theorem of Novik (necessity) and Browder (sufficiency) that characterizes the face numbers of CM subcomplexes of the join of the boundaries of simplices.     

A Short Simplicial h -Vector and the Upper Bound Theorem

Abstract. The Upper Bound Conjecture is verified for a class of odd-dimensional simplicial complexes that in particular includes all Eulerian simplicial complexes with isolated singularities. The proof relies on a new invariant of simplicial complexes—a short simplicial h -vector.     

Reverse lexicographic and lexicographic shifting

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δ_lex—an operation that transforms a monomial ideal of S = K[x_i: i ∈ ℕ] that is finitely generated in each degree into a squarefree strongly stable ideal—is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a squarefree strongly stable ideal I ⊂ S is fixed by lexicographic shifting if and only if I is a universal squarefree lexsegment ideal (abbreviated USLI) of S. Moreover, in the case when I is finitely generated and is not a USLI, it is verified that all the ideals in the sequence } are distinct. The limit ideal is well defined and is a USLI that depends only on a certain analog of the Hilbert function of I. Research partially supported by NSF grants DMS 0070571 and DMS 0100141.     

Centrally symmetric polytopes with many faces

We present explicit constructions of centrally symmetric polytopes with many faces: (1) we construct a d-dimensional centrally symmetric polytope P with about 3 ^d/4 ≈ (1.316) ^d vertices such that every pair of non-antipodal vertices of P spans an edge of P, (2) for an integer k ≥ 2, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitrarily large number N of vertices such that for some 0 < δ _k < 1 at least (1 ? (δ _k ) ^d )( _k ^N ) k-subsets of the set of vertices span faces of P, and (3) for an integer k ≥ 2 and α > 0, we construct a centrally symmetric polytope Q with an arbitrarily large number of vertices N and of dimension d = k ^1+o(1) such that at least $(1 - k^{ - \alpha } )(_k^N )$ k-subsets of the set of vertices span faces of Q.