Classification of the space spanned by theta series and applications

We determine a class of functions spanned by theta series of higher degree. We give two applications: A simple proof of the inversion formula of such theta series and a classification of skew-holomorphic Jacobi forms.

     

Some time change representations of stable integrals, via predictable transformations of local martingales

From the predictable reduction of a marked point process to Poisson, we derive a similar reduction theorem for purely discontinuous martingales to processes with independent increments. Both results are then used to examine the existence of stochastic integrals with respect to stable Lévy processes, and to prove a variety of time change representations for such integrals. The Knight phenomenon, where possibly dependent but orthogonal processes become independent after individual time changes, emerges as a general principle.     

Random time change and an integral representation for marked stopping times

Summary Consider the set of all possible distributions of triples (, , ), such that is a finite stopping time with associated mark in some fixed Polish space, while is the compensator random measure of (, ). We prove that is convex, and that the extreme points of are the distributions obtained when the underlying filtration is the one induced by (, ). Moreover, every element of has a corresponding unique integral representation. The proof is based on the peculiar fact that EV _, =0 for every predictable processV which satisfies a certain moment condition. From this it also follows thatT _, isU(0, 1) wheneverT is a predictable mapping into [0, 1] such that the image of , a suitably discounted version of , is a.s. bounded by Lebesgue measure. Iterating this, one gets a time change reduction of any simple point process to Poisson, without the usual condition of quasileftcontinuity. The paper also contains a very general version of the Knight-Meyer multivariate time change theorem.Research supported by NSF grant DMS-8703804     

Synthesis and X-ray crystal structures of six [TeL4][MF6] salts, where L is ethylene- or trimethylene-thiourea, and M is Si, Ge or Sn. Five Te(II) complexes with a novel type of structure linked together by unusual N–HF hydrogen bonds

The complexes [Te(etu)₄][SiF₆] (1), [Te(etu)₄][SiF₆] · H₂O (2), [Te(trtu)₄][SiF₆] (3), [Te(etu)₄][GeF₆] · H₂O (4), [Te(trtu)₄][GeF₆] (5) and [Te(etu)₄][SnF₆] (6) (etu = ethylenethiourea, trtu = trimethylenethiourea) have been prepared and their crystal structures determined by X-ray crystallographic methods. The crystals of 1, 3 and 5 are tetragonal; space groups P4cc (No. 103) with Z = 4 for 1, P4nc (No. 104) with Z = 2 for 3, and I4 (No. 79) with Z = 2 for 5. The crystals of 2, 4 and 6 are orthorhombic, space group Pccn (No. 56) with Z = 8 for 2 and 4 and Z = 4 for 6; those of 2 and 4 being isomorphous. The cations contain square planar or slightly distorted square planar TeS₄ coordination groups. In 1, 3 and 5 the Te atoms are located on fourfold rotation axes; the cations have fourfold rotational symmetry and the four thiourea ligands extend to the same side of the TeS₄ plane. These are the first examples of [TeL₄]²⁺ conformers of this type. In 2 and 4 the Te atoms lie on general positions; the cations are distorted versions of those in 1, and also in these the four ligands extend to the same side of the TeS₄ plane. In 6 the Te atoms are located on twofold rotation axes, the conformation of the cations corresponds to the point group C₂ with two neighbouring ligands extending to one side of the coordination plane and the remaining two to the opposite side. In 1–5 each of the four ligands forms a N–HF bond to the same F atom in the counter ion. The crystals of 1–5 are red, and those of 6 are yellow. The red colour is attributed to interactions of Te and S lone electron pairs caused by ligand TeS₄/TeSC tilt angles markedly different from 90°.     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday     

From primary to dual affine variety codes over the Klein quartic

Designs, Codes and Cryptography - In Geil and Özbudak (Cryptogr Commun 11(2):237–257, 2019) a novel method was established to estimate the minimum distance of primary affine variety...     

Survey of linear programming for standard and nonstandard Markovian control problems. Part II: Applications

This paper deals with some applications of Markov decision models for which the linear programming method is efficient. These models are replacement models (with the optimal stopping problem as special case), separable models (including the inventory model as special case) and the multi-armed bandit model. In the companion paper Survey of linear programming for standard and nonstandard Markovian control problems. Part I: Theory, general linear programming methods are discussed. These linear programming formulations are the starting point for the efficient methods that will be derived for the special models.     

INVESTIGATION OF THE ALLOMERIZATION REACTION OF CHLOROPHYLL a: USE OF DIODE ARRAY HPLC, MASS SPECTROMETRY AND CHEMOMETRIC FACTOR ANALYSIS FOR THE DETECTION OF EARLY PRODUCTS

Abstract –The products of chlorophyll allomerization in methanol were isolated and analyzed by open column sucrose chromatography, liquid chromatography mass spectrometry (LCMS) and DAD-HPLC (diode-array high-performance liquid chromatography). Four main bands were found with molecular ions of (a) 908, (b) 938, (c) 938 and (d) 938, consistent with the structures (a) 13²-hydroxy-chlorophyll a (II), (b) and (c) Mg(II)-3¹,3²-didehydro-15¹-hydroxy-15¹-methoxy-rhodochlorin-15 acetic acid δ-lactone 15²-methyl 17³-phytyl ester and its epimer (III) and (d) Mg(II)-3¹,3²-didehydro-rhodochlorin-15-glyoxylic acid 13¹,15²-dimethyl 17³-phytyl ester (IV), evidence enhanced by UV/visible spectroscopy, chromatographic coelutions and chemometrics. Chlorophyll a was degraded both in the dark and light, under O₂ and N². DAD-HPLC of the resultant degradation mixtures were analyzed using the chemometric heuristic-evolving latent projection method for resolution. Ultraviolet/visible spectra of II and III are reproducibly extracted from the mixtures after a short degradation time, whereas III and IV are the dominant compounds after longer degradation times. Changes in relative elution order of IV using open column chromatography and reverse-phase HPLC are established. A possible allomerization pathway is proposed.     

Molecular structure and conformation of gaseous bromoacetyl chloride and bromoacetyl bromide as determined by electron diffraction

Bromoacetyl chloride and bromoacetyl bromide are studied by gas phase electron diffraction at nozzle-tip temperatures of 70°C and 77°C, respectively. Both compounds exist as mixtures of anti and gauche conformers. The mole fraction anti, with uncertainties estimated at 2σ, was found to be 0.474(0.080) for bromoacetyl chloride and 0.615(0.069) for bromoacetyl bromide. The results for the distance (r_a)and angle (∠α) parameters, with parenthesized uncertainties of 2σ including estimated uncertainty in the electron wave length and correlation effects are as follows: (1) bromoacetyl chloride, r(C-H) = 1.086(0.062) Å, r(CO) = 1.188(0.009) Å, r(C-C) = 1.519(0.018) Å, r(C-Cl) = 1.789(0.011) Å, r(C-Br) = 1.935(0.012) Å, ∠C-CO = 127.6(1.3)°, ∠C-C-Cl = 111.3(1.1)°, ∠C-C-Br = 111.0(1.5)°, ∠H-C-H = 109.5°(assumed), $\text{}\text{?}$/o (gauche torsion angle relative to 0° for the anti form) = 110.0°(assumed); (2) bromoacetyl bromide, r(C-H) =1.110(0.088) Å, r(C=O) = 1.175(0.013) Å, r(C-C) = 1.513(0.020) Å, r(CO-Br) = 1.987(0.020) Å, r(CH₂-Br) = 1.915(0.020) Å, ∠C-CO = 129.4(1.7)°, ∠CH₂-CO-Br = 110.7(1.5)°, ∠CO-CH₂-Br = 111.7(1.8)°, ∠H-C-H = 109.5°(assumed), ∠ø (gauche torsion angle relative to 0° for the anti form) = 105.0°(assumed). The structural results are discussed in connection with the structures of related molecules.