Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Solid-state structures and conformational studies of four 1,2,3,4-tetrahydroacridine Alzheimer's disease therapeutics

The solid-state structures of four 1,2,3,4-tetrahydroacridines [tacrine hydrochloride monohydrate (1), 7-methoxytacrine hydrochloride monohydrate (2), velnacrine hydrogenmaleate (3) and suronacrine hydrogenmaleate (4)] were determined from single-crystal X-ray diffraction analysis. (1): monoclinic,P2₁/n, a=8.778(1),b=8.521(1),c=17.603(2)Å, =101.34(1)°. (2): monoclinic,C2/c, a=12.326(7),b=18.050(9),c=13.822(8)Å, =113.70(4)°. (3): triclinic, ,a=7.349(2),b=9.417(3),c=12.557(4)Å, =109.62(2), =98.12(2), =101.18(2)°. (4): monoclinic,P2₁/n, a=8.513(6),b=18.74(1),c=13.401(6)Å, =91.21(5)°. FinalR factors for compounds(1)–(4) are 0.047, 0.057, 0.057, 0.11, respectively. The overall arrangement of the common aminotetrahydroacridine skeleton looks similar in all derivatives. However, whereas enantiomerization of the unsubstituted cyclohexenyl rings occurs in (1) and (2), onlyquasi-axially hydroxyl substituted diastereomers are found for (3) and (4). This is presumably due to the different propensities for hydrogen bonding of axially vs. equatorially disposed hydroxyl groups with the hydrogenmaleate anions. Empirical and semiempirical calculations were performed to examine the conformational behavior of the four compounds, bothin vacuo and in solution.     

Solid state conformational parameters in dibenzo[b,f]heteroepin drugs: Crystal structures of 3-methoxy-10-methyl-11-phenyldibenzo[b,f]thiepine and 3-allyloxy-10-ethyl-11-phenyldibenzo[b,f]oxepine

The structures of 3-methoxy-10-methyl-11-phenyldibenzo[b, f]thiepine (I) [C₂₂H₁₈OS, tetragonal,I4₁/a, witha=33.81(1),c=6.065(5)Å,Z=16] and 3-allyloxy-10-ethyl-11-phenyldibenzo[b,f]oxepine (II) [C₂₅H₂₂O₂, mono-clinic,P2₁/c,a=12.115(7),b=16.316(9),c=10.136(7)Å,=105.05(9)°,Z=4] have been determined by the symbolic addition procedure and refined by least-squares method to anR of 0.090 for 784 diffractometer-measured reflections (I) and to anR of 0.083 for 442 reflections (II). The dihedral angle between the phenyl-ring mean planes is 111.3° in (I) and 121.1° in (II), the middle seven-membered ring has the boat conformation, and the tricyclic moiety has twist and skew values of 6° and 0.42 Å in (I) and 0.3° and 0.79 Å in (II). The overall conformational characteristic for the tricyclic (6, 7, 6)-dibenzo[b,f]heteroepin derivatives have been reviewed to gain a better understanding of what requirements may be important for interaction of drugs of this class at the receptor site.     

Polycarbide nickel clusters containing interstitial Ni(eta2-C2)4 and Ni2(micro-eta2-C2)4 acetylide moieties: mimicking the supersaturated Ni-C solutions preceding the catalytic growth of CNTs with the structures of [HNi25(C2)4(CO)32]3- and [Ni22(C2)4(CO)28Cl]3-

Reaction of [Ni(6)(CO)(12)](2-) with CCl(4) in CH(2)Cl(2) gives the [HNi(25)(C(2))(4)(CO)(32)](3-) and [Ni(22)(C(2))(4)(CO)(28)Cl](3-) carbonyl clusters containing interstitial Ni(eta(2)-C(2))(4) and Ni(2)(micro-eta(2)-C(2))(4) acetylide moieties.     

Multitechnique investigation of conformational features of small molecules: the case of methyl phenyl sulfoxide

The conformational distribution of methyl phenyl sulfoxide (a molecule representative of a very important class of reagents widely used in asymmetric synthesis) has been studied in two different phases of matter (gas phase and solution) by a comprehensive approach including theoretical calculations, microwave spectroscopy, liquid crystal NMR experiments, and atomistic molecular dynamics computer simulations. The aim was to investigate the combined action of intra- and intermolecular interactions in determining the molecule's conformational equilibrium, upon which important physicochemical properties (inter alia, the chemoselectivity) significantly depend. Basically, the results converge in describing the tendency of the molecule to favor stable conformations governed by intramolecular interactions (in particular, the expected optimization between steric repulsion and conjugation of pi systems). However, significant solvent effects (whose "absolute" magnitude is actually difficult to assess, due to a certain "method-dependence" of the results) have been also detected.     

Molecular recognition of chiral conformers: a rotational study of the dimers of glycidol

Two homochiral dimers of glycidol, deriving from two different conformers, have been characterized by rotational spectroscopy in a supersonic expansion.     

Sn-centred icosahedral Rh carbonyl clusters: synthesis and structural characterization and 13C-{103Rh} HMQC NMR studies

The reaction of [Rh(7)(CO)(16)](3-) with SnCl(2).2H(2)O in a 1 : 1 molar ratio under N(2) results in the formation of the new heterometallic cluster, [Rh(12)Sn(CO)(27)](4-), in very high yield (ca. 86%). Further controlled additions of SnCl(2).2H(2)O, or solutions of HCl, or [RhCl(COD)](2), give [Rh(12)(micro-Cl)(2)Sn(CO)(23)](4-). Similarly, addition of HBr to [Rh(12)Sn(CO)(27)](4-) gives the related cluster [Rh(12)(micro-Br)(2)Sn(CO)(23)](4-). Notably, if the addition of SnCl(2).2H(2)O to [Rh(12)Sn(CO)(27)](4-) is carried out under a CO atmosphere, the reaction takes a different course and leads to the formation of the new cluster, [Rh(12)Sn(micro(3)-RhCl)(CO)(27)](4-). All the above clusters have been shown by single-crystal X-ray diffraction studies to have a metal framework based on an icosahedron, which is centred by the unique Sn atom. Their chemical reactivity and (13)C-{(103)Rh} HMQC NMR spectroscopic characterization are also reported.     

Conformational preferences of chiral molecules: free jet rotational spectrum of 1-phenyl-1-propanol

The rotational spectra of normal and O-d species of the two most stable conformers of chiral 1-phenyl-1-propanol, obtained by free jet millimetre-wave absorption spectroscopy reveal that both conformers are stabilized by a O-H[dot dot dot]pi interaction, and have the Calpha-Cbeta-bond oriented nearly perpendicular to the plane of the benzene ring. The methyl group is trans with respect to the phenyl group for the most stable conformer (T), while it is gauche with respect to the phenyl group and entgegen with respect to the hydroxyl group for the second most stable conformer (GE). The energy difference (E(GE)-E(T)) was estimated to be 50(50) cm(-1) from relative intensity measurements.     

Synthesis and X-ray structure of the [{Fe3(CO)9(micro3-O)}2H]3- trianion: dimerization of a metal carbonyl cluster via formation of an exceptionally short hydrogen bond

The synthesis, structure and characterization of the [{Fe3(CO)9(micro3-O)}2H]3- trianion in its [Cs(THF)0.33]+ and [NEt4]+ salt are reported. The title dimeric cluster has been obtained by protonation in water or in organic solvent of the [Fe3(CO)9(micro3-O)]2- dianion to the hydroxo [Fe3(CO)9(micro3-OH)]- derivative and crystallization. The solid state structure of [Cs(THF)0.33]3[{Fe3(CO)9(micro3-O)}2H] is based on ionic packing of [Cs(THF)0.33]+ cations and [{Fe3(CO)9(micro3-O)}2H]3- trianions. The fractional formula is due to the particular packing of Cs+ cations, which are at the vertices of fused cuboctahedral and trigonal antiprismatic polyhedrons. Each cuboctahedron encapsulates a [{Fe3(CO)9(micro3-O)}2H]3- trianion, whereas each trigonal antiprism encapsulates a THF molecule. The possibility that the structure of the [{Fe3(CO)9(micro3-O)}2H]3- trianion could be affected by its confinement in the cuboctahedral cage of Cs+ ions and the heavy disorder of the THF molecule urged a further structural determination of the trianion with a completely different cation. The corresponding [NEt4]3[{Fe3(CO)9(micro3-O)}2H] salt has been, therefore, prepared and structurally characterized. The [{Fe3(CO)9(micro3-O)}2H]3- trianion displays an identical structure and almost coincident molecular parameters in both salts. Its most notable feature is represented by the unique hydrogen atom symmetrically bridging the micro3-O atoms of two different [Fe3(CO)9(micro3-O)]2- molecules and displaying one of shortest O...H...O interaction so far reported in organic, inorganic and organometallic literature. The structure of [Cs(THF)]2[Fe4(CO)13], which has been obtained as a by-product of the synthesis of [Cs(THF)0.33]3[{Fe3(CO)9(micro3-O)}2H], is also briefly reported.