Statistical Inference with Fractional Brownian Motion

We give a test between two complex hypothesis; namely we test whether a fractional Brownian motion (fBm) has a linear trend against a certain non-linear trend. We study some related questions, like goodness-of-fit test and volatility estimation in these models.     

Crosslinked polystyrene with improved mechanical properties

The synthesis of some divinyl monomers—bis(vinylphenyl)ethane ( 2 ), bis(vinylbenzyloxy)hexane ( 3a ), and bis(vinylbenzyloxy)dodecane ( 3b ) is reported. Copolymers of the new monomers and styrene were evaluated as an alternative to divinylbenzene-crosslinked polymers for use as matrices and absorbents. The mechanical properties and the amount of residual double bonds in the copolymers were compared. It was found that the new copolymers, unlike the divinylbenzene-crosslinked polymers, retained their mechanical strength even at high crosslinking degrees. Stress at break values of 79, 68, and 18 N/mm² were found for the polymers crosslinked with 20 mol % of 3a, 2 , and divinylbenzene; 5, 25 and 45% of the divinyl units in these polymers were left as pendant double bonds. Porous styrene– 2 copolymers were synthesized and shown to have lower surface areas than the corresponding divinylbenzene-crosslinked polymers. The pore size distribution showed that this was due to the absence of the smallest pores which are found in the divinylbenzene-crosslinked polymers in between heavily crosslinked nodules. © 1993 John Wiley & Sons, Inc.     

Indolizine derivatives. IX. Preparation of 1-acylpyrrolo[2,1,5-cd]indolizines via cycloaddition of 3-acyloxyindolizines to active ethylenes and acetylenes

3-Indolizinyl acetates and propionates 4 react with ethylenic and acetylenic ketones or carboxylic esters to give 1-acylpyrrolo[2,1,5-cd]indolizines 5-12 in excellent yields.     

Cyclohexanone Dimethyl Acetals: A 13C NMR, Thermodynamic, and Ab Initio Study

The spatial structures of a number of mono- and disubstituted 1,1-dimethoxycyclohexanes (cyclohexanone dimethyl acetals) were studied by ¹³C NMR spectroscopy. In the monosubstituted acetals, substituents (Me, Et, i-Pr, and MeO) on C-2 are axially oriented, contrary to their normal, equatorial orientation on C-3 and C-4. Besides the spectroscopic study, the relative thermodynamic stabilities of the cis-trans isomers of a few 2,X-dialkyl (X = 3, 4, 5, or 6) derivatives of the parent cyclohexanone dimethyl acetal were determined by acid-catalyzed chemical equilibration in MeOH solution. In the most stable isomeric form, the 2-substituent is axial and the other equatorial. In the less stable isomer, both substituents are equatorial, excluding the cis-2,6-dimethyl derivative, where the ¹³C NMR shift data point to a predominance of the diaxial form. In general, the enthalpy difference between the isomeric forms is ca. 9 kJ mol^–1, while the entropy term favors the less stable isomer by 4 to 16 J K^–1 mol^–1. In the 2,6-dimethyl derivatives, however, the trans form is favored by only 0.8 kJ mol^–1 in G _m at 298.15 K. The main findings of the experimental work are in good agreement with ab initio calculations.     

Relative thermodynamic stabilities of 2-substituted 4-methylene-1,3-dioxolanes and 4-methyl-1,3-dioxoles

The relative thermodynamic stabilities of 24 pairs of carbon-carbon double-bondexo-endo isomeric 2-substituted 4-methylene-1,3-dioxolanes (a) and 4-methyl-1,3-dioxoles (b) have been determined by base-catalyzed chemical equilibration in DMSO solution. In all cases, theendo isomer (b) is the favored species at thermodynamic equilibrium. A single alkyl substitutent on C-2 gives only a negligible contribution to the relative stability of the isomeric forms, but the presence of two alkyl groups on C-2 increases the relative stability of theendo isomer by 2–3 kL mol^–1. A still higher effect in favor of theendo isomer is produced by introduction of a single alkoxy group on C-2; this effect is further slightly accentuated by 2,2-dialkoxy substitution at C-2. The origin of the favorable effect of 2-alkoxy substitution on the relative stability of theendo isomer is not clear, but it seems to arise from an unexpected stability of theendo isomer rather than from an enhanced destabilization of theexo form.     

IR Study of p–π Conjugation in 2-Substituted 4-Methylene-1,3-dioxolanes and 4-Methyl-1,3-dioxoles

Selected group frequencies of the IR spectra of a number of 2-substituted 4-methylene-1,3-dioxolanes (a) and their endocyclic isomers, 2-substituted 4-methyl-1,3-dioxoles (b), have been studied to establish their usefulness as a measure of the strength of p– conjugation in the O—C=C moieties of the title compounds. In the exo compounds (a), the C=C stretching frequencies C=C and the in-phase, out-of-plane bending (wagging) frequencies CH₂ w of the =CH₂ group were found to be linearly related, besides to each other, also to the electron-donating character of the substituents and the ¹³C NMR chemical shift of the C atom of the exocyclic CH₂ group. This suggests that the two IR group frequencies of the exo isomers are linearly related to the strength of p– conjugation in the O—C=C moiety. The C=C stretching absorption of the exo compounds in the 1600–1700 cm^–1 region appeared as a doublet, shown to arise from Fermi resonance of the C=C fundamental with the CH₂ w overtone. The C=C frequencies of the endo compounds support some previous findings of an unexpected strength of p– conjugation in the 2-alkoxy derivatives. Finally, DFT calculations at the B3LYP/6-31G* level of theory are shown to give accurate predictions of the effect of 2-substituents on the group frequencies.     

TEM Imaging of Mass-selected Polymer Molecules

Polyethylene glycol (PEG) molecules with masses below 1300amu are electrosprayed (ES) from solution, mobility-selected at high resolution in a differential mobility analyzer (DMA), collected on a grid and imaged by transmission electron microscopy (ES–DMA–TEM). The DMA resolves individual n-mers, and selects only one out of the many present in the original sample. Ion identity is established from parallel mass spectra (ES-MS). The images reveal spherical particles 1.46nm in diameter, in good agreement with the known ion mass and bulk density. The DMA-selection technique opens new paths for the study of very small particles.     

Relative Thermodynamic Stabilities of Isomeric Vinyl Ethers Derived from 2-Acetyland 2-Isobutyryltetrahydrofurans. An Experimental and DFT Study

The relative thermodynamic stabilities of four isomeric vinyl ethers obtained by acid-catalyzed cleavage of MeOH from the dimethyl acetals of both 2-acetyltetrahydrofuran and 2-isobutyryltetrahydrofuran have been determined by chemical equilibration in cyclohexane solution. In addition, the structures and relative energies of many of these compounds have also been studied theoretically by DFT calculations. In each series of compounds, the endocyclic isomers, 5-(1-methoxyethyl)-2,3-dihydrofuran and 5-(1-methoxy-2-methylpropyl)-2,3-dihydrofuran, respectively, show the highest thermodynamic stabilities. This is particularly prominent for the vinyl ethers derived from 2-isobutyryltetrahydrofuran in which the equilibrium mixture consists of 90% of the endocyclic isomer at room temperature. The geometrical (exocyclic) isomers of the latter series of compounds show unexpected relative thermodynamic stabilities, but on the basis of the geometry-optimized structures provided by the DFT calculations, a reasonable explanation can be found.     

Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data

The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity.     

Small molecule antagonists of cell-surface heparan sulfate and heparin–protein interactions

Surfen, bis-2-methyl-4-amino-quinolyl-6-carbamide, was previously reported as a small molecule antagonist of heparan sulfate (HS), a key cell-surface glycosaminoglycan found on all mammalian cells. To generate structure–activity relationships, a series of rationally designed surfen analogs was synthesized, where its dimeric structure, exocyclic amines, and urea linker region were modified to probe the role of each moiety in recognizing HS. An in vitro assay monitoring inhibition of fibroblast growth factor 2 binding to wild-type CHO cells was utilized to quantify interactions with cell surface HS. The dimeric molecular structure of surfen and its aminoquinoline ring systems was essential for its interaction with HS, and certain dimeric analogs displayed higher inhibitory potency than surfen and were also shown to block downstream FGF signaling in mouse embryonic fibroblast cells. These molecules were also able to antagonize other HS–protein interactions including the binding of soluble RAGE to HS. Importantly, selected molecules were shown to neutralize heparin and other heparinoids, including the synthetic pentasaccharide fondaparinux, in a factor Xa chromogenic assay and in vivo in mice. These results suggest that small molecule antagonists of heparan sulfate and heparin can be of therapeutic potential for the treatment of disorders involving glycosaminoglycan–protein interactions.