Unbiased estimators for spatial distribution functions of classical fluids

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density rho(r) in the vicinity of a fixed solute and the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.     

Convergence of set-valued mappings: Equi-outer semicontinuity

The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascolì theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is related to the outer semicontinuity of epigraphical mappings. Finally, some examples involving set-valued mappings are re-examined in terms of the concepts introduced here.Research supported in part by a grant of the National Science Foundation.     

Does the Boltzmann Principle Need a Dynamical Correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln(E) via the thermodynamic relation 1/T=S / E by additional terms of dynamical character, which are argued to correct and generalize the Boltzmann principle for small systems (here (E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker–Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the volume entropy S = k ln (E) via the thermodynamic relation above for systems of any number of degrees of freedom ((E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.     

Axial structure of oxathiane benzyl sulfonium perchlorate

It is shown that the S-benzyl substituent, in the S-benzyl sulfonium perchlorate 2 derived from Eliel's oxathiane, has an axial position in the solid state (X Ray analysis of a single crystal) as well as in solution (2D ¹H NMR), probably due to 1-3-anomeric effect between the lone-pairs of oxygen and sulfur.     

A simple and reliable stir bar sorptive extraction-liquid chromatography procedure for the determination of chlorpromazine and trifluoperazine in human serum using experimental design methodology

A sensitive and reproducible stir bar sorptive extraction and HPLC-UV detection method was used for the therapeutic drug monitoring of chlorpromazine and trifluoperazine in human serum. The separation was achieved using a C(18) column. The mobile phase consisted of methanol/sodium acetate buffer (pH 4.1; 0.1 M) (95:5, v/v) including 0.5% triethylamine. This miniaturized method can result in faster analysis, lower solvent consumption and less workload per sample while maintaining or even improving sensitivity. In the second part, stir bar sorptive extraction/HPLC-UV method was optimized by a chemometrics approach. An experimental design was therefore used to evaluate the statistically influential and/or interacting factors, among those described in the literature, and to find the best extraction and desorption conditions. Optimal sample volume of 1 mL, extraction time of 24 min at 31°C with pH 8.1 were obtained in a screening 2(5) half fractional factorial design followed by a Box-Behnken design. For the desorption conditions, a Box-Behnken design showed that the best conditions were 150 μL mobile phase for 20 min at 50°C. The optimized method was repeatable (CV<10%, linear (LOQ-500 ng/mL)), with the LOQs equal to 0.7 and 1.5 ng/mL for chlorpromazine and trifluoperazine, respectively.     

Solvent-free reaction between acenaphthoquinone, various benzils and ammonium acetate: synthesis of 9,10-diaryl-7H-benzo[d,e]imidazo[2,1-a]isoquinolin-7-ones

A simple synthesis of benzo[d,e]imidazo[2,1-a]isoquinolines is described. Heating a mixture of acenaphthoquinone, a benzil, and ammonium acetate under solvent-free conditions afforded 9,10-diaryl-7H-benzo[d,e]imidazo[2,1-a]isoquinolin-7-ones in good to excellent yields.     

Preparation of a novel sorptive stir bar based on vinylpyrrolidone‐ethylene glycol dimethacrylate monolithic polymer for the simultaneous extraction of diazepam and nordazepam from human plasma

A new monolithic coating based on vinylpyrrolidone‐ethylene glycol dimethacrylate polymer was introduced for stir bar sorptive extraction. The polymerization step was performed using different contents of monomer, cross‐linker and porogenic solvent, and the best formulation was selected. The quality of the prepared vinylpyrrolidone‐ethylene glycol dimethacrylate stir bars was satisfactory, demonstrating good repeatability within batch (relative standard deviation < 3.5%) and acceptable reproducibility between batches (relative standard deviation < 6.0%). The prepared stir bar was utilized in combination with ultrasound‐assisted liquid desorption, followed by high‐performance liquid chromatography with ultraviolet detection for the simultaneous determination of diazepam and nordazepam in human plasma samples. To optimize the extraction step, a three‐level, four‐factor, three‐block Box–Behnken design was applied. Under the optimum conditions, the analytical performance of the proposed method displayed excellent linear dynamic ranges for diazepam (36–1200 ng/mL) and nordazepam (25–1200 ng/mL), with correlation coefficients of 0.9986 and 0.9968 and detection limits of 12 and 10 ng/mL, respectively. The intra‐ and interday recovery ranged from 93 to 106%, and the relative standard deviations were less than 6%. Finally, the proposed method was successfully applied to the analysis of diazepam and nordazepam at their therapeutic levels in human plasma. The novelty of this study is the improved polarity of the stir bar coating and its application for the simultaneous extraction of diazepam and its active metabolite, nordazepam in human plasma sample. The method was more rapid than previously reported stir bar sorptive extraction techniques based on monolithic coatings, and exhibited lower detection limits in comparison with similar methods for the determination of diazepam and nordazepam in biological fluids.     

Solvent-free and three-component synthesis of 1H,6H-6λ5-[1,2]benzoxaphospholo[2,3-b][1,2]benzoxaphosphol-1-ones

A concise and facile synthesis of a new class of P,O-heterocycles is described. Knoevenagel condensation reaction of a salicylaldehyde and a cyclohexane-1,3-dione forms an α,β-unsaturated intermediate, which undergoes nucleophilic addition of a trialkyl phosphite under solvent-free conditions to afford the title compounds in good to excellent yields.     

Microwave-assisted reaction between 2-aminobenzoic acids, 2-hydroxybenzaldehydes,and arylboronic acids: a one-pot three-component synthesis of bridgehead bicyclo[4.4.0]boron heterocycles

A one-pot three-component synthesis of 6-aryl-8H-dibenzo[d,h][1,3,7,2]dioxazaborecin-8-ones is described. A mixture of 2-aminobenzoic acid, 2-hydroxybenzaldehyde, and arylboronic acid undergo a 1:1:1 addition reaction in CCl₄ under microwave irradiation to produce bridgehead bicyclo[4.4.0]boron heterocycles in excellent yields.