Stability of Semiconductor States with Insulating and Contact Boundary Conditions

We prove the existence of global smooth solutions near a given steady state of the hydrodynamic model of the semiconductors in a bounded domain with physical boundary conditions. The steady state and the doping profile are permitted to be of large variation but the initial velocity must be small. Two cases are considered. In the first one the problem is three-dimensional, the boundary conditions are insulating and the steady state velocity vanishes. In the second one, the problem is one-dimensional, the boundary is of contact type and the steady state velocity does not vanish.     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC ² norm, then a uniqueC ¹ solution to this system is shown to exist on all of spacetime.Research supported in part by NSF DMS 85-20662 and NSF DMS 84-20957     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Broadening the scope of 1,2,4-triazine synthesis by the application of microwave technology

By the application of microwave technology, a general protocol has been developed for the rapid synthesis of diverse 3,5,6-trisubstituted 1,2,4-triazines in excellent yield and purity, including many previously unknown 3-heterocyclic-1,2,4-triazines.     

Relative Lewis basicities of six AI(ORF)4- superweak anions and the structures of LiA

The relative Lewis basicities of six Al(ORF)4- ions, Al[OC(CH3)(CF3)2]4-, Al(OC(CF3)3]4-, Al(OCPh(CF3)2]4-, Al[OC[4-C6H4(tBu)](CF3)2]4-, Al(OC(Cy)(CF3)2]4-, and Al(OCPh2(CF3)]4-, have been determined by measuring their relative coordinating abilities towards Li+ in dichloromethane. The relative Li- Lewis basicities of the Al(ORF)4- ions are linearly related to the aqueous pKa values of the corresponding parent HORF fluoroalcohols. The Lewis basicity of Al[OCH(CF3)2]4- could not be measured because two of these anions can coordinate to one Li+ cation. The structures of LiAl[OCH(CF3)2]4 and [1-Et-3-Me-1,3-C3H3N2][Li[Al[OCH(CF3)2)4]2] were determined.     

The dynamics of rotational isomerism in crystals as studied by vibrational spectroscopy

Vibrational spectroscopy is uniquely capable of determining the structure and dynamics arising from the rotational degrees of freedom in molecular solids. Vibrational spectroscopy is sensitive to phenomena occurring on a time scale between the slow scale of magnetic, resonance methods and fast scale of diffraction methods; a time scale appropriate for both internal and overall rotation. Rotational motion of molecules in crystals provide examples of very simple reactions. Our understanding of the spectra of reacting molecules can thus be tested on these systems, and we conclude that Redfield equations can describe such spectra.A rich variety of motional effects are described: (1) The libration of the water of hydration in sodium perchlorate which illustrates a simple reacting system. (2) The libration of the adamantane molecule in both its ordered and disordered crystal phases which illustrates intermolecular interactions in organic crystals and the consequences of disorder. (3) The libration of the ammonium ion in crystals of ammonium salts which illustrated both change of orientational position by tunneling and the subtle orientating effects of isotopic substitution. (4) The internal rotation in n-alkane crystals which illustrates the ability to determine conformers and the relationship between the occurrence of disordered conformers and the occurrence of phase transitions.     

Carbon nanodots revised: the thermal citric acid/urea reaction

Luminescent compounds obtained from the thermal reaction of citric acid and urea have been studied and utilized in different applications in the past few years. The identified reaction products range from carbon nitrides over graphitic carbon to distinct molecular fluorophores. On the other hand, the solid, non-fluorescent reaction product produced at higher temperatures has been found to be a valuable precursor for the CO₂-laser-assisted carbonization reaction in carbon laser-patterning. This work addresses the question of structural identification of both, the fluorescent and non-fluorescent reaction products obtained in the thermal reaction of citric acid and urea. The reaction products produced during autoclave–microwave reactions in the melt were thoroughly investigated as a function of the reaction temperature and the reaction products were subsequently separated by a series of solvent extractions and column chromatography. The evolution of a green molecular fluorophore, namely HPPT, was confirmed and a full characterization study on its structure and photophysical properties was conducted. The additional blue fluorescence is attributed to oligomeric ureas, which was confirmed by complementary optical and structural characterization. These two components form strong hydrogen-bond networks which eventually react to form solid, semi-crystalline particles with a size of ∼7 nm and an elemental composition of 46% C, 22% N, and 29% O. The structural features and properties of all three main components were investigated in a comprehensive characterization study.

Products of the thermal reaction of citric acid and urea have been identified as a complex mixture of fluorophores and particles.     

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.¹ Received: 11 August 2001 Accepted: 22 February 2002