Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part II

(Accepted July 23, 1996)     

Distinguishing sceneries by observing the scenery along a random walk path

LetG be an infinite connected graph with vertex setV. Ascenery onG is a map ξ :V → 0, 1 (equivalently, an assignment of zeroes and ones to the vertices ofG). LetS _{n n≥0} be a simple random walk onG, starting at some distinguished vertex v₀. Now let ξ and η be twoknown sceneries and assume that we observe one of the two sequences ξ(S _n) _n≥0 or {η(S _n)} _n≥0 but we do not know which of the two sequences is observed. Can we decide, with a zero probability of error, which of the two sequences is observed? We show that ifG = Z orG = Z², then the answer is “yes” for each fixed ξ and “almost all” η. We also give some examples of graphsG for which almost all pairs (ξ, η) are not distinguishable, and discuss some variants of this problem.     

Method of evaluation of the bitterness of clarithromycin dry syrup

The degree of bitterness of clarithromycin (CAM) dry syrup was evaluated using several methods. Using the inversion method, shaking method, and paddle method, a reasonable correlation between the bitter taste and the amount dissolved was not observed. A mini-column with inner diameter of 0.76 cm and height of 5 cm packed with CAM dry syrup was used for the release test. The release rate of CAM in test solution, which passed through the mini-column, was then measured to evaluate bitterness. The release rate of CAM in the release test using the mini-column correlated well with the results of a sensory test for the bitterness of CAM dry syrup. The dissolution rate constant, defined as the percentage of CAM dissolved from the unit void surface multiplied by the void volume, was inversely proportional to the linear velocity of the test solution. The critical factors affecting evaluation of bitterness were the void volume of the column and linear velocity of the test solution. The optimum linear velocity and void volume were 0.048-0.021 cm/min and 0.27-0.12 cm3, respectively. In addition, the threshold of bitterness of CAM dry syrup was defined as the concentration at which half of the volunteers recognized bitterness in the sensory test. This threshold was found to be 135 microg/ml using the mini-column.     

Toward a realistic description of NO(x) storage in BaO: the aspect of BaCO3

NO(x) storage over hexagonal BaCO3(110) is investigated using first-principles calculations. Special focus is put on the importance of surface decarbonation. Upon decarbonation, supported BaO quasi-molecules are formed and a small drive toward (BaO)n cluster formation is predicted. Introduction of NO2 makes the decarbonation energetically relevant, while forming NO2-BaO-NO2 units, on the decarbonated surface. With this configuration, it is possible to replace all surface carbonates with nitrites and nitrates, forming a BaCO3 supported BaNO3NO2 overlayer. Thermodynamic considerations are employed to elaborate on the thermal stability of the formed NO(x) overlayers.     

Stereoselective Access to Fully Substituted Aldehyde‐Derived Silyl Enol Ethers by Iridium‐Catalyzed Alkene Isomerization

An in situ generated cationic Ir‐catalyst isomerizes simple allylic silyl ethers into valuable, fully substituted aldehyde‐derived silyl enol ethers. Importantly, by judicious choice of substrate, either of the two possible stereoisomers of a given enolate derivative is accessible with complete stereoselectivity. One‐pot isomerization‐aldol and isomerization‐allylation processes illustrate the synthetic utility of this method.     

Formulation design of an oral, fast-disintegrating dosage form containing taste-masked particles of famotidine

A fast-disintegrating dosage form has been developed as a user-friendly formulation that disintegrates in the mouth immediately. Patients can take it without water like a liquid formulation. In this study famotidine taste-masking technology was applied to the new fast-disintegrating tablet in an attempt to produce a novel, taste-masked, fast-disintegrating tablet. Partial granulation was found to be an effective and practical way to address content uniformity, however, oral disintegration time tended to become longer as content uniformity improved. The disintegration time was improved considerably by controlling ambient humidity during the compression process (>50% RH). Furthermore, since the new fast-disintegrating technology made it possible to use low compression force, there was no change in the structure or dissolution rate of the taste-masked particles after compression. Therefore, this system can produce a taste-masked fast-disintegrating tablet with satisfactory attributes.     

The structure of ions and zwitterionic lipids regulates the charge of dipolar membranes

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ～10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.     

Exponential Clogging Time for a One Dimensional DLA

In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187–223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686–5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.