An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

The quest for modular nanocages: tbo-MOF as an archetype for mutual substitution, functionalization, and expansion of quadrangular pillar building blocks

A new blueprint network for the design and synthesis of porous, functional 3D metal-organic frameworks (MOFs) has been identified, namely, the tbo net. Accordingly, tbo-MOFs based on this unique (3,4)-connected net can be exclusively constructed utilizing a combination of well-known and readily targeted [M(R-BDC)](n) MOF layers [i.e., supermolecular building layers (SBLs)] based on the edge-transitive 4,4 square lattice (sql) (i.e., 2D four-building units) and a novel pillaring strategy based on four proximal isophthalate ligands from neighboring SBL membered rings (i.e., two pairs from each layer) covalently cross-linked through an organic quadrangular core (e.g., tetrasubstituted benzene). Our strategy permits the rational design and synthesis of isoreticular structures, functionalized and/or expanded, that possess extra-large nanocapsule-like cages, high porosity, and potential for gas separation and storage, among others. Thus, tbo-MOF serves as an archetypal tunable, isoreticular MOF platform for targeting desired applications.     

A quantile domain perspective on the relationships between optimal grouping, spacing and stratification problems

The relationships between two distributions having the same solutions for problems of optimal spacing selection for the asymptotically best linear unbiased estimator of a location or scale parameter or for problems of optimal stratification for estimation of a population mean are investigated. Easily checked necessary and sufficient conditions under which two distributions have identical solutions to these problems are given in terms of their quantile and density-quantile functions. As an application of these results a quantile domain analoque of a theorem due to Adatia and Chan (1981) on the equivalence of optimal grouping, spacing and stratification problems is obtained.     

On the relationship between functions with the same optimal knots in spline and piecewise polynomial approximation

The relationship between functions with the same optimal knots for L₂[0, 1] approximation by kth order splines or piecewise polynomials is investigated. It is shown that if two functions have positive continuous kth derivatives they will have the same optimal knots if and only if they differ by a polynomial of order k. An application to design selection for continuous time regression is considered and extensions to L_p approximation are also provided.     

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is "bleached"), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.     

Biological Applications of Electron Paramagnetic Resonance Viscometry Using a 13C-Labeled Trityl Spin Probe

Alterations in viscosity of biological fluids and tissues play an important role in health and diseases. It has been demonstrated that the electron paramagnetic resonance (EPR) spectrum of a ¹³C-labeled trityl spin probe (¹³C-dFT) is highly sensitive to the local viscosity of its microenvironment. In the present study, we demonstrate that X-band (9.5 GHz) EPR viscometry using ¹³C-dFT provides a simple tool to accurately measure the microviscosity of human blood in microliter volumes obtained from healthy volunteers. An application of low-field L-band (1.2 GHz) EPR with a penetration depth of 1–2 cm allowed for microviscosity measurements using ¹³C-dFT in the living tissues from isolated organs and in vivo in anesthetized mice. In summary, this study demonstrates that EPR viscometry using a ¹³C-dFT probe can be used to noninvasively and rapidly measure the microviscosity of blood and interstitial fluids in living tissues and potentially to evaluate this biophysical marker of microenvironment under various physiological and pathological conditions in preclinical and clinical settings.