Zero distribution and division results for exponential polynomials

An exponential polynomial of order q is an entire function of the form

$$g(z) = {P_1}(z){e^{{Q_1}(z)}} + ...{P_k}(z){e^{{Q_k}(z)}},$$

where the coefficients P_j(z),Q_j(z) are polynomials in z such that

$$\max \{ deg({Q_j})\} = q.$$

It is known that the majority of the zeros of a given exponential polynomial are in domains surrounding finitely many critical rays. The shape of these domains is refined by showing that in many cases the domains can approach the critical rays asymptotically. Further, it is known that the zeros of an exponential polynomial are always of bounded multiplicity. A new sufficient condition for the majority of zeros to be simple is found. Finally, a division result for a quotient of two exponential polynomials is proved, generalizing a 1929 result by Ritt in the case q = 1 with constant coefficients. Ritt’s result is closely related to Shapiro’s conjecture that has remained open since 1958.

     

Polymer dynamics in torsion space

The large scale motion of proteins, or covalently bonded polymers in general, is governed by the dynamics of the torsion angles, with bond lengths and bond angles kept approximately constant. In the present work, the Lagrangian equations of torsion motion are derived for a general macromolecule. The dynamics is implemented numerically for a test protein, using the velocity Verlet method as the integrator. The results indicate time steps of up to about 30 fs can be used for short time (up to at least 20 ps) simulations, before the dynamics and energy start to differ significantly from results obtained with smaller time steps. For longer time simulations, up to 1000 ps, a time step of 10 fs is relatively safe. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Elliptic boundary value problems with Gaussian white noise loads

Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. The challenging cases of Neumann and Robin BVPs are considered.The main obstacle for usual variational methods is the irregularity of the load. In particular, the Neumann boundary values are not well-defined.In this work, the BVP is formulated by replacing the continuity of boundary trace mappings with measurability. Instead of variational methods alone, the novel BVP derives also from Cameron–Martin space techniques.The new BVP returns the study of irregular white noise to the study of $L^2$-loads.     

Effect of microfibrillated cellulose and fines on the drainage of kraft pulp suspension and paper strength

Different types of microfibrillated cellulose (MFC) and fines suspensions were produced, characterized, and then added to a papermaking pulp suspension. High and medium molar mass cationic polyelectrolytes were used as fixatives. The drainage behavior of the pulp suspensions with additives were evaluated against the strength properties of hand sheets made thereof. The effects of salt concentration, pH, fixative type, dosage and type of fibrillar material on drainage were examined. All the MFC and fines samples produced had clearly different properties due to their dissimilar production methods, and they also introduced specific responses on the measured drainage and paper strength. Generally, the addition of MFC decreased the drainage rate of pulp suspension and increased the strength of paper. However, it was shown that by optimum selection of materials and process conditions an enhancement of the strength properties could be achieved without simultaneously deteriorating the drainage.     

Mappings of Finite Distortion:¶Discreteness and Openness

We establish a sharp integrability condition on the partial derivatives of a mapping with L ^p -integrable distortion for some p>n? 1 to guarantee discreteness and openness. We also show that a mapping with exponentially integrable distortion and integrable Jacobian determinant is either constant or both discrete and open. We give an example demonstrating the preciseness of our criterion.     

Quantum chemical calculations on the Peterson olefination with alpha-silyl ester enolates

The reaction of stabilized Peterson reagents (alpha-silyl ester enolates) with ketones has been studied theoretically and experimentally. Enolate geometry was studied by trapping experiments and NMR spectroscopy and was found to differ markedly with the nature of the base (LiHMDS vs LDA vs KHMDS). The chelating effect of the lithium counterion was found to be critical for the reaction. For the two ketones studied, the combined weight of experimental and computational data assigns geometrical selectivity to the initial addition transition state, though in general there appears to be a fine balance between three possible choices for the rate-determining step.     

Comparison of Experimental Strategies to Study l-Type Amino Acid Transporter 1 (LAT1) Utilization by Ligands

l-Type amino acid transporter 1 (LAT1), expressed abundantly in the brain and placenta and overexpressed in several cancer cell types, has gained a lot of interest in drug research and development, as it can be utilized for brain-targeted drug delivery, as well as inhibiting the essential amino acid supply to cancer cells. The structure of LAT1 is today very well-known and the interactions of ligands at the binding site of LAT1 can be modeled and explained. However, less is known of LAT1′s life cycle within the cells. Moreover, the functionality of LAT1 can be measured by several different methods, which may vary between the laboratories and make the comparison of the results challenging. In the present study, the usefulness of indirect cis-inhibition methods and direct cellular uptake methods and their variations to interpret the interactions of LAT1-ligands were evaluated. Moreover, this study also highlights the importance of understanding the intracellular kinetics of LAT1-ligands, and how they can affect the regular function of LAT1 in critical tissues, such as the brain. Hence, it is discussed herein how the selected methodology influences the outcome and created knowledge of LAT1-utilizing compounds.     

On functions with derivatives in a Lorentz space

We establish a sharp integrability condition on the partial derivatives of a Sobolev mapping to guarantee that sets of measure zero get mapped to sets of measure zero. This condition is sharp also for continuity and differentiability almost everywhere. Received: 6 January 1999 / Revised version: 5 May 1999     

Particle number fractionalization of an atomic Fermi-Dirac gas in an optical lattice

We show that a dilute two-species gas of Fermi-Dirac alkali-metal atoms in a periodic optical lattice may exhibit fractionalization of the particle number when the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. This results in fractional eigenvalues of the spin operator with vanishing fluctuations. The fractional part can be accurately controlled by modifying the effective detuning of the electromagnetic field.