Half-range completeness for the Fokker-Planck equation

Half-range completeness theorems are proved for eigenfunctions associated to the one-dimensional Fokker-Planck equation in a semi-infinite medium. Existence and uniqueness results for perfectly absorbing, partially absorbing, and purely specularly reflecting boundary conditions are deduced for the stationary and time-dependent problems. Similar results are obtained for a slab geometry.     

STABLE PERIODIC BEHAVIOR IN PIONEER-CLIMAX COMPETING SPECIES MODELS WITH CONSTANT RATE FORCING

Two-dimensional pioneer-climax models of competing species differential equations are studied where the per capita growth rates are functions of weighted densities of the populations. The per capita growth rate of the pioneer species is monotonically decreasing whereas the per capita growth rate of the climax species is a one-humped function of the total weighted density. Constant rate forcing is introduced into the model representing stocking or harvesting. General formulas are calculated for determining the stability of the periodic orbit arising from a Hopf bifurcation.     

Parametric integer linear programming: A synthesis of branch and bound with cutting planes

A branch and bound algorithm is designed to solve the general integer linear programming problem with parametric right-hand sides. The right-hand sides have the form b + θd where b and d are comformable vectors, d consists of nonnegative constants, and θ varies from zero to one.The method consists of first determining all possible right-hand side integer constants and appending this set of integer constants to the initial tableau to form an expanded problem with a finite number of family members. The implicit enumeration method gives a lower bound on the integer solutions. The branch and bound method is used with fathoming tests which allow one family member possibly to fathom other family members. A cutting plane option applies a finite number of cuts to each node before branching. In addition, the cutting plane method is invoked whenever some members are feasible at a node and others are infeasible. The branching and cutting process is repeated until the entire family of problem has been solved.     

A LEED study of adsorbed neon on graphite

Neon monolayers on graphite have been investigated by high resolution LEED in the range 14.5 < T < 7.5 K and 10^?8 < p < 10^?4 Torr. The fluid-solid transition line has the form ln$\text{(}\text{p}\text{Torr}\text{)= ?}\text{A}\text{T + B}\text{,}\text{with}\text{A = 740 ± 45}\text{K and}\text{B = 31.0 ± 2.8}$. The solid is an incommensurate rotated phase whose lattice parameter decreases and rotation angle increases away from the transition line. Comparison is made with other thermodynamic and diffraction studies, and a preliminary phase diagram is constructed. Extrapolation of these data to higher temperatures and pressure suggests that this rotated solid monolayer is stable up to 23–25 K (P = 3?10 Torr) at coverage x = 1, and is stable over the range 0.88 < x < 1.0 at T = 16 K (2 × 10^?7 < p 1.5 × 10^?2 Torr). Extrapolation to lower temperatures gives the 2D triple point pressure in the range p = (0.3?3) × 10^?10 Torr. The steep slope of the fluid-solid transition line is consistent with the fluid phase having a high density (x?0.80) in the temperature range studied.     

A minimax problem for semilinear nonlocal competitive systems

A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.This research has been partially sponsored by DARPA under Contract No. 1868-A037-A1 with Martin Marietta Energy Systems, Inc., under Contract No. DE-AC05-84OR21400 with U.S. Department of Energy. S. Lenhart's work was also partially supported by an NSF grant.     

Kinetic selectivity in the N-alkylation of 2-pyridyl porphyrins: a facile approach to the alphaalphabetabeta scaffold

meso-Tetrakis(2-pyridyl)-porphyrin (2-PyP) was tetra-N-alkylated with three different alpha-bromoacetamides to generate a series of water-soluble N-alkylpyridinium porphyrins (1-3). The product mixtures showed a marked preference for the formation of the alphaalphabetabeta atropisomer. With alpha-bromo-N-n-butylacetamide, the corresponding alphaalphabetabeta 2-tetrakis (N-n-butylacetamido)-pyridyl porphyrin (2-TnBuPyP, 3) was obtained in 69% isolated yield in a single step. Prolonged heating lead to equilibration of the rotational isomers for the less bulky alkyl groups, indicating that the observed preference is a kinetic effect. The intermediate products for the N-bornyl case were identified by LC/ESI-MS to deduce an explanation for the observed nonstatistical selectivity.     

Solid-state NMR evidence for a protonation switch in the binding pocket of the H1 receptor upon binding of the agonist histamine

G protein coupled receptors (GPCRs) represent a major superfamily of transmembrane receptor proteins that are crucial in cellular signaling and are major pharmacological targets. While the activity of GPCRs can be modulated by agonist binding, the mechanisms that link agonist binding to G protein coupling are poorly understood. Here we present a method to accurately examine the activity of ligands in their bound state, even at low affinity, by solid-state NMR dipolar correlation spectroscopy and confront this method with the human H1 receptor. The analysis reveals two different charge states of the bound agonist, dicationic with a charged imidazole ring and monocationic with a neutral imidazole ring, with the same overall conformation. The combination of charge difference and pronounced heterogeneity agrees with converging evidence that the active and inactive states of the GPCR represent a dynamic equilibrium of substates and that proton transfer between agonist and protein side chains can shift this equilibrium by stabilizing the active receptor population relative to the inactive one. In fact, the data suggest a global functional analogy between H1 receptor activation and the meta I/meta II charge/discharge equilibrium in rhodopsin (GPCR). This corroborates current ideas on unifying principles in GPCR structure and function.