Nonlinear optimal control of population systems: applications in ecosystems

This article investigates the chaotic Lotka–Volterra system as an optimal nonlinear design problem for biological pest control strategies. In the biological control strategy, natural enemies are introduced such that the pest density is stabilized below the economic injury level, and the population of natural enemies remains sufficiently high to control the pests. Applying dynamic programming, this problem was reduced to the Hamilton–Jacobi–Bellman equation. The functions satisfying the reduced equation were obtained among the correspondent Lyapunov functions of the considered Lotka–Volterra system. A closed-form optimal feedback control law was derived. The effectiveness of the method is verified by numerical simulations of biological pest control. The biological implications of these results are also discussed.     

Experimental optical diabolos

The canonical point singularity of elliptically polarized light is an isolated point of circular polarization, a C point. As one recedes from such a point the surrounding polarization figures evolve into ellipses characterized by a major axis of length a, a minor axis of length b, and an azimuthal orientational angle alpha: at the C point itself, alpha is singular (undefined) and a and b are degenerate. The profound effects of the singularity in alpha on the orientation of the ellipses surrounding the C point have been extensively studied both theoretically and experimentally for over two decades. The equally profound effects of the degeneracy of a and b on the evolving shapes of the surrounding ellipses have only been described theoretically. As one recedes from a C point, a and b generate a surface that locally takes the form of a double cone (i.e., a diabolo). Contour lines of constant a and b are the classic conic sections, ellipses or hyperbolas depending on the shape of the diabolo and its orientation relative to the direction of propagation. We present measured contour maps, surfaces, cones, and diabolos of a and b for a random ellipse field (speckle pattern).     

There is no low maximal d. c. e. degree – Corrigendum

We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Signs of proximate 31P, 19F and 19F, 19F spin–spin coupling constants in 2-trifluoromethylphenyldifluorophosphine

In 2-trifluoromethylphenyldifluorophosphine the proximate couplings ⁴J(¹⁹F³¹P) and ⁵J(¹⁹F¹⁹F) are + 68.3 and + 8.3 Hz, respectively. ¹J(¹³C³¹P) is ?57.0 Hz, ²J(¹³C-1, ¹⁰F) is + 9.9 Hz and ²J(¹³C-6, ¹³C-6, ³¹P) is + 10.1 Hz. The trifluoromethyl substituent induces substantial changes in some coupling constants, particularly those between the ³¹P and ring ¹³C nuclei.     

Quadratic helicities and the energy of magnetic fields

Two new nonlocal asymptotic invariants of magnetic fields frozen into a finite domain filled with an ideal liquid conducting medium are introduced. The velocity of variation of the invariants in a nonideal medium is estimated for magnetic fields described by the induction equation. The invariants are used to study the spectral characteristics of magnetic fields.     

Signature OH absorption spectrum from cluster models of solvation: a solvent-to-solute charge transfer state

Ab initio electronic structure theory calculations on cluster models support the characterization of the signature absorption spectrum of a solvated hydroxyl OH radical as a solvent-to-solute charge transfer state modulated by the hydrogen-bonding environment. Vertical excited states in OH(H2O)n clusters (n = 0-7, 16) calculated at the TDDFT level of theory (with companion calculations at the EOM-CCSD level of theory for n 相似文献   

Nonregular structure-property relationships for inclusion parameters of tert-butylcalix[5]arene

The effect of macrocycle size on the structure-property relationships was studied for inclusion compounds of tert-butylcalix[n]arenes (n=4,5) with volatile organic guests having various molecular size and group composition. Vapor-sorption isotherms, guest-inclusion stoichiometry and Gibbs energy, thermostability parameters and decomposition enthalpies were determined for host-guest compounds (clathrates) obtained using saturation of solid calixarene powder with guest vapor. The increase of the host macrocycle in the studied calixarene pair changes the observed structure-property relationship from the guest-binding selectivity mostly seen in inclusion Gibbs energy to the high sensitivity for guest structure in inclusion stoichiometry. The host with the larger macrocycle has more clathrates with stepwise formation and decomposition. Specific types of guest binding with solid hosts are discussed.     

Synthesis and characterization of Li(I)-M(II) (M = Co, Ni) heterometallic complexes as molecular precursors for LiMO2

Lithium-containing heterometallic complexes with cobalt (Li₂Co₂(Piv)₆(2,4-Lut)₂ (2, Piv is the pivalate anion) and Li₂Co₂(O₂CCH₂Bu^t)₆(2,4-Lut)₂ (3)) and with nickel (Li₂Ni₂(Piv)₆(DME)₂ (4) and Li₂Ni₂(Piv)₆(2,2′-bpy)₂ (5)) were synthesized. The structures of the complexes were established by X-ray diffraction. The magnetic properties of complexes 2 and 4 were studied. The thermal behavior of compounds 2, 3, and 5 was investigated. It was shown that the compounds under study can be used as molecular precursors for the synthesis of lithium cobaltate and nickelate.     

The catalytic mechanism of an aspartic proteinase explored with neutron and X-ray diffraction

Hydrogen atoms play key roles in enzyme mechanism, but as this study shows, even high-quality X-ray data to a resolution of 1 A cannot directly visualize them. Neutron diffraction, however, can locate deuterium atoms even at resolutions around 2 A. Both neutron and X-ray diffraction data have been used to investigate the transition state of the aspartic proteinase endothiapepsin. The different techniques reveal a different part of the story, revealing the clearest picture yet of the catalytic mechanism by which the enzyme operates. Room temperature neutron and X-ray diffraction data were used in a newly developed joint refinement software package to visualize deuterium atoms within the active site of the enzyme when a gem-diol transition state analogue inhibitor is bound at the active site. These data were also used to estimate their individual occupancy, while analysis of the differences between the bond lengths of the catalytic aspartates was performed using atomic resolution X-ray data. The two methods are in agreement on the protonation state of the active site with a transition state analogue inhibitor bound confirming the catalytic mechanism at which the enzyme operates.