On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

Bounded speed of propagation for solutions to radiative transfer equations

The Radiative Transfer Equation is the nonlinear transport equation

Generalized solutions of a class of nuclear-space-valued stochastic evolution equations

Generalized solutions are defined for stochastic evolution equations of the formdY _t =A ^* Y _t dt + dZ _t on the nuclear triplel(R ^d ) L²(R ^d ) l(R ^d ), whereA does not mapl(R ^d ) into itself. One case which is treated in detail involvesA = –(–) ^/2 ,0 < < 2. This example arises as the Langevin equation for the fluctuation limit of a system of particles migrating according to a symmetric stable process and undergoing critical branching in a random medium.The research of D. A. Dawson was supported by the Natural Sciences and Engineering Research Council of Canada. L. G. Gorostiza's research was supported in part by CONACyT Grants PCEXCNA-040319 and 140102 G203-006, Mexico.     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.     

A comparative study of several HPLC methods for determining free amino acid profiles in honey

A study of the viability of three derivatizing reagents for obtaining amino acid profiles in honey through high performance liquid chromatography (HPLC) is presented. A method using diode array detection based on a reaction with diethyl ethoxymethylene malonate (DEMM) and two other methods using fluorescence detection based on derivatization with fluorenylmethyl chloroformate (FMOC-Cl) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) have been developed. The three methods yield detection limits close to the ppb level, but vary in relation to other analytical characteristics. The use of methyl chloroformate derivatives allows the profile to be obtained with the greatest sensitivity within a short time frame. On applying such methods to honey samples of diverse botanical origin, we observe that the proline values obtained are always lower than those found using the official spectrophotometric method, thereby underlining the advisability of using HPLC methods to reduce uncertainty in these results.     

Application of preparative high-speed counter-current chromatography for the separation of flavonoids from the leaves of Byrsonima crassa Niedenzu (IK)

The methanolic extract of the leaves of the medicinal plant Byrsonima crassa (Malpighiaceae) contain flavonoids with antioxidant activity. They were separated in a preparative scale using high-speed counter-current chromatography. The optimum solvent system used was composed of a mixture of ethyl acetate-n-propanol-water (140:8:80 (v/v/v)) and led to a successful separation between monoglucosilated flavonoids (quercetin-3-O-alpha-L-arabinoside, quercetin-3-O-beta-D-galactoside) and the biflavonoid amentoflavone in only 3.5 h. The purities of quercetin-3-O-alpha-L-arabinoside (95 mg), quercetin-3-O-beta-D-galactoside (16 mg) and the biflavonoid amentoflavone (114 mg) were all isolated at purity over 95%. Identification was performed by 1H NMR, 13C NMR and UV analyses.     

Inorganic-metalorganic hybrids based on copper(II)-monosubstituted Keggin polyanions and dinuclear copper(II)-oxalate complexes. Synthesis, X-ray structural characterization, and magnetic properties

Reaction of in situ generated copper(II)-monosubstituted Keggin polyoxometalates and copper(II)-bipyridine-oxalate complexes in the corresponding alkaline acetate buffer led to the formation of hybrid metal organic-inorganic compounds K(2)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)].14H(2)O (1), K(14)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}](2)[SiW(11)O(39)Cu(H(2)O)].55H(2)O (2), (NH(4))(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (3), and Rb(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (4). Their structures have been established by single-crystal X-ray diffraction. The main structural feature of these compounds is the presence of copper(II)-monosubstituted alpha-Keggin polyoxoanions as inorganic building blocks, on which the mu-oxalatodicopper metalorganic blocks are supported. Compound 1contains the discrete hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)](2)(-), whereas the polymeric hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}(2)](n)(4)(n)(-) gives a monodimensional character to compounds 2-4. Magnetic and EPR results are discussed with respect to the crystal structure of the compounds. DFT calculations on both the [Cu(2)(bpy)(2)(H(2)O)(4)(mu-ox)](2+) cationic complex and the metalorganic blocks have been performed in order to determine the optimized geometry and the magnetic coupling constants, respectively.