Ein beliebig startender SIMPLEX-Algorithmus

Zusammenfassung Die betrachtete Aufgabe der linearen Programmierung lautet: man maximiereC _T x unter den Bedingungenx0,A xd, wobeix,c R ⁿ ,d R ^m ,A=(m×n)-Matrix. Fallsd0, muß man nach herkömmlichen Verfahren zuerst einen zulässigen Ausgangspunkt finden, um den eigentlichen SIMPLEX-Algorithmus starten zu können. Die beschriebene Methode wendet den eigentlichen SIMPLEX-Algorithmus sofort solange auf jeweils noch verletzte Restriktionend _i <0 an, bis entweder alle eingehalten sind, und optimiert schließlich die gegebene Zielfunktion, oder gibt an, daß eine zulässige Lösung der Aufgabe nicht existiert.

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Consider the linear programming problem: maximizec ^T x s.t.x0,A xd, wherex,cR _n ,d R _m ,A=(m×n)-matrix. Ifd0, the ordinary SIMPLEX-algorithm can only be started after some feasible solution has been found. The above procedure instead takes advantage of the SIMPLEX-algorithm from the very beginning by using violated constraints as objective functions until either all of them hold (which allows subsequent optimization of the original objective function) or it can be stated that there exists no feasible solution at all.

     

Intervalence transitions in the mixed-valence monocations of bis(triarylamines) linked with vinylene and phenylene-vinylene bridges

(E)-4,4'-Bis[bis(4-methoxyphenyl)amino]stilbene, 1, (E,E)-1,4-bis[4-[bis(4-methoxyphenyl)amino]styryl]benzene, 2, and two longer homologues, (E,E,E)-4,4'-bis[4-[bis(4-methoxyphenyl)amino]styryl]stilbene, 3, and (E,E,E,E)-1,4-bis(4-[4-[bis(4-methoxyphenyl)amino]styryl]styryl)benzene, 4, have been oxidized to their mono- and dications using tris(4-bromophenyl)aminium hexachloroantimonate. The intervalence charge-transfer (IVCT) band of 1(+) is narrow and asymmetric and exhibits only weak solvatochromism. Analysis of this band indicates that 1(+) is a class-III or class-II/III borderline mixed-valence species. In contrast, a broad, strongly solvatochromic IVCT band is observed for 2(+), indicating that this species is a class-II mixed-valence species. The assignment of 1(+ ) and 2(+) as symmetric class-III and unsymmetric class-II species, respectively, is also supported by AM1 calculations. Hush analysis of the IVCT bands of both 1(+) and 2(+) gives larger electronic couplings, V, than for their analogues in which the double bonds are replaced with triple bonds. The diabatic electron-transfer distance, R, in 1(+) can be estimated by comparison of the V estimated by Hush analysis and from the IVCT maximum; it is considerably less than the geometric N-N separation, a result supported by quantum-chemical estimates of R for 1(+)-4(+). In 3(+) and 4(+), the IVCT is largely obscured by an intense absorption similar to a band seen in the corresponding dications and to that observed in the monocation of a model compound, (E,E,E)-1-[bis(4-methoxyphenyl)amino]-4-[4-[4-(4-tert-butylstyryl)styryl]styryl]benzene, 5, containing only one nitrogen redox center; we attribute this band to a bridge-to-N(+) transition. The corresponding dications 1(2+)-4(2+) show a complementary trend in the coupling between redox centers: the shortest species is diamagnetic, while the dication with the longest bridge behaves as two essentially noninteracting radical centers.     

A unification of chirality measures

A general classification of chirality measures is suggested, based on a new unifying scheme. Two classes of measures - congruity and resolution type — are defined All chirality measures so far reported in the literature are found to belong to one of these two classes. At a higher level of unification, a more general construction is suggested that includes congruity and resolution measures as limiting cases. It is shown that congruity measures are nested in clusters of eight, generated by 2³ combinations of their possible choice of a reference object (chiral vs. achiral), representation form (optimized vs. factorized) and type of chiral object under consideration (discrete vs. continuous). Each of the eight cases can have an infinite number of variations depending on the choice of averaging scheme. The problem of dimensionality is discussed for congruity measures and is shown to be unresolvable only for the case of chirality measures based on the discrete metric (e.g. overlap measures).     

Polymerized bicontinuous cubic nanoparticles (cubosomes) from a reactive monoacylglycerol

Bicontinuous cubic phases of monoacylglycerides/Poloxamer 407 (PEO98PPO67PEO98)/water can be dispersed into submicron particles, which are termed "cubosomes". Technological applications of these nanoparticles may be possible, if their nonlamellar architecture can be rendered more robust. To accomplish this goal, a polymerizable heterobifunctional monoacylglycerol, 3-(2,4,13-(E,E)-tetradecatrienoyl)-sn-glycerol (1), was synthesized and combined with water to form an optically transparent gel. In the presence of Poloxamer 407 and excess water the cubic phase of 1 was dispersed by ultrasonication into 300-nm diameter nanoparticles. The polymerization of these reactive cubosomes could be initiated either by the use of a photoinitiator or with redox chemistry. The polymerized cubosomes remained stable even after the addition of excess Triton X-100, in a manner consistent with executing cross-linking in the nanostructures.     

Empirical relations between σI, σoR and taft σ* values of alkyl,acyl, benzoyl and substituted phenyl groups

The X(X) values¹ of the halogens (which resemble the Pauling electronegativities) and of some oxa substituents can be interpreted in terms of the inductive and resonance parameters σ_I and σ^o_R according to the regression equation

and η*_R=η(X)?η(R) it is found that for some substituted methyl, phenyl and benzoyl groups [σ*]^X_R=αη^X_R where α equals ?10.6 and ?10.9 for R = Me and R = Ph, CHO and PhCO respectively. Thus [σ*]^X_Rand η^x_r represent Taft σ* and [σ_I(X)?σ_oR(X)] values relative to that of the parent R group. The hydroxyl frequencies of phenol, and benzoic, acrylic, acetic and formic acids measured in dilute carbon tetrachloride solutions correlate with σ_I(X) and σ^o_R(X) according to the equations v(OH) = ?423.0 σ_I(X) + 3654.7 v(OH) = ?270.0 σ⁰_R(X) + 3586.7 where X = Ph, PhCO, CH₂=CHCO, MeCO and HCO. From these results, it is inferred that the σ* values of substituents having an α sp² hybridized carbon atom are proportional to σ⁰_R according to the equation σ*(X) = 3.97 σ⁰_R(X) + 1 New σ_I σ^o_R and σ* values of some acyi, benzoyl and substituted phenyl groups are presented.     

Propellanes. Part LXXVIII. Preparation of Several Triaza[3.3.3]propellanes and an Oxadiaza[3.3.3]propellane

3,7,10-Tribenzyl-3,7,10-triaza[3.3.3]propellane ( 4a ), 3,7-dibenzyl-10-phenyl-3,7,10-triaza[3.3.3]propellane ( 4c ), 3,7-dibenzyl-10-(p-tolyl)-3,7,10-triaza[3.3.3]propellane ( 4b ), and 3-oxa-7,10-diaza[3.3.3]propellane ( 6 ) have been prepared.     

Determination of chromophore charge states in the low pH color transition of the fluorescent protein Rtms5 via time-dependent DFT

The red fluorescent protein Rtms5^H146S displays a transition from blue (absorbance λ_max 590 nm) to yellow (absorbance λ_max 453 nm) upon titration to low pH. The pK_a of the reaction depends on the concentration of halide, offering promise for new expressible halide sensors. The protonation state involved in the low pH form of the chromophore remains, however, ambiguous. We report calculated excitation energies of different protonation states of an RFP chromophore model. These suggest that the relevant titration site is the phenoxy moiety of the chromophore, and the relevant base and conjugate acid are anionic and neutral chromophore species, respectively.     

Elucidating drug-metalloprotein interactions with tris(pyrazolyl)borate model complexes

The tetrahedral zinc complex [(Tp(Me,Ph))ZnOH] (Tp(Me,Ph) = hydrotris(5,3-methylphenylpyrazolyl)borate) was combined with acetohydroxamic acid, 3-mercapto-2-butanone, N-(methyl)mercaptoacetamide, beta-mercaptoethanol, 3-mercapto-2-propanol, and 3-mercapto-2-butanol to generate the complexes [(Tp(Me,Ph))Zn(ZBG)] (ZBG = zinc-binding group). These complexes were prepared to determine the mode of binding for three different types of thiol-derived matrix metalloproteinase (MMP) inhibitors. The solid-state structures of all six metal complexes were determined by X-ray crystallography. The structures reveal that while beta-mercaptoketones and beta-mercaptoamides bind the zinc ion in a bidentate fashion, the three beta-mercaptoalcohol compounds only demonstrate monodentate coordination via the sulfur atom. Prior to this work, no experimental data were available for the binding conformation of these types of inhibitors to the zinc active site of MMPs. The results of these model studies reveal different binding modes for these ZBGs and are useful for explaining the results of inhibition assays and in second-generation drug design. This work demonstrates the utility of model complexes as a tool for revealing drug-metalloprotein interactions.     

High charge-carrier mobility in an amorphous hexaazatrinaphthylene derivative

An isomeric mixture of a tris(pentafluorobenzyl ester) derivative of hexaazatrinaphthylene forms stable amorphous films with an effective charge-carrier mobility of 0.02 cm2/Vs, while the pure 2,8,15-isomer exhibits widely differing morphologies and carrier mobilities (0.001-0.07 cm2/Vs), depending critically on the processing conditions.