Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u _t = m ₀ u + Q(x)u + u _xx + d|u|² u ?|u|⁴ u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u ₀ with stationary localized structures which accumulate at the Maxwell point m ₀ = ?3d ²/16. When spatial forcing is included its wavelength is imprinted on u ₀ creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.     

Cotorsion pairs associated with Auslander categories

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝⁿ. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes. Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590     

Synthesis,Antiprotozoal Activity,and Cheminformatic Analysis of 2-Phenyl-2H-Indazole Derivatives

Indazole is an important scaffold in medicinal chemistry. At present, the progress on synthetic methodologies has allowed the preparation of several new indazole derivatives with interesting pharmacological properties. Particularly, the antiprotozoal activity of indazole derivatives have been recently reported. Herein, a series of 22 indazole derivatives was synthesized and studied as antiprotozoals. The 2-phenyl-2H-indazole scaffold was accessed by a one-pot procedure, which includes a combination of ultrasound synthesis under neat conditions as well as Cadogan’s cyclization. Moreover, some compounds were derivatized to have an appropriate set to provide structure-activity relationships (SAR) information. Whereas the antiprotozoal activity of six of these compounds against E. histolytica, G. intestinalis, and T. vaginalis had been previously reported, the activity of the additional 16 compounds was evaluated against these same protozoa. The biological assays revealed structural features that favor the antiprotozoal activity against the three protozoans tested, e.g., electron withdrawing groups at the 2-phenyl ring. It is important to mention that the indazole derivatives possess strong antiprotozoal activity and are also characterized by a continuous SAR.     

Capillary electrophoresis for the detection of PMP22 gene duplication: study in Mexican patients

Charcot-Marie-Tooth (CMT) disease is the most common inherited disorder of the human peripheral nerve, with an estimated overall prevalence of 17-40/10 000 [1]. The typical phenotype presents peroneal muscular atrophy and pes cavus [2]. CMT is usually divided into two large types, about two-thirds of the patients have CMT type 1 (CMT1), that affects the layer of myelin (demyelination). In type 2 (CMT2) the nerve fibers are affected (axonal). CMT diseases have autosomal dominant, autosomal recessive, and X-linked inheritance [1]. The most frequent subtype is 1A (CMT1A) with autosomal dominant transmission, secondary in most cases to a tandem duplication of a 1.5 Mb DNA fragment on chromosome 17p11.2-p12 [4-7]. In this region, the codification of the peripheral myelin protein 22 (PMP22) takes place. The severity of the disease varies among patients, even within the same family, from almost no symptoms to severe foot-drop and sensory loss. The PMP22 gene has four exons and is regulated by two promoters located toward the extreme 5'. The origin of the duplication that causes the disease is an uneven exchange of the chromatids during the meiosis. This unequal recombination occurs between two regions that limit the PMP22 gene, described as REP places of 24 kb, proximal and distal [3, 4].     

Evaluation of individual particle capillary electrophoresis experiments via quantile analysis

The number of particles in a sample heavily influences the shape of a distribution corresponding to the individual particle measurements. Selecting an adequate number of particles that prevents biases due to sample size is particularly difficult for complex biological systems in which statistical distributions are not normal. Quantile analysis is a powerful statistical technique that can rapidly compare differences between multiple distributions of individual particles. This report utilizes quantile analysis to show that the number of events detected affects the mobility distributions for rat liver and mouse liver mitochondria, sample individual particles, when analyzed via capillary electrophoresis with laser-induced fluorescence. When the mitochondrial sample is small (e.g. <78), there are not enough events to obtain statistically relevant mobility data. Adsorption to the capillary surface also significantly affects the mobility distribution at a small number of events in uncoated and dynamically coated capillaries. These adsorption effects can be overcome when the mitochondrial load on the capillary is sufficiently large (i.e. >609 and >1426 events for mouse liver on uncoated capillaries and rat liver on dynamically coated capillaries, respectively). It is anticipated that quantile analysis can be used to study other distributions of individual particles, such as nanoparticles, organelles, and biomolecules, and that distributions of these particles will also be dependent on sample size.     

Bemerkung zur Gleichheit der Aufspaltungen ΔI (zwischen den ersten beiden π-Ionisationspotentialen) und ΔE (zwischen den entsprechenden π* ← π Übergangsenergien) des Spiro[4,4]nonatetraens. Vorläufige Mitteilung

For a given molecule M, the difference ΔI between the first two vertical ionization potentials I_v,2 and I_v,2 (from MOs ψ₁ and ψ₂) and ΔE between the corresponding singlet-singlet excitation energies E₁ and E₂ (transitions ψ?₁ ←₁, ψ?₁ ψ₂) are related by ΔE = ΔI- (J_2,?1?J_1,?1) ?2(K_1,?1 ? K_2,?1), using Koopmans approximation. A simple MO model suggests that under certain conditions of symmetry and quasi-alternancy (e. g. in spiro[4,4]nonatetraene 1 ) the bracketed differences between the Coulomb- and exchange-integrals should vanish to first order, thus leading to the simple (almost) equality ΔE = ΔI. It is shown that the results from a photoelectron- and electron-spectroscopic investigation of 1 support this conclusion i.e. ΔI = 1.23 eV, ΔE = 1.19 to 1.23 eV.     

Thermophysics of alkali and related azides II. Heat capacities of potassium,rubidium, cesium,and thallium azides from 5 to 350 K

The heat capacities of potassium, rubidium, cesium, and thallium azides were determined from 5 to 350 K by adiabatic calorimetry. Although the alkali-metal azides studied in this work exhibited no thermal anomalies over the temperature range studied, thallium azide has a bifurcated anomaly with two maxima at (233.0±0.1) K and (242.04±0.02) K. The associated excess entropy was 0.90 cal_th K^?1 mol^?1. The thermal properties of the azides and the corresponding structurally similar hydrogen difluorides are nearly identical. Both have linear symmetrical anions. However, thallium azide shows a solid-solid phase transition not exhibited by thallium hydrogen difluoride. At 298.15 K the values of C_p^o, S^o, and $\text{?{G}{}^{\mathrm{o}}\text{(T)?H}{}^{\mathrm{o}}\text{(0)}}\text{T}$, respectively, are 18.38, 24.86, and 12.676 cal_th K^?1 mol^?1 for potassium azide; 19.09, 28.78, and 15.58 cal_th K^?1 mol^?1 for rubidium azide; 19.89, 32.11, and 18.17 cal_th K^?1 mol^?1 for cesium azide; and 19.26, 32.09, and 18.69 cal_th K^?1 mol^?1 for thallium azide. Heat capacities at constant volume for KN₃ were deduced from infrared and Raman data.     

Electronic States of 1,5-Cyclooctadiyne Radical Cation and of Related Systems: The electronic structure of cis-bent carbon-carbon triple bonds

The photoelectron spectra of 1,5-cyclooctadiyne ( 2 ) and of 1,6-dithiacyclodeca-3,8-diyne ( 3 ) have been recorded. The first four ( 2 ) or six ( 3 ) PE. bands have been assigned as follows; in increasing order of ionization potentials: The relative sequence and the positions of the PE. bands are explained in terms of through-bond and through-space interactions between the basis π-orbitals and σ-orbitals of appropriate symmetry behaviour. An analysis of the PE. spectroscopic data for cyclooctyne ( 1 ) and for ( 2 ) indicates that a cis-bend of the acetylene moiety by θ < 20° leads to a split in energy of the in-plane and out-of-plane basis π-orbitals which is smaller than ∽ 0.2 eV. This is in agreement with the predictions derived from semiempirical models (MINDO/2, SPINDO) and qualitative orbital arguments. However, it is shown by using orbital localization procedures, that the rationales underlying the two semiempirical models differ significantly.     

Interpretation der Absorptionsspektren der Komplexionen [Mo(CN)8]4−, [Mo(CN)8]3−, [W(CN)8]4− und [W(CN)8]3−

Zusammenfassung Die Absorptions- und Reflexionsspektren der Oktocyanokomplexe desMo(IV) undW(IV) sowie die Absorptionsspektren der Oktocyanotomplexe desMo(V) undW(V) werden mitgeteilt. Die Spektren werden unter Zugrundelegung der durch Raman- und IR-spektroskopische Untersuchungen gefordertenD _4d-Symmetrie dieser Verbindungen interpretiert. Die beobachteten Banden niedriger Intensität (log<3) werden Übergängen in einem Termsystem zugeordnet, das für die Konfigurationend ² undd ₁ und die SymmetrieD _4d berechnet worden ist. Banden hoher Intensität (log>3) werden auf Übergänge in antibindende Zustände zurückgeführt, an denen höherep-Zustände des Zentralions sowie Ligandenzustände beteiligt sind. Die erhaltenen Werte des Feldparameters stimmen mit ligandenfeldtheoretischen Erwartungen überein.

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Absorption and reflection spectra of the octacyanides ofMo(IV) andW(IV) and the absorption spectra of the octacyanides ofMo(V) andW(V) are presented. The spectra are interpreted in terms of theD _4d symmetry of the compounds supported by investigations of Raman and infrared spectra. Bands of low intensity (log<3) correspond to transitions between levels obtained in the case of the configurationsd ² andd ¹ respectively, in a field ofD _4d symmetry. Bands of high intensity (log>3) are attributed to transitions into antibonding levels in which p-orbitals of the central ion and ligand orbitals participate. The values of the field parameter obtained are in accord with ligand field theory.

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Résumé Les spectres d'absorption et de réflexion des complexes octocyanurés duMo(IV) et duW(IV) ainsi que les spectres d'absorption des mêmes complexes deMo(V) et de W(V) sont présentés. Les spectres sont interprétés en supposant la symétrieD _4d des molécules indiquée par des analyses des spectres Raman et infrarouges. Les bandes de faible intensité (log<3) sont attribuées à des transitions dans un système de niveaux, calculé pour les configurationsd ² etd ¹, respectivement, en symétrieD _4d. Des bandes de forte intensité (log>3) sont attribuées à des transitions vers des niveaux antiliants auxquels participent des fonctions élevéesp de l'ion central et des fonctions des groupes liés. Les valeurs obtenues pour le paramètre de champ sont en accord avec les prévisions de la théorie.