Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.     

Polyselenide mit langkettigen Tetraalkylammoniumionen Die Kristallstruktur von Trimethyl-tetradecyl-ammonium-hexaselenid

Polyselenides with Long-chain Tetraalkylammonium Ions. Crystal Structure of Trimethyltetradecyl-ammonium Hexaselenide Na₂Se₂ and Na₂Se react with various tetraalkylammonium halides in ethanol and in presence of grey selenium and catalytic quantities of iodine forming different polyselenides Se_n^2? (n = 3, 5—9). In the solutions equilibria of polyselenides seem to occur; cooling of saturated solutions causes crystallization of polyselenides with a composition depending on the cation. Tri- and pentaselenide are dark green. The higher members form black crystals, all compounds are sensitive to oxygen. The i.r. spectra are reported. [(CH₃)₃N(CH₂)₁₃CH₃]₂Se₆ is characterized by a crystallographic structure determination with X-ray data: space group P2₁2₁2, Z = 4, a = 5043, b = 734.2, c = 600.3 pm (986 observed independent reflexions. R = 0.072). The compound consists of trimethyl tetradecylammonium ions and angular Se₆^2? chains of symmetry C₂ with Se? Se bond lengths of 227 and 235 pm.     

Synthesis of Some Novel 2‐Anilinothiophene, 2,3′‐Bithienyl and Thienylthiopyridine Derivatives Resistance to Penicillium Digitatum Effect the Fruit

Reaction of benzotriazol‐1‐yl acetone 1 with phenyl isothiocyanate followed with α‐chloroacetone or ethyl‐α‐chloroacetate afforded 2‐anilinothiophenes 3 or 4 , respectively. Treatment of 3 with malononitrile at different reaction conditions afforded 6 or 7 . Reaction of 1 with CS₂ in DMF and phenacylbromide afforded S‐alkylated thiophene 10 . Reactions of the latter compound with different active methylene nitriles afforded thienylthiopyridine derivatives 14 and 15 . Condensation of 10 with hydrazine hydrate afforded hydrazon derivative 16 . Reaction of thiophene 17 with formamide in DMF afforded 19 which converted to N‐thienylpyrimidine 20 when treated with malononitrile. The structure of the newly synthesized compounds has been established on the basis of their analytical and spectral data. The compounds were also investigated for antibacterial and antifungal activities.     

Synthesis of 1,2,4-Triazol-3-ylmethyl-, 1,3,4-Oxa-, and -Thiadiazol-2-ylmethyl-1H-[1,2,3]-triazolo[4,5-d]pyrimidinediones

1-Carbethoxymethyl-4,6-dimethyl-1H-[1,2,3]triazolo[4,5-d]pyrimidine-5,7(4H,6H)-dione was synthesized and treated with hydrazine hydrate to give the corresponding hydrazide. The latter hydrazide was treated either with phenylisothiocyanate or with carbon disulfide/alc. KOH to afford the corresponding thiosemicarbazide and oxadiazole derivatives. Alkylation of 2-mercapto-1,3,4-oxadiazole with dimethyl sulfate or ethyl chloroacetate gave the corresponding 2-methylthio-, and 2-ethylthioglycolate derivatives. Formation of 1,3,4-thiadiazole, 5-mercapto-1,2,4-triazole, and 1,3,4-oxadiazole were carried out by treating of the latter thiosemicarbazide with conc. H₂SO₄, NaOH/HCl, and HgO. Treating of 5-mercapto-1,2,4-triazole with ethyl chloroacetate afforded the thioglycolate ester. Hydrolysis of the latter with hydrazine hydrate afforded the hydrazide derivatives. Condensation of these hydrazides with monosaccharide aldoses gave the corresponding sugar hydrazones. The novel compounds were tested for antiviral activity against hepatitis B virus and showed moderate activities.     

Enhancement of selectivity and resolution in the enantioseparation of uncharged compounds using mixtures of oppositely charged cyclodextrins in capillary electrophoresis

The enantiomeric separation of some nonsteroidal anti-inflammatory drugs (NSAIDs) was investigated in capillary electrophoresis (CE) using dual systems with mixtures of charged cyclodextrin (CD) derivatives. A significant enhancement of selectivity and resolution could be achieved in the enantioseparation of these analytes in their uncharged form by the simultaneous addition of two oppositely charged CD derivatives to the background electrolyte. The combination of the single-isomer cationic CD, permethyl-6-monoamino-6-monodeoxy-beta-CD (PMMAbetaCD) and the single-isomer polyanionic CD, heptakis-6-sulfato-beta-cyclodextrin (HSbetaCD) in a pH 2.5 phosphoric acid-triethanolamine buffer, was designed and employed for the enantioseparation of profens. The improvement in selectivity and resolution can be attributed to the fact that the two CDs, which lead to independent and enantioselective complexation with the analyte enantiomers, have not only opposite effects on the electrophoretic mobility of these compounds but also opposite affinity patterns towards the enantiomers of these compounds. Binding constants for these enantiomers with each CD were determined using linear regression approach, in order to be able to predict the effect of the concentrations of the two CDs on enantiomeric selectivity and resolution in such dual systems.     

Nickel(II) complexes of 3-acetyl-4,5-dihydro-1,2,4-triazole hydrazones

3-Acetyl-1,2,4-triazole hydrazones (3b,c) and methylhydrazone (4d) were prepared by reacting triazoles (1b–d) with an excess of hydrazines at room temperature. Square planar nickel(II) complexes (8b,c) of (3b,c) were obtained from their reaction with Ni(OAc)₂ in a 2:1 mol ratio in EtOH at room temperature. The spectral data suggest structures (8b,c) for the obtained complexes, which result from ring opening of the triazole ring followed by recyclization to give the 5-arylhydrazono-2,3-dihydro-4H-1,2,4-triazine ligand (7b,c). The reaction of triazole methylhydrazone (4d) with Ni(OAc)₂ in EtOH resulted, however, in the formation of the starting triazole (1d). All new compounds were characterized by elemental analysis, i.r., ¹H-n.m.r. ¹³C-n.m.r. and hrms.     

Super spline spaces of smoothnessr and degreed≥3r+2

The problem of computing the dimension of spaces of splines whose elements are piecewise polynomials of degreed withr continuous derivatives globally has attracted a great deal of attention recently. We contribute to this theory by obtaining dimension formulae for certain spaces of super splines, including the case where varying amounts of additional smoothness is enforced at each vertex. We also explicitly construct minimally supported bases for the spaces. The main tool is the Bernstein-Bézier method.Communicated by Klaus Höllig.     

Indirect atomic absorption and atomic emission spectrometric determination of antazoline,hydralazine and amiloride hydrochlorides and quinine sulphate

Ion-association complexes of antazoline HCl [I], hydralazine HCl [II], amiloride HCl [III] and quinine sulphate [IV] with [Co(SCN)₄]^2– and [Co(NO₂)₆]^3– were precipitated and the excess unreacted cobalt complex was determined. A new method using atomic emission and atomic absorption spectrometry for the determination of the above drugs in pure solutions and pharmaceutical preparations is given. The drugs can be determined in the ranges 0.3–3.0, 0.19–1.96, 0.3–3.0, and 0.78–7.82 mg/25 ml solutions of I, II, III, and IV, respectively, with mean relative standard deviations of 0.65–2.03 % and recovery values of 95.76–101.2% indicating high precision and accuracy.     

Synergistic effects of ion-pairing in the enantiomeric separation of basic compounds with cyclodextrin derivatives in nonaqueous capillary electrophoresis

The enantiomeric separation of various kinds of basic pharmaceuticals has been investigated in nonaqueous capillary electrophoresis (NACE) systems using an ion-pairing reagent in combination with cyclodextrins (CDs). The simultaneous addition to the methanolic background electrolyte (BGE) of (+)-S-camphorsulfonate or alkanesulfonates and an anionic beta-cyclodextrin derivative, heptakis(2,3-dimethyl-6-sulfato)-beta-cyclodextrin (HDMS-beta-CD), led to partial or complete enantioresolution in most cases. In the absence of ion-pairing reagent, the enantiomeric resolution obtained with this CD derivative was most often completely lost or strongly reduced, indicating the important role of ion-pairing in the chiral recognition mechanism in these NACE systems. The influence of the nature and concentration of the counterion and the anionic CD derivative on the enantioseparation of basic compounds was studied. Synergistic effects between these two kinds of charged additives were clearly observed.