Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Detecting organic vapors using a conductometric sensor prepared from Ardel®D-100 and graphite

The composites of graphite with Ardel^?D-100 which is a trademark of a polyester of bisphenol-A with terephthalic and isophthalic acid were used as a sensing material in a conductometric vapor sensor. The magnitudes of responses are increased in the order of benzene, isobutyl acetate, isoamyl acetate, ethyl benzene and chloro benzene. This suggests that Ardel^?D-100 can be used as a sensing material for chlorobenzene, ethyl benzene and isoamyl acetate. On the other hand, specific retention volumes of the sensed vapors on Ardel^?D-100 coated on graphite were determined by inverse gas chromatography at temperatures between 200 and 260 °C. The distribution coefficient, K _s of the vapors between stationary and mobile phases in the column was obtained. It was revealed for the first time that the logarithm of K _s of the solvents varies almost linearly with their responses based on conductometric resistance of the sensing polymer composite. Subsequently, the study suggests that gas chromatographic retention data can be used in prediction of the conductometric responses of a polymeric sensor to vapors. Correspondence: Ferdane Karaman, Department of Chemistry, Yildiz Technical University, 34220 Istanbul-Esenler, Turkey     

Synthesis of pyrazoles via electrophilic cyclization

Electrophilic cyclizations of α,β-alkynic hydrazones by molecular iodine were investigated for the synthesis of 4-iodopyrazoles. α,β-Alkynic hydrazones were readily prepared by the reactions of hydrazines with propargyl aldehydes and ketones. When treated with molecular iodine in the presence of sodium bicarbonate, α,β-alkynic hydrazones underwent electrophilic cyclization to afford 4-iodopyrazoles in good to high yields. Iodocyclization was general for a wide range of α,β-alkynic hydrazones and tolerated the presence of aliphatic, aromatic, heteroaromatic, and ferrocenyl moieties with electron-withdrawing and electron-donating substituents.     

Phthalocyanine with a giant dielectric constant

Compound 1 has been prepared by the reaction of 4-nitrophthalonitrile and trans-2-methoxy-4-(2-nitrovinil)phenol by the common method of nucleophilic substitution of an activated nitro group in an aromatic ring. The metallophthalocyanines 2, 3 were prepared by the reaction of a dinitrile derivative with Co(OAc)(2) or Zn(OAc)(2) in DMSO. The lutetium bis-(phthalocyaninato) complex 4 was obtained by treating the dinitrile derivative with lutetium acetate and DBU in 1-hexanol. The new compounds were characterized by elemental analyses, FT-IR, (1)H-NMR, MALDI-TOF MS and UV/Vis spectral data. The spectroscopic data of the new compounds were in accordance with the structures. The temperature and frequency dependence of dielectric and conduction properties of the spin coated film of compounds (2-4) have been studied by fabricating metal-Pc-metal structures. The results show that compound 2 has giant dielectric constant. At a low range of frequency and room temperature, ε' is found to be equal to 2.33 × 10(6), 1.53 × 10(4) and 1.03 × 10(4) for 2, 3 and 4, respectively. The giant dielectric behavior of 2 is mainly attributed to Maxwell-Wagner polarization. The obtained results also indicated that the frequency dependence of the dielectric permittivity, ε'(ω), exhibits non-Debye type relaxation for all temperatures investigated. The ac conductivity results gave a temperature dependent frequency exponent s. The results were compared with the prediction of the Quantum Mechanical Tunneling and Correlated Barrier Hopping models.     

Self-tuning fuzzy logic control of a non-linear structural system with ATMD against earthquake

Self-tuning fuzzy logic controllers (STFLC) for the active control of Marmara Kocaeli earthquake excited building structures are studied in this paper. Vibration control using intelligent controllers, such as fuzzy logic has attracted the attention of structural control engineers during the last few years, because fuzzy logic can handle nonlinearities, uncertainties, and heuristic knowledge effectively and easily. The improved seismic control performance can be achieved by converting a simply designed static gain into a real time variable dynamic gain through a self-tuning mechanism. Self-tuning fuzzy logic controller is designed to reduce the story-drift of each floor. The simulated system has a nine-degree-of-freedom, which is modeled using nonlinear behavior of the base-structure interaction. Modeled system was simulated against the ground motion of the Marmara Kocaeli earthquake (M _w=7.4) in Turkey on 17 August, 1999. At the end of the study, the time history of the story displacements, accelerations, ATMD displacements, control voltage, and frequency responses of the both uncontrolled and controlled cases are presented. The robustness of the controller has been checked through the uncertainty in stiffness of the structure. Performance of the designed STFLC has been demonstrated for the different disturbance using ground motion of the Kobe earthquake. Simulations of an earthquake excited nine story structure are performed to prove the validity of proposed control strategy.     

Gadolinium triflate catalyzed alkylation of pyrroles: efficient synthesis of 3-oxo-2,3-dihydro-1H-pyrrolizine derivatives

Novel 2-alkylated pyrrole derivatives were synthesized regioselectively by Gd(OTf)₃ catalyzed addition reactions of pyrrole to substituted dimethyl 2-benzylidenemalonate derivatives under mild reaction conditions. 2-Alkylated pyrrole derivatives are used for the construction of the 3-oxo pyrrolizine skeleton. Intramolecular cyclization of alkylated pyrrole derivatives afforded new diastereoselective 3-oxo-2,3-dihydro-1H-pyrrolizine derivatives with good to high yields.     

Erdős Type Problems in Modules over Cyclic Rings

In the present paper, we study various Erd?s type geometric problems in the setting of the integers modulo q, where \(q=p^l\) is an odd prime power. More precisely, we prove certain results about the distribution of triangles and triangle areas among the points of \(E\subset \mathbb {Z}_q^2\).     

Superconductivity of F-substituted LnOBiS2 (Ln=La,Ce, Pr,Nd, Yb) compounds

Polycrystalline samples of F-substituted LnOBiS₂ (Ln?=?La, Ce, Pr, Nd, Yb) compounds were synthesized by solid-state reaction. The samples were characterized by X-ray diffraction measurements and found to have the ZrCuSiAs crystal structure. Electrical resistivity and magnetic susceptibility measurements were performed on all of the samples and specific heat measurements were made on those with Ln?=?La, Ce, and Yb. All of these compounds exhibit superconductivity in the range 1.9?K–5.4?K, which has not previously been reported for the compounds based on Ce, Pr, and Yb. The YbO_0.5F_0.5BiS₂ compound was also found to exhibit magnetic order at ～2.7?K that apparently coexists with superconductivity below 5.4?K.