The volume measure for flat connections as limit of the Yang–Mills measure

We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang–Mills measure defined in terms of the heat-kernel for the gauge group. In doing this we also give a rigorous proof of Witten’s formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinants of matrices along with a careful accounting of certain dense subsets of full measure in the moduli space.     

New Representation of the Self-Duality and Exact Solutions for Yang–Mills Equations

In this paper, we found a new representation for self-duality . In addition, exact solution class of the classical SU(2) Yang–Mills field in four-dimensional Euclidean space and two exact solution classes for SU(2) Yang–Mills when ρ is a complex analytic function are also obtained. PACS numbers: 11.15.-q Gauge field theories, 11.15.Kc Semiclassical theories in gauge fields, 12.10.-g, 12.15.-y Yang–Mills fields     

Removal of Phenolic and Lignin Compounds from Bleached Kraft Mill Effluent by Fly Ash and Sepiolite

This study aimed to remove phenolic and lignin compounds from paper mill industry (4500 m³/h) wastewaters, which is discharged to sea from a plant located in the western Turkey. As adsorbent, fly ash, raw sepiolite and heat-activated sepiolite were used. The effect of factors such as, particle size, temperature and pH on adsorption process was investigated. From kinetic studies, equilibrium time was found as 1 h for both. The kinetic data supports pseudo-second order model but shows very poor fit for pseudo-first order model. Intraparticle model also shows that there are two separate stages in sorption process, namely, external diffusion and pore diffusion. Adsorption isotherms for fly ash and activated sepiolite were obtained at two different temperatures. From experiments carried out at different pHs, it was observed that pH plays an important role in the adsorption process in removing of both lignin and phenolic compounds, providing both ionizating the compounds and modifying sorbent surfaces. It was also observed that heat-activated sepiolite is more effective than raw sepiolite and fly ash to remove these compounds. Adsorption of lignin and phenolic compounds increases with decreasing particle size. In addition, the efficiency of adsorption decreases with increasing adsorption temperature for both fly ash and untreated sepiolite.     

Exploring correlations in the stochastic Yang–Mills vacuum

The correlation lengths of nonperturbative-nonconfining and confining stochastic background Yang–Mills fields are obtained by means of a direct analytic path-integral evaluation of the Green functions of the so-called one- and two-gluon gluelumps. Numerically, these lengths turn out to be in a good agreement with those known from the earlier, Hamiltonian, treatment of such Green functions. It is also demonstrated that the correlation function of nonperturbative-nonconfining fields decreases with the deviation of the path in this correlation function from the straight-line one.     

A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality

A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected.     

Simultaneous determination of ginsenoside Rb1, ginsenoside Rg1, paeoniflorin,albiflorin and oxypaeoniflorin in rat plasma by liquid chromatography–tandem mass spectrometry: Application to a pharmacokinetic study of wen‐Yang‐Huo‐Xue soft capsule

A simple and sensitive HPLC–MS/MS method was developed and fully validated for simultaneous determination of ginsenoside Rb1, ginsenoside Rg1, paeoniflorin, albiflorin and oxypaeoniflorin in rat plasma. Plasma samples were pretreated with protein precipitation using acetonitrile. The chromatographic separation was carried out on a C₁₈ column with a gradient mobile phase consisting of acetonitrile and water (containing 0.1% formic acid). All analytes and digoxin (internal stand, IS) were quantitated through electrospray ionization in negative ion multiple reaction monitoring mode. All calibration curves exhibited good linearity (r > 0.9960) over a wide concentration range for all components. The intra‐day and inter‐day precisions (RSD) at three different levels were all <12.0% and the accuracies (RE) ranging from −6.1 to 6.2%. The extraction recoveries of the five compounds ranged from 89.2 to 97.1%. The validated method was successfully applied in a comparative pharmacokinetic study of Wen‐Yang‐Huo‐Xue soft capsule (WYHXSC) in rats. Compared with single pure component, the exposure of the investigated components, except for oxypaeoniflorin, increased after oral administration of WYHXSC in rats, which suggested a synergistic effects between the herbs in the WYHXSC preparations.     

Soliton interactions and Yang–Baxter maps for the complex coupled short-pulse equation

The complex coupled short-pulse equation (ccSPE) describes the propagation of ultrashort optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton solutions: fundamental solitons, fundamental breathers, composite breathers (generic or nongeneric), as well as so-called self-symmetric composite solitons. In this work, we use the dressing method and the Darboux matrices corresponding to the various types of solitons to investigate soliton interactions in the focusing ccSPE. The study combines refactorization problems on generators of certain rational loop groups, and long-time asymptotics of these generators, as well as the main refactorization theorem for the dressing factors that leads to the Yang–Baxter property for the refactorization map and the vector soliton interactions. Among the results obtained in this paper, we derive explicit formulas for the polarization shift of fundamental solitons that are the analog of the well-known formulas for the interaction of vector solitons in the Manakov system. Our study also reveals that upon interacting with a fundamental breather, a fundamental soliton becomes a fundamental breather and, conversely, that the interaction of two fundamental breathers generically yields two fundamental breathers with a polarization shifts, but may also result into a fundamental soliton and a fundamental breather. Explicit formulas for the coefficients that characterize the fundamental breathers, as well as for their polarization vectors are obtained. The interactions of other types of solitons are also derived and discussed in detail and illustrated with plots. New Yang–Baxter maps are obtained in the process.     

Elliptic Yang–Mills flow theory

We lay the foundations of a Morse homology on the space of connections on a principal G‐bundle over a compact manifold Y, based on a newly defined gauge‐invariant functional on . While the critical points of correspond to Yang–Mills connections on P, its L²‐gradient gives rise to a novel system of elliptic equations. This contrasts previous approaches to a study of the Yang–Mills functional via a parabolic gradient flow. We carry out the analytical details of our programme in the case of a compact two‐dimensional base manifold Y. We furthermore discuss its relation to the well‐developed parabolic Morse homology over closed surfaces. Finally, an application of our elliptic theory is given to three‐dimensional product manifolds .     

The crystal and molecular structure of sodium 4‐(2,4,6‐triisopropylbenzoyl)benzoate in terms of the photochemical behaviour of the anion

Contrary to the known 4‐(2,4,6‐triisopropylbenzoyl)benzoate salts, di‐μ‐aqua‐bis[tetraaquasodium(I)] bis[4‐(2,4,6‐triisopropylbenzoyl)benzoate] dihydrate, [Na₂(H₂O)₁₀](C₂₃H₂₇O₃)₂·2H₂O, (1), does not undergo a photochemical Norrish–Yang reaction in the crystalline state. In order to explain this photochemical inactivity, the intermolecular interactions were analyzed by means of the Hirshfeld surface and intramolecular geometrical parameters describing the possibility of a Norrish–Yang reaction were calculated. The reasons for the behaviour of the title salt are similar crystalline environments for both the o‐isopropyl groups in the anion, resulting in similar geometrical parameters and orientations, and that these interaction distances differ significantly from those found in salts where the photochemical reaction occurs.