On an Extension of a Hardy-Hilbert-Type Inequality with Multi-Parameters

Making use of weight coefficients as well as real/complex analytic methods, an extension of a Hardy–Hilbert-type inequality with a best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression with the norm, and a few particular cases are also considered.

A new Hardy–Mulholland-type inequality with a mixed kernel

By the use of weight coefficients and techniques of real analysis, we establish a new Hardy–Mulholland-type inequality with a mixed kernel and a best possible constant factor in terms of the hypergeometric function. Equivalent forms, an operator expression with the norm and reverses are also considered.

The spin Drude weight of the XXZ chain and generalized hydrodynamics

Based on a generalized free energy we derive exact thermodynamic Bethe ansatz formulas for the expectation value of the spin current, the spin current-charge, charge-charge correlators, and consequently the Drude weight. These formulas agree with recent conjectures within the generalized hydrodynamics formalism. They follow, however, directly from a proper treatment of the operator expression of the spin current. The result for the Drude weight is identical to the one obtained 20 years ago based on the Kohn formula and TBA. We numerically evaluate the Drude weight for anisotropies \Delta=\cos(\gamma)Δ=cos(γ) with \gamma = \pi n/mγ=πn/m, n\leq mn≤m integer and coprime. We prove, furthermore, that the high-temperature asymptotics for general \gamma=\pi n/mγ=πn/m—obtained by analysis of the quantum transfer matrix eigenvalues—agrees with the bound which has been obtained by the construction of quasi-local charges.

Spectrums of Solvable Pantograph Differential-Operators for First Order

By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

VALIDITY OF THE GELL-MANN FORMULA FOR sl(n, ℝ) AND su(n) ALGEBRAS

The so-called Gell-Mann formula, a prescription designed to provide an inverse to the Inönü–Wigner Lie algebra contraction, has a great versatility and potential value. This formula has no general validity as an operator expression. The question of applicability of Gell-Mann's formula to various algebras and their representations was only partially treated. The validity constraints of the Gell-Mann formula for the case of sl(n, ℝ) and su(n) algebras are clarified, and the complete list of representations spaces for which this formula applies is given. Explicit expressions of the sl(n, ℝ) generators matrix elements are obtained for all these cases in a closed form by making use of the Gell-Mann formula.

Engineering and overexpression of periplasmic forms of the penicillin-binding protein 3 of Escherichia coli

Replacement of the 36 and 56 N-terminal amino acid residues of the 588-amino-acid-residue membrane-bound penicillin-binding protein 3 (PBP3) of Escherichia coli by the OmpA signal peptide allows export of F37-V577 PBP3 and G57-V577 PBP3 respectively into the periplasm. The modified ftsI genes were placed under the control of the fused lpp promoter and lac promoter/operator; expression of the truncated PBP3s was optimized by varying the copy number of the recombinant plasmids and the amount of LacI repressor, and export was facilitated by increasing the SecB content of the producing strain. The periplasmic PBP3s (yield 8 mg/l of culture) were purified to 70% protein homogeneity. They require the presence of 0.25 M NaCl to remain soluble. Like the membrane-bound PBP3, they undergo processing by elimination of the C-terminal decapeptide I578-S588, they bind penicillin in a 1:1 molar ratio and they catalyse hydrolysis and aminolysis of acyclic thioesters that are analogues of penicillin. The membrane-anchor-free PBP3s have ragged N-termini. The G57-V577 PBP3, however, is less prone to proteolytic degradation than the F37-V577 PBP3.