Simultaneous difference equations on a restricted domain

Aequationes mathematicae - Given a set $$Tsubset (0, +infty )$$ , a function $$c:Trightarrow mathbb R$$ and a real number p we study continuous solutions $$varphi $$ of the simultaneous...     

Absolutely summing multipliers on abstract Hardy spaces

We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces.     

Nonexistence of small,odd breathers for a class of nonlinear wave equations

In this note, we show that for a large class of nonlinear wave equations with odd nonlinearities, any globally defined odd solution which is small in the energy space decays to 0 in the local energy norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations, such as the sine-Gordon equation and \(\phi ^4\) and \(\phi ^6\) models. It also partially answers a question of Soffer and Weinstein (Invent Math 136(1): 9–74, p 19 1999) about nonexistence of breathers for the cubic NLKG in dimension one.     

Automatic approximation using asymptotically optimal adaptive interpolation

Numerical Algorithms - We present an asymptotic analysis of adaptive methods for Lp approximation of functions f ∈ Cr([a, b]), where $1le ple +infty $ . The methods rely on piecewise...     

Vibrational characterization of L-leucine phosphonate analogues: FT-IR, FT-Raman, and SERS spectroscopy studies and DFT calculations

This study reports the Raman (FT-Raman) and absorption infrared (FT-IR) spectra, based on calculated wavenumbers and normal modes of vibrations, of the following compounds: L-Leu-D-NH-CH(Me)-PO(3)H(2) (LI), L-Leu-NH-C(Me)(2)-PO(3)H(2) (LII), L-Leu-D-NH-CH(Et)-PO(3)H(2) (LIII), L-Leu-L-NH-CH(Et)-PO(3)H(2) (LIV), L-Leu-L-NH-CH(EtOH)-PO(3)H(2) (LV), L-Leu-NH-C(Me)(Et)-PO(3)H(2) (LVI), L-Leu-L-NH-CH(PrA)-PO(3)H(2) (LVII), L-Leu-L-NH-CH(c-Pr)-PO(3)H(2) (LVIII), L-Leu-L-NH-CH(t-Bu)-PO(3)H(2) (LIX), L-Leu-L-NH-CH(BuA)-PO(3)H(2) (LX), L-Leu-L-NH-CH(c-Bu)-PO(3)H(2) (LXI), and L-Leu-L-NH-C(Adm)-PO(3)H(2) (LXII). The equilibrium geometries and vibrational wavenumbers were calculated using density functional theory (DFT) at the B3LYP, 6-311++G** level using Gaussian 03, Raint, GaussSum 0.8, and Gar2ped software. We briefly compare and analyze the experimental and calculated vibrational wavenumbers in the range 4000-400 cm(-1). In addition, the Raman wavenumbers are compared to those from the surface-enhanced Raman scattering (SERS) spectra for the phosphono analogues of l-leucine (l-Leu) adsorbed on a colloidal silver surface in an aqueous solution. The geometries of these molecules etched on the silver surface were deduced from observed changes in both the intensity and broadness of Raman bands in the spectra of the bound versus free species. For example, LVI appears to adsorb onto the colloidal silver particles mainly through the amine group and amide bond, which assists in the adsorption process, whereas LII shows strongly enhanced SERS bands due to the rocking, twisting, and stretching vibrations of the N(amid)C(sg)(Me)(2)P fragment, suggesting that this peptide's interaction with the silver surface occurs mainly via this fragment. On the other hand, the most dominant SERS bands of LIII and LIV due to the P═O bond stretches reflect P═O···Ag complex formation.     

Estimation of the breakthrough volume of selected steroids for C‐18 solid‐phase extraction sorbent using retention data from micro‐thin layer chromatography

SPE method is a very popular technique, and is commonly used for the prepurification, concentration, and isolation of different organic compounds from variable matrices. In this work, the optimization of SPE process was carried out. The breakthrough volume of solid sorbents based on octadecylsilane was determined and three methods were compared: (1) calculation one – the breakthrough volume was calculated using retention factor k determined with micro‐TLC method, frontal analysis – (2) breakthrough volume was determined as volume of whole elution peak, and (3) breakthrough volume was determined as the center of peak gravity. For calculation method, the k values of key estrogens and progestogens were derived from the micro‐TLC experiment reported previously. By combining these three methods, we can point the start of elution, the maximum concentration of analyte in eluate, and the whole eluent volume, which is necessary to achieve an appropriate selectivity and high extraction recovery. Proposed calculation method allows to estimate the beginning of the steroid peak, when the analyte appears in the eluate flowing from the sorbent. Such observation advances the SPE optimization protocol that was described before and was based on the correlation between raw k_SPE and k_micro‐TLC data.     

Scaling Properties of the Number of Random Sequential Adsorption Iterations Needed to Generate Saturated Random Packing

The properties of the number of iterations in random sequential adsorption protocol needed to generate finite saturated random packing of spherically symmetric shapes were studied. Numerical results obtained for one, two, and three dimensional packings were supported by analytical calculations valid for any dimension d. It has been shown that the number of iterations needed to generate finite saturated packing is subject to Pareto distribution with exponent \(-1-1/d\) and the median of this distribution scales with packing size according to the power-law characterized by exponent d. Obtained results can be used in designing effective random sequential adsorption simulations.     

Locking entanglement with a single qubit

We study the loss of entanglement of a bipartite state subjected to discarding or measurement of one qubit. Examining behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, logarithmic negativity, and one-way distillable entanglement are lockable measures in that they can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically noncontinuous measure is lockable. As a consequence, all the convex-roof measures can be locked. The relative entropy of entanglement is shown to be a nonlockable measure.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.