On $${\mathcal {I}}_{

Tóth  János T.  Filip  Ferdinánd  Bukor  József  Zsilinszky  László 《Periodica Mathematica Hungarica》2021,82(2):125-135

Analytic implementation of the duals of some spaces of infinitely differentiable functions

Using the Fourier-Laplace transform for functionals, we describe the duals of some spaces of the infinitely differentiable functions given on convex compact sets or convex domains in ?^N and such that the growth of their derivatives is determined by weight sequences of a general form.     

Spin-lattice relaxation in multiple-pulse experiments as contrast parameter in NMR imaging of solids

The molecular motion contrast parameter for NMR imaging of solids and quasi-solids based on the spin-lattice relaxation (T _leff) in multiple-pulse experiments is discussed. For Ostroff-Waugh multiple-pulse sequence theT _leff contrast parameter is evaluated in slow and fast molecular motion regime and compared with spin-lattice relaxation in the rotating frame contrast parameter. It is shown thatT _leff is offering a good molecular motion contrast in NMR imaging of polymer systems. The radio-frequency pulse scheme forT _leff-imaging using magic-echo phase-encoding procedure for recording spatial distribution in solids is introduced. A method forT _leff-weighted imaging using gradient spin-echo valid for weak dipolar solids is also discussed. The one-dimensional protonT _leff image using Ostroff-Waugh pulse sequence in combination with frequency-encoding imaging procedure is presented for a phantom of poly(ethyleneoxide) and poly(methylmethacrylate). The distribution of mechanical stresses in a acrylate film on glass is investigated by protonT _leff-imaging. A proton spin-density image weighted byT _leff, for a mixture of two elastomers with different crosslink density is also shown.     

Stagnation point flow of a micropolar fluid towards a stretching sheet

The steady two-dimensional stagnation point flow of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation point, has been studied in this paper. The resulting equations of non-linear ordinary coupled differential equations are solved numerically using the Keller-box method. The results obtained for velocity, microrotation and skin friction are shown in tables and graphs. Comparison with the recent results of Mahapatra and Gupta {Heat Mass Transfer 38 (2002) 517} for the corresponding problem of a viscous fluid (K=0) has been done and it has been shown that the results are in excellent agreement.     

Inhibition of homogeneous condensation of SF6 by vibrational excitation

Vibrational excitation of SF₆ by a 10.6 μm CO₂ laser is shown to reduce lifetimes for SF₆ dimers in supersonically expended flows. A possible utility of this phenomenon in controlling condensation rates to separate isotopes is discussed, and a kinetic analysis of the expected isotopic composition of SF₆ in a supersonically expanded stream is presented.     

Implications of enzymatic, acidic and thermal hydrolysis of DNA on the occurrence of cross-linked melphalan DNA adducts

Calf thymus DNA was treated with melphalan, a nitrogen mustard, and the formation of melphalan cross-linked DNA adducts was investigated. These cross-linked adducts could not be detected either in the enzymatically or in the thermally generated DNA hydrolysates. However, a search for DNA cross-linked adducts in the hydrolysates obtained under acidic conditions revealed the presence of different types of cross-links, mainly containing an adenine moiety. These results are very important because they show that the detection of cross-links is dependent on the hydrolytic procedure used and that these cross-linked adducts are formed under totally different reaction conditions from those in in vivo situations. This can explain the very low abundance or even the absence of cross-linked adducts in nitrogen mustard treated animals. The generally accepted theory that the anti-cancer activity of bifunctional mustards such as melphalan is due to cross-linking of DNA strands remains therefore from our point of view questionable.     

Synthesis of Clicked Imidazolium‐Containing Biosourced Copolymers and Application in Carbon Nanotube Dispersion

New polyesters incorporating a variable quantity of imidazolium rings along the backbone are synthesized by Huisgen 1,3‐dipolar cycloaddition (“click” reaction). Subsequently, the imidazolium‐grafted copolymers reveal an efficient dispersing ability toward the carbon nanotubes (CNTs) through supramolecular interactions in organic media. Interestingly, these compounds offer a simple and reliable strategy to control the quantity of dispersed CNTs as a function of imidazolium content. This approach is particularly suitable for the elaboration of biosourced and biodegradable materials based on poly(butylene succinate) with high‐performance properties.     

Tolerance of continuous-variables quantum key distribution to the noise in state preparation

We address the applicability of the continuous-variables quantum key distribution in the realistic conditions of noisy preparation, channel loss and detection noise and investigate the possibility to increase its tolerance to the state preparation noise. The two types of preparation noise, either phase-sensitive or phase-insensitive excess noise, are considered in the assumption of optimal attacks performed by an eavesdropper within the setup based on the entangled source and either homodyne or heterodyne measurements. We show that preparation noise is destructive for the secure channel upon even low noise variances in the conditions of channel loss, while detection noise just decreases the key rate. We propose the method of sender-side attenuation to suppress the preparation noise in the entanglements-based scheme and show that it enables the secure key transmission upon arbitrary high preparation noise of both types and any pure channel loss against both individual and collective attacks.     

Families Of K3 surfaces and Lyapunov exponents

Consider a family of K3 surfaces over a hyperbolic curve (i.e., Riemann surface). Their second cohomology groups form a local system, and we show that its top Lyapunov exponent is a rational number. One proof uses the Kuga–Satake construction, which reduces the question to Hodge structures of weight 1. A second proof uses integration by parts. The case of maximal Lyapunov exponent corresponds to modular families coming from the Kummer construction.