Transfinite interpolation on the medians of a triangle and best L 1-approximation

Let be a triangle in and let be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on The interpolants are of type f(₁)+g(₂)+h(₃), where (₁,₂,₃) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L¹-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C³().Received: 17 December 2003     

Geodesic Equivalence via Integrability

We suggest a construction that, given an orbital diffeomorphism between two Hamiltonian systems, produces integrals of them. We treat geodesic equivalence of metrics as the main example of it. In this case, the integrals commute; they are functionally independent if the eigenvalues of the tensor g ⁱg¯_j are all different; if the eigenvalues are all different at least at one point then they are all different at almost each point and the geodesic flows of the metrics are Liouville integrable. This gives us topological obstacles to geodesic equivalence.     

The fourfold escape threshold law

The dependence of an ionization function on the total energy near the break-up threshold has been derived making use of the classical theory. The threshold exponent for the triple ionization by electron impact on neutral target assumes the value κ = 3.525.     

Localization of the electromagnetic field in the vicinity of gold nanoparticles: Surface modification of different substrates

Theoretical predictions and experimental results for nanosized modification of metal (Au), semiconductor (Si), or dielectric (soda lime glass) substrates using near-electromagnetic field enhancement in the vicinity of gold nanoparticles are presented. The near field properties for the system consisting of an isolated gold nanoparticle or nanoparticle aggregate deposited on the substrates, which is irradiated by electromagnetic wave, are investigated using Finite Difference Time Domain Simulation technique. The influence of the substrate material on the near field distribution characteristics is predicted. The results reveal that the field on the substrate surface is enhanced in the three investigated cases, but its spatial distribution and magnitude depend on the substrate material. In the case of the metal and semiconductor substrate the enhanced near field is strongly localized in the vicinity of the contact point with the particle, in an area with diameter smaller than the particle's one. The intensity of the enhanced field on the glass is more than an order of magnitude lower than the case of using silicon substrate. The properties of the near field on the substrate surface also depend on the particle arrangement. For a two-dimensional gold nanoparticle array, when the particles are closely arrayed, the intensity of the enhanced field on the substrate surface is minimal. With the increase of the interparticle distance the near field intensity increases. The validity of the obtained theoretical results is confirmed experimentally.     

Low-Regularity Solutions of the Periodic Camassa–Holm Equation

We prove local existence and uniqueness of weak solutions of the Camassa–Holm equation with periodic boundary conditions in various spaces of low-regularity which include the periodic peakons. The proof uses the connection of the Camassa–Holm equation with the geodesic flow on the diffeomorphism group of the circle with respect to the L ² metric.     

Synthesis and Characterization of Novel Cycloalkanespiro-5-Hydantoin Phosphonic Acids

A series of new cycloalkanespiro-5-hydantoin phosphonic acids have been synthesized and characterized. The mixture of [(2,4-dioxo-1,3-diazaspiro-alkane-3-yl)-methyl]phosphonic acids and [(2,4-dioxo-1,3-diazaspiro-alkane-1,3-diyl)dimethyl]diphospho-nic acids was obtained from cycloalkanespiro-5-hydantoins, formaldehyde, and phosphorus trichloride in a molar ratio of 1:2:2, by a procedure modified by us. Their structures were proved by means of IR, ¹H, ¹³C{¹H} and ³¹P NMR spectroscopy.     

Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties

We show that the class of locally finite varieties omitting type 1 has the following properties. This class is:

1. definable by an idempotent, linear, strong Mal’cev condition in a language with one 4-ary function symbol;
2. not definable by an idempotent, linear, strong Mal’cev condition in a language with only one function symbol of arity strictly less than 4;
3. definable by an idempotent, linear, strong Mal’cev condition in a language with two 3-ary function symbols;
4. not definable by an idempotent, linear, strong Mal’cev condition in a language with function symbols of arity less than 4 unless at least two of the symbols have arity 3.

     

Periodic Solutions of the Burgers-Hopf Equation with Small Parameter and its Cellular Neural Network Model

This paper deals with the periodic solutions of the Cauchy problem to the Burgers-Hopf equation containing small viscosity term. We propose at first an explicit formula for the exact solution of the Cauchy problem and then we give an approximate formula. We use CNN approach for constructing the approximate solution and we find precise estimates of the remainder term. This work was supported by the NATO Grant ICS.NR.CLG 981757.     

Characterization and quantitative analysis of surfactants in textile wastewater by liquid chromatography/quadrupole-time-of-flight mass spectrometry

A method based on the application of ultra-performance liquid chromatography (UPLC) coupled to hybrid quadrupole-time-of-flight mass spectrometry (QqTOF-MS) with an electrospray (ESI) interface has been developed for the screening and confirmation of several anionic and non-ionic surfactants: linear alkylbenzenesulfonates (LAS), alkylsulfate (AS), alkylethersulfate (AES), dihexyl sulfosuccinate (DHSS), alcohol ethoxylates (AEOs), coconut diethanolamide (CDEA), nonylphenol ethoxylates (NPEOs), and their degradation products (nonylphenol carboxylate (NPEC), octylphenol carboxylate (OPEC), 4-nonylphenol (NP), 4-octylphenol (OP) and NPEO sulfate (NPEO-SO4). The developed methodology permits reliable quantification combined with a high accuracy confirmation based on the accurate mass of the (de)protonated molecules in the TOFMS mode. For further confirmation of the identity of the detected compounds the QqTOF mode was used. Accurate masses of product ions obtained by performing collision-induced dissociation (CID) of the (de)protonated molecules of parent compounds were matched with the ions obtained for a standard solution. The method was applied for the quantitative analysis and high accuracy confirmation of surfactants in complex mixtures in effluents from the textile industry. Positive identification of the target compounds was based on accurate mass measurement of the base peak, at least one product ion and the LC retention time of the analyte compared with that of a standard. The most frequently surfactants found in these textile effluents were NPEO and NPEO-SO4 in concentrations ranging from 0.93 to 5.68 mg/L for NPEO and 0.06 to 4.30 mg/L for NPEO-SO4. AEOs were also identified.     

Wormlike morphology formation and stabilization of "pluronic p123" micelles by solubilization of pentaerythritol tetraacrylate

A transition from spherical to wormlike micelles of a poly(ethylene oxide) 20- block-poly(propylene oxide) 70- block-poly(ethylene oxide) 20 triblock copolymer Pluronic P123 induced by solubilization of a tetrafuctional monomer, Pentaerythritol tetraacrylate (PETA), in aqueous media has been studied. The wormlike micelles shape was locked by UV cross-linking of PETA within the micelles resulting in stabilized polymeric micelles (SPMs). The stability of SPMs in a good solvent for both polyether blocks like THF, and upon dilution below the critical micelle concentration (CMC) of P123 in water was confirmed by dynamic light scattering (DLS) and scanning force microscopy (SFM). Formation of cadmium sulfide (CdS) nanoparticles within the wormlike SPMs was carried out via the reduction of Cd (2+) with NaS and analyzed by transmission electron microscopy (TEM) and UV-vis absorption measurements. A stable water-dispersible hybrid system consisting of CdS quantum dots embedded into the wormlike SPMs was obtained.