Variable degree polynomial splines are Chebyshev splines

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms based on knot insertion. We consider variable degree polynomial splines of order $k\geqslant 2$ spanned by $\{ 1,x,\ldots x^{k-3},(x-x_i)^{m_i-1},(x_{i+1}-x)^{n_i-1} \}$ on each subinterval $[x_i,x_{i+1}\rangle\subset [0,1]$ , i?=?0,1, ...l. Most of the paper deals with non-polynomial case m _i ,n _i ?∈?[4,?∞?), and polynomial splines known as VDP–splines are the special case when m _i , n _i are integers. We describe VDP–splines as being piecewisely spanned by a Canonical Complete Chebyshev system of functions whose measure vector is determined by positive rational functions p(x), q(x). These functions are such that variable degree splines belong piecewisely to the kernel of the differential operator $\frac{d}{dx} p \frac{d}{dx} q \frac{d^{k-2}} {dx^{k-2}}$ . Although the space of splines is not based on an Extended Chebyshev system, we argue that total positivity and variation diminishing still holds. Unlike the abstract results, constructive properties, like Marsden identity, recurrences for quasi-Bernstein polynomials and knot insertion algorithms may be more involved and we prove them only for VDP splines of orders 4 and 5.     

On possible dependence structures of a set of random variables

We give a constructive proof of existence of random vectors and discrete-time random processes with arbitrary nonsingular marginal distributions and arbitrary dependence structure. A corollary of this fact regarding Gaussian distributions is also established, as well as some abstract properties of dependence structures.     

Separation of hypoviral double-stranded RNA on monolithic chromatographic supports

A procedure based on BIA Separations CIM DEAE anion-exchange chromatography was developed to separate double-stranded (ds) RNA of hypovirus infecting phytopathogenic fungus Cryphonectria parasitica. Using a linear gradient of 25 mM 4-morpholinepropanesulfonic acid (MOPS), pH 7.0 as a binding buffer, and 25 mM MOPS, 1.5 M NaCl, 0.1 mM EDTA, 15% isopropanol (v/v), pH 7.0 as an elution buffer, hypoviral dsRNA was additionally purified from nucleic acid species present in preparations partially purified by standard CF-11 cellulose chromatography. Moreover, crude phenol/chloroform extracts of the fungal tissue were also applied to monolithic supports and CIM DEAE chromatograms revealed clear evidence for hypoviral presence without CF-11 chromatography, nucleic acid precipitation, and electrophoresis.     

Synthesis,Kinetics, and Molecular Docking of Novel 9‐(2‐Hydroxypropyl)purine Nucleoside Analogs as Ligands of Herpesviral Thymidine Kinases

In the context of broadening the knowledge on substrate specificity of Herpes simplex virus type 1 thymidine kinase (HSV‐1 TK) and Varicella‐Zoster virus thymidine kinase (VZV TK), new derivatives of 9‐(2‐hydroxypropyl)‐substituted adenine, chloropurine, hypoxanthine, guanine, thiopurine, and (methylsulfanyl)purine were synthesized and subjected to in vitro phosphorylation and binding affinity assays. The interactions between the compounds and the crystallographically determined active site residues of HSV‐1 TK have been studied by molecular modeling with the Lamarckian genetic algorithm of docking program AutoDock 3.0. All compounds mentioned bind to both enzymes in the low mM to sub‐mM range, comparable to binding affinities of existing prodrugs. Findings from the docking procedure indicate multiple binding modes for all of the compounds and are in accordance with the results of phosphorylation and binding‐affinity studies. Furthermore, the studies reveal that hypoxanthine derivatives represent a new class of TK substrates and thiopurine derivatives a new class of TK inhibitors.     

Migration Testing of GPPS and HIPS Polymers: Swelling Effect Caused by Food Simulants Compared to Real Foods

Migration kinetic data from general purpose polystyrene (GPPS) and high impact polystyrene (HIPS) were generated for a set of model substances as well as styrene monomer and oligomers at different temperatures (20 °C, 40 °C, 60 °C) using food simulants stipulated in the European Regulation (EU) 10/2011 and real foods like milk, cream and olive oil (20 °C, 40 °C). The extent of polymer swelling was characterized gravimetrically and visual changes of the test specimens after migration contact were recorded. Isooctane and 95% ethanol caused strong swelling and visual changes of HIPS, overestimating real migration into foods especially at high temperatures; GPPS was affected by isooctane only at 60 °C. With 50% ethanol, after 10 days contact at 60 °C or 40 °C both polymers were slightly swollen. Contrary, most of the real foods analyzed caused no detectable swelling or visual changes of the investigated polymers. This study demonstrates that the recommendations provided by EU regulations are not always in agreement with the physicochemical properties of styrenic polymers. The critical point remains the selection of adequate food simulants/testing conditions, since the high overestimation of aggressive media can lead to non-compliance of polystyrene materials even if the migration into real food would be of no concern.     

Synthesis and biological evaluation of 99mTc tricarbonyl complex of O,O′‐diethylethylenediamine‐N,N′‐di‐3‐propanoate as potential tumour diagnostic agent

The extensive development of radiopharmaceuticals towards early tumour detection and treatment has increased the demand for new ligands with higher tumour selectivity. Research has been done on the potential of the novel O,O′‐diethylethylenediamine‐N,N′‐di‐3‐propanoate ( L ) ligand as a radionuclide vehicle for tumour targeting. Under alkaline conditions, L hydrolyses and produces half ester ligand ( L' ) and diacid ligand ( L'' ), with characteristic donor atom array N,N,O. Ligand L was successfully labelled with ^99mTc at pH = 9 by coordination with the octahedral fac‐[^99mTc(CO)₃(H₂O)₃]⁺ intermediate, forming the main radioproduct fac‐[^99mTcL′(CO)₃] (Tc1). The ^99mTc complex showed a low lipophilic character (log P = 0.48) and low binding affinity to human serum albumin (2.51 ± 0.48%). In vitro stability studies in saline and human plasma, as well as challenge studies with cysteine and histidine, revealed high stability of the complex during 24 h. Biodistribution studies of Tc1 in female C57BL/6 mice bearing B16/F1 melanoma metastases showed significant tumour uptake: 9.81 ± 1.19%ID g^?1 in the liver, 5.87 ± 0.54%ID g^?1 in the lungs and 3.17 ± 0.33%ID g^?1 in the ovary at 30 min post‐injection. Favourable physicochemical properties, satisfactory in vitro/in vivo stability and biodistribution profile in the experimental metastatic melanoma model indicate the possible application of the radiolabelled ligand in tumour diagnosis. Copyright © 2015 John Wiley & Sons, Ltd.     

Next Generation Access Network Deployment in Croatia: Optical Access Networks and Current IoT/5G Status

This paper gives an overview and background of optical access network deployment in Croatia. Optical access network development in Croatia has been put into a global as well as in the European Union context. All the challenges and the driving factors for optical access networks deployment are considered. Optical access network architectures that have been deployed by most of the investors in Croatian telecommunication market are presented, as well as the architectures that are in early phase of deployment. Finally, an overview on current status of mobile networks of the fifth generation and Internet of Things is given.     

Hydrogen Bonding and Solvent Effects on Complexation of Alkali Metal Cations by Lower Rim Calix[4]arene Tetra(O-[N -acetyl-D -phenylglycine methyl ester]) Derivative

Complexation of alkali metal cations with 5,11,17,23-tetra-tert-butyl-26,28,25,27-tetrakis(O-methyl-D-α-phenylglycylcarbonylmethoxy)calix[4]arene (L) was studied by means of spectrophotometric, conductometric and potentiometric titrations at 25 °C. The solvent effect on the binding ability of L was examined by using two solvents with different affinities for hydrogen bonding, viz. methanol and acetonitrile. Despite the presence of intramolecular NH···O=C hydrogen bonds in L, which need to be disrupted to allow metal ion binding, this calix[4]arene amino acid derivative was shown to be an efficient binder for smaller Li⁺ and Na⁺ cations in acetonitrile (lg K_LiL > 5, lg K_NaL = 7.66), moderately efficient for K⁺ (lg K_KL = 4.62), whereas larger Rb⁺ and Cs⁺ did not fit in its hydrophilic cavity. The complex stabilities in methanol were significantly lower (lg K_NaL = 4.45, lg K_KL = 2.48). That could be explained by different solvation of the cations and by competition between the cations and methanol molecules (via hydrogen bonds) for amide carbonyl oxygens. The influence of cation solvation on complex stability was most pronounced in the case of Li⁺ for which, contrary to the quite stable LiL⁺ complex in acetonitrile, no complexation was observed in methanol under the conditions used.     

Photoinduced gelation by stilbene oxalyl amide compounds

Oxalyl amide derivatives bearing 4-dodecyloxy-stilbene as a cis-trans photoisomerizing unit were synthesized. The trans derivative acted as a versatile gelator of various organic solvents, whereas the corresponding cis derivative showed a poor gelation ability or none at all. In diluted solution (c = 2.0 x10(-5) mol dm(-3), ethanol), the cis isomer was photochemically converted into the trans isomer within 4 min. Depending on the radiation wavelength, the trans isomer was stable or liable to photodecomposition. When exposed to irradiation, a concentrated solution of the cis isomer (c = 2.0 x 10(-2) mol dm(-3), ethanol) turned into a gel. The FT-Raman, FT-IR, and 1H NMR spectra demonstrated that the gelation process occurred because of a rapid cis --> trans photoisomerization followed by a self-assembly of the trans molecules. Apart from the formation of hydrogen bonding between the oxalyl amide parts of the molecules, confirmed by FT-IR spectroscopy, it was assumed that the pi-pi stacking between the trans-stilbene units of the molecule and a lipophilic interaction between long alkyl chains were the interactions responsible for gelation.