Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.     

Glass–metal objects from archaeological excavation: corrosion study

This paper contributes to the investigations on history, technology, and degradation of middle age objects (metallic rings with mounted glass beads) recently excavated under the Main Square in Krakow (Poland). Moreover, they were discovered in soil layers differing by chemical composition and microclimate parameters. Historical material is indeed very limited in terms of quantity and sample size, and the following nondestructive analyses were applied: scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDXS), X-ray diffraction (XRD), and X-ray fluorescence spectroscopy (XRF). The glass and the metal were separately tested. Metallography on cross-sections (by both optical and scanning electron microscopy) was applied only on microfragments sampled from metallic rings. The achieved results pointed out how the local microclimate affected the degradation of the analyzed rings developing locally different corrosion processes. Each tested glass of “ring eye” shows a specific chemical composition. All glass pieces were covered by silica gel, and locally more advanced corrosion has been found.     

Experimental and Theoretical Studies of the Optical Properties of the Schiff Bases and Their Materials Obtained from o-Phenylenediamine

Two macrocyclic Schiff bases derived from o-phenylenediamine and 2-hydroxy-5-methylisophthalaldehyde L1 or 2-hydroxy-5-tert-butyl-1,3-benzenedicarboxaldehyde L2, respectively, were obtained and characterized by X-ray crystallography and spectroscopy (UV-vis, fluorescence and IR). X-ray crystal structure determination and DFT calculations for compounds confirmed their geometry in solution and in the solid phase. Moreover, intermolecular interactions in the crystal structure of L1 and L2 were analyzed using 3D Hirshfeld surfaces and the related 2D fingerprint plots. The 3D Hirschfeld analyses show that the most numerous interactions were found between hydrogen atoms. A considerable number of such interactions are justified by the presence of bulk tert-butyl groups in L2. The luminescence of L1 and L2 in various solvents and in the solid state was studied. In general, the quantum efficiency between 0.14 and 0.70 was noted. The increase in the quantum efficiency with the solvent polarity in the case of L1 was observed (λ_ex = 350 nm). For L2, this trend is similar, except for the chloroform. In the solid state, emission was registered at 552 nm and 561 nm (λ_ex = 350 nm) for L1 and L2, respectively. Thin layers of the studied compounds were deposited on Si(111) by the spin coating method or by thermal vapor deposition and studied by scanning electron microscopy (SEM/EDS), atomic force microscopy (AFM), spectroscopic ellipsometry and fluorescence spectroscopy. The ellipsometric analysis of thin materials obtained by thermal vapor deposition showed that the band-gap energy was 3.45 ± 0.02 eV (359 ± 2 nm) and 3.29 ± 0.02 eV (377 ± 2 nm) for L1/Si and L2/Si samples, respectively. Furthermore, the materials of the L1/Si and L2/Si exhibited broad emission. This feature can allow for using these compounds in LED diodes.     

Insights into Antimalarial Activity of N-Phenyl-Substituted Cinnamanilides

Due to the urgent need of innovation in the antimalarial therapeutic arsenal, a series of thirty-seven ring-substituted N-arylcinnamanilides prepared by microwave-assisted synthesis were subjected to primary screening against the chloroquine-sensitive strain of P. falciparum 3D7/MRA-102. The lipophilicity of all compounds was experimentally determined as the logarithm of the capacity factor k, and these data were subsequently used in the discussion of structure-activity relationships. Among the screened compounds, fourteen derivatives exhibited IC₅₀ from 0.58 to 31 µM, whereas (2E)-N-(4-bromo-2-chlorophenyl)-3-phenylprop-2-enamide (24) was the most effective agent (IC₅₀ = 0.58 µM). In addition, (2E)-N-[2,6-dibromo-4-(trifluoromethyl)- phenyl]-3-phenylprop-2-enamide (36), (2E)-N-[4-nitro-3-(trifluoromethyl)phenyl]-3-phenylprop- 2-enamide (18), (2E)-N-(2-bromo-5-fluorophenyl)-3-phenylprop-2-enamide (23), and (2E)-3-phenyl-N-(3,4,5-trichlorophenyl)prop-2-enamide (33) demonstrated efficacy in the IC₅₀ range from 2.0 to 4.3 µM, comparable to the clinically used standard chloroquine. The results of a cell viability screening performed using THP1-Blue™ NF-κB cells showed that none of these highly active compounds displayed any significant cytotoxic effect up to 20 μM, which makes them promising Plasmodium selective substances for further investigations.     

Diurnal variations in the photosynthesis-respiration activity of a cyanobacterial bloom in a freshwater dam reservoir: an isotopic study

The stable isotopic analyses of molecular oxygen dissolved in water (delta18O(DO)) and dissolved inorganic carbon (delta13C(DIC)), supplemented with basic chemical measurements, have been carried out on a diurnal basis to better understand the dynamics of photosynthesis and respiration in freshwater systems. Our observations have been carried out in a lowland dam reservoir, the Sulejow Lake (central Poland), during the summer cyanobacterial bloom. All data obtained, isotopic, hydrochemical, and biological, show a high mutual consistency. Namely, the lowest delta18O(DO) values, obtained at 10:00 and 14:00 (16.0 and 15.5 per thousand, respectively), correspond to the highest amount of cyanobacterial cells observed (66 and 63 mg dm(-3), respectively), whereas the minimum delta13C(DIC) (-10.6 per thousand) obtained at 22:00 corresponds to the maximum content of organic matter (110 mg dm(-3)). This evidence suggests that isotopic assays of delta18O(DO) and delta13C(DIC) are a reliable tool for the quantitative study of biochemical processes in freshwater systems.     

Polyethyleneimine coating renders polycarbonate resistant to organic solvents

We propose a method for the modification of surfaces of microchannels in chips fabricated in polycarbonate (PC) that makes the devices resistant to a range of organic solvents. Coating of PC with branched polyethyleneimine (BPEI) with the use of trimethylpropane triglycidyl ether (TTE) as a linker renders the devices resistant to toluene, benzene, acetonitrile, tetrahydrofuran, dioxane and ethylene dichloride. The optimized procedure of modification allows for continuous operation of the chips for several hours without dissolution of PC. Additional modification with the use of Krytox? allows for the use of Fluorinert (FC-40) as the continuous phase and for generation and handling of droplets of organic solvents that are miscible with water.     

Effect of the orientation of the optic axis on simulated scattering matrix elements of small birefringent particles

We study how the orientation of the optic axis affects single-scattering properties for small, birefringent calcite particles simulated using DDSCAT 7.1.1. We consider two irregular model particles, a flake and a rhomboid, in either a (i)?fixed or (ii)?random orientation. Simulations are performed for three volume-equivalent radii of 0.1, 0.45, and 1.0?μm. For each target, we repeat the computations for three sets of orientations of the optic axis. When a fixed spatial orientation of the target is considered, the simulations are significantly affected by the orientation of the optic axis. However, the effect is considerably weaker when assuming the same targets in random spatial orientation.     

Thermodynamic dissociation constants of silychristin, silybin, silydianin and mycophenolate by the regression analysis of spectrophotometric data

Mixed dissociation constants of four drug acids, i.e. silychristin, silybinin, silydianin and mycophenolate at various ionic strengths I of range 0.01 and 0.30 and at temperatures of 25 and 37 °C were determined using the SQUAD(84) regression analysis program applied to pH-spectrophotometric titration data. The proposed strategy of an efficient experimentation in a protonation constants determination, followed by a computational strategy for the chemical model with a protonation constants determination, is presented on the protonation equilibria of silychristin. The thermodynamic dissociation constant pK_a^T was estimated by non-linear regression of {pK_a, I} data at 25 and 37 °C: for silychristin pK_a,1^T=6.52(16) and 6.62(1), pK_a,2^T=7.22(13) and 7.41(5), pK_a,3^T=8.96(9) and 8.94(9), pK_a,4^T=10.17(7) and 10.03(8), pK_a,5^T=11.89(4) and 11.63(7); for silybin pK_a,1^T=7.00(4) and 6.86(5), pK_a,2^T=8.77(11) and 8.77(3), pK_a,3^T=9.57(8) and 9.62(1), pK_a,4^T=11.66(3) and 11.38(1); for silydianin pK_a,1^T=6.64(7) and 7.10(6), pK_a,2^T=7.78(5) and 8.93(1), pK_a,3^T=9.66(9) and 10.06(11), pK_a,4^T=10.71(7) and 10.77(7), pK_a,5^T=12.26(5) and 12.14(5); for mycophenolate pK_a^T=8.32(1) and 8.14(1). Goodness-of-fit tests for various regression diagnostics enabled the reliability of parameter estimates to be found.