Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.     

Solving the robust two-stage capacitated facility location problem with uncertain transportation costs

In this study, we start from a multi-source variant of the two-stage capacitated facility location problem (TSCFLP) and propose a robust optimization model of the problem that involves the uncertainty of transportation costs. Since large dimensions of the robust TSCFLP could not be solved to optimality, we design a memetic algorithm (MA), which represents a combination of an evolutionary algorithm (EA) and a modified simulated annealing heuristic (SA) that uses a short-term memory of undesirable moves from previous iterations. A set of computational experiments is conducted to examine the impact of different protection levels on the deviation of the objective function value. We also investigate the impact of variations of transportation costs that may occur on both transhipment stages on the total cost for a fixed protection level. The obtained results may help in identifying a sustainable and efficient strategy for designing a two stage capacitated transportation network with uncertain transportation costs, and may be applicable in the design and management of similar transportation networks.     

Calderón problem for connections

In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9 Dos Santos Ferreira, D., Kenig, C., Salo, M., Uhlmann, G. (2009). Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178:119–171.[Crossref], [Web of Science ®] , [Google Scholar]] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11 Dos Santos Ferreira, D., Kurylev, Y., Lassas, M., Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. J. Eur. Math. Soc., 18:2579–2626.[Crossref], [Web of Science ®] , [Google Scholar]]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy.     

Influence of selected mobile phase properties on the TLC retention behavior of ziprasidone and its impurities

ABSTRACT

Influence of nine different solvents, either alone or in a mixture, on the retention behavior of ziprasidone and its five impurities were examined by normal-phase thin-layer chromatography. Migration distances of the examined compounds obtained under the examined chromatographic conditions were correlated with calculated mobile phase properties, such as Snyder polarity and Hansen solubility. Linear or second-order polynomial relationships with high correlation coefficients were established between investigated variables. The obtained mathematical functions and statistical results indicated that selected mobile phase properties can be used for the prediction of the retention behavior of ziprasidone and its five impurities.     

New gold(III) chlorophenyl terpyridine complex: Biomolecular interactions and anticancer activity against human oral squamous cell carcinoma

In this work we synthesized new monofunctional gold(III) complex [Au(Cl-Ph-tpy)Cl]Cl₂ (Cl-Ph-tpy = 4′-[4-chlorophenyl]-2,2′:6′, 2″-terpyridine). This complex was characterized by UV–Vis, NMR, IR, and ESI-MS spectrometry. The kinetic study of the substitution reactions of the Au-Cl-Ph-tpy complex with biomolecules showed that the rate constants depend on the nature of the entering nucleophile. Based on the calculated values of entropy (∆H^≠ > 0) and enthalpy (∆S^≠ < 0) the proposed substitution mechanism is associative. Additionally, the relative stability and thermodynamic properties of Au-Cl-Ph-tpy complex were compared with the analogue Au-tpy complex by the B3LYP/def2-svp method. DNA/BSA binding studies showed that Au-Cl-Ph-tpy complex interacts with CT DNA through the intercalation and moderately quenches the fluorescence of tryptophan residues in serum albumin (BSA). Molecular docking confirmed results obtained by spectroscopic experiments and suggested site I (subdomain IIA) for binding of Au complex to BSA. We demonstrated that the Au chlorophenyl terpyridine complex possessed significant in vitro cytotoxic activity against human oral squamous carcinoma cells (CAL-27), induced apoptosis, inhibited proliferation of CAL-27 cells, and induced cell cycle disturbance. Treatment of CAL-27 cells with the Au complex enhanced expression of cyclin-dependent kinase inhibitors p21 and p27, resulting in cell cycle arrest in the G1 phase, reduced the percentage of CAL-27 cells in S phase and decreased expression of Ki-67. Additionally, Au complex reduced expression of phosphorylated STAT3 and downstream regulated molecules associated with cancer stemness, NANOG, and Sox2 protein.     

Efficient templated synthesis of donor-acceptor rotaxanes using click chemistry

The mild reaction conditions, remarkable functional group compatibility, and complete regioselectivity of the Cu-catalyzed Huisgen 1,3-dipolar cycloaddition ("click chemistry") between organic azides and terminal alkynes have led to a threading-followed-by-stoppering approach to the synthesis of donor-acceptor rotaxanes incorporating cyclobis(paraquat-p-phenylene) (CBPQT4+) as the pi-accepting ring component. Rotaxane formation is initiated by reacting azide-functionalized pseudorotaxanes containing pi-donating 1,5-dioxynaphthalene (DNP) recognition units with appropriate alkyne-functionalized stoppers. The high yields obtained in this efficient, kinetically controlled post-assembly covalent modification, as well as the excellent convergence of the synthetic protocol, are demonstrated by the preparation of [2]-, [3]-, and [4]rotaxanes containing multiple DNP/CBPQT4+ donor-acceptor recognition motifs.     

Thermally stimulated depolarization current of novolac resin

A novolac phenol-formaldehyde resin was investigated via the thermally stimulated depolarization current, using integral and partial measurements in the temperature range from 137 to 270 K. Tow broadened peaks, assigned as Β₁, and Β₂, appeared at about 160 and 190 K. The influence of water and ¯M_n was investigated. The activation energy E_a vs. T relationship was analysed, and a search was made for compensation phenomena. The distribution of the relaxing dipolesN vs. E_a was approximated. Three different relaxation ranges were distinguished. All the motions were attributed to the rotation of the phenyl rings. The differences found are due to the heterogeneity in the resin. Contamination with water increases the polarizability, decreases the structure differences and relieves the motions in the resin. A resin with a smaller ¯M_n exhibits a higher polarizability and a decreases in structure variety.     

Silver(I) mediated folding of a molecular basket

We have investigated Ag(I) mediated folding of a tridentate compound, containing three pyridine flaps tethered to a semirigid scaffold, into a molecular basket, using both experimental and theoretical methods. The basket formation has been shown to be highly favorable in organic media (Delta G degrees = -7.2 kcal/mol), with the assembly process allowing for another ligand to bind preferentially on the outer side.