Optimal control of continuity equations

An optimal control problem for the continuity equation is considered. The aim of a “controller” is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular case of the problem, where an initial distribution is absolutely continuous with smooth density and the target set has certain regularity properties, a necessary optimality condition is derived. It is shown that for the general problem one may construct a perturbed problem that satisfies all the assumptions of the necessary optimality condition, and any optimal control for the perturbed problem, is nearly optimal for the original one.     

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre–Pólya class are investigated. The main result of this paper establishes new moment inequalities for a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre–Pólya class and the Riemann -function.     

Chirality of nuclear rotation

It is shown that the rotating mean field of triaxial nuclei can break the chiral symmetry. Two nearly degenerate DeltaI=1 rotational bands originate from the left-handed and right-handed solutions.     

Synthesis and characterization of two intensely colored tris(benzoylcyanoxime)iron(II) anionic complexes

Two intensely blue-colored complexes, P(C 6H 5) 4[Fe(BCO) 3] ( 1) and Na[Fe(BCO) 3] ( 2), where BCO (-) is the benzoylcyanoxime anion, have been prepared and characterized in solution and in the solid state. The crystal structure of 1 has been determined at several temperatures (100, 155, 225, and 293 K) and consists of layers of P(C 6H 5) 4 (+) cations and [Fe(BCO) 3] (-) anions. The latter exist as a pair of fac-Delta and Lambda enantiomers in a monoclinic unit cell in the P2(1)/ n space group. Iron(II) has a trigonal-prismatic N 3O 3 coordination environment with average Fe-N and Fe-O bond distances of 1.866 and 1.956 A, respectively, bonds that are unusually short and indicate a (1)A 1g low-spin ground state for iron(II). A sample of 1 prepared with iron-57 has been studied by Mossbauer spectroscopy between 4.2 and 430 K and found to be low-spin iron(II) in studied temperature range. The stepwise formation constants for 1 in aqueous solution at 296 K and pH of 7 are log beta 1 = 0.85 +/- 0.1, log beta 2 = 3.55 +/- 0.15, and log beta 3 = 6.36 +/- 0.15. Both 1 and 2 exhibit irreversible oxidation of iron(II) at approximately 1.0 V, indicating a significant degree of the ligand-to-iron charge transfer. Thus, 1 and 2 are rare examples of highly colored iron(II) anionic complexes that do not contain aromatic heterocyclic amine ligands, such as bipyridine or phenanthroline.     

Synthesis and Characterization of Titanium Oxide Nanoparticles by Plasma in Contact with Liquid

Plasma Chemistry and Plasma Processing - Two types of plasma in contact with water were employed for the synthesis of mixed-phase TiO2 in a liquid. This is glow discharge with a metal cathode and...     

Versatile Reactivity of MnII Complexes in Reactions with N-Donor Heterocycles: Metamorphosis of Labile Homometallic Pivalates vs. Assembling of Endurable Heterometallic Acetates

Reaction of 2,2′-bipyridine (2,2′-bipy) or 1,10-phenantroline (phen) with [Mn(Piv)₂(EtOH)]_n led to the formation of binuclear complexes [Mn₂(Piv)₄L₂] (L = 2,2′-bipy (1), phen (2); Piv⁻ is the anion of pivalic acid). Oxidation of 1 or 2 by air oxygen resulted in the formation of tetranuclear Mn^II/III complexes [Mn₄O₂(Piv)₆L₂] (L = 2,2′-bipy (3), phen (4)). The hexanuclear complex [Mn₆(OH)₂(Piv)₁₀(pym)₄] (5) was formed in the reaction of [Mn(Piv)₂(EtOH)]_n with pyrimidine (pym), while oxidation of 5 produced the coordination polymer [Mn₆O₂(Piv)₁₀(pym)₂]_n (6). Use of pyrazine (pz) instead of pyrimidine led to the 2D-coordination polymer [Mn₄(OH)(Piv)₇(µ₂-pz)₂]_n (7). Interaction of [Mn(Piv)₂(EtOH)]_n with FeCl₃ resulted in the formation of the hexanuclear complex [Mn^II₄Fe^III₂O₂(Piv)₁₀(MeCN)₂(HPiv)₂] (8). The reactions of [MnFe₂O(OAc)₆(H₂O)₃] with 4,4′-bipyridine (4,4′-bipy) or trans-1,2-(4-pyridyl)ethylene (bpe) led to the formation of 1D-polymers [MnFe₂O(OAc)₆L₂]_n·2nDMF, where L = 4,4′-bipy (9·2DMF), bpe (10·2DMF) and [MnFe₂O(OAc)₆(bpe)(DMF)]_n·3.5nDMF (11·3.5DMF). All complexes were characterized by single-crystal X-ray diffraction. Desolvation of 11·3.5DMF led to a collapse of the porous crystal lattice that was confirmed by PXRD and N₂ sorption measurements, while alcohol adsorption led to porous structure restoration. Weak antiferromagnetic exchange was found in the case of binuclear Mn^II complexes (J_Mn-Mn = −1.03 cm⁻¹ for 1 and 2). According to magnetic data analysis (J_Mn-Mn = −(2.69 ÷ 0.42) cm⁻¹) and DFT calculations (J_Mn-Mn = −(6.9 ÷ 0.9) cm⁻¹) weak antiferromagnetic coupling between Mn^II ions also occurred in the tetranuclear {Mn₄(OH)(Piv)₇} unit of the 2D polymer 7. In contrast, strong antiferromagnetic coupling was found in oxo-bridged trinuclear fragment {MnFe₂O(OAc)₆} in 11·3.5DMF (J_Fe-Fe = −57.8 cm⁻¹, J_Fe-Mn = −20.12 cm⁻¹).     

Synthesis and Antiviral Activity of Camphene Derivatives against Different Types of Viruses

To date, the ‘one bug-one drug’ approach to antiviral drug development cannot effectively respond to the constant threat posed by an increasing diversity of viruses causing outbreaks of viral infections that turn out to be pathogenic for humans. Evidently, there is an urgent need for new strategies to develop efficient antiviral agents with broad-spectrum activities. In this paper, we identified camphene derivatives that showed broad antiviral activities in vitro against a panel of enveloped pathogenic viruses, including influenza virus A/PR/8/34 (H1N1), Ebola virus (EBOV), and the Hantaan virus. The lead-compound 2a, with pyrrolidine cycle in its structure, displayed antiviral activity against influenza virus (IC₅₀ = 45.3 µM), Ebola pseudotype viruses (IC₅₀ = 0.12 µM), and authentic EBOV (IC₅₀ = 18.3 µM), as well as against pseudoviruses with Hantaan virus Gn-Gc glycoprotein (IC₅₀ = 9.1 µM). The results of antiviral activity studies using pseudotype viruses and molecular modeling suggest that surface proteins of the viruses required for the fusion process between viral and cellular membranes are the likely target of compound 2a. The key structural fragments responsible for efficient binding are the bicyclic natural framework and the nitrogen atom. These data encourage us to conduct further investigations using bicyclic monoterpenoids as a scaffold for the rational design of membrane-fusion targeting inhibitors.     

Effects of Curcumin and Ferulic Acid on the Folding of Amyloid-β Peptide

The polyphenols curcumin (CU) and ferulic acid (FA) are able to inhibit the aggregation of amyloid-β (Aβ) peptide with different strengths. CU is a strong inhibitor while FA is a weaker one. In the present study, we examine the effects of CU and FA on the folding process of an Aβ monomer by 1 µs molecular dynamics (MD) simulations. We found that both inhibitors increase the helical propensity and decrease the non-helical propensity of Aβ peptide. They prevent the formation of a dense bulk core and shorten the average lifetime of intramolecular hydrogen bonds in Aβ. CU makes more and longer-lived hydrogen bonds, hydrophobic, π–π, and cation–π interactions with Aβ peptide than FA does, which is in a good agreement with the observed stronger inhibitory activity of CU on Aβ aggregation.     

Benz(2-heteroaryl)cyanoximes and their Tl(i) complexes: new room temperature blue emitters

A series of five 2-heteroarylcyanoximes such as: alpha-oximino-(2-benzimidazolyl)acetonitrile (HBIHCO), alpha-oximino-(N-methy-l-2-benzimidazolyl)acetonitrile (HBIMCO), alpha-oximino-(2-benzoxazolyl)acetonitrile (HBOCO), alpha-oximino-(2-benzothiazolyl)acetonitrile (HBTCO) and alpha-oximino-(2-quinolyl)acetonitrile (HQCO) and their monovalent thallium(i) complexes were synthesized and characterized using spectroscopic methods ((1)H, (13)C NMR, IR, UV-visible, mass-spectrometry) and X-ray analysis. The HBIMCO (as monohydrate) adopts planar trans-anti configuration in the solid state. The crystal structure of "HBOCO" revealed the presence of nitroso anion a, BOCO(-), and protonated oxime cation b, H(2)BOCO(+), that form a H-bonded dimer in the unit cell. Both molecules adopt planar structures, but different configurations: cis-anti in the molecule a, and trans-anti for b. This is the first reported case of a zwitterionic pair in oximes and the coexistence of the two geometrical cis/trans isomers in the same crystal. All 2-heteroarylcyanoximes form yellow anions upon deprotonation, which exhibit significant negative solvatochromism in solution. Heterogeneous reactions between hot aqueous solutions of Tl(2)CO(3) and solid protonated 2-heteroarylcyanoximes HL afford yellow TlL. The crystal structure of Tl(BTCO) shows the formation of centrosymmetrical dimers, which connect with each other to form a double-stranded one-dimensional coordination polymer. The oxygen atom of the oxime group acts as a bridge between the three different Tl(i) centers. The anion is non-planar and adopts a trans-anti configuration in the complex. The polymeric motif in the complex represents a ladder-type structure. Staggered pi-pi interactions between benzothiazolyl groups provide additional stabilization of the structure. Both organic ligands and their Tl(i) complexes exhibit strong room temperature blue emission in the solid state.     

Complex of calcium receptor blocker nifedipine with glycyrrhizic acid

Physicochemical methods were used to explore the regularities of complexing between the calcium channel blocker nifedipine (NF) and pharmaceutically acceptable complex-forming glycyrrhizic acid (GA) in view of the discovered influence of GA on the therapeutic activity of NF. 1H NMR (including relaxation measurements) and UV-vis spectra have produced illustrative evidence that NF forms stable complexes with GA within a wide concentration range, from 0.05 to 5 mM. At low GA concentrations, below 0.5 mM, NF forms an inclusion complex where each NF molecule is bound by two molecules of GA. Computer simulations of the NMR experimental data have shown that, in aqueous solution, the stability constant of this complex, K, is about 10(5) M(-1). At higher concentrations, GA forms large micelle-like aggregates which increase the water solubility of NF. Quenching of chemically induced dynamic nuclear polarization effects in the photoinduced interaction of the NF-GA complex with tyrosine suggests that complex formation with GA completely blocks the single electron-transfer step between NF and the amino acid. This, arguably, could explain the increased therapeutic activity of GA complexes, since GA might protect the drug molecule from the reaction with amino acid residues of the receptor binding site.