Quadratic stochastic operators on Banach lattices

We study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval \(S = [0, f]\) of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.     

The Bolzano mean-value theorem and partial differential equations

We study the existence of solutions to abstract equations of the form $0=Au+F(u)$, $u\in K?E$, where A is an abstract differential operator acting in a Banach space E, K is a closed convex set of constraints being invariant with respect to resolvents of A and a perturbation F satisfies a certain tangency condition. Such problems are closely related to the so-called Poincaré–Miranda theorem, being the multi-dimensional counterpart of the celebrated Bolzano intermediate value theorem. In fact our main results should be regarded as infinite-dimensional variants of Bolzano and Miranda–Poincaré theorems. Along with single-valued problems we deal with set-valued ones, yielding the existence of the so-called constrained equilibria of set-valued maps. The abstract results are applied to show existence of (strong) steady state solutions to some weakly coupled systems of drift reaction–diffusion equations or differential inclusions of this type. In particular we get the existence of strong solutions to the Dirichlet, Neumann and periodic boundary problems for elliptic partial differential inclusions under the presence of state constraints of different type. Certain aspects of the Bernstein theory for bvp for second order ODE are studied, too. No assumptions concerning structural coupling (monotonicity, cooperativity) are undertaken.     

Green Synthesis of Silver Nanoparticles Using Natural Extracts with Proven Antioxidant Activity

Natural extracts are a rich source of biomolecules that are useful not only as antioxidant drugs or diet supplements but also as complex reagents for the biogenic synthesis of metallic nanoparticles. The natural product components can act as strong reducing and capping substrates guaranteeing the stability of formed NPs. The current work demonstrates the suitability of extracts of Camellia sinensis, Ilex paraguariensis, Salvia officinalis, Tilia cordata, Levisticum officinale, Aegopodium podagraria, Urtica dioica, Capsicum baccatum, Viscum album, and marine algae Porphyra Yezoensis for green synthesis of AgNPs. The antioxidant power of methanolic extracts was estimated at the beginning according to their free radical scavenging activity by the DPPH method and reducing power activity by CUPRAC and SNPAC (silver nanoparticle antioxidant capacity) assays. The results obtained by the CUPRAC and SNAPC methods exhibited excellent agreement (R²~0.9). The synthesized AgNPs were characterized by UV-vis spectroscopy, Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDX), dynamic light scattering (DLS) particle size, and zeta potential. The UV-vis absorption spectra showed a peak at 423 nm confirming the presence of AgNPs. The shapes of extract-mediated AgNPs were mainly spherical, spheroid, rod-shaped, agglomerated crystalline structures. The NPs exhibited a high negative zeta potential value in the range from −49.8 mV to −56.1 mV, proving the existence of electrostatic stabilization. FTIR measurements indicated peaks corresponding to different functional groups such as carboxylic acids, alcohol, phenol, esters, ethers, aldehydes, alkanes, and proteins, which were involved in the synthesis and stabilization of AgNPs. Among the examined extracts, green tea showed the highest activity in all antioxidant tests and enabled the synthesis of the smallest nanoparticles, namely 62.51, 61.19, and 53.55 nm, depending on storage times of 30 min, 24 h, and 72 h, respectively. In turn, the Capsicum baccatum extract was distinguished by the lowest zeta potential, decreasing with storage time from −66.0 up to −88.6 mM.     

Spectroscopic Studies of Quinobenzothiazine Derivative in Terms of the In Vitro Interaction with Selected Human Plasma Proteins. Part 1

Plasma proteins play a fundamental role in living organisms. They participate in the transport of endogenous and exogenous substances, especially drugs. 5-alkyl-12(H)-quino[3,4-b][1,4]benzothiazinium salts, have been synthesized as potential anticancer substances used for cancer treatment. Most anticancer substances generate a toxic effect on the human body. In order to check the toxicity and therapeutic dosage of these chemicals, the study of ligand binding to plasma proteins is very relevant. The present work presents the first comparative analysis of the binding of one of the 5-alkyl-12(H)-quino[3,4-b][1,4]benzothiazinium derivatives (Salt1) with human serum albumin (HSA), α-1-acid glycoprotein (AGP) and human gamma globulin (HGG), assessed using fluorescence, UV-Vis and CD spectroscopy. In order to mimic in vivo ligand–protein binding, control normal serum (CNS) was used. Based on the obtained data, the Salt1 binding sites in the tertiary structure of all plasma proteins and control normal serum were identified. Both the association constants (K_a) and the number of binding site classes (n) were calculated using the Klotz method. The strongest complex formed was Salt1–AGP_complex (K_a = 7.35·10⁴ and 7.86·10⁴ mol·L⁻¹ at excitation wavelengths λ_ex of 275 and 295 nm, respectively). Lower values were obtained for Salt1–HSA_complex (K_a = 2.45·10⁴ and 2.71·10⁴ mol·L⁻¹) and Salt1–HGG_complex (K_a = 1.41·10⁴ and 1.33·10⁴ mol·L⁻¹) at excitation wavelengths λ_ex of 275 and 295 nm, respectively, which is a positive phenomenon and contributes to the prolonged action of the drug. Salt1 probably binds to the HSA molecule in Sudlow sites I and II; for the remaining plasma proteins studied, only one binding site was observed. Moreover, using circular dichroism (CD), fluorescence and UV-Vis spectroscopy, no effect on the secondary and tertiary structures of proteins in the absence or presence of Salt1 has been demonstrated. Despite the fact that the conducted studies are basic, from the scientific point of view they are novel and encourage further in vitro and in vivo investigations. As a next part of the study (Part 2), the second new synthetized quinobenzothiazine derivative (Salt2) will be analyzed and published.     

High Density Polyethylene Containing Antibacterial Silver Nanoparticles for Medical Applications

High density polyethylene (HDPE) and composites with silver nanoparticles were processed via extrusion and injection moulding. The materials thus produced were tested against Gram-positive Staphylococcus aureus and Gram-negative Escherichia coli. The release of silver ions Ag⁺ from composites was measured by means of ICP-MS method. Surface parameters such as wettability and roughness were determined because of their effect on the most important processes at biomaterial interface. Scanning electron microscopy was used to investigate the microstructure. Durability tests of polymer and composite materials were carried out in a simulated biological solution by monitoring the pH and electrical conductivity, mass changes as well as the longitudinal ultrasonic wave measurements. Antibacterial tests prove that nanosilver modified materials have bactericidal activity against tested bacteria. Biological durability studies reveal stable behavior of incubated materials. Spectrometric analysis shows that the amount of silver release depends on the immersion time and the amount of nanopowder introduced into the polymer matrix.     

Geometry of isotypic Kronecker webs

An isotypic Kronecker web is a family of corank m foliations such that the curve of annihilators t ↦ (T _x F _t )^⊥ ∈ Gr _m (T _x * M) is a rational normal curve in the Grassmannian Gr _m (T _x *M) at any point x ∈ M. For m = 1 we get Veronese webs introduced by I. Gelfand and I. Zakharevich [Gelfand I.M., Zakharevich I., Webs, Veronese curves, and bi-Hamiltonian systems, J. Funct. Anal., 1991, 99(1), 150–178]. In the present paper, we consider the problem of local classification of isotypic Kronecker webs and for a given web we construct a canonical connection. We compute the curvature of the connection in the case of webs of equal rank and corank. We also show the correspondence between Kronecker webs and systems of ODEs for which certain sets of differential invariants vanish. The equations are given up to contact transformations preserving independent variable. As a particular case, with m = 1 we obtain the correspondence between Veronese webs and ODEs.     

Uniqueness of solutions to an Abel type nonlinear integral equation on the half line

We consider a convolution-type integral equation u = k ? g(u) on the half line (???; a), a ?? ?, with kernel k(x) = x ^???1, 0 < ??, and function g(u), continuous and nondecreasing, such that g(0) = 0 and 0 < g(u) for 0 < u. We concentrate on the uniqueness problem for this equation, and we prove that if ?? ?? (1, 4), then for any two nontrivial solutions u ₁, u ₂ there exists a constant c ?? ? such that u ₂(x) = u ₁(x +c), ??? < x. The results are obtained by applying Hilbert projective metrics.     

Revisiting the Reactivity of Uracil During Collision Induced Dissociation: Tautomerism and Charge-Directed Processes

In our recent work towards the nontarget identification of products of nucleic acid (NA) damage in urine, we have found previous work describing the dissociation of NA bases not adequate to fully explain their observed reactivity. Here we revisit the gas-phase chemistry of protonated uracil (U) during collision induced dissociation (CID) using two modern tandem mass spectrometry techniques; quadrupole ion trap (QIT) and quadrupole time of flight (Q-TOF). We present detailed mechanistic proposals that account for all observed products of our experiments and from previous isotope labeling data, and that are supported by previous ion spectroscopy results and theoretical work. The diverse product-ions of U cannot be explained adequately by only considering the lowest energy form of protonated U as a precursor. The tautomers adopted by U during collisional excitation make it possible to relate the complex reactivity observed to reasonable mechanistic proposals and feasible product-ion structures for this small highly conjugated heterocycle. These reactions proceed from four different stable tautomers, which are excited to a specific activated precursor from which dissociation can occur via a charge-directed process through a favorable transition state to give a stabilized product. Understanding the chemistry of uracil at this level will facilitate the identification of new modified uracil derivatives in biological samples based solely on their reactivity during CID. Our integrated approach to describing ion dissociation is widely applicable to other NA bases and similar classes of biomolecules.     

Enhanced mobility in P3HT-based OTFTs upon blending with a phenylene-thiophene-thiophene-phenylene small molecule

An enhancement in charge transport capacity in a poly(3-hexylthiophene) (P3HT) semicrystalline film, up to field-effect mobilities approaching 0.1 cm(2) V(-1) s(-1), has been achieved by co-deposition with a small molecule, i.e. 5,5'-bis(4-n-hexylphenyl)-2,2'-bithiophene (dH-PTTP), forming highly ordered crystals bridging large polymeric domains.