Self-assembling diblock copolymers of poly[N-(2-hydroxypropyl)methacrylamide] and a beta-sheet peptide

The self-assembly of hybrid diblock copolymers composed of poly(HPMA) and beta-sheet peptide P11 (CH(3)CO-QQRFQWQFEQQ-NH(2)) blocks was investigated. Copolymers were synthesized via thiol-maleimide coupling reaction, by conjugation of semitelechelic poly(HPMA)-SH with maleimide-modified beta-sheet peptide. As expected, CD and CR binding studies showed that the peptide block imposed its beta-sheet structural arrangement on the structure of diblock copolymers. TEM and AFM proved that peptide and these copolymers had the ability to self-assemble into fibrils.     

A new Fenchel dual problem in vector optimization

We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.     

Adiabatic Non-Equilibrium Steady States in the Partition Free Approach

Consider a small sample coupled to a finite number of leads and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a non-equilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jakšić–Pillet–Ruelle approach. Thus we partly settle a question asked by Caroli et al. (J. Phys. C Solid State Phys. 4(8):916–929, 1971) regarding the (non)equivalence between the partitioned and partition-free approaches.     

A Planning Algorithm for Correction Therapies After Allogeneic Stem Cell Transplantation

In this paper we continue the investigation of a basic mathematical model describing the dynamics of three cell lines after allogeneic stem cell transplantation: normal host cells, leukemic host cells and donor cells, whose evolution ultimately lead either to the normal hematopoietic state achieved by the expansion of the donor cells and the elimination of the host cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the other cell lines. A theoretical basis for the control of post-transplant evolution is provided. We describe several scenarios of change of system parameters by which a bad post-transplant evolution can be corrected and turned into a good one and we propose therapy planning algorithms for guiding the correction treatment.     

Dissipation anomaly and energy cascade in 3D incompressible flows

The purpose of this Note is to present a mathematical evidence of the dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical scales of 3D incompressible flows recently introduced by the authors.     

Spinning black strings in five-dimensional Einstein–Gauss–Bonnet gravity

We construct generalizations of the D=5$D=5$ Kerr black string by including higher curvature corrections to the gravity action in the form of the Gauss–Bonnet density. These uniform black strings satisfy a generalized Smarr relation and share the basic properties of the Einstein gravity solutions. However, they exist only up to a maximal value of the Gauss–Bonnet coupling constant, which depends on the solutions? mass and angular momentum.     

New Polymeric Adsorbents Functionalized with Aminobenzoic Groups for the Removal of Residual Antibiotics

In this paper, we present the synthesis of new polymeric adsorbents derived from macroporous chloromethylated styrene–divinylbenzene (DVB) copolymers with different cross-linking degrees functionalized with the following aminobenzoic groups: styrene—6.7% DVB (PAB1), styrene—10% DVB (PAB2), and styrene—15% DVB (PAB3). The new polymeric products, PAB1, PAB2, and PAB3, were characterized by FTIR spectroscopy, thermogravimetric analysis, and EDX, SEM, and BET analysis, respectively. The evolution of the functionalization reaction was followed by FTIR spectroscopy, which revealed a decrease in the intensity of the γCH₂Cl band at 1260 cm⁻¹, and, simultaneously, the appearance of C=O carboxylic bands from 1685–1695 cm⁻¹ and at 1748 cm⁻¹. The thermal stability increased with the increase in the cross-linking degree. The data obtained from the EDX analysis of the novel cross-linked copolymers confirmed the functionalization with aminobenzoic groups through the presence and content of nitrogen, as follows: PAB1: N% = 0.47; PAB2: N% = 0.85; and PAB3: N% = 1.30. The adsorption performances of the novel polymeric adsorbents, PAB1, PAB2, and PAB3, were tested in the adsorption of three antibiotics, tetracycline, sulfamethoxazole, and amoxicillin, from aqueous solutions, by using extensive kinetic, equilibrium, and thermodynamic studies. The best adsorption capacity was demonstrated by the tetracycline. Amoxicillin adsorption was also attempted, but it did not show positive results.     

Unprecedented Relaxivity Gap in pH-Responsive FeIII-Based MRI Probes

Two mononuclear ferric complexes are reported that respond to a pH change with a 27- and 71-fold jump, respectively, in their capacity to accelerate the longitudinal relaxation rate of water-hydrogen nuclei, and this starting from a negligible base value of only 0.06. This unprecedented performance bodes well for tackling the sensitivity issues hampering the development of Molecular MRI. The two chelates also excel in the fully reversible and fatigue-less nature of this phenomenon. The structural reasons for this performance reside in the macrocyclic nature of the hexa-dentate ligand, as well as the presence of a single pendant arm displaying a five-membered lactam or carbamate which show (perturbed) pK_a values of 3.5 in the context of this N6 N5O1 coordination motif.     

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Mathematical Programming - We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control...     

Positive radial solutions for Dirichlet problems via a Harnack-type inequality

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving $\varphi$-Laplacian operators in a ball. In particular, $p$-Laplacian and Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to a Harnack-type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.