Strongly regular graphs associated with ternary bent functions

We prove a new characterization of weakly regular ternary bent functions via partial difference sets. Partial difference sets are combinatorial objects corresponding to strongly regular graphs. Using known families of bent functions, we obtain in this way new families of strongly regular graphs, some of which were previously unknown. One of the families includes an example in [N. Hamada, T. Helleseth, A characterization of some {3v₂+v₃,3v₁+v₂,3,3}-minihypers and some [15,4,9;3]-codes with B₂=0, J. Statist. Plann. Inference 56 (1996) 129-146], which was considered to be sporadic; using our results, this strongly regular graph is now a member of an infinite family. Moreover, this paper contains a new proof that the Coulter-Matthews and ternary quadratic bent functions are weakly regular.     

Lanthanide-based hexanuclear complexes usable as molecular precursors for new hybrid materials

Lanthanide containing octahedral hexanuclear complexes with general chemical formula [Ln₆O(OH)₈(NO₃)₆(H₂O)_x].2NO₃.yH₂O where Ln = Ce–Lu (except Pm) or Y, x = 0, 6, 12, 14 or 16 and y = 0, 2, 4 or 5 constitute a great family of polymorphic compounds. The synthesis and the crystal structures of all these compounds are overviewed. The hydration/dehydration processes that allow the structural transitions from one compound to another are described. The crystal structure of compounds with general chemical formula [Ln₆O(OH)₈(NO₃)₆(H₂O)₆].2NO₃ where Ln = Ce–Lu (except Pm) or Y is described. It has been solved on the basis of a powder XRD diagram. The use of such hexanuclear complexes as molecular precursors for new materials is also discussed.     

Weighted multiple interpolation and the control of perturbed semigroup systems

In this paper, the controllability and admissibility of perturbed semigroup systems are studied, using tools from the theory of interpolation and Carleson measures. In addition, there are new results on the perturbation of Carleson measures and on the weighted interpolation of functions and their derivatives in Hardy spaces, which are of interest in their own right.     

A new class of symmetric (v,k, λ)-designs

We construct new families of symmetric (v, k, )-designs with parameters

Ueber den Arsengehalt des Glases und der Alkalien

Ohne Zusammenfassung     

An estimate for weighted Hilbert transform via square functions

We show that the norm of the Hilbert transform as an operator on the weighted space is bounded by a constant multiple of the power of the constant of , in other words by . We also give a short proof for sharp upper and lower bounds for the dyadic square function.

     

On the Linear Complexity of the Sidelnikov-Lempel-Cohn-Eastman Sequences

In [6] and [10], a construction of binary sequences with an (almost) optimal autocorrelation spectrum is suggested. We continue the study of the linear complexity and the linear feedback polynomial of these sequences over $ \mathbb{F} $ ₂, originated in [4].     

β-Carotene: Preventive Role for Type 2 Diabetes Mellitus and Obesity: A Review

Carotenoids are vital antioxidants for plants and animals. They protect cells from oxidative events and act against the inflammatory process and carcinogenesis. Among the most abundant carotenoids in human and foods is β-carotene. This carotenoid has the highest level of provitamin A activity, as it splits into two molecules of retinol through the actions of the cytosolic enzymes: β-carotene-15,15′-monooxygenase (β-carotene-15,15′-oxygenase 1) and β-carotene-9′,10′-dioxygenase (β-carotene-9′,10′-oxygenase 2). The literature supports the idea that β-carotene acts against type 2 diabetes mellitus, cardiovascular diseases, obesity, and metabolic syndrome. Due to the many processes involved in β-carotene biosynthesis and metabolic function, little is known about such components, since many mechanisms have not yet been fully elucidated. Therefore, our study concisely described the relationships between the consumption of carotenoids, with emphasis on β-carotene, and obesity and type 2 diabetes mellitus and its associated parameters in order to understand the preventive role of carotenoids better and encourage their consumption.     

Effect of Photobiomodulation on Repairing Pressure Ulcers in Adult and Elderly Patients: A Systematic Review

Evaluation of photobiomodulation therapy (PBMT) in the treatment of pressure ulcers in adults and the elderly. Systematic review, based on the recommendations of the handbook, proposed by Cochrane. The search was carried out in databases, records of randomized clinical trials, list of references cited in the selected articles, as well as a manual search in meetings and specialized journals. A total of 1342 studies were identified, 18 were preselected and 5 were included in this review. Clinical heterogeneity of the participants was observed, in addition to variation in the laser parameters and predominance of studies of low methodological quality. PBMT with the use of laser (658 nm; 4 J cm⁻²;50 mw) showed complete wound healing (P < 0.001) when compared to lasers (990 nm and 808 nm). However, there was no statistically significant difference in relation to time to complete wound healing and in area reduction compared to standard care. PBMT in the infrared wavelength showed efficacy in the healing of the pressure ulcer, similar to the standard care presented in the different studies. PBMT (658 nm) was effective in promoting healing when compared to standard care. Laser can be a therapy of choice in the treatment of pressure ulcers, since no evidence has been found to refute its clinical application.