Decomposition of a recursive family of polynomials

We describe a decomposition of the polynomials f _n := f _n,B,a defined by where B and a are rational numbers. We also present an application to related Diophantine equations. The authors were supported by the Ministry of Science, Education and Sports, Republic of Croatia, grant 0037110.     

Nitrogen activation and cleavage by a multimetallic uranium complex

Multimetallic-multielectron cooperativity plays a key role in the metal-mediated cleavage of N₂ to nitrides (N³⁻). In particular, low-valent uranium complexes coupled with strong alkali metal reducing agents can lead to N₂ cleavage, but often, it is ambiguous how many electrons are transferred from the uranium centers to cleave N₂. Herein, we designed new dinuclear uranium nitride complexes presenting a combination of electronically diverse ancillary ligands to promote the multielectron transformation of N₂. Two heteroleptic diuranium nitride complexes, [K{U^IV(OSi(O^tBu)₃)(N(SiMe₃)₂)₂}₂(μ-N)] (1) and [Cs{U^IV(OSi(O^tBu)₃)₂(N(SiMe₃)₂)}₂(μ-N)] (3-Cs), containing different combinations of OSi(O^tBu)₃ and N(SiMe₃)₂ ancillary ligands, were synthesized. We found that both complexes could be reduced to their U(iii)/U(iv) analogues, and the complex, [K₂{U^IV/III(OSi(O^tBu)₃)₂(N(SiMe₃)₂)}₂(μ-N)] (6-K), could be further reduced to a putative U(iii)/U(iii) species that is capable of promoting the 4e⁻ reduction of N₂, yielding the N₂⁴⁻complex [K₃{U^V(OSi(O^tBu)₃)₂(N(SiMe₃)₂)}₂(μ-N)(μ-η²:η²-N₂)], 7. Parallel N₂ reduction pathways were also identified, leading to the isolation of N₂ cleavage products, [K₃{U^VI(OSi(O^tBu)₃)₂(N(SiMe₃)₂)( N)}(μ-N)₂{U^V(OSi(O^tBu)₃)₂(N(SiMe₃)₂)}]₂, 8, and [K₄{(OSi(O^tBu)₃)₂U^V)( N)}(μ-NH)(μ-κ²:C,N-CH₂SiMe₂NSiMe₃)-{U^V(OSi(O^tBu)₃)₂][K(N(SiMe₃)₂]₂, 9. These complexes provide the first example of N₂ cleavage to nitride by a uranium complex in the absence of reducing alkali metals.

Combinations of ligands were used to tune U N U complexes yielding a U(iii)/U(iii) nitride, which activates N₂. Parallel N₂ reduction pathways were identified, leading to the first example of N₂ cleavage by U without external alkali reducing agents.     

The Evaluation of Healing Properties of Galium verum-Based Oral Gel in Aphthous Stomatitis in Rats

Although oral ulcers represent one of the most frequent oral mucosal diseases, the available treatment is not sufficient to provide complete ulcer recovery without side-effects. Therefore, the aim of our study was to prepare a mucoadhesive oral gel based on Galium verum ethanol extract (GVL gel) and reveal its healing effects in the model of aphthous stomatitis in rats. Rats with oral ulcers were divided into the following groups: control (untreated), gel base (ulcer was treated with the gel base, three times per day for 10 days), and GVL gel group (the ulcer was treated with GVL gel in the same way as the gel base). Animals from each group were sacrificed on days 0, 3, 6, and 10 for collecting blood and ulcer tissue samples. Healing properties of oral gel were determined by clinical evaluation, as well as biochemical and histopathological examinations. Our findings suggest a significant decrease in the ulcer size in GVL gel group, with healing effects achieved through the alleviation of oxidative stress, reduction in COX-2 immunopositivity, and increase in collagen content in buccal tissue. Significant ulcer repairing potential of GVL gel highlights this oral mucoadhesive gel as a promising tool for prevention and treatment of RAS.     

Comparative thermodynamic analysis of the Pb-Au0.7Sn0.3 section in the Pb-Au-Sn ternary system

The results of comparative thermodynamic analysis of Pb-Au_0.7Sn_0.3 section in Pb-Au-Sn system are presented in this paper. Investigation was done comparatively by calorimetric measurements and thermodynamic calculation according to the general solution model. Thermodynamic parameters, such as partial and integral molar quantities, were determined at different temperatures. The comparison between experimental and calculated results showed mutual agreement. Demixing tendency of lead, presented in the positive deviation from ideal behavior, was confirmed through the study of concentration fluctuation in the long-wavelength limit. Also, chosen alloys in the investigated section were characterized using SEM-EDX analysis.     

Retraction closure property

We say that an algebra ${\mathcal{A}}$ has the retraction closure property (RCP) if the set of all retractions of ${\mathcal{A}}$ is closed with respect to fundamental operations of ${\mathcal{A}}$ applied pointwise. In this paper we investigate this property, both “locally” (one algebra) and “globally” (in some variety of algebras), especially emphasizing the case of groupoids. We compare the retraction closure property with the endomorphism closure property on both levels and prove that a necessary and sufficient condition for a variety V of algebras to have RCP is that V is a variety of entropic algebras that satisfy the diagonal identities.     

The effect of crosslinking on properties of low‐density polyethylene filled with organic filler

Scanning electron microscopy was employed to investigate the effect of peroxide‐initiated crosslinking on behaviour of composites of low‐density polyethylene filled with wood flour. The improved wetting of the filler by the matrix and/or the increase in the matrix/filler adhesion was shown to be the main consequence of crosslinking, with the obvious influence on the physical, especially mechanical properties.     

Recent Studies of Hypernuclei Formation with Electron Beams at MAMI

At the Mainz Microtron MAMI exploratory experiments on the spectroscopy of mesonic weak decays (MWD) of electroproduced Λ-hypernuclei were performed. A unique setup was realized to use the broad momentum-band kaon spectrometer Kaos at zero degree angle with respect to the high-intensity electron beam direction to tag strangeness producing processes. A sample of order 10³ MWD from a beryllium target was collected by the coincidence technique with the high-resolution multi-spectrometer facility of the A1 Collaboration. It is conjectured that this sample contains monochromatic two-body decays from stopped hyperfragment decays as well as a wide momentum distribution of quasi-free produced Λ- and Σ-hyperon decays and three-body decays from hyperfragments. Stopped hyperfragments will be identified as monochromatic peaks in the π ^? momentum spectrum from which their masses can be extracted with a precision of 50 keV/c ².     

A note on the reservoir routing problem

The reservoir routing problem has been recognized and managed for quite some time, but this paper presents a consistent mathematical approach by applying only the mass conservation principle (instead of various ‘ad hoc’ approaches). Application of the mass conservation principle facilitates the presentation of integral and differential formulations based on either the water volume or the water level of an arbitrarily-shaped reservoir. For the solution, new functions with a clear physical meaning are introduced. An error analysis is performed using a new approach based on spectral operators (traditionally, Richardson extrapolation has been used). It becomes evident that the integral formulations are more advantageous in terms of stability; however, they take more time to program and to calculate. The calculations in the examples are based on actual data from an artificial water reservoir (lake) Botonega in Croatia using the authors’ computer program that was created in the Mathcad environment.     

Single frame blind image deconvolution by non-negative sparse matrix factorization

Novel approach to single frame multichannel blind image deconvolution has been formulated recently as non-negative matrix factorization problem with sparseness constraints imposed on the unknown mixing vector that accounts for the case of non-sparse source image. Unlike most of the blind image deconvolution algorithms, the novel approach assumed no a priori knowledge about the blurring kernel and original image. Our contributions in this paper are: (i) we have formulated generalized non-negative matrix factorization approach to blind image deconvolution with sparseness constraints imposed on either unknown mixing vector or unknown source image; (ii) the criteria are established to distinguish whether unknown source image was sparse or not as well as to estimate appropriate sparseness constraint from degraded image itself, thus making the proposed approach completely unsupervised; (iii) an extensive experimental performance evaluation of the non-negative matrix factorization algorithm is presented on the images degraded by the blur caused by the photon sieve, out-of-focus blur with sparse and non-sparse images and blur caused by atmospheric turbulence. The algorithm is compared with the state-of-the-art single frame blind image deconvolution algorithms such as blind Richardson-Lucy algorithm and single frame multichannel independent component analysis based algorithm and non-blind image restoration algorithms such as multiplicative algebraic restoration technique and Van-Cittert algorithms. It has been experimentally demonstrated that proposed algorithm outperforms mentioned non-blind and blind image deconvolution methods.     

Propolis Extract and Its Bioactive Compounds—From Traditional to Modern Extraction Technologies

Propolis is a honeybee product known for its antioxidant, anti-inflammatory, anticancer, and antimicrobial effects. It is rich in bioactive molecules whose content varies depending on the botanical and geographical origin of propolis. These bioactive molecules have been studied individually and as a part of propolis extracts, as they can be used as representative markers for propolis standardization. Here, we compare the pharmacological effects of representative polyphenols and whole propolis extracts. Based on the literature data, polyphenols and extracts act by suppressing similar targets, from pro-inflammatory TNF/NF-κB to the pro-proliferative MAPK/ERK pathway. In addition, they activate similar antioxidant mechanisms of action, like Nrf2-ARE intracellular antioxidant pathway, and they all have antimicrobial activity. These similarities do not imply that we should attribute the action of propolis solely to the most representative compounds. Moreover, its pharmacological effects will depend on the efficacy of these compounds’ extraction. Thus, we also give an overview of different propolis extraction technologies, from traditional to modern ones, which are environmentally friendlier. These technologies belong to an open research area that needs further effective solutions in terms of well-standardized liquid and solid extracts, which would be reliable in their pharmacological effects, environmentally friendly, and sustainable for production.