The Endomorphism Monoid of the Random Graph has Uncountably Many Ideals

In this note we prove that the monoid End(R) of all endomorphisms of the random graph R is not simple. On the contrary, the lattice of ideals of End(R) embeds the poset of all subsets of , the set of natural numbers.     

Synthesis and structural characterization of copper(II) complexes with the 2′-[1-(2-pyridinyl)ethylidene]oxalohydrazide ligand

The octahedral copper(II) complex with two 2-[1-(2-pyridinyl)ethylidene]oxalohydrazide molecules was synthesized from bis(acetylacetonato)copper(II) and 2-[1-(2-pyridinyl)ethylidene]oxamohydrazide (Hapsox). The complex is unstable when not in solution. X-ray analysis confirmed the tridentate coordination of the ligands in the monoanionic form. In addition, the stable tetrahedral copper(II) complex with one ligand molecule coordinated as a tridentate in the dianionic form was prepared by direct synthesis from Cu(NO₃)₂·3H₂O and Hapsox, and characterized by elemental analysis, magnetic measurements and by i.r. and u.v./vis. spectrophotometry.     

Nondipole Effects in Atomic Ionization Induced by an Intense Counter-Rotating Bicircular Laser Field

Nondipole effects occurring in the process of atomic ionization by an intense, mid-infrared, counter-rotating bicircular laser field are investigated using the strong-field approximation with leading-order nondipole corrections. The time integrals appearing in the expression for the differential ionization rate are computed in two ways: numerically, and by applying the saddle-point approximation. The nondipole corrections introduce an asymmetry in the photoelectron momentum distribution along the field propagation direction. The asymmetry is quantified by the partial average value of the propagation-direction momentum component of the photoelectrons and by the normalized difference of the differential ionization rates computed including and excluding the nondipole corrections. Using the saddle-point approximation, it is investigated how the nondipole corrections change the solutions for direct photoelectrons and how this affects the momentum spectra. The impact of nondipole corrections increases with increasing photoelectron energy. Analysis of the complete photoelectron spectra including both direct and rescattered photoelectrons shows that, in the low-energy region, a shift against the propagation direction occurs. The partial average of the propagation–direction momentum component in the rescattering region exhibits a plateau structure and also a local minimum structure that was recently observed in an experiment with a linearly polarized laser field (Lin et al., Phys Rev. Lett. 128, 023201 (2022)).     

Nanovesicles Loaded with Origanum onites and Satureja thymbra Essential Oils and Their Activity against Food-Borne Pathogens and Spoilage Microorganisms

Food poisoning is a common cause of illness and death in developing countries. Essential oils (EOs) could be effective and safe natural preservatives to prevent and control bacterial contamination of foods. However, their high sensitivity and strong flavor limit their application and biological effectiveness. The aim of this study was firstly the chemical analysis and the antimicrobial evaluation of the EOs of Origanum onites L. and Satureja thymbra L. obtained from Symi island (Greece), and, secondly, the formulation of propylene glycol-nanovesicles loaded with these EOs to improve their antimicrobial properties. The EOs were analyzed by GC-MS and their chemical contents are presented herein. Different nanovesicles were formulated with small average sizes, high homogeneity, and optimal ζ-potential. Microscopic observation confirmed their small and spherical shape. Antibacterial and antifungal activities of the formulated EOs were evaluated against food-borne pathogens and spoilage microorganisms compared to pure EOs. Propylene glycol-nanovesicles loaded with O. onites EO were found to be the most active formulation against all tested strains. Additionally, in vitro studies on the HaCaT cell line showed that nanovesicles encapsulated with EOs had no toxic effect. The present study revealed that both EOs can be used as alternative sanitizers and preservatives in the food industry, and that their formulation in nanovesicles can provide a suitable approach as food-grade delivery system.     

Survey of Dipeptidyl Peptidase III Inhibitors: From Small Molecules of Microbial or Synthetic Origin to Aprotinin

Dipeptidyl peptidase III (DPP III) was originally thought to be a housekeeping enzyme that contributes to intracellular peptide catabolism. More specific roles for this cytosolic metallopeptidase, in the renin-angiotensin system and oxidative stress regulation, were confirmed, or recognized, only recently. To prove indicated (patho)physiological functions of DPP III in cancer progression, cataract formation and endogenous pain modulation, or to reveal new ones, selective and potent inhibitors are needed. This review encompasses natural and synthetic compounds with experimentally proven inhibitory activity toward mammalian DPP III. Except for the polypeptide aprotinin, all others are small molecules and include flavonoids, coumarin and benzimidazole derivatives. Presented are current strategies for the discovery or development of DPP III inhibitors, and mechanisms of inhibitory actions. The most potent inhibitors yet reported (propioxatin A and B, Tyr-Phe- and Phe-Phe-NHOH, and JMV-390) are active in low nanomolar range and contain hydroxamic acid moiety. High inhibitory potential possesses oligopeptides from the hemorphin group, valorphin and tynorphin, which are poor substrates of DPP III. The crystal structure of human DPP III-tynorphin complex enabled the design of the transition-state peptidomimetics inhibitors, effective in low micromolar concentrations. A new direction in the field is the development of fluorescent inhibitor for monitoring DPP III activity.     

Mathematical Modeling of Combustion of Single Porous Pulverized Coal Particle Using Lattice Approach

Novel model of coal particle combustion was developed. The aim of proposed model is to describe all possible mechanisms for particle combustion and their sensitivity to combustion conditions. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radioactivity in Montenegro beach sands and assessment of the corresponding environmental risk

Activity concentrations of the naturally occurring radionuclides ²²⁶Ra, ²³²Th, ⁴⁰K and anthropogenic ¹³⁷Cs in sand samples collected from 20 renowned beaches on the Coast of Montenegro have been determined using an HPGe (high purity Ge spectrometer). The average activity concentrations were found to be 7.4, 5.2, 97.3 and 0.5 Bq kg^?1, respectively. For all sand samples, the radium equivalent activity has been evaluated and found to be lower than the limit of 370 Bq kg^?1. External and internal hazard indices were less than unity. The gonadal dose equivalent was estimated to be on average 75 μSv y^?1, which is about four times lower than the global average for soil (0.3 mSv y^?1). Calculated values of absorbed dose rates showed the range from 3.1 to 28 nGy h^?1, which is below the world median of average values (57 nGy h^?1). The effective dose rate in the range from 3.8 to 34.4 μSv y^?1 was significantly below the recommended limit value for the public (1 mSv y^?1). The highest dose rate was found for the Velika Plaza locality, which also showed heavy metal contents (As, B, Cd, Hg, Cr, Cu, Mn, Ni, Pb, Zn and Ba) significantly higher than in the sand from Jaz, a locality with one of the lowest dose rates.     

π‐electron currents in polycyclic conjugated hydrocarbons: Coronene and its isomers having five and seven member rings

We have outlined novel graph theoretical model for computing π‐electron currents in π‐electron polycyclic conjugated hydrocarbons. We start with Kekulé valence structures of a polycyclic conjugated hydrocarbon and their conjugated circuits. To each 4n+2 conjugated circuits we assign counter clockwise current i and to each 4n conjugated circuit we assign clockwise current i. By adding the contributions from all conjugated circuits in a single Kekulé valence structure one obtains π‐electron current pattern for the particular Kekulé valence structure. By adding the conjugated circuit currents in all Kekulé valence structure one obtains the pattern of π‐electron currents for considered molecule. We report here π‐electron current patters for coronene and 17 its isomers, which have been recently considered by Balaban et al., obtained by replacing one or more pairs of peripheral benzene rings with five and seven member rings. Our results are compared with their reported π‐electron current density patters computed by ab initio molecular orbital (MO) computations and satisfactory parallelism is found between two so disparate approaches. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Adding Value to the Oil Cake as a Waste from Oil Processing Industry: Production of Lipase and Protease by <Emphasis Type="Italic">Candida utilis</Emphasis> in Solid State Fermentation

Olive oil cake is a by-product from the olive oil processing industry and can be used for the lipase and protease production by Candida utilis in solid state fermentation. Different carbon and nitrogen sources were evaluated, and the results showed that the supplementation of the substrate with maltose and starch as carbon sources and yeast extract as a nitrogen source significantly increased the lipase production. The best results were obtained with maltose, whereas rather low lipase and protease activities were found with glucose and oleic acid. Response surface methodology and a five-level–three-factor central composite rotatable design were used to evaluate the effects of the initial moisture content, inoculum size and fermentation time on both lipase and protease activity levels. A lipase activity value of ≈25 U g^-1 and a protease activity value of 110 U g^-1 were obtained under the optimized fermentation conditions. An alkaline treatment of the substrate appeared to be efficient, leading to increases of 39% and 133% in the lipase and protease production, respectively. The results showed that the olive cake could be a good source for enzyme production by solid state fermentation.     

Some new extensions of Banach’s contraction principle to partial metric space

In S.G. Matthews [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183–197], the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this work we study fixed point results for new extensions of Banach’s contraction principle to partial metric space, and we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.