On dilworth’s theorem in the in finite case

The following theorem is proved: Letc be an infinite cardinal. There exists a partially ordered set of cardinalc, which contains no infinite independent subset, and which is not decomposable into less thanc chains.     

Quasi-equational bases for graphs of semigroups,monoids and groups

The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. Let denote by the class of all graphs of algebras from a class . We prove that if is a class of semigroups possessing a nontrivial member with a neutral element, then does not have finite quasi-equational basis. We deduce that, for a class of monoids or groups with a nontrivial member, also does not have finite quasi-equational basis.     

A quantitative thermal analysis of cyclists’ thermo-active base layers

It is well known that clothes used in sporting activity are a barrier for heat exchange between the environment and athlete, which should help in thermoregulation improvement. However, it is difficult to evaluate which top is best for each athlete according to the characteristics of the sport. Researchers have tried to measure the athlete’s temperature distribution during exercise at the base layers of tops with different approaches. The aim of this case study was to investigate the use of thermography for thermo-active base layer evaluation. Six new base layers were measured on one cyclist volunteer during a progressive training on a cycloergometer. As a control condition, the skin temperature of the same volunteer was registered without any layer with the same training. A training protocol was selected approximate to cycling race, which started from the warm-up stage, next the progressive effort until the race finished and at the end “cool-down” stage was over. In order to show which layer provided the strongest and weakest barrier for heat exchange in comparison with environment, the temperature parameters were taken into consideration. The most important parameter in the studies was the temperature difference between the body and the layers, which was changing during the test time. The studies showed a correlation between the ergometer power parameter and the body temperature changes, which has a strong and significant value. Moreover, the mass of every layer was checked before and after the training to evaluate the mass of the sweat exuded during the test. From this data, the layer mass difference parameter was calculated and taken into consideration as a parameter, which may correspond with the mean heart rate value from each training. A high and positive correlation coefficient was obtained between the average heart rate and the mass difference for the base layers. Thermal analysis seems to have a new potential application in the objective assessment of sports clothing and may help in choosing the proper clothes, which could support heat transfer during exercising and protect the body from overheating.

     

Radiocaesium pollution of fly agaric Amanita muscaria in fruiting bodies decreases with developmental stage

Amanita muscaria collected from a forested area in northern Poland in 2015 were analysed for activity concentrations of ¹³⁷Cs and ⁴⁰K. Total K concentration values were calculated from ⁴⁰K data. Mushrooms were grouped in six fruiting bodies size classes regarding to their developmental stage. The ¹³⁷Cs activity concentrations declined in A. muscaria as the fruiting bodies maturated. The contents of ⁴⁰K/K activity remained constant in caps at different developmental stage, while for stipes an increase was around twofold (⁴⁰K from 925?±?55 Bq kg^?1 dry biomass in the baby individuals and 1600?±?63–1700?±?53 Bq kg^?1 dry biomass in two oldest classes). A. muscaria is a weak accumulator of ¹³⁷Cs, while a steep drop in activity concentrations of this nuclide in the fruiting bodies as they maturate has not been reported earlier for mushrooms. Clearly, a fate of ¹³⁷Cs in A. muscaria is highly different from that of ⁴⁰K/K that is an essential element to fungi. In parallel, an observed increase in the content of ⁴⁰K/K in stipes of fruiting bodies with developmental state can be related to its ‘hardening’ and more fibrous nature with age and basic function to support the cap, but this has not been studied.     

Photoinduced Mo−CN Bond Breakage in Octacyanomolybdate Leading to Spin Triplet Trapping

The photoinduced properties of the octacoordinated complex K₄Mo^IV(CN)₈⋅2 H₂O were studied by theoretical calculations, crystallography, and optical and magnetic measurements. The crystal structure recorded at 10 K after blue light irradiation reveals an heptacoordinated Mo(CN)₇ species originating from the light-induced cleavage of one Mo−CN bond, concomitant with the photoinduced formation of a paramagnetic signal. When this complex is heated to 70 K, it returns to its original diamagnetic ground state, demonstrating full reversibility. The photomagnetic properties show a partial conversion into a triplet state possessing significant magnetic anisotropy, which is in agreement with theoretical studies. Inspired by these results, we isolated the new compound [K(crypt-222)]₃[Mo^IV(CN)₇]⋅3 CH₃CN using a photochemical pathway, confirming that photodissociation leads to a stable heptacyanomolybdate(IV) species in solution.     

In a Quest for Selectivity Paired with Activity: A Ruthenium Olefin Metathesis Catalyst Bearing an Unsymmetrical Phenanthrene-Based N-Heterocyclic Carbene

Robust, selective, and stable in the presence of ethylene, ruthenium olefin metathesis pre-catalyst, {[3-benzyl-1-(10-phenyl-9-phenanthryl)]-2-imidazolidinylidene}dichloro(o-isopropoxyphenylmethylene)ruthenium(II), Ru-3 , bearing an unsymetrical N-heterocyclic carbene (uNHC) ligand, has been synthesized. The initiation rate of Ru-3 was examined by ring-closing metathesis and cross-metathesis reactions with a broad spectrum of olefins, showing an unprecendented selectivity. It was also tested in industrially relevant ethenolysis reactions of olefinic substrates from renewable feedstock with very good yields and selectivities.     

Some results on Vizing’s conjecture and related problems

The well-known conjecture of Vizing on the domination number of Cartesian product graphs claims that for any two graphs $G$ and $H$, $\gamma \left(G\square H\right)\ge \gamma \left(G\right)\gamma \left(H\right)$. We disprove its variations on independent domination number and Barcalkin–German number, i.e. Conjectures 9.6 and 9.2 from the recent survey Bre?ar et al. (2012) [4]. We also give some extensions of the double-projection argument of Clark and Suen (2000) [8], showing that their result can be improved in the case of bounded-degree graphs. Similarly, for rainbow domination number we show for every $k\ge 1$ that ${\gamma }_{rk}\left(G\square H\right)\ge \frac{k}{k+1}\gamma \left(G\right)\gamma \left(H\right)$, which is closely related to Question 9.9 from the same survey. We also prove that the minimum possible counterexample to Vizing’s conjecture cannot have two neighboring vertices of degree two.     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

An Asymptotic Ratio in the Complete Binary Tree

Let T _n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 _n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T _n as follows A(n;T)=|{S T _n  : 1 _n ∈S, S≅T}|, and B(n;T)=|{S T _n :1 _n ∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  _n→∞[A(n;T)/B(n;T)]=2^ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.