Structure solution of the Al69.2Cu20Cr10.8 ϕ phase

The stable ϕ phase that forms below ∼923 K around the Al69.2Cu20.0Cr10.8 composition was found to be hexagonal [P63, a = 11.045 (2), c = 12.688 (2) Å] and isostructural to the earlier reported Al6.2Cu2Re X phase [Samuha, Grushko & Meshi (2016). J. Alloys Compd. 670, 18–24]. Using the structural model of the latter, a successful Rietveld refinement of the XRD data for Al69.5Cu20.0Cr10.5 was performed. Both ϕ and X were found to be structurally related to the Al72.6Cu11.0Cr16.4 ζ phase [P63/m, a = 17.714, c = 12.591 Å; Sugiyama, Saito & Hiraga (2002). J. Alloys Compd. 342, 148–152], with a close lattice parameter c and a τ-times-larger lattice parameter a (τ is the golden mean). The structural relationship between ζ and ϕ was established on the basis of the similarity of their layered structures and common features. Additionally, the strong-reflections approach was successfully applied for the modeling of the ϕ phase based on the structural model of the ζ phase. The latter and the experimental structural model (retrieved following Rietveld refinement) were found to be essentially identical.

On Catastrophic Increase in Mortality and Measures to Save the People in Russia

How is it that in Russia, unlike in other countries, during the coronavirus pandemic the total mortality increased by a record amount and the income and consumption of the population decreased to the greatest extent? The point is that the crisis, caused by the coronavirus pandemic, is completely different from previous ones. It highlights the dilemma: should we use forces and means to prevent an economic recession with lower costs for anti-crisis measures, or focus on saving people's lives while minimizing additional mortality and maintaining real incomes of the population? Each country, depending on objectives, prevailing conditions and opportunities, chooses its “golden mean”. In many cases such choice is not fully conscious, since it's not possible to forecast with any certainty even over the near term. Decisions have to be taken up along the way, based on the situation and assessing the probability of certain events, including in view of the other countries' experience in combating the pandemic.

Russian Idea" of F.M. Dostoevsky: from Soilness to Universality

The author reveals Fyodor Dostoevsky's works main features, his importance for Russian and world philosophy. The researcher analyzes the concept of "Russian Idea" introduced by Dostoyevsky, which became a study subject in Russian philosophy's subsequent history. The polemics that arose regarding the characteristics of Dostoevsky's soilness ( Pochvennichestvo ) ideology and his interpretation of the Russian Idea in his Pushkin Speech and subsequent comments in A Writer's Diary are unveiled. The author concludes that Dostoevsky overcomes the limitations of soilness and comes to universalism. The universal for him does not have a rootless cosmopolitan character but is born from the national's heyday. Diversity adorns the truth, and national diversity enamels humankind. People's real unity is in that all-human value that is found in the highest examples of each national culture. The truth is not in rootless cosmopolitanism or nationalism - it is in the "golden mean," which, in our opinion, the writer-philosopher sought to express. Dostoevsky wanted to rise above the dispute, to recognize the points of view of the Slavophiles and Westernizers as one-sided, to get out of any particularity to universality.

On Maximum-Sized Golden-Mean Matroids

<p>A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of all simple rank-r matroids in that class. Maximum-sized matroids have been classified for various classes of matroids: regular (Heller, 1957); dyadic (Kung and Oxley, 1988-90); k-regular (Semple, 1998); near-regular and sixth-root-of-unity (Oxley, Vertigan, and Whittle, 1998). Golden-mean matroids are matroids that are representable over the golden-mean partial field. Equivalently, a golden-mean matroid is a matroid that is representable over GF(4) and GF(5). Archer conjectured that there are three families of maximum-sized golden-mean matroids. This means that a proof of Archer’s conjecture is likely to be significantly more complex than the proofs of existing maximum-sized characterisations, as they all have only one family. In this thesis, we consider the four following subclasses of golden-mean matroids: those that are lifts of regular matroids, those that are lifts of nearregular matroids, those that are golden-mean-graphic, and those that have a spanning clique. We close each of these classes under minors, and prove that Archer’s conjecture holds in each of them. It is anticipated that the last of our theorems will lead to a proof of Archer’s conjecture for golden-mean matroids of sufficiently high rank.</p>

On Maximum-Sized Golden-Mean Matroids

<p>A rank-r simple matroid is maximum-sized in a class if it has the largest number of elements out of all simple rank-r matroids in that class. Maximum-sized matroids have been classified for various classes of matroids: regular (Heller, 1957); dyadic (Kung and Oxley, 1988-90); k-regular (Semple, 1998); near-regular and sixth-root-of-unity (Oxley, Vertigan, and Whittle, 1998). Golden-mean matroids are matroids that are representable over the golden-mean partial field. Equivalently, a golden-mean matroid is a matroid that is representable over GF(4) and GF(5). Archer conjectured that there are three families of maximum-sized golden-mean matroids. This means that a proof of Archer’s conjecture is likely to be significantly more complex than the proofs of existing maximum-sized characterisations, as they all have only one family. In this thesis, we consider the four following subclasses of golden-mean matroids: those that are lifts of regular matroids, those that are lifts of nearregular matroids, those that are golden-mean-graphic, and those that have a spanning clique. We close each of these classes under minors, and prove that Archer’s conjecture holds in each of them. It is anticipated that the last of our theorems will lead to a proof of Archer’s conjecture for golden-mean matroids of sufficiently high rank.</p>

Golden-Mean and Secret Sharing Matroids

<p>Maximum-sized results are an important part of matroid theory, and results currently exist for various classes of matroids. Archer conjectured that the maximum-sized golden-mean matroids fall into three distinct classes, as op- posed to the one class of all current results. We will prove a partial result that we hope will lead to a full proof. In the second part of this thesis, we look at secret sharing matroids, with a particular emphasis on the class of group-induced p-representable matroids, as introduced by Matúš. We give new proofs for results of Matúš', relating to M(K₄), F₇ and F⁻₇. We show that the techniques used do not extend in some natural ways, and pose some unanswered questions relating to the structure of secret sharing matroids.</p>

Golden-Mean and Secret Sharing Matroids

<p>Maximum-sized results are an important part of matroid theory, and results currently exist for various classes of matroids. Archer conjectured that the maximum-sized golden-mean matroids fall into three distinct classes, as op- posed to the one class of all current results. We will prove a partial result that we hope will lead to a full proof. In the second part of this thesis, we look at secret sharing matroids, with a particular emphasis on the class of group-induced p-representable matroids, as introduced by Matúš. We give new proofs for results of Matúš', relating to M(K₄), F₇ and F⁻₇. We show that the techniques used do not extend in some natural ways, and pose some unanswered questions relating to the structure of secret sharing matroids.</p>

On Catastrophic Increase in Mortality and Measures to Save the People in Russia

How is it that in Russia, unlike in other countries, during the coronavirus pandemic the total mortality increased by a record amount and the income and consumption of the population decreased to the greatest extent? The point is that the crisis, caused by the coronavirus pandemic, is completely different from previous ones. It highlights the dilemma: should we use forces and means to prevent an economic recession with lower costs for anti-crisis measures, or focus on saving people's lives while minimizing additional mortality and maintaining real incomes of the population? Each country, depending on objectives, prevailing conditions and opportunities, chooses its “golden mean”. In many cases such choice is not fully conscious, since it's not possible to forecast with any certainty even over the near term. Decisions have to be taken up along the way, based on the situation and assessing the probability of certain events, including in view of the other countries' experience in combating the pandemic.

Fluctuating Number of Energy Levels in Mixed-Type Lemon Billiards

In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by B=0.1953,0.083, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry–Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as E, in agreement with the theoretical prediction by Steiner.