General Position Research Articles

Bis[tris-(diiso-butyl-dithio-carbamato)-μ3-sulfido-tri-μ2-di-sulfido-trimolybdenum(IV)] sulfide tetra-hydro-furan monosolvate.

The title compound, [Mo3(C9H18NS2)3(S2)3S]2S, crystallizes on a general position in the monoclinic space group P21/n (No. 14). The cationic [Mo3S7(S2CNiBu2)3]+ fragments are joined by a mono-sulfide dianion that forms close S⋯S contacts to each of the di-sulfide ligands on the side of the Mo3 plane opposite the μ3 2- ligand. The two Mo3 planes are inclined at an angle of 40.637 (15)°, which gives the assembly an open clamshell-like appearance. One μ6-S2-⋯S2 2- contact, at 2.4849 (14) Å, is appreciably shorter than the remaining five, which are in the range 2.7252 (13)-2.8077 (14) Å.

Maximal cocliques and the chromatic number of the Kneser graph on chambers of PG(3,q) $(3,q)$

AbstractLet be the graph whose vertices are the chambers of the finite projective 3‐space , with two vertices being adjacent if and only if the corresponding chambers are in general position. We show that a maximal independent set of vertices of contains , or , or at most elements. For the structure of the largest maximal independent sets is described. For the structure of the maximal independent sets of the three largest cardinalities is described. Using the cardinality of the second largest maximal independent sets, we show that the chromatic number of is .

Synthesis, crystal structure and properties of the trigonal-bipyramidal complex tris-(2-methyl-pyridine N-oxide-κO)bis-(thio-cyanato-κN)cobalt(II).

Reaction of Co(NCS)2 with 2-methyl-pyridine N-oxide in a 1:3 ratio in n-butanol leads to the formation of crystals of tris-(2-methyl-pyridine N-oxide-κO)bis-(thio-cyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)3]. The asymmetric unit of the title compound consists of one CoII cation two thio-cyanate anions and three crystallographically independent 2-methyl-pyridine N-oxide coligands in general positions. The CoII cations are trigonal-bipyramidally coordinated by two terminal N-bonding thio-cyanate anions in the trans-positions and three 2-methyl-pyridine N-oxide coligands into discrete complexes. These complexes are linked by inter-molecular C-H⋯S inter-actions into double chains that elongate in the c-axis direction. Powder X-ray diffraction (PXRD) measurements prove that all batches are always contaminated with an additional and unknown crystalline phase. Thermogravimetry and differential analysis of crystals selected by hand reveal that the title compound decomposes at about 229°C in an exothermic reaction. At about 113°C a small endothermic signal is observed that, according to differential scanning calorimetry (DSC) measurements, is irreversible. PXRD measurements of the residue prove that a poorly crystalline and unknown phase has formed and thermomicroscopy indicates that some phase transition occurs that is accompanied with a color change of the title compound.

On the finiteness of meromorphic mappings sharing few hyperplanes without multiplicities

In this paper, we show that the set of meromorphic mappings from Cm to Pn(C) which share 2n+1 hyperplanes in general position regardless of multiplicities has at most two elements, provided n≥12.

All-path convexity: two characterizations, general position number, and one algorithm

All-path convexity: two characterizations, general position number, and one algorithm

Posttraumatic growth and rehabilitative resources of the combatants and demobilized servicemen

The combat experience of military and demobilized persons combines the influence of combat and non-combat stressors with combat conditions and stressors associated with being in the combat zone, which leads to severe personal injury, symptoms of posttraumatic stress disorder and severe stress adaptive capacity. The resource of mastering combat stress is vitality, which is confirmed by the general viable position of the subjects, focused on effective self-development. Combatants show marked signs of maladaptation, but half of them report an increase in the value of life, spiritual growth and a general trend of personal growth, with women significantly exceeding men in terms of increasing personal strength. The aim of the research is to reveal the indicators of posttraumatic growth and personality rehabilitative resources of combatants and demobilized servicemen. Therefore, the posttraumatic growth of combatants goes hand in hand with attempts to adapt to a difficult situation. The main strategies for resisting stress in these conditions are cognition and recourse to physical activity. It is the resource of physical activity that is significantly positively correlated with indicators of posttraumatic personal growth. Personality posttraumatic growth indicators have been substantiated: change in attitude toward others, emergence of new opportunities, increase in strength of personality, spiritual changes, increase in the value of life, and general posttraumatic growth. The resource of rehabilitation potential, which is little used, is the appeal to the sphere of imagination and emotional sphere. The military does not sufficiently use the resources of faith and search for social support, which in crisis conditions are productive strategies. Sustainability is an important component of personal rehabilitation potential, but at this stage of a difficult situation, the personal resources involved are a person’s activity in overcoming difficulties, his/her desire to act and win, the desire not to lose this meaning, to express their personal potential.

Volunteering and Catholicism in Europe. The Inside Perspective Part 2: Empirical

In the paper we analyse the social activity practices of Catholic persons, as a set of individual and collective action emerging from the Catholic identity and – to more or less extent – structuralised under the Church-related formal non-profit initiatives. The purpose of the study is to clarify: (1) to what extent the Catholic unpaid social activities of different kinds could be classified as forms of volunteering and (2) to what extent the third sector definitions of volunteering are included in specific Catholic activities. Three tendencies have been observed with respect to not including religion-oriented volunteering in voluntary studies. Firstly, while using tools for collecting data adequate for the secular world, researchers face methodological difficulties to successfully cover social activities organized in parishes and congregations. Secondly, a reductionist approach reflects the ideological-rooted tendency to treat religion as a matter of private life. Thirdly, some religious-based entities tend to keep social activities of the believers within the Church-related circle. From the Catholic perspective, volunteer engagement represents an important aspect of faith-based every day activities, the so-called lived religion. At the same time, social engagement of believers provided within the Church-related entities, as well as outside them, usually fulfils all main features of volunteering. The relation between volunteering and religion is to be referred not only to the general position of faith-based and religious organizations in the public sphere, but also to the embeddedness of religious life in the society, as in fact both religion and volunteering are categories social per se. We illustrate our reflection on volunteering and Catholicism by presenting empirical evidence from the 2018 panel expert research among representatives of 29 Catholic Bishops Conferences across Europe.

The system of images in A. Varlamov's novel "The Mental Wolf"

This article is devoted to the study of the images of the main characters of the novel, representing the author's complex view of the pre-Soviet period of Russian history, the First World War and the Revolution. Each character is characterized by his own system of ideological coordinates that form the picture of the world in the novel, expressing the national and cultural consciousness of the era. The character's deep characterization is based on a value paradigm, the constituent elements of which are attitude to nature, religion, homeland, and war. It is considered how these value characteristics are reflected in the life position of each character represented in the novel.The purpose of the article is to consider the system of images in A. Varlamov's novel "The Mental Wolf". The need to consider this problem is determined by the general literary position that the author's idea of life is expressed through a system of characters. The author uses the following research methods: comparative, hermeneutical and comparative typological. With the help of a systematic approach, an analytical study of images is provided. The analysis of the image system in the novel allowed us to correlate the images with the compositional structure of the work, to consider their position in the chronotope, to determine the characterological conflict in the novel. As the analysis made it possible to determine, the characters of Varlamov's novel form a system. Its main feature is the complex connections between the characters. The system of images in the novel is based on the idea of their attraction – repulsion. Relevance is seen in addressing one of the key problems of literary criticism based on the work of a modern author. It is established that complex connections of attraction, repulsion and pair interaction are established between the characters of the novel, which ultimately allows us to talk about a complex ideological concept of the novel depicting a person and his spiritual world in an era of changing social, cultural and political paradigms.

Extremal Edge General Position Sets in Some Graphs

A set of edges X⊆E(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X\\subseteq E(G)$$\\end{document} of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number gpe(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{gp}}_{\ extrm{e}}(G)$$\\end{document} of G is the cardinality of a largest edge general position set in G. Graphs G with gpe(G)=|E(G)|-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{gp}}_{{\ extrm{e}}}(G) = |E(G)| - 1$$\\end{document} and with gpe(G)=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{gp}}_{{\ extrm{e}}}(G) = 3$$\\end{document} are respectively characterized. Sharp upper and lower bounds on gpe(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{gp}}_{{\ extrm{e}}}(G)$$\\end{document} are proved for block graphs G and exact values are determined for several specific block graphs.

Quantum K-theory of incidence varieties

We prove a conjecture of Buch and Mihalcea in the case of the incidence variety X=Fl(1,n-1;n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X=\ extrm{Fl}\\hspace{0.55542pt}(1,n-1;n)$$\\end{document} and determine the structure of its (T-equivariant) quantum K-theory ring. Our results are an interplay between geometry and combinatorics. The geometric side concerns Gromov–Witten varieties of 3-pointed genus 0 stable maps to X with markings sent to Schubert varieties, while on the combinatorial side are formulas for the (equivariant) quantum K-theory ring of X. We prove that the Gromov–Witten variety is rationally connected when one of the defining Schubert varieties is a divisor and another is a point. This implies that the (equivariant) K-theoretic Gromov–Witten invariants defined by two Schubert classes and a Schubert divisor class can be computed in the ordinary (equivariant) K-theory ring of X. We derive a positive Chevalley formula for the equivariant quantum K-theory ring of X and a positive closed formula for Littlewood–Richardson coefficients in the non-equivariant quantum K-theory ring of X. The Littlewood–Richardson rule in turn implies that non-empty Gromov–Witten varieties given by Schubert varieties in general position have arithmetic genus 0.

Disparity of cycad leaves dispels the living fossil metaphor

The living fossil metaphor is tightly linked with the cycads. This group of gymnosperms is supposed to be characterised by long-term morphological stasis, particularly after their peak of diversity and disparity in the Jurassic. However, no formal test of this hypothesis exists. Here, we use a recent phylogenetic framework and an improved character matrix to reconstruct the Disparity Through Time for cycad leaves using a Principal Coordinate Analysis and employing Pre-Ordination Ancestral State Reconstruction to test the impact of sampling on the results. Our analysis shows that the cycad leaf morsphospace expanded up to the present, with numerous shifts in its general positioning, independently of sampling biases. Moreover, they also show that Zamiaceae expanded rapidly in the Early Cretaceous and continued to expand up to the present, while now-extinct clades experienced a slow contraction from their peak in the Triassic. We also show that rates of evolution were constantly high up to the Early Cretaceous, and then experienced a slight decrease in the Paleogene, followed by a Neogene acceleration. These results show a much more dynamic history for cycads, and suggest that the ‘living fossil’ metaphor is actually a hindrance to our understanding of their macroevolution.

The Neognostic Myth in Cyberspace

The subject of the study is the functioning of the neognostic myth in cyberspace. Such aspects of the topic as the relationship between religion and the Internet from a non-instrumental point of view on technology are considered in detail. Digital and network technologies are seen as a modern repository of religious beliefs, and not as tools for proselytizing or proclaiming the good news. With the help of an archaeological approach to technical media, the author proposes to determine the deep times of the digital disclosure of technological mysticism, depending on a specific technical materiality characterized by wireless networks and mobile devices. Currently, there are trends in world culture towards the construction of a syncretic myth, which contains elements of the dying Christian paradigm and trends introduced into it from the outside or emerging again. The categorical apparatus developed in the discourse of postmodern aesthetics makes it possible to apply such methods as phenomenological, discursive, hermeneutic and archetypal analysis to the analysis of visual culture. In the study of visual neognostic myth, the concepts of archetypal models, plots, cliches, the theory of the evolution of symbols, general cultural positions of psychoanalysis and the concept of myth are used. The main conclusions of the study are as follows. Gnostic epistemology underlies the imagination of cyberspace. There is a constant in the history of the West that Eric Davis calls "techno-gnosis." In this regard, cybergnosis would be only the latest incarnation of a profound phenomenon. In the world of cyberculture, technognosis manifests itself in hacker ethics, cyberpunk literature, science fiction films and video games. With the help of an archaeological approach to technical media, the deep moments of the digital are determined, showing that there is a technological mysticism in video games that depends on a specific materiality. The new metamodern perception of the world recognizes not only the possibility of perceiving various logical and irrational paradigms of the world order and gaining knowledge about it, but also gives a positive connotation to pluralism itself, when diversity becomes more desirable than truth, which is characteristic of cyberspace. The novelty of the research lies in the fact that the research is the basis for the formation of a clear conceptual understanding of the phenomenon of the neognostic myth in its visual form (as opposed to verbal) as a dynamic cultural model generated by digital art strategies and implemented today in media culture.

General Position Polynomials

A subset of vertices of a graph G is a general position set if no triple of vertices from the set lie on a common shortest path in G. In this paper we introduce the general position polynomial as ∑i≥0aixi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sum _{i \\ge 0} a_i x^i$$\\end{document}, where ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_i$$\\end{document} is the number of distinct general position sets of G with cardinality i. The polynomial is considered for several well-known classes of graphs and graph operations. It is shown that the polynomial is not unimodal in general, not even on trees. On the other hand, several classes of graphs, including Kneser graphs K(n, 2), with unimodal general position polynomials are presented.

Symmetry of f-Vectors of Toric Arrangements in General Position and Some Applications

A toric hyperplane is the preimage of a point in a circle of a continuous surjective group homomorphism from the n-torus to the circle. A toric hyperplane arrangement is a finite collection of such hyperplanes. In this paper, we study the combinatorial properties of toric hyperplane arrangements on n-tori which are spanning and in general position. Specifically, we describe the symmetry of f-vectors arising in such arrangements and a few applications of the result to count configurations of hyperplanes.

Negative flows and non-autonomous reductions of the Volterra lattice

We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown that, in the case of general position, such a reduction is equivalent to the stationary equation for a sum of the scaling symmetry and the negative flows, and is written as $(m+1)$-component difference equations of the Painlev\'e type generalizing the dP$_1$ and dP$_{34}$ equations. For these reductions, we present the isomonodromic Lax pairs and derive the B\"acklund transformations which form the $\mathbb{Z}^m$ lattice.

Peeling Sequences

AbstractGiven a set of n labeled points in general position in the plane, we remove all of its points one by one. At each step, one point from the convex hull of the remaining set is erased. In how many ways can the process be carried out? The answer obviously depends on the point set. If the points are in convex position, there are exactly n! ways, which is the maximum number of ways for n points. But what is the minimum number? It is shown that this number is (roughly) at least $$3^n$$ 3 n and at most $$12.29^n$$ 12 . 29 n .

Assessment of quality of life in follow-up patients with COVID-19 pneumonia: A prospective, observational study from a tertiary care center.

This study intended to assess the quality of life (QOL) with telephonic interview using the Short Form 12 (SF-12) Scale in follow-up patients admitted to the intensive care unit (ICU) with COVID-19 pneumonia. This prospective, noninterventional follow-up study was conducted at a tertiary care center. COVID-19 pneumonia patients discharged from ICU were recruited for telephonic interviews. Interviews were performed using SF-12 Scale to assess QOL 6 months after discharge. The SF-12 survey measures general health status in eight domains. A radar chart was used for the interpretation of health component scores. One hundred and fifty patients could complete the telephonic interview. The first-stage depression risk was 50%, which was 30% more than general position incidence (20%). As compared to the general population, physical component summary (PCS-12) was 60% below and mental component summary (MCS-12) was 67% below the general norm. Role emotional was the most affected followed by role physical. QOL in follow-up ICU patients with COVID-19 pneumonia was worse in terms of physical and mental scores. By employing a comprehensive, longitudinal assessment of QOL in follow-up patients, using validated SF-12 Scale, this study captures a multifaceted view of their health status postrecovery.

Cadmium phosphates Cd2(PO4)OH and Cd5(PO4)2(OH)4 crystallizing in mineral structures

Single crystals of two basic cadmium phosphates, dicadmium orthophosphate hydroxide, Cd2(PO4)OH, and pentacadmium bis(orthophosphate) tetrakis(hydroxide), Cd5(PO4)2(OH)4, were obtained under hydrothermal conditions. Cd2(PO4)OH adopts the triplite [(Mn,Fe)2(PO4)F] structure type. Its asymmetric unit comprises two Cd, one P and five O sites, all situated at the general Wyckoff position 8 f of space group I2/a; two of the O atoms are positionally disordered over two sites, and the H atom could not be localized. Disregarding the disorder, distorted [CdO6] polyhedra form a tri-periodic network by edge-sharing with neighbouring [CdO6] units and by vertex-sharing with [PO4] units. The site associated with the OH group is coordinated by four Cd atoms in a distorted tetrahedral manner forming 1 ∞[(OH)Cd4/2] chains parallel to [001]. The oxygen environment around the OH site suggests multiple acceptor atoms for possible O—H...O hydrogen-bonding interactions and is the putative reason for the disorder. Cd5(PO4)2(OH)4 adopts the arsenoclasite [Mn5(AsO4)2(OH)4] structure type. Its asymmetric unit comprises five Cd, two P, and twelve O sites all located at the general Wyckoff position 4 a of space group P212121; the H atoms could not be localized. The crystal structure of Cd5(PO4)2(OH)4 can be subdivided into two main sub-units. One consists of three edge-sharing [CdO6] octahedra, and the other of two edge- and vertex-sharing [CdO6] octahedra. Each sub-unit forms corrugated ribbons extending parallel to [100]. The two types of ribbons are linked into the tri-periodic arrangement through vertex-sharing and through common [PO4] tetrahedra. Quantitative structure comparisons are made with isotypic M 5(XO4)2(OH)4 crystal structures (M = Cd, Mn, Co; X = P, As, V).

Synthesis and crystal structure of diisothiocyanatotetrakis(4-methylpyridine N-oxide)cobalt(II) and diisothiocyanatotris(4-methylpyridine N-oxide)cobalt(II) showing two different metal coordination polyhedra

The reaction of Co(NCS)2 with 4-methylpyridine N-oxide (C6H7NO) leads to the formation of two compounds, namely, tetrakis(4-methylpyridine N-oxide-κO)bis(thiocyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)4] (1), and tris(4-methylpyridine N-oxide-κO)bis(thiocyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)3] (2). The asymmetric unit of 1 consists of one CoII cation located on a centre of inversion, as well as one thiocyanate anion and two 4-methylpyridine N-oxide coligands in general positions. The CoII cations are octahedrally coordinated by two terminal N-bonding thiocyanate anions in trans positions and four 4-methylpyridine N-oxide ligands. In the extended structure, these complexes are linked by C—H...O and C—H...S interactions. In compound 2, two crystallographically independent complexes are present, which occupy general positions. In each of these complexes, the CoII cations are coordinated in a trigonal–bipyramidal manner by two terminal N-bonding thiocyanate anions in axial positions and by three 4-methylpyridine N-oxide ligands in equatorial positions. In the crystal, these complex molecules are linked by C—H...S interactions. For compound 2, a nonmerohedral twin refinement was performed. Powder X-ray diffraction (PXRD) reveals that 2 was nearly obtained as a pure phase, which is not possible for compound 1. Differential thermoanalysis and thermogravimetry data (DTA–TG) show that compound 2 start to decompose at about 518 K.

Semiotic Violence

Semiotic Violence