The reaction of zinc iodide with 2,3-dimethylpyrazine (C 6 H 8 N 2 ) in ethanol leads to the formation of [ZnI 2 (C 6 H 8 N 2 )] n ( 1 ), that according to powder X-ray diffraction was obtained as a pure phase. When the same reaction was performed in a mixture of ethanol and water as solvent, a few crystals of [ZnI 2 (C 6 H 8 N 2 )(H 2 O)]·0.5C 6 H 8 N 2 ·0.5H 2 O ( 2 ) were serendipitiously obtained in a mixture with compound 1 as the major phase. The asymmetric unit of 1 consists of one zinc cation, two crystallographically independent iodide anions and one 2,3-dimethylpyrazine ligand all of them located in general positions. In the extended structure, the Zn cations are tetrahedrally coordinated by two iodide anions and two symmetry-related 2,3-dimethylpyrazine ligands and are linked by bridging 2,3-dimethylpyrazine ligands into helical chains that proceed along the c -axis direction in the uncommon space group P 3 2 . Within these chains, intrachain C—H...I hydrogen bonding is observed. The asymmetric unit of 2 consists of two crystallographically independent [ZnI 2 (C 6 H 8 N 2 )(H 2 O)] complexes as well as one water molecule and one none-coordinating 2,3-dimethylpyrazine ligand. In the complexes, the Zn cations are tetrahedrally coordinated by two iodide anions, one 2,3-dimethylpyrazine ligand and one water molecule. These complexes are packed in such a way that cavities are formed, which are filled by water and 2,3-dimethylpyrazine solvate molecules that are hydrogen bonded to each other.

The synthesis and crystal structure of an unprecedented compound, zinc phosphorus heptachloride or catena -poly[phosphorus tetrachloride [[dichloridozinc]-μ-chlorido]], ZnPCl 7 or {[PCl 4 ][ZnCl 3 ]} n , are reported. The reaction of ZnCl 2 with PCl 5 in a 1:1 molar ratio at 623 K produced single crystals of ZnPCl 7 , which crystallizes in the orthorhombic space group Ama2 . The Zn and P atoms lie on crystallographic mirror planes, as do four of the Cl atoms. One Cl atom lies on a twofold axis and one occupies a general position. Its extended structure features isolated [PCl 4 ] + tetrahedra and one-dimensional chains of corner-sharing ZnCl 2 Cl 2/2 tetrahedra. Bond-valence sum calculations support the assignment of formal oxidation states. This discovery extends the compositional and structural landscape of mixed-metal halides.

Abstract A compromise process describes the evolution of opinions through binary interactions. Opinions are real numbers, and at each step, two randomly selected agents reach a compromise by averaging their pre-interaction opinions. We prove that if the number $N$ of agents is a power of two, then consensus emerges after a finite number of compromise events with probability one; otherwise, consensus cannot be reached in a finite number of steps, provided the initial opinions are in a general position. The number of steps required to reach consensus is random for $N=2^k$ with $k\geq 2$. We prove that the smallest number of steps is $k\cdot 2^{k-1}$ when the initial opinions are in a general position. For $N=4$, we determine the distribution of the number of steps. In particular, we show that it has a purely exponential tail and compute all cumulants.

Moving through Cartesian products, coronas and joins in general position

This paper investigates the dynamical behavior of Lotka–Volterra type operators defined on the four and five dimensional simplexes, focusing on their fixed points and structural representation through directed graphs (tournaments). For several classes of such operators, we derive algebraic and combinatorial conditions under which the configuration of fixed points exhibits transitive, cyclic, or homogeneous structures. Using methods from algebraic graph theory, Lyapunov stability theory, and Young’s inequality, explicit criteria are established for the existence, uniqueness, and stability of interior and boundary fixed points. A detailed analysis is provided for the class of operators whose associated skew-symmetric matrices are in general position. The connection between the minors of these matrices and the orientation of arcs in the tournament is clarified, revealing how dynamical transitions correspond to changes in tournament type. Furthermore, we demonstrate that under certain parameter regimes, fixed points coincide with evolutionarily stable strategies (ESS) in replicator dynamics, thus bridging discrete population models and evolutionary game theory. The obtained results enrich the theory of quadratic stochastic and Lotka–Volterra operators, providing new insights into nonlinear mappings on simplexes, combinatorial dynamics, and applications to models of interacting populations.

Abstract Outer, dual, and total general position sets are studied on strong and lexicographic products of graphs. Sharp lower and upper bounds are proved for the outer and the dual general position number of strong products and several exact values are obtained. For the lexicographic product, the outer general position number is determined in all the cases, and the dual general position number is established in many cases. The total general position number is determined for both products. Along the way some results on outer general position sets are also derived.

We present a microscopic analysis and evaluation of the dielectric susceptibility of a dielectric medium consisting of vector-type two-energy-level atoms, responding to a weak probe mode, when the atoms are driven by a strong coherent field. Each atom, in an environment of others, exists as a quasiparticle, further structuring the bulk medium. In a limit of dilute atomic gas, the dynamics of each atom follows the Mollow-type nonlinear excitation regime, and the medium susceptibility collectivizes the individual atomic responses to the probe mode. We outline how the collective dynamics can be interpolated up to a dense medium, and we argue from general positions that in such a medium, the optical nonlinearity and, in particular, its parametric part could be significantly magnified by manipulating both the coherent pump and the sample density. This indicates certain limitations for potential capabilities of quantum communication protocols utilizing entangled photons created by a parametric process as a main resource of quantum correlations.

The article examines the features of the administrative and legal regulation of the implementation of individual instruments of democracy during the period of the legal regime of martial law in Ukraine. It is established that the implementation and development of democracy during martial law consists in temporarily restricting or prohibiting the implementation of its individual forms (elections, referendums, other forms of public administrative initiative) while granting special powers to public authorities. The range of positions in the field of legal science regarding the state of administrative and legal regulation of prohibitions, restrictions and permissions for the implementation of instruments of democracy during the period of legislative restrictions of the legal regime of martial law and the formation of a substantiated author’s proposal in this area of public and administrative relations is investigated. It is established that the majority of representatives of legal science support the general position regarding the expediency of restricting relations of democracy (holding parliamentary, presidential, local elections and national and local referendums, etc.) during martial law. It is proposed to conduct research in the direction of forming administrative and legal principles for the introduction of direct electronic democracy. The state of regulatory and legal regulation of various types of mass gatherings as instruments for the implementation of democracy in legislative, and especially in subordinate administrative and legal acts (orders of the Ministry of Internal Affairs of Ukraine) is characterized. It is determined that such instruments for the implementation of citizens’ rights as public hearings and general meetings of condominium associations do not fall under any of the types of peaceful gatherings (events) that are prohibited by law during the legal regime of martial law and can be held both through direct gatherings of citizens, as well as in the telecommunications regime with compliance with all security measures, provided that the military command together with the military administration, in accordance with the powers assigned to them by law, have not prohibited the holding of such events.

Humans have exceptional object manipulation skills. By combining feed-forward and feedback control, the sensori motor system is able to predictively scale grip and manipulation forces and quickly adapt to environmental changes. Using technologies such as virtual reality, researchers can investigate the underlying mechanisms in ways that are not possible in the physical world. Here, we present our custom-built virtual reality setup, including an open-source software framework, and show its validity in human motor control studies. We replicated two well-established experiments involving physical objects that investigated how humans adapt to different object mass and center of mass. Our results show that the general force and position control strategies employed in the virtual experiment closely mirrored those observed in the real world. Specifically, participants scaled grip forces with object mass and coordinated digit positions and forces according to the object's center of mass and shape. However, the trial-by-trial adaptation rate was slower, and the grip forces were slightly increased in the virtual setup, likely due to increased uncertainty arising from the 2D visual feedback and the lack of cutaneous feedback. Additionally, we tested the effect of visual feedback complexity by comparing a simple and detailed representation of the fingers, finding that participants exhibited similar manipulation strategies across both conditions. Our results validate this setup as a reliable platform for future studies in human motor control.

The title compound, C 11 H 9 Cl 3 O 2 , (common name: β-aryl-β-methoxyvinyl trichloromethylketone) was crystallized from a chloroform solution at room temperature. The asymmetric unit comprises one molecule with all atoms in general positions and the E isomerism about the central vinyl entity could be undoubtedly determined. Weak intramolecular interactions between the ketone and the phenyl groups can be suggested, as two O...C distances [2.9154 (17) and 2.9780 (15) Å] are shorter than the van der Waals radii sum for the respective atoms (3.35 Å). As a result of the sp 3 C atoms and the C—C single bond between the phenyl ring and the central alkene fragment, the molecule is not planar. In the crystal, the molecules are linked by Cl...O weak interactions along the a -axis direction (2.962 Å intermolecular distances, compared to the 3.34 Å for the vdW radius sum) and these contacts were observed over the Hirshfeld surfaces set as d norm , shape-index and curvedness modes. The Hirshfeld surface analysis mapped over the d norm property indicates that four major contributions for the crystal cohesion are the H...Cl/Cl...H (34.2%), H...H (22.2%), H...C/C...H (13.5%) and H...O/O...H (10.6%) contacts. In addition, quantum-mechanical properties were calculated using the B3LYP/6–31 G( d , p ) monomer wavefunctions model. The calculations were performed from a single molecular entity within a radial cluster of symmetry-generated molecules, with the radius set to 3.8 Å, and the total intermolecular energies between the molecular pairs range from −3.5 kJ/mol to −22.4 kJ mol −1 . An expanded structure section, set to 3 × 3 × 3 unit cells, was used for the visualization of the energy-framework (only the total energy property was selected and the energy cut-off was set to 10.0 kJ/mol). The synthesis and 1 H/ 13 C NMR data of the title compound are already published in the literature [Siqueira et al. (1994). Quim. Nova , 17 , 24–26].

ABSTRACT The heterogeneity in the far-right parties’ foreign policy positions becomes especially visible when they face a dilemma of which side(s) to take in highly salient military conflicts that currently shape European and international politics: the war in Ukraine and the conflict between Israel and Palestine. Comparative studies have argued that these parties react differently given ideological and strategic concerns related to anti-Semitism, Islamophobia, Russophilia, and anti-Atlanticism and their positions are shaped by both domestic and international contexts. However, the impact of internal differences, which could lead to an ambivalent general position of a party on an issue, remains understudied. This study fills this gap by concentrating on an illustrative case of one of the most divided far-right parties, the Alternative for Germany (AfD). As the AfD is often depicted as a staunch supporter of Russia and Israel, the study also empirically assesses the plausibility of these arguments.

Direct observation of strongly tilted Dirac points at general positions in the reciprocal space

Purpose This research reveals the effect of gender on corporate risk management. Female involvement in business and management has been a hot topic in recent years. The authors use emerging market data to determine the effects of female chairpersons and general managers on risk management and corporate governance. In particular, the authors consider the combination of different genders of the chairperson and general manager positions and test their contributions to risk control. This study aims to contribute to the academic community while making policy contributions and providing gender equality opportunities for female involvement at the management level. Design/methodology/approach This research uses empirical methods to show the effects of different chairperson and general manager gender combinations, with firm share crash risk and volatility used as risk indicators. This study considers several specific issues, such as bank–firm relationships and a firm’s political connections, which may increase the degree of risk-taking incentives at the firm’s management level. It also further explores the effect of female involvement as the chairperson and the general manager in those specific situations. Findings The results show that when the chairperson and the general manager are both male, the firm has significantly greater risk. Once a female assumes the chairperson or general manager position, the regression coefficient of gender becomes statistically insignificant, indicating lower risk level. When a firm has a director or manager who has expertise in bank relationships, a female general manager could reduce the degree of risk. A similar situation occurs when a firm has political connections, and the female chairperson can better monitor and supervise the firm and reduce the risk of share price crashes and volatility. Originality/value This research, unlike most past research, uses manager and chairperson combinations rather than merely female involvement to demonstrate that females at the management level could alleviate a firm’s degree of corporate risk. The effects of the female chairperson, who plays the monitoring role, and the female general manager, who operates the firm, are separated and analyzed. Furthermore, it extends such influences to contribution when the chairperson and general managers are of different genders.

Abstract The persistent homology transform, Betti function transform, and Euler characteristic transform represent a shape with a multiset of persistence diagrams, Betti functions, or Euler characteristic functions, respectively, parameterized by the sphere of directions in the ambient space. In this work, we give the first explicit construction of finite sets of directions discretizing the verbose variants of these transforms and show that such discretizations faithfully represent the underlying shape. Our discretization, while exponential in the dimension of the shape, does not depend on any restrictions on the particular immersion beyond general position, and is stable with respect to various perturbations.

The search of multiple topological phases (TPs) and their transitions by tuning different parameters through chemical substitutions, electric field, magnetic field, strain and Floquet engineering, etc has garnered a widespread attention in recent time. In spite of great effort, the observations of multiple TPs in a single material and multiple TP transitions in the presence of one parameter remain elusive. Here we demonstrate the presence of multiple TPs and their transitions with uniaxial compressive strain (UCS) in orthorhombic Cu2SnS3by usingstate-of-the-artab-initiocalculations. In the absence of spin-orbit coupling (SOC), the Cu2SnS3exhibits only one (type-II) nodal-ring and in the presence of SOC, it hosts Weyl phase with seven Weyl points (three at Γ and four at general positions) along with nodal arcs. On the application of UCS, the system exhibits a type-II nodal ring for UCS<5.5%, which further evolves into type-III nodal-ring for5.5%⩽UCS<5.6%, thereby marking a TP transition in the nodal topology. Interestingly, at 5.6% of UCS, it shows Weyl phase with four Weyl nodes even in the absence of SOC. All the above-mentioned seven Weyl points persist below 5% of UCS. For5%⩽UCS<5.6%, four Weyl points (at general positions) disappear and nodal-arcs remain intact in all the studied range of UCS. The TPs observed in the absence of SOC appears to arise due to the presence of strain driven topological flat band, which is typically reported to be seen in kagome and Lieb lattices.

Abstract A finite point set in $\mathbb{R}^d$ is in general position if no $d + 1$ points lie on a common hyperplane. Let $\alpha _d(N)$ be the largest integer such that any set of $N$ points in $\mathbb{R}^d$ , with no $d + 2$ members on a common hyperplane, contains a subset of size $\alpha _d(N)$ in general position. Using the method of hypergraph containers, Balogh and Solymosi showed that $\alpha _2(N) \lt N^{5/6 + o(1)}$ . In this paper, we also use the container method to obtain new upper bounds for $\alpha _d(N)$ when $d \geq 3$ . More precisely, we show that if $d$ is odd, then $\alpha _d(N) \lt N^{\frac {1}{2} + \frac {1}{2d} + o(1)}$ , and if $d$ is even, we have $\alpha _d(N) \lt N^{\frac {1}{2} + \frac {1}{d-1} + o(1)}$ . We also study the classical problem of determining $a(d,k,n)$ , the maximum number of points selected from the grid $[n]^d$ such that no $k + 2$ members lie on a $k$ -flat, and improve the previously best known bound for $a(d,k,n)$ , due to Lefmann in 2008, by a polynomial factor when $k$ = 2 or 3 (mod 4).

ABSTRACT How has the media influenced the evolution of roles and identity in Kenyan women? This study examines the interplay between traditional roles and modern media culture, focusing on how media has shaped the roles and identities of Kenyan women. It introduces the concept of cultural hybridity to explain the emergence of a hybrid identity, where women navigate between established norms and new representations shaped by media. Using a mixed-method design with a narrative qualitative approach, the study draws on literature, media content, interviews, and observations to examine how Kenyan women adapt to changing social roles. Grounded in mediatization theory, our research highlights Kenyan women’s adaptation to modern roles through their engagement with media. Findings indicate that historically rigid roles of women in Kenya have become fluid, influenced by the dynamic interplay between global media narratives and local cultural contexts. There is an unclear distinction between men’s and women’s roles and identities in various realms, such as domestic, corporate, politics, and the general positioning in social structures. This interaction provides a platform for women to redefine their individual and collective identities. This article contributes to understanding the media’s transformative impact on women’s lived experiences in a globalized, culturally diverse Kenya.

The article actualizes the contradiction about the identity of female tutors, mentors, supervisors and educators of women’s institutions, which contributed not only to the ease in the practice of using these names as synonyms, but also to the actual historical error, which led to the confusion of the meaning of the activities of the mentioned subjects in the system of women’s education in the Russian Empire. This contribution is quite widespread in the historical and pedagogical literature. The purpose of this article is to clarify the use of the term “female tutorˮ in the context of the development of women’s education in pre-revolutionary Russia and to restore the historical semantics of this specific teaching position. The use of historical and pedagogical reconstruction of the term “female tutorˮ allows us to present the transformation of this pedagogical term through the analysis of its origin, changes, and meaning in the historical context. In turn, the application of historical-systematic and typological analysis has contributed to the clarification of the conceptual framework under study. The comparative analysis allowed us to collate the names of various specific pedagogical positions in women’s educational institutions of the Russian Empire in the late 18th and early 20th centuries, demonstrating both similarities as a result of their common ancestry and specific features determined by the goals of the educational institution. It is concluded that the concept of “female tutorˮ can be conditionally accepted as a historical and pedagogical stereotype that is familiar to the public consciousness, implying a general pedagogical position in women’s educational institutions in pre-revolutionary Russia. Formally, a female tutor is a special pedagogical position that was included into the staff of closed women’s institutions in the Russian Empire in the late 18th and early 20th centuries, with a wide range of organizational, household, and educational obligations

2-Picolinium tetra-chlorido-aurate(III), (C6H8N)[AuCl4] or (2-PicH)[AuCl4], 1, and 2-picolinium tetra-bromido-aurate(III), (C6H8N)[AuBr4] or (2-PicH)[AuBr4], 2, both crystallize in the space group P1 with Z = 4, but are not isotypic. Bis(2-picolinium) tetra-bromido-aurate(III) bromide, (C6H8N)2[AuBr4]Br or (2-PicH)2[AuBr4]Br, 3, crystallizes in the space group P1 with Z = 2. All atoms of 1-3 lie on general positions. 3-Picolinium tetra-bromido-aurate(III), (C6H8N)[AuCl4] or (3-PicH)[AuBr4], 4, crystallizes in the space group P21/c with Z = 4; the two independent anions each display inversion symmetry. trans-Di-bromido-bis-(4-picoline)gold(III) tetra-bromido-aurate(III) nitro-methane mono-sol-vate, [AuBr2(C6H7N)2](AuBr4]·CH3NO2 or [(4-Pic)2AuBr2](AuBr4]·CH3NO2, 5, and 4-picolinium tetra-bromido-aurate(III), (C6H8N)[AuBr4] or (4-PicH)[AuBr4], 6, both crystallize in the space group P1 with Z = 2; both involve two independent anions with inversion symmetry. 2,4-Lutidinium tetra-bromido-aurate(III), (C7H10N)[AuBr4] or (2,4-LutH)[AuBr4], 7, crystallizes in the space group P212121 with Z = 4. All the gold(III) species show the expected square-planar geometry. The main inter-est centres on the packing patterns. In 1, hydrogen bonds, Cl⋯Cl contacts, axial Au⋯Cl contacts ('coinage bonds') and Cl⋯π contacts combine to form layers parallel to (101). In 2, similar contacts (but involving Br) link the residues to form corrugated layers parallel to the ac plane. In 3, classical hydrogen bonds, Br⋯Br contacts and a coinage bond, all involving the free bromide ion, combine to produce rings of composition Au2Br4, which are then linked by another Br⋯Br contact, to form chains of residues parallel to [011]. In 4, hydrogen bonds and a Br⋯Br contact generate chains of residues parallel to [101], which are in turn linked by a Br⋯π contact. In 5, Br⋯Br contacts and coinage bonds link the anions and cations to form a corrugated layer structure parallel to the ac plane, involving six-membered Au2Br4 and ten-membered Au4Br6 rings. A similar combination of contacts in 6 leads to a layer structure parallel to the ab plane, also involving a pattern of six- and ten-membered rings topologically analogous to that of 5. However, the angles in the rings of the two layers differ appreciably, and 6 also contains a short Br⋯π contact. In 7, a hydrogen bond combines with a coinage bond to produce a ribbon of residues parallel to the a axis. Three further, longer and perhaps borderline, Br⋯Br and Br⋯Cg contacts link the ribbons to form a three-dimensional pattern.

The critical threat of the risk of genocide became especially acute in the late twentieth and first third of the twenty-first century and has become a major influence on global security. The study is devoted to the specifics of the genocidal policy of the Russian Federation as part of the concept of the formation of Russian national ideology. The research methodology included analysis and synthesis, systematization, comparison, generalization, and abstraction. The analysis of the rhetoric of Russian officials and publications in the media and mass media allowed us to conclude that the idea of genocide is present, supported by the general national position of the Russian Federation and actively financed by the federal budget. The retransmission of the official ideology in the context of anti-Ukrainian materials contains calls for “restoring historical justice” and “denazification” of Ukrainians. The study examines the system of Russian “denazification” measures, which are accompanied by censorship, ideological pressure, and the destruction of its own political opposition against the background of the functioning of cross-cutting ideas of genocidal policy. The author substantiates the presence of a consistent policy of the Russian Federation towards Ukrainians, which has signs of genocidal intentions. The article proves that genocidal propaganda within the political narrative of the Russian Federation has a suggestive character, which ensures the consistent formation of ideological hatred towards the Ukrainian people in society. The destructive critical consequences of the genocidal ideology of the Russian Federation for the security of global geopolitical development are substantiated.