Group Elements Research Articles

On the combinatorial rank of quantum groups of type F4

In this paper, we calculate the combinatorial rank of the positive part [Formula: see text] of the multiparameter version of the small Lusztig quantum group, where [Formula: see text] is a simple Lie algebra of type [Formula: see text]. For this purpose, we also present the basis and relations of the quantum algebra, calculate the coproduct of its PBW-generators and determine all skew-primitive elements of this quantum group. In conclusion, we obtain that the combinatorial rank of [Formula: see text] is 4.

Towards Catalytic C–H Activation Using Main Group Elements

AbstractCatalytic C–H activation reactions are now established as a means to directly transform organic molecules and are commonly associated with metals such as palladium, rhodium, ruthenium and iridium. This Account will describe a short number of reports demonstrating that structures containing main group elements can facilitate C–H activation processes. In particular, boron-based catalysts can promote catalytic arene C–H borylation reactions, and an emerging approach using phosphenium ions can also cleave sp2 C–H bonds. These processes use a Lewis acidic main group atom combined with a pendant base to cleave C–H bonds, which compares with metal-catalyzed reactions that proceed via concerted metalation deprotonation mechanisms.1 Introduction2 Metal-Catalyzed C–H Activation via CMD/AMLA Mechanisms3 C–H Borylation via Boron-Based Catalysts4 C–H Activation Using Phosphenium Ions5 Conclusions

Optimizing the heat capacities of sphalerite phases as single system, or how nuclear physics can help physical chemistry

The correct mathematical description of heat capacities Cp in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of Cp or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe Cp in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (114Fl) closing this group. There should be no other elements in this group according to the fine structure constant (α) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (114Fl) and has a value of Cp = 30.5 ± 0.3 J · mol-at−1 · K−1. This value was obtained as a maximal virtual point Cp of the last element (114Fl) of group IV and corresponds to Ln (Cp/R) = 1.30 ± 0.01 for the isotherms ln (Cp/R) vs Ln(N), where N is an atomic number of an element of group IV or the sum of the atomic numbers of AIIIBV or AIIBVI compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations Ср/R vs Ln(N) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to α. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at−1·K−1 with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at−1·K−1. To describe the set of the isostructural experimental data Cp(T) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence Cp(T) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(N), where N is the atomic number or the demi sum of the atomic numbers of phases AIIBVI or AIIIBV. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(N).

Cayley Linear-Time Computable Groups

This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We show that the groups $\mathbb{Z}_2 \wr \mathbb{Z}^2$, $\mathbb{Z}_2 \wr \mathbb{F}_2$ and Thompson's group $F$ have normal forms for which the right multiplication by a group element is computed in linear time on a $2$-tape Turing machine. This refines the results previously established by Elder and the authors that these groups are Cayley polynomial-time computable.

Do Economic Complexity Drivers Differ by Income Level? Insights From a Global Perspective

This study examines the drivers of economic complexity for 97 countries over the period 1995 to 2020 by income sub-groups. To investigate determinants of complexity, we develop five novel indexes. Using two-step system GMM (2SGMM) regression with the robust standard errors method, we found that institutional quality, health dimensions and macroeconomic conditions were enormously significant economic complexity drivers. However, the findings vary according to the country groups with different income levels. While the importance of openness and health dimensions are prominent in low and middle-income countries, capital stock and openness are the principal elements in the high-income group. The institutional quality is statistically significant and considerably affects on complexity in each group and across the panel. The education dimension of human capital has a positive effect only in the high-income group and across the panel, while it is negative in the middle and low-income groups, but its effect is weak. Moreover, these findings are valid in the long run. From a policy perspective, the findings suggest that macroeconomic policies focused on institutional quality, openness and healthcare as critical components of economic complexity should be crucial goals, especially for low and middle-income countries. JEL Classification: O11, O43, I15, I25.

SN 2020udy: A New Piece of the Homogeneous Bright Group in the Diverse Iax Subclass

We present optical observations and analysis of the bright type Iax supernova SN 2020udy hosted by NGC 0812. The evolution of the light curve of SN 2020udy is similar to that of other bright type Iax SNe. Analytical modeling of the quasi-bolometric light curves of SN 2020udy suggests that 0.08 ± 0.01 M ⊙ of 56Ni would have been synthesized during the explosion. The spectral features of SN 2020udy are similar to those of the bright members of type Iax class, showing a weak Si ii line. The late-time spectral sequence is mostly dominated by iron group elements with broad emission lines. Abundance tomography modeling of the spectral time series of SN 2020udy using TARDIS indicates stratification in the outer ejecta; however, to confirm this, spectral modeling at a very early phase is required. After maximum light, uniform mixing of chemical elements is sufficient to explain the spectral evolution. Unlike in the case of normal type Ia SNe, the photospheric approximation remains robust until +100 days, requiring an additional continuum source. Overall, the observational features of SN 2020udy are consistent with the deflagration of a carbon–oxygen white dwarf.

Chemical Aristocracy: He3 Dication and Analogous Noble-Gas-Exclusive Covalent Compounds.

Herein, we predict the first set of covalently bonded triatomic molecular compounds composed exclusively of noble gases. Using a combination of double-hybrid DFT, CCSD(T), and MRCI+Q calculations and a range of bonding analyses, we explored a set of 270 doubly charged triatomics, which included various combinations of noble gases and main group elements. This extensive exploration uncovered nine noble-gas-exclusive covalent compounds incorporating helium, neon, argon, or combinations thereof, exemplified by cases such as He32+ and related systems. This work brings to light a previously uncharted domain of noble gas chemistry, demonstrating the potential of noble gases in forming covalent molecular clusters.

Exceptional sequences and rooted labeled forests

We give a representation-theoretic bijection between rooted labeled forests with [Formula: see text] vertices and complete exceptional sequences for the quiver of type [Formula: see text] with straight orientation. The ascending and descending vertices in the forest correspond to relatively injective and relatively projective objects in the exceptional sequence. We conclude that every object in an exceptional sequence for linearly oriented [Formula: see text] is either relatively projective or relatively injective or both. We construct a natural action of the extended braid group on rooted labeled forests and show that it agrees with the known action of the braid group on complete exceptional sequences. We also describe the action of [Formula: see text], the Garside element of the braid group, on rooted labeled forests using representation theory and show how this relates to cluster theory.

Revisit of a Diaconis urn model

Let G be a finite Abelian group of order d. We consider an urn in which, initially, there are labeled balls that generate the group G. Choosing two balls from the urn with replacement, observe their labels, and perform a group multiplication on the respective group elements to obtain a group element. Then, we put a ball labeled with that resulting element into the urn. This model was formulated by P. Diaconis while studying a group theoretic algorithm called MeatAxe (Holt and Rees, 1994). Siegmund and Yakir (2005) partially investigated this model. In this paper, we further investigate and generalize this model. More specifically, we allow a random number of balls to be drawn from the urn at each stage in the Diaconis urn model. For such a case, we verify that the normalized urn composition converges almost surely to the uniform distribution on the group G. Moreover, we obtain the asymptotic joint distribution of the urn composition by using the martingale central limit theorem.

Chemical Bonding and the Role of Node-Induced Electron Confinement.

The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial and has been responsible for fierce debate over the past century. Here, we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms [node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction, and polarization] that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure, and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements.

Chinese Mythological Elements and Contemporary Art Works

"Contemporary art" is an "alternative construction" that seeks a way out in the context of "modernity". It is a work of art constructed using the way of thinking of contemporary people; it is the development of post-modern art and continues after modern art and is derived from it; it is a new concept, new form, and new path. Chinese totem aesthetic art has substantial symbolic value and significance. Among the art categories, dance dramas with mythological themes deeply explore elements of various regions, ethnic groups, and dance types and incorporate traditional dance vocabulary. A large amount of vocabulary is used in dance dramas with mythological themes. This vocabulary not only makes the dance dramas present a unique national style but also sorts out and excavates the cultural relics of different mythological themes, effectively promoting the fullness of dance dramas with mythological themes.

MV polytopes and reduced double Bruhat cells

When G is a complex reductive algebraic group, MV polytopes are in bijection with the non-negative tropical points of the unipotent group of G . By fixing w from the Weyl group, we can define MV polytopes whose highest vertex is labelled by w . We show that these polytopes are in bijection with the non-negative tropical points of the reduced double Bruhat cell labelled by w^{-1} . To do this, we define a collection of generalized minor functions \Delta_{\gamma}^{\mathrm{new}} which tropicalize on the reduced Bruhat cell to the BZ data of an MV polytope of highest vertex w . We also describe the combinatorial structure of MV polytopes of highest vertex w . We explicitly describe the map from the Weyl group to the subset of elements bounded by w in the Bruhat order which sends u \mapsto v if the vertex labelled by u coincides with the vertex labelled by v for every MV polytope of highest vertex w . As a consequence of this map, we prove that these polytopes have vertices labelled by Weyl group elements less than w in the Bruhat order.

Relativistic effect influencing the diverse bonding character of the interfacial Ag staple motifs in thiolate-protected nanoclusters.

Thiolate-protected noble-metal nanoclusters have recently attracted extensive attention due to their appealing properties in optics, catalysis, etc. Within the same group element, experiments indicate that Ag staples exhibit di-, tri-, or even tetra-coordination, in contrast to the di-coordination observed in Au staples, rendering the structures of Ag nanoclusters more intricate. However, the underlying chemical insight of the bonding feature of multiple-coordinated Ag staples remains unclear. In this study, we employed density functional theory coupled with all-electron scalar relativistic calculations to elucidate the critical role of relativistic effect in determining the conformational complexity of Ag staples. Unlike Au, the relatively weaker relativistic effect induces fewer contributions of d orbitals in bonding for the Ag atom, showing an extreme sensitivity to the structural architecture in liganded clusters. A relatively higher d orbital percentage favors di-coordination with a shortened Ag-S bond, while a relatively lower d orbital percentage favors tri- and tetra-coordinations with an elongated Ag-S bond. The Lewis structures of the multi-coordinated Ag motifs were also unveiled. In addition, two AgNCs, including the [Ag29(SCH3)18]3- cluster with tri-coordinated Ag motifs and [Ag29(SCH3)18(PCH3)6]3- with tetra-coordinated Ag motifs, were predicted after clarifying the bonding characters of the multiple-coordinated Ag motifs. This work not only deepens the understanding of the bonding characteristics of the Ag staple motif in AgNCs and AuAg alloy clusters but also provides a new perspective to understand the relativistic effect in the thiolate-protected noble-metal nanocluster.

Pattern identification in data about unmodified waste eggshell application as an adsorbent for metal ion removal from aqueous media

Abstract In recent years, a significant increase in the amount of research published about the application of eggshells for the removal of metal ions from aqueous solutions has been observed. The paper presents different aspects of metal adsorption from aqueous solutions on untreated eggshells. Pretreatment procedures and tested parameters for the adsorption differ significantly across all the reviewed data, providing a source of variance for the results. For untreated eggshells, the range of the reported BET surface area is from 0.07 m2/g to 8.941 m2/g. Correlation between particle size and BET surface area has been highlighted. Reported removal efficiencies for the untreated eggshell have been compared. Reported results show that eggshell is most employed for the removal of Pb(II), Cd(II), and Cu(II) from aqueous solutions. Eggshell capacity to remove metal ions from the main group elements has also been demonstrated. While results look promising, not enough data are present to make reliable conclusions about its efficiency with other (mainly transition) metal ions – which makes it a possible research direction. Based on the reported data, multiple removal pathways are involved. Several eggshell modification methods and possibilities of creating new adsorbents using eggshells only as a part of the raw material have been assessed. Finally reported eggshell modification methods have been assessed and it is clear that to compare different material’s effectiveness as an adsorbent, comparing only materials adsorption capacities is insufficient. Certain environmental water pollution removal studies using adsorption demand further study, such as metal ion specification in aqueous solution, in different processing water, and even in wastewater.

Pnictogen-Rich Heterocycles Derived from a Phosphadiazonium Cation.

Heterocycles that pair main group elements and nitrogen are extremely important within the π-conjugated heterocycles research community. Compared to the vast number of boron-nitrogen heterocycles, those that include phosphorus are less common. Furthermore, the use of phosphorus-nitrogen triple bonds of any type to prepare such compounds is unprecedented. Here, we pair pyridyl hydrazonide ligands with phosphadiazonium cations and demonstrate that the chelated Mes*NP group is directly implicated in the photophysical and redox properties observed for the resulting heterocycles. In doing so, we introduce a novel building block for the production of phosphorus-containing heterocycles that could find use in small molecule activation and catalysis or as the functional component of emerging organic electronics.

Potential cellular targets of platinum in the freshwater microalgae Chlamydomonas reinhardtii and Nitzschia palea revealed by transcriptomics.

Platinum group element levels have increased in natural aquatic environments in the last few decades, in particular as a consequence of the use of automobile catalytic converters on a global scale. Concentrations of Pt over tens of μg L-1 have been observed in rivers and effluents. This raises questions regarding its possible impacts on aquatic ecosystems, as Pt natural background concentrations are extremely low to undetectable. Primary producers, such as microalgae, are of great ecological importance, as they are at the base of the food web. The purpose of this work was to better understand the impact of Pt on a cellular level for freshwater unicellular algae. Two species with different characteristics, a green alga C. reinhardtii and a diatom N. palea, were studied. The bioaccumulation of Pt as well as its effect on growth were quantified. Moreover, the induction or repression factors of 16 specific genes were determined and allowed for the determination of possible intracellular effects and pathways of Pt. Both species seemed to be experiencing copper deficiency as suggested by inductions of genes linked to copper transporters. This is an indication that Pt might be internalized through the Cu(I) metabolic pathway. Moreover, Pt could possibly be excreted using an efflux pump. Other highlights include a concentration-dependent negative impact of Pt on mitochondrial metabolism for C. reinhardtii which is not observed for N. palea. These findings allowed for a better understanding of some of the possible impacts of Pt on freshwater primary producers, and also lay the foundations for the investigation of pathways for Pt entry at the base of the aquatic food web.

First-principles calculations to investigate impact of doping by chalcogen elements on the electronic, structural, and optical properties of SrTiO3 compounds

Doping techniques are commonly utilized to effectively modify the physical properties of a desired compound. In this study, we employed the first-principles DFT calculations with a GGA + TB-mBJ approach as implemented by the Wien2k code, by investigating the effects of oxygen group element concentrations on the structural, electronic, and optical properties of the perovskite substance SrTiO3. We calculated the formation energies of each doped structure to assess the viability of synthesis. The band gap is equal to 1.355 eV, 0.653 eV, and 0.632 eV for 12.5 % S, Se, and Te doped SrTiO3, respectively. For the pure SrTiO3, the band gap is 2.584 eV. According to our findings, raising the chalcogen concentrations resulted in a considerable decrease in band gaps and an improvement in the ability to absorb light in the visible range (380–790 nm), exceeding 105 cm−1 for Te doped SrTiO3 (STO). At zero frequency, the dielectric constant was found (ε1 (0)) to be 4.432 for SrTiO3 pure and 6.332 for SrTiO3 doped with Te (12.5 %) in GGA-PBE and (ε1 (0)) = 4.432 and 12.217 for GGA + mBJ. The optical conductivity of SrTO3 doped with Te is determined to be 0.322 * 104 /Ω.cm, in comparison to a value of 0.377 * 104/Ω.cm for mBJ. Our research revealed that raising the chalcogen concentrations significantly enhanced the electrical conductivity, as predicted, along with improvements in optical conductivity and reflectivity. SrTiO3-xYx (Y = S, Se, or Te) represents one of our quaternary alloys, demonstrating substantial potential as a promising material for advanced photovoltaic and solar cell applications. Our findings revealed that the doped materials exhibited significantly high absorption rates and productivity. We also examined additional optical parameters, including optical band gap, Urbach energy, and optical conductivity.

Evaluation of urinary trace element levels in patients with opioid use disorder undergoing methadone treatment in western Iran

The monitoring of essential and toxic elements in patients with Opioid Use Disorder (OUD) undergoing methadone treatment (MT) is important, and there is limited previous research on the urinary levels of these elements in MT patients. Therefore, the present study aimed to analyze certain elements in the context of methadone treatment compared to a healthy group. In this study, patients with opioid use disorder undergoing MT (n = 67) were compared with a healthy group of companions (n = 62) in terms of urinary concentrations of some essential elements (selenium (Se), zinc (Zn), copper (Cu), iron (Fe), manganese (Mn), calcium (Ca)) and toxic elements (lead (Pb), cadmium (Cd), arsenic (As), and chromium (Cr)). Urine samples were prepared using the acid digestion method with a mixture of nitric acid and perchloric acid and assessed using the ICP-MS method. Our results showed that the two groups had no significant differences in terms of gender, education level, occupation, and smoking status. Urinary concentrations of Se, Cu, and Fe levels were significantly lower in the MT group compared to the healthy subjects. However, the concentrations of Pb, Cd, As, Mn, Cr, and Ca in the MT group were higher than in the healthy group (p < 0.05). No significant difference was established between the levels of Zn in the two groups (p = 0.232). The results of regression analysis revealed that the differences between the concentration levels of all metals (except Zn) between two groups were still remained significant after adjusting for all variables (p < 0.05). The data obtained in the current study showed lower urinary concentrations of some essential elements and higher levels of some toxic elements in the MT group compared to the healthy subjects. These findings should be incorporated into harm-reduction interventions.

Low-sulfide platinum–metal deposits in the Kola region: A comparative analysis of the Yuzhnosopchinskoye ore occurrence and the Fedorova Tundra deposit

Research subject. Platinum–metal objects of the Kola region (contact type mineralization), including the Yuzhnosopchinskoye ore occurrence within the same-name massif belonging to the Early Proterozoic Monchetundra intrusion and the Fedorova Tundra deposit located in the western part of the Early Proterozoic Fedorovo-Pansky layered complex. Aim. To establish the formation conditions of platinum-metal ores in the Yuzhnosopchinskoye ore occurrence and the Fedorova Tundra deposit. Methods. Comparison of the geological structure and petro-geochemical features of rocks and ores from the two objects using statistical analysis. Results. Both the Yuzhnosopchinskoye ore occurrence and the Fedorova Tundra deposit belong to the contact type of platinum group element deposits. The main characteristic feature is confinement of the ore zone to the contact of two magmatic phases. In the contact zone, igneous breccia, pegmatoid, and vein bodies are widespread, with the latter being especially common in the Yuzhnosopchinskoye ore occurrence. In Yuzhnosopchinskoye ore occurrence, breccia fragments are represented by orthopyroxenites and melanocratic norites of the early magmatic phase (layered series of rocks). They were cemented by barren gabbroids of the later magmatic phase. In the Fedorova Tundra deposit, breccia zone fragments are also composed of orthopyroxenites and melanocratic norites of the early magmatic phase (layered series of rocks). They were cemented by taxitic ore-bearing gabbronorites of the late magmatic phase. Rocks of the two objects with a similar nomenclature demonstrate slight systematic differences in the composition of petrogenic components, as well as in REE and rare elements. Taxitic gabbronorites (rocks of the marginal series) from the Fedorova Tundra deposit have no rock analogues in Yuzhnosopchinskoye ore occurrence. A comparison of similar amounts of two data sets (more than 2000 samples each) of Pt, Pd, Au, Ni, and Cu sampling showed that the content of all precious metals in the Fedorova Tundra deposit was consistently higher than that in the Yuzhnosopchinskoye ore occurrence. The Fedorova Tundra deposit is homogeneous, with an average Pd/Pt ratio of 4.5. The Yuzhnosopchinskoye ore occurrence is heterogeneous and, on average, slightly more ‘platinum’ and less ‘palladium’ than the Fedorova Tundra deposit. Conclusions. The two ore objects of the contact type are similar in many respects, mainly differing in the conditions of mineralization formation. The Yuzhnosopchinskoye ore occurrence entered the contact zone from the rocks of the layered series due to the activation of the ore matter during intrusion of the late gabbroid intrusive phase. The Fedorova Tundra deposit entered the contact zone together with the late ore-bearing gabbronorite magmatic phase.

There are at most finitely many singular moduli that are S-units

We show that for every finite set of prime numbers $S$ , there are at most finitely many singular moduli that are $S$ -units. The key new ingredient is that for every prime number $p$ , singular moduli are $p$ -adically disperse. We prove analogous results for the Weber modular functions, the $\lambda$ -invariants and the McKay–Thompson series associated with the elements of the monster group. Finally, we also obtain that a modular function that specializes to infinitely many algebraic units at quadratic imaginary numbers must be a weak modular unit.