Index Theory Research Articles

Supramolecular Assemblies in Mn (II) and Zn (II) Metal–Organic Compounds Involving Phenanthroline and Benzoate: Experimental and Theoretical Studies

Two new Mn(II) and Zn(II) metal–organic compounds of 1,10-phenanthroline and methyl benzoates viz. [Mn(phen)2Cl2]2-ClBzH (1) and [Zn(4-MeBz)2(2-AmPy)2] (2) (where 4-MeBz = 4-methylbenzoate, 2-AmPy = 2-aminopyridine, phen = 1,10-phenanthroline, 2-ClBzH = 2-chlorobenzoic acid) were synthesized and characterized using elemental analysis, TGA, spectroscopic (FTIR, electronic) and single crystal X-ray diffraction techniques. The crystal structure analysis of the compounds revealed the presence of various non-covalent interactions, which provides stability to the crystal structures. The crystal structure analysis of compound 1 revealed the formation of a supramolecular dimer of 2-ClBzH enclathrate within the hexameric host cavity formed by the neighboring monomeric units. Compound 2 is a mononuclear compound of Zn(II) where flexible binding topologies of 4-CH3Bz are observed with the metal center. Moreover, various non-covalent interactions, such as lp(O)-π, lp(Cl)-π, C–H∙∙∙Cl, π-stacking interactions as well as N–H∙∙∙O, C–H∙∙∙O and C–H∙∙∙π hydrogen bonding interactions, are found to be involved in plateauing the molecular self-association of the compounds. The remarkable enclathration of the H-bonded 2-ClBzH dimer into a supramolecular cavity formed by two [Mn(phen)2Cl2] complexes were further studied theoretically using density functional theory (DFT) calculations, the non-covalent interaction (NCI) plot index and quantum theory of atoms in molecules (QTAIM) computational tools. Synergistic effects were also analyzed using molecular electrostatic potential (MEP) surface analysis.

Contact instantons with Legendrian boundary condition: A priori estimates, asymptotic convergence and index formula

In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with Legendrian boundary condition, and prove an asymptotic exponential [Formula: see text]-convergence result at a puncture under the uniform [Formula: see text] bound. We prove that the asymptotic charge of contact instantons at the punctures under the Legendrian boundary condition vanishes. This eliminates the phenomenon of the appearance of spiraling cusp instanton along a Reeb core, which removes the only remaining obstacle towards the compactification and the Fredholm theory of the moduli space of contact instantons in the open string case, which plagues the closed string case. Leaving the study of [Formula: see text]-estimates and details of Gromov-Floer-Hofer style compactification of contact instantons to [27], we also derive an index formula which computes the virtual dimension of the moduli space. These results are the analytic basis for the sequels [27]–[29] and [36] containing applications to contact topology and contact Hamiltonian dynamics.

98 Adding parasite resistance to the breeding objective in hair sheep

Abstract Economic selection indexes provide the best method to achieve genetic gain for multiple traits simultaneously. Hair sheep enterprises, particularly in environments with substantial gastrointestinal nematode challenge, may benefit from incorporating parasite resistance in a selection index. However, obtaining the relative economic value (REV) for parasite resistance is challenging; information on its impact on productivity is incomplete, as are the costs of treatment given anthelmintic resistance. The National Sheep Improvement Program (NSIP) currently provides producers with an index designed to increase total weight of lamb weaned per ewe lambing (TW). Our objective was to assess the effects of including fecal egg count, an indicator of parasite resistance, as an additional goal trait. Including the benchmark scenario with TW as its sole objective, 10 indexes were constructed using standard index theory. Post-weaning fecal egg count (PFEC) was added to this breeding objective with a REV of -1 and the REV for TW was varied from +1 to +5 at +0.5 increments. Weaning weight, number of lambs born and weaned, and PFEC were the selection criteria, modelled as either phenotypes or estimated breeding values (EBV). Phenotypes and EBV were simulated for 1,000 lambs by Cholesky decomposition and used to generate index scores. Ten replicates were run and the top 3% of males and 26% of females were retained on index scores. Annual responses in the goal traits were estimated. Responses in PFEC were expressed as a percentage, assuming a mean PFEC of 2,089 eggs/g as in NSIP. Concordances with those selected in the benchmark scenario were determined. Using EBV as selection criteria, TW increased by 1.7 kg/yr in the benchmark scenario (Table 1). However, unfavorably, PFEC increased by 2.3%/yr. When phenotypic criteria were used, TW increased by 0.5 kg/yr, and PFEC by 0.3%/yr. Once added to the breeding objective, PFEC decreased regardless of the REV of TW. However, response in TW also reduced, although less so as its REV increased. With EBV as the criteria, the REV of +3 for TW appeared preferable: PFEC reduced by 7.1%/yr with 98% of the response in TW retained. With phenotypic selection criteria, PFEC reduced by 5.2%/yr with 94% of the response in TW retained. With +3 REV for TW and EBV as the selection criteria, on average 65% and 82% of males and females, respectively, were chosen in common with the benchmark. When phenotypic criteria were used, those percentages were 60% and 80%, respectively. Implementing a more holistic index with REV of +3 for TW and -1 for PFEC would result in reasonable responses in both traits. However, producers will need to decide if reduced gains in TW is acceptable to improve parasite resistance in a hair sheep breeding program.

On generalized logistic equations with non-local term of feedback control type

We consider a problem of finding functions λ(x),u(x) such that −Δpu=λf(x,u,∇u)−g(x,u) in Ω and u=0 on ∂Ω, λ(x)∈F(x,u(x)) a.e. in Ω. Assume that, the single-valued functions f,g and the multi-valued function F satisfy certain growth conditions. Using the fixed point index theory for multi-valued operators with non-necessary convex values, we prove the existence of one or two nontrivial non-negative solutions of the problem.

Improving the quality and toxicity of rice husk liquid smoke to control edamame soybean pests

Purpose of the research to improve the quality and toxicity of husk charcoal liquid smoke which is effective and selective in controlling edamame soybean plant pests, safe for predatory and pollinators arthropods, and does not contain the dangerous compound Benzo(a)pyrene. The resulting product can be used as a substitute for synthetic insecticides which are non-selective and unsafe for predators, pollinators and human health. The technique used was to set the temperature of the pyrolysis process between 200-300°C to produce grade 3 and distillation of grade 3 to grade 2 with a temperature of 80-100°C. Research was carried out at Jember State Polytechnic, from August to September 2023. The observation parameters were content of grade 3 and grade 2 compounds using GCMS, Bioassay tests against S. litura 3rd instar using concentrations of 0%, 1%. 2%, 3%, 4% and 5% each for 10 test insects, with 3 repetitions, using the feed immersion method. LC50 and LC95 test used PoloPlus 1.0. Field tests compared arthropod diversity, grade 3, grade 2 and Imidacloprid treatments, using the Kruskal-Wallis test. The diversity index uses the Shannon-Wiener (H’) and Sympson Dominance Index (C’) formulas. Conclusion LC95 grade 3 was 3%, Grade 2 was 4%. Both were not found Benzo(a)pyrene. The grade 3 pest population was not significantly different compared to Imidacloprid. Grade 3 and grade 2 predators and pollinators were higher than Imidacloprid, the diversity of Grade 3, grade 2 and Imidacloprid treatments were moderate diversity, balanced ecosystem and no species dominance found.

Correction to: Local index theorem for orbifold Riemann surfaces

Correction to: Local index theorem for orbifold Riemann surfaces

Assessment and spatialization of vulnerability of Benin coast to sea level rise using composite/blended approach

Climate change, particularly sea level rise, poses significant challenges to global coastal regions, necessitating a profound understanding of their vulnerability for effective mitigation and adaptation strategies. This study focuses on enhancing scientific insight into West African coastal vulnerability, aiming to assist policymakers and coastal managers in developing sustainable coastal zone management strategies. The methodology employed combines Geographic Information System (GIS) and remote sensing techniques with the Coastal Vulnerability Index (CVI) formula. Parameters such as slope, topography, distance to shoreline, population density, accessibility, land cover, and soil and vegetation types are assessed for their contribution to physical and socio-economic changes induced by sea level rise. These parameters undergo weighting using the Analytic Hierarchy Process (AHP). The socio-economic vulnerability is quantified using the Community-Based Risk Screening Tool-Adaptation and Livelihoods (CRiSTAL). The assessment of the Benin coast reveals significant vulnerability, with very high vulnerability (36.69–70.4, indicated by red cells) and high vulnerability (30.84–36.69, indicated by orange cells) observed in all coastal municipalities (Grand-Popo, Ouidah, Abomey-Calavi, Cotonou, Sèmè-Kpodji), encompassing 40 % and 21 % of the study area, respectively. Moderate (25.69–30.84) and low (10.87–25.69) vulnerability areas are situated at higher elevations inland, covering 35 % and 4 % of the total study area, respectively. No areas of very low vulnerability have been identified. This research contributes significantly to coastal management decisions, adaptation strategies, and climate change policies in Benin by advancing scientific understanding of coastal vulnerability and facilitating the development of sustainable strategies.

Existence of solutions for boundary value problems for first order impulsive difference equations

  In this work, we establish sufficient conditions for the existence of nonnegative solutions for a class of first order impulsive difference equations with a family of nonlinear boundary conditions. To prove our main result we use a new topological approach on the fixed point index theory for the sum of two operators in Banach spaces. An example is given to illustrate the main result.

Predictors of Remission or Combined Remission and Low Disease Activity in Rheumatoid Arthritis Patients in Taiwan: A Prospective Cohort Study.

Objectives: This study aimed to identify predictors of remission or low disease activity (LDA) in patients with rheumatoid arthritis (RA) and low-ultrasound inflammation. Methods: A total of 80 patients with RA who fulfilled the 1987 ACR criteria for RA with a disease activity score of 28 joints (DAS28) > 3.2 were recruited. Over 1 year of therapy, we conducted blood tests every 6 months to examine erythrocyte sedimentation rate (ESR), C-reactive protein (CRP), monocyte chemotactic protein-1 (MCP-1), neuraminidase 3 (Neu3), and α-2,3-sialyltrasnferse I (ST3Gal-1) levels in B cells and monocytes. Additionally, we evaluated physical function by using the Health Assessment Questionnaire-Disability Index (HAQ-DI). Data on demographic and clinical parameters were collected, and musculoskeletal ultrasonography was performed twice a year on 12 specific joints to assess synovial changes. One year later, we compared all collected data and laboratory or ultrasound results between patients achieving remission or LDA and those who did not in order to determine the predictors. Results: Age, the presence or absence of rheumatoid factor, and the number of conventional disease-modifying anti-rheumatic drugs used were not correlated with remission or LDA for DAS28 or Simplified Disease Activity Index formulas. However, male sex, low CRP levels, low ESR levels, and low HAQ-DI scores were associated with a higher likelihood of achieving remission or LDA for DAS28-ESR. Negative anticyclic citrullinated peptide (CCP) and low HAQ-DI scores were predictors of remission or LDA for DAS28-MCP-1. Interestingly, having less than two comorbidities is a good predictor of a combined remission/low disease activity state for SDAI and DAS28-MCP-1. Furthermore, Neu3 and ST3Gal-1 levels and ST3Gal-1/Neu3 ratios in B cells and monocytes had no significant correlation with total ultrasound scores. Nevertheless, monocyte ST3Gal-1 and Neu3 correlated significantly with DAS28-ESR >5.1 and DAS-MCP-1 >4.8 (both categories belong to high disease activity), respectively (rho = 0.609 with p = 0.012, and rho = 0.727 with p = 0.011, respectively). Monocyte ST3Gal-1/Neu3 ratios connected with DAS28-ESR >5.1 and 3.3 < SDAI ≦ 11 (low disease activity), respectively (rho = 0.662 with p = 0.005, and rho = 0.342 with p = 0.048, respectively). Conclusions: In patients with RA in Taiwan, male sex, low CRP levels, low ESR levels, and low HAQ-DI scores are predictors of remission or LDA for DAS28-ESR, which differ from the predictors for DAS28-MCP-1. Moreover, monocyte ST3Gal-1, Neu3, and their ratios correlated with different disease activity categories of DAS28-ESR, DAS28-MCP-1, and SDAI scores.

Development of Android-Based Video Series on Climate Change Topic to Empower Students’ Environmental Literacy

Learning in the 21st century requires students to have problem-solving and critical thinking skills. In problem-solving related to the environment, students need a strong foundation in environmental literacy. The environmental literacy of eighth-grade students still falls relatively low within the unfavorable category. It was found that several students still needed to increase their awareness of protecting the environment. Students still need assistance in learning about climate change because there are several abstract concepts to grasp. The characteristics of Generation Z include a low attention span and a dislike for lengthy explanations. The purposes of this study were to (1) determine the characteristics of Generation Z, (2) assess the feasibility of utilizing Android-based video series as a learning medium, and (3) analyze the response of Generation Z to such educational content. This research and development method refers to the ADDIE model, which includes the stages of analysis, design, development, implementation, and evaluation. The outcome of this research and development is a video series focusing on climate change, presented in the form of an android. Observation, interviews, and questionnaires are data collection techniques. Learning media validation was conducted by two media experts: a subject matter expert and a language expert. The validity test results were calculated using Aiken’s V index formula. The results obtained for the three experts were 0.92, 0.93, and 0.90. The results of the analysis of teacher and student response tests form the expected characteristics of the video series, receiving very positive feedback.

Evaluation of the Interaction-Based Hazard Index Formula Using Data on Four Trihalomethanes from U.S. EPA’s Multiple-Purpose Design Study

The interaction-based hazard index (HIINT), a mixtures approach to characterizing toxicologic interactions, is demonstrated and evaluated by statistically analyzing data on four regulated trihalomethanes (THMs). These THMs were the subject of a multipurpose toxicology study specifically designed to evaluate the HIINT formula. This HIINT evaluation uses single, binary and quaternary mixture THM data. While this research is considered preliminary, the results provide insights on the application of HIINT when toxicology mixture data are available and on improvements to the method. The results for relative liver weight show the HIINT was generally not conservative but did adjust the additive hazard index (HI) in the correct direction, predicting greater than dose-additivity, as seen in the mixture data. For the liver serum enzyme endpoint alanine aminotransferase, the results were mixed, with some indices giving an estimated effective dose lower than the observed mixture effective dose and others higher; in general, the HIINT adjusted the HI in the correct direction, predicting less than dose-additivity. In addition, a methodological improvement was made in the calculation of maximum interaction magnitude. Suggested refinements to the HIINT included mixture-specific replacements for default parameter values and approaches for supplementing the usual qualitative discussions of uncertainty with numerical descriptions.

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Sombor index is a newly developed degree-based topological index which involves the degree of the vertex in a simple connected graph. The Sombor index is known as the square root of the sum of the squared degrees of two adjacent vertices in a graph. Meanwhile, the noncommuting graph associated to a group is a graph where its vertices are the non-central elements of the group and two vertices are adjacent if and only if they do not commute. In this study, a new notion called the Sombor polynomial is introduced. Then, the general formula of the Sombor index and the Sombor polynomial of the noncommuting graph associated to some finite groups are determined by using their definitions and some preliminaries. The groups involved in this research are the dihedral groups, the quasidihedral groups, and the generalized quaternion groups. The results found can help the chemists and biologists to predict the chemical and physical properties of the molecules without involving any laboratory work.

Spatial and temporal characteristics of drought in the Mu Us Sandy Land based on the Standardized Precipitation Index

The environment of the Mu Us Sandy Land, northern Shaanxi, is fragile, so the temporal and spatial evolution of drought can provide a reference for ecological construction and agricultural production. Based on the daily precipitation data of five meteorological stations from 1967 to 2020, the spatial and temporal evolution characteristics of drought in the Mu Us Sandy Land of northern Shaanxi were analyzed using the methods Standardized Precipitation Index (SPI) and run-length theory. The results show that 1) the smaller the time scale, the higher the sensitivity of the SPI to primary precipitation. 2) The annual, summer, autumn, and winter SPI showed an upward and a wetting trend, and the fastest wetting speed is observed in summer, while spring showed an increasing trend of drought. 3) In the past 54 years, the duration, degree, and intensity of drought events at SPI-3 and SPI-12 scales in the Mu Us Sandy Land of northern Shaanxi showed an insignificant decreasing trend, but the decreasing rate at the SPI-12 scale was faster than that at the SPI-3 scale. The serious periods of drought are November 2018 to May 2019 and April 1999 to July 2021. 4) The duration of drought events at two timescales in each region showed a decreasing trend. The longest durations of drought were in Yulin and Jingbian; Shenmu and Dingbian are the regions with the fastest reduction rate of drought degree at the two scales. Hengshan shows rapid reduction of drought intensity at the two scales and also the region with large average drought intensity. These results are helpful in understanding and describing drought events for drought risk management under the condition of global warming.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2 spectrum, and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance (NMR) experiments of high multiple waterflooding. A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores. The remaining oil viscosity in the core is positively correlated with the displacing water multiple. The remaining oil viscosity increases rapidly when the displacing water multiple is low, and increases slowly when the displacing water multiple is high. The variation of remaining oil viscosity is related to the reservoir heterogeneity. The stronger the reservoir homogeneity, the higher the content of heavy components in the remaining oil and the higher the viscosity. The reservoir wettability changes after water injection: the oil-wet reservoir changes into water-wet reservoir, while the water-wet reservoir becomes more hydrophilic; the degree of change enhances with the increase of displacing water multiple. There is a high correlation between the time-varying oil viscosity and the time-varying wettability, and the change of oil viscosity cannot be ignored. The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott (spontaneous imbibition) wettability index, which agrees more with the time-varying law of reservoir wettability.

Topological insulators and K-theory

We analyze topological invariants, in particular Z2 invariants, which characterize time reversal invariant topological insulators, in the framework of index theory and K-theory. After giving a careful study of the underlying geometry and K-theory, we formalize topological invariants as elements of KR theory. To be precise, the strong topological invariants lie in the higher KR groups of spheres; KR̃−j−1(SD+1,d). Here j is a KR-cycle index, as well as an index counting off the Altland-Zirnbauer classification of Time Reversal Symmetry (TRS) and Particle Hole Symmetry (PHS)—as we show. In this setting, the computation of the invariants can be seen as the evaluation of the natural pairing between KR-cycles and KR-classes. This fits with topological and analytical index computations as well as with Poincaré Duality and the Baum–Connes isomorphism for free Abelian groups. We provide an introduction starting from the basic objects of real, complex and quaternionic structures which are the mathematical objects corresponding to TRS and PHS. We furthermore detail the relevant bundles and K-theories (Real and Quaternionic) that lead to the classification as well as the topological setting for the base spaces.

Factors Impacting Women Gaining Leadership Roles in the Jordanian Construction Sector: Architects and Civil Engineers

The persistent underrepresentation of women in leadership positions within the construction industry remains a global concern. In Jordan, despite comprising 60.45% and 22.4% of the total workforce of architects and civil engineers, respectively, women’s contribution to management roles is significantly low. Therefore, there is an urgent necessity to examine the factors hindering women’s advancement in the construction sector and their ability to attain leadership positions. This research aims to provide an overview of the current situation in Jordan, focusing specifically on the architectural and civil engineering professions. It presents findings from a desktop study, a survey questionnaire, and focus groups. The Severity Index (SI) formula is utilised to identify critical barriers in the Jordanian context, derived from both the literature review and questionnaire responses. Additionally, the Interpretive Structural Modelling (ISM) technique is employed to establish a hierarchy of critical barriers and analyse their interrelationships. The study reveals that the obstacles impeding women from assuming leadership roles in the Jordanian construction sector primarily stem from 20 critical barriers categorised across 11 levels in ISM. Notably, the lack of childcare programmes is identified as a fundamental barrier at the lower level, while informal networks formed by men emerge as the highest-rated barrier at level 11. Addressing and mitigating these challenges is crucial to facilitating women’s progression into leadership positions within the sector and is anticipated to contribute significantly to addressing the growing complexity of modern construction projects.

Kirchhoff‐type critical fractional Laplacian system with convolution and magnetic field

AbstractIn this paper, we consider a class of upper critical Kirchhoff‐type fractional Laplacian system with Choquard nonlinearities and magnetic fields. With the help of the limit index theory and the concentration–compactness principles for fractional Sobolev spaces, we establish the existence of infinitely many nontrivial radial solutions for the above system. A distinguished feature of this paper is that the above Kirchhoff‐type system is degenerate, that is, the Kirchhoff term is zero at zero.

Distribution of Seats in the New 2021 Czech Government Coalition in Terms of Coalition Theories and Power Indices of Political Parties

This study is theoretically anchored in the office-seeking approach and coalition theory of political science. It is based on the most widespread theories of portfolio distribution in executive and legislative bodies (proportionality, power index, voting weights), and it tests these theories using data related to coalition negotiations in the Czech Republic for the new 2021 government coalition, a case of a surplus majority government. The study investigates the distribution of ministerial positions in the government, the office of President (Speaker) of the Chamber of Deputies, and the chairs of permanent parliamentary committees. The analysis also explores the types of electoral coalitions formed; the SPOLU coalition was a superadditive coalition, while the PirSTAN coalition was only an additive coalition. Grounded in the theory of electoral games, the Shapley-Shubik and Banzhaf power indices and the theory of coalition formation are applied in order to analyse the possible minimal winning coalitions that could be formed following the 2021 elections to the Chamber of Deputies.

On the Maximal Subspaces of Discrete Hamiltonian Systems

In this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester’s inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.

Localization of energies in Navier–Stokes models with reaction terms

We analyze a general class of coupled systems of stationary Navier–Stokes type equations with variable coefficients and non-homogeneous terms of reaction type in the incompressible case. Existence of solutions satisfying the homogeneous Dirichlet condition in a bounded domain in [Formula: see text], [Formula: see text], and localization results for the corresponding kinetic energy and enstrophy are obtained by using a variational approach and the fixed point index theory.