Index Theory Research Articles

Classification of contact seaweeds

A celebrated result of Gromov ensures the existence of a contact structure on any connected, non-compact, odd-dimensional Lie group. In general, such structures are not invariant under left translation. The problem of finding which Lie groups admit a left-invariant contact structure resolves to the question of determining when a Lie algebra g is contact; that is, admits a one-form φ∈g⁎ such that φ∧(dφ)k≠0.In full generality, this remains an open question; however we settle it for the important category of the evocatively named seaweed algebras by showing that an index-one seaweed is contact precisely when it is quasi-reductive. Seaweeds were introduced by Dergachev and Kirillov who initiated the development of their index theory – since completed by Joseph, Panyushev, Yakimova, and Coll, among others. Recall that a contact Lie algebra has index one – but not characteristically so. Leveraging recent work of Panyushev, Baur, Moreau, Duflo, Khalgui, Torasso, Yakimova, and Ammari, who collectively classified quasi-reductive seaweeds, our equivalence yields a full classification of contact seaweeds. We remark that since type-A and type-C seaweeds are de facto quasi-reductive (by a result of Panyushev), in these types index one alone suffices to ensure the existence of a contact form.

An Achievement Test in Mathematics in the Modern World Course: The Standardization Process

This study aimed to construct and standardize an achievement test in Mathematics in the Modern World (MMW) course. Achievement test evaluates a student’s performance after a given period of instruction. Using the instrumentation research design, the data were gathered among 273 tertiary students of Notre Dame University enrolled during the second semester of Academic Year 2020-2021. Among these, 38 pilot tested and 213 tested the reliability of the instrument. This study further utilized the following: a 4-point Likert scale for the validation of the instrument, difficulty value and discrimination index formulas for the analysis of each item, and KR20 reliability for internal consistency. Furthermore, a test manual for the MMW achievement test was also established. The preliminary total number of Items before MMW teachers’ validation was 42 items covering the topics for the first 12 hours of the MMW Syllabus. These items were validated through Aiken’s Item Validity method which resulted in the acceptance of 42 items. After rigorous processes, it resulted in the acceptance of 34 items for the MMW achievement test. The instrument’s average validity is 0.935, and the reliability is 0.701 which means that this tool has high validity and acceptable reliability.

Prognostic value of the oxygenation index measured during mechanical ventilation and weaning. A retrospective cohort study.

The aim of this study was to investigate the predictive value of the ratio of oxygen saturation (ROX) index calculated during mechanical ventilation (MV) and the weaning period in evaluating readiness to weaning and the success of the spontaneous breathing trial (SBT), extubation, and mortality. We also compared the results of the ROX index calculated with partial arterial oxygen pressure (PaO2), arterial oxygen saturation (SaO2%), and probe oxygen saturation (SpO2%). In this retrospective cohort study, the ROX index was calculated by SpO2%, PaO2, and SaO2% separately using the ROX index formula (PaO2 or SaO2 or SpO2 /FiO2)/respiratory rate. ROX was calculated during the first three days of MV treatment and the weaning period daily (SBT). Positive end-expiratory pressure and peak inspiratory pressure values were also recorded during these measurements. These ROX values were used to analyze whether they predict weaning readiness, SBT, extubation failure (EF), and mortality. The study included 107 mechanically ventilated patients. Weaning could be tried in 64 (60%) of the 107 patients; 44 (69%) of the 64 patients succeeded, and extubation was performed. 19 (43%) of 44 patients had EF. ROX values calculated with PaO2 during MV and SBT predicted readiness to wean, EF, and mortality better than ROX values calculated with SaO2 and SpO2. ROX values calculated with PaO2 during the third day of MV had the highest sensitivity and specificity for EF (sensitivity: 81%, specificity: 70% for the ROX<11 value). The results of this study suggest that the calculation of ROX index, not only with SpO2% but also with arterial blood gas PaO2 and SaO2% values, may be helpful in predicting the weaning readiness evaluation, SBT, and extubation success and mortality. Further studies with more patients are necessary to verify and standardize these results.

Index Formula for Hamiltonian Loop Group Spaces

Index Formula for Hamiltonian Loop Group Spaces

Influence of residential physical environments on occupant experience: considering the moderating effects of indoor plants and climate zones

PurposeHome is a place/system/product that becomes increasingly occupied with various tasks used to be performed in workplaces. However, the knowledge of the relationship between residential physical environments and occupant experience is limited, especially when considering the effect of indoor plants (IPs) and climate zones. To address the gap, this study conducted a questionnaire survey in three cities across different regions in China.Design/methodology/approachBased on User Experience and Customer Satisfaction Index theory, following the research paradigm, a total of 627 valid samples were collected and analyzed in a stepwise statistical analysis, including descriptive statistics, reliability and validity test, correlation test and region comparison, then the model of PROCESS was adopted to examine the hypotheses that are given based on the former studies.FindingsThe results showed that residential physical environments have a significant effect on occupant satisfaction (OS) in all regions, as well as OS on occupant performance. However, regional differences were found that OS is a complete mediator in the Middle region, while a partial mediator in the North and South. A slight moderating effect of IPs was also found in the region of South. Nevertheless, both the number of plants and plant types have a significant moderating effect on the mechanism.Originality/valueBesides combining two theories and confirming the mechanism in the residential physical environment, it is also the first study to consider the moderating effects of IPs and climate zones, providing potential empirical support for not only design and management stages but also facing global challenges of working at home and climate changes.

Study of Drought Using the Theory of Run and Hydrological Drought Index and its Relationship to Reservoir Storage at the Batubai Dam and Pengga Dam

Drought is a frequent disaster in Indonesia, particularly in areas with long dry seasons. Several factors influencing drought in Indonesia include irregular rainfall patterns, climate change, and unsustainable water resource usage. This study was conducted to provide an overview of drought and its impact on the storage of the Batujai Dam and Pengga Dam. This research utilizes drought analysis and reservoir simulation analysis. The results of this study are as follows: a) The drought condition at the Batujai Dam based on the Theory of Run method has a maximum deficit value of -644.66 mm, and the drought based on the Hydrological Drought Index using inflow data from 2013 to 2022 has a maximum deficit value of -2.88 m³/s. Meanwhile, the drought condition at the Pengga Dam based on the Theory of Run method has a maximum deficit value of -407.86 mm, and the drought based on the Hydrological Drought Index using inflow data has a maximum deficit value of -2.371 m³/s. b) The impact of drought on the simulation of the Batujai Dam and Pengga Dam over specific periods shows that the Batujai Dam was full (overflowing) for 7 dekadal periods, whereas under existing conditions, it was never full. The Pengga Dam was full (overflowing) for 6 dekadal periods, while under existing conditions, it was only full once, with a K Factor (ratio of water supply to water demand) having a minimum value of 20% from October I to October III, 2018.

Democratic Aggregation: Issues and Implications for Consumer Price Indexes

AbstractThis paper constructs and compares consumer price indexes (CPI) using weighting methods that differentially incorporate inflation disparities across households. Plutocratic CPIs, commonly used by statistical agencies, weight households based on their total expenditure, while democratic CPIs equally weight households to better represent average consumer experiences. I estimate democratic versions of the Bureau of Labor Statistics' CPI and Chained CPI (C‐CPI) for all urban consumers using the Lowe and Törnqvist formulas, respectively. From December 2002 to June 2021, the democratic CPI‐U exceeds its plutocratic counterpart by approximately 0.08 percentage points per year, on average, while the democratic C‐CPI‐U surpasses the plutocratic by 0.19 percentage points per year. The results indicate a negative correlation between inflation and household expenditure level over the study period. I also find weight frequency to be more important than index formula for explaining why larger differences occur for the C‐CPI‐U.

Connes fusion of spinors on loop space

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers the fusion of loops, i.e. the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish novel relations between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.

Spectral properties of Sombor matrix of threshold graphs

We investigate the Sombor spectral properties of threshold graphs, a formula for the Sombor index is presented, the Sombor eigenvalues are given, graphs with simple Sombor eigenvalues are characterized, bounds on the smallest/largest Sombor eigenvalues are presented, the multiplicities of the Sombor eigenvalues are discussed, formulae for trace and determinant of the associated quotient matrix are given, the Sombor spread bound and the bounds on the Sombor energy along with the characterization of extremal graphs. At the end, the conclusion states that all our results are valid for adjacency matrix and other adjacency type matrices.

A Birkhoff–Kellogg Type Theorem for Discontinuous Operators with Applications

By means of fixed point index theory for multivalued maps, we provide an analogue of the classical Birkhoff–Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general and can be applied, for example, to eigenvalues and parameter problems for ordinary differential equations with discontinuities. We illustrate in detail this fact for a class of second-order boundary value problem with deviated arguments and discontinuous terms. In a specific example, we explicitly compute the terms that occur in our theory.

Influence of News Media Contents on Policy Makers

The research explores the influence of news media content on policymakers, using Indexing Theory and the Cascade Model to provide an empirical basis. Policymakers were interviewed, and the resulting data was analyzed through thematic analysis. The study found that media content has a significant, multifaceted impact on policy-making, particularly during the agenda-setting phase. Policymakers noted an increasing trend of media interactions affecting their decisions. While media attention can shape policy priorities, there is also a concern about the sensationalism prevalent in Pakistani media. Policymakers believe that if this sensationalism can be regulated and brought under control, the media could become a more credible and valuable source of information. This would enhance its role in contributing to sustainable governance. The study highlights the dual role of media as both an influencer and a potential partner in governance. Further research is recommended to delve deeper into these dynamics and to develop strategies for leveraging media influence constructively. The findings underscore the importance of understanding media's impact on policy-making and the need for a balanced approach to media consumption and regulation to support informed and effective governance.

Cost-effectiveness analysis of optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection

HIV and Varicella-Zoster co-infection has been threatens the lives and livelihood of millions of individuals all over the world. In various nations of the world the co-infection disease is presently a major health problem. Although, various researchers carried out studies related with HIV and Zoster single infections, no one has carried out a study on the co-infection disease. Therefore, investigating the HIV and Varicella-Zoster co-infection transmission dynamics using mathematical modeling approach is relatively necessary. The main objective of this study is to investigate the cost-effective analysis of the proposed optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection in the community using compartmental modeling approach. Qualitatively, we have computed the model equilibrium points and analyze their local stabilities using Routh-Hurwitz stability criteria, the effective reproduction numbers by using the next generator matrix operator method, we re-formulated the optimal control problem of the complete co-infection model by implementing five time dependent optimal control strategies, analyzed the optimal control problem by applying the Pontryagin's Maximum/Minimum principle. Sensitivity analysis and numerical simulations have been carried out using the forward sensitivity index formula and the fourth order Runge-Kutta numerical methods respectively and verified the analytic results. Finally, we have performed the cost effective analysis for the proposed controlling strategies and from the result we have observed that implementing strategy four (treatment of Varicella-Zoster infected individuals to increase their recovery rate and recovery period) is the most cost effective-strategy as compared with other alternatives.

Estimating the elasticity of substitution when compiling the CES cost of living index on scanner data

AbstractScanner data are electronic transaction data that specify turnover and the number of items sold by barcodes, e.g., the Global Trade Article Number. These data are of particular value and interest to theorists and practitioners who wish to measure the Cost of Living Index or the Consumer Price Index, since their complete content makes it possible to compute any price index formula, including superlative indices or CES (Constant Elasticity Substitution) indices. Since the CES index requires the estimation of the elasticity of substitution, this paper focuses on verifying various methods of estimating this parameter based on scanner data. The paper considers both algebraic methods and methods based on the panel regression approach. The main achievement of the paper is the separation of the main factors that affect the estimated value of the elasticity of substitution, i.e., the type of data filter used and the level of data aggregation. The paper also verifies how the elasticity of substitution estimates affect the differences between the values of the CES indices based on these estimates.

The Morse index theorem for mechanical systems with reflections

We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.

Positive Radial Symmetric Solutions of Nonlinear Biharmonic Equations in an Annulus

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵2u=f(u,▵u) on an annular domain Ω in RN with the Navier boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:R+×R−→R+ is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f(ξ,η) to have superlinear or sublinear growth on ξ,η as |(ξ,η)|→0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones.

A resolution theorem for extriangulated categories with applications to the index

Quillen's Resolution Theorem in algebraic K-theory provides a powerful computational tool for calculating K-groups of exact categories. At the level of K0, this result goes back to Grothendieck. In this article, we first establish an extriangulated version of Grothendieck's Resolution Theorem.Second, we use this Extriangulated Resolution Theorem to gain new insight into the index theory of triangulated categories. Indeed, we propose an index with respect to an extension-closed subcategory N of a triangulated category C and we prove an additivity formula with error term. Our index recovers the index with respect to a contravariantly finite, rigid subcategory X defined by Jørgensen and the second author, as well as an isomorphism between K0sp(X) and the Grothendieck group of a relative extriangulated structure CRX on C when X is n-cluster tilting. In addition, we generalize and enhance some results of Fedele. Our perspective allows us to remove certain restrictions and simplify some arguments.Third, as another application of our ExtriangulatedResolution Theorem, we show that if X is n-cluster tilting in an abelian category, then the index introduced by Reid gives an isomorphism K0(CRX)≅K0sp(X).

Antibiotyping, RAPD- and ERIC-PCR fingerprinting of Klebsiella pneumoniae clinical isolates at a tertiary reference hospital in Denpasar, Bali, Indonesia.

Klebsiella pneumoniae is a healthcare-associated infections agent and could be an extended spectrum β-lactamase (ESBL) producer. Understanding the transmission of this bacterium in a hospital setting needs accurate typing methods. An antibiogram is used to detect the resistance pattern of the isolates. Random Amplified Polymorphic DNA (RAPD) and Enterobacterial Repetitive Intergenic Consensus (ERIC)-PCR are rapid, technically simple, and easy-to-interpret DNA typing methods. This study aimed to evaluate the use of antibiotyping, RAPD-, and ERIC-PCR to investigate the heterogeneity of K. pneumoniae isolated from clinical specimens. The antibiograms of 46 K. pneumoniae clinical isolates were determined by Vitek® 2 Compact. All isolates underwent RAPD-PCR using AP4 primer and ERIC-PCR using ERIC-2 primer. The dendrogram was generated using the GelJ software and analyzed to determine its similarity. The analysis of antibiogram and the molecular typing diversity index was calculated using the formula of the Simpson's diversity index. About 71.7% of the isolates were ESBL-producers, and more than 80% of isolates were susceptible to amikacin, ertapenem, and meropenem. The antibiotyping produced 32 diverse types with DI = 0.964. In addition, the RAPD-PCR produced 47 different types with DI = 1, while ERIC-PCR was 46 (DI=0.999). Antibiotyping, RAPD- and ERIC-PCR showed powerful discrimination power among the isolates, supported the diversity of K. pneumoniae isolates in current study. These combination could be promising tools for clonal relationship determination, including in tracking the transmission of the outbreak's agent in hospital setting.

Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodynamic model to identify a topological mode called topological Alfvén sound wave in magnetized plasmas. Published by the American Physical Society 2024

Light management of solar cells by implementation of nano/microstructures

Research on the improvement of the photoelectric conversion efficiency of solar cells is always the focus. In this paper, an efficient anti-reflection micro/nanostructure is proposed to improve the conversion efficiency of the solar cell. Graded effective refractive index theory is used to achieve the anti-reflection effect while the simulation model is established by FDTD. A specific periodic nanostructure is obtained, which can achieve a good anti-reflection effect. According to the simulation model, the reflectivity of the solar cell is reduced by 0.85% and the transmittance is increased by 0.85% in the band range of 200 nm to 1000 nm. Specifically, high anti-reflection phenomena are obtained in the band range of ultraviolet and blue light, in which the reflectivity is reduced by 1.56% and the transmittance is increased by 1.55%. Based on the simulation results, the array nanostructure is produced by etching the self-assembled polystyrene (PS) microspheres. Finally, the required structure is formed on the silicon wafer by nanoimprinting and etching technology. The reflectivity of 2.8% is obtained on silicon, which can potentially increase the opto-electrical performance of the solar cell.

Gastropods are faced with potential environmental hazards in Kuala Langsa, Aceh

The Kuala Langsa Peninsula is a geographical region that is often developed as a site of habitat. The surrounding nature of Kuala Langsa is an environment of biodiversity that contains gastropods. There are also several mangrove areas throughout Kuala Langsa with certain characteristics, under certain conditions and status, which are ecological or non-ecological conservation. The purpose of this investigation is to determine the level of pollution that occurs in the port of Kuala Langsa by looking at the value of the index of gastropodic diversity. The research uses the quantitative method with the Shannon-Wienner diversity index formula and sampling using the square tranche technique. The results show that diversity from common and detected low quality is based on the total number of species in a community found, as well as very similar types of organisms, resulting in low diversity coefficient values and water quality belonging to moderate pollution. The conclusion is that the total number of gastropods is 1,064 individuals from 9 families and 19 species on the three research locations. It can be concluded that the highest value of the diversity index obtained with the data is at station II, which is 2, whereas the lowest diversity Index value at station III is at 1.86 and is followed by station I at 1.91, as long as from the data the variability index value belongs to the type of moderate polluted waters.