Distribution Properties Research Articles

Connecting student development of use of grouping and mathematical properties

Understanding algebraic properties is a key component of building mathematical thinking across grades K-8, yet less is known about the development of students' use of mathematical properties within their strategies. This article presents results from four conversations with 24 5th-grade students over a school year, that focus on examining the development of students grouping within strategies for multiplication and division problems. Findings add to previous research on student strategies within multiplication and division by detailing some of the nuances in students' use of grouping. Additionally, a focus on student strategies reveals students' progression in more explicit use of grouping underlies the development of more planful use of the distributive and associative properties of multiplication.

Distribution, Chemical Constituents and Biological Properties of Genus Malaxis.

The genus Malaxis (family Orchidaceae), comprises nearly 183 species available across the globe. The plants of this genus have long been employed in traditional medical practices because of their numerous biological properties, like the treatment of infertility, hemostasis, burning sensation, bleeding diathesis, fever, diarrhea, dysentery, febrifuge, tuberculosis, etc. Various reports highlight their phytochemical composition and biological activities. However, there is a lack of systematic review on the distribution, phytochemistry, and biological properties of this genus. Hence, this study aims to conduct a thorough and critical review of Malaxis species, covering data published from 1965 to 2022 with nearly 90 articles. Also, it examines different bioactive compounds, their chemistry, and pharmacotherapeutics as well as their traditional uses. A total of 189 unique compounds, including the oil constituents were recorded from Malaxis species. The highest active ingredients were obtained from Malaxis acuminata (103) followed by Malaxis muscifera (49) and Malaxis rheedei (33). In conclusion, this review offers an overview of the current state of knowledge on Malaxis species and highlights prospects for future research projects on them. Additionally, it recommends the promotion of domestication studies for rare medicinal orchids like Malaxis and the prompt implementation of conservation measures.

Enhanced Insurance Risk Assessment using Discrete Four-Variate Sarmanov Distributions and Generalized Linear Models

This research paper investigated multivariate risk assessment in insurance, focusing on four risks of a singular person and their interdependence. This research examined various risk indicators in non-life insurance which was under-writing for organizations with clients that purchase several non-life insurance policies. The risk indicators are probabilities of frequency claims and correlations of two risk lines. The closed forms of probability mass functions evaluated the probabilities of frequency claims. Three generalized linear models of four-variate Sarmanov distributions were proposed for marginals, incorporating various characteristics of policyholders using explanatory variables. All three models were discrete models that were a combination of Poisson and Gamma distributions. Some properties of four-variate Sarmanov distributions were explicitly shown in closed forms. The dataset spanned a decade and included the exposure of each individual to risk over an extended period. The correlations between the two risk types were evaluated in several statistical ways. The parameters of the three Sarmanov model distributions were estimated using the maximum likelihood method, while the results of the three models were compared with a simpler four-variate negative binomial generalized linear model. The research findings showed that Model 3 was the most accurate of all three models since the AIC and BIC were the lowest. In terms of the correlation, it was found that the risk of claiming auto insurances was related to claiming home insurances. Model 1 could be used for the risk assessment of an insurance company that had customers who held multiple types of insurances in order to predict the risks that may occur in the future. When the insurance company can forecast the risks that may occur in the future, the company will be able to calculate appropriate insurance premiums.

A new unit distribution: properties, estimation, and regression analysis

This research commences a unit statistical model named power new power function distribution, exhibiting a thorough analysis of its complementary properties. We investigate the advantages of the new model, and some fundamental distributional properties are derived. The study aims to improve insight and application by presenting quantitative and qualitative perceptions. To estimate the three unknown parameters of the model, we carefully examine various methods: the maximum likelihood, least squares, weighted least squares, Anderson–Darling, and Cramér-von Mises. Through a Monte Carlo simulation experiment, we quantitatively evaluate the effectiveness of these estimation methods, extending a robust evaluation framework. A unique part of this research lies in developing a novel regressive analysis based on the proposed distribution. The application of this analysis reveals new viewpoints and improves the benefit of the model in practical situations. As the emphasis of the study is primarily on practical applications, the viability of the proposed model is assessed through the analysis of real datasets sourced from diverse fields.

Exact Characterization of the Jointly Optimal Restocking and Auditing Policy in Inventory Systems with Record Inaccuracy

We present a continuous-time stochastic model of an inventory system with record inaccuracy. In this formulation, demand is modeled by a point process and is observable only when it leads to sales. In addition to demand that can reduce the stock, an unobservable stochastic loss process can also reduce the stock. The retailer’s goal is to identify the restocking and auditing policy that minimizes the expected discounted cost of carrying a product over an infinite horizon. We analytically characterize the optimal restocking and jointly optimal auditing policy. We prove that the optimal restocking policy is a threshold policy. Our proof of this result is based on a coupling argument that is valid for any demand and loss model. Unlike the optimal restocking policy, the jointly optimal auditing policy is not of threshold type. We show that a complete proof of this statement cannot be obtained by solely resorting to the first-order stochastic dominance property of the Bayesian shelf stock distribution induced by the demand and loss process. Instead, our characterization of the jointly optimal auditing policy is based on proving that the dynamics of the shelf stock distribution constitute a (strictly) sign-regular kernel. To our knowledge, this is the first paper that characterizes the optimal policy of a complex control problem by establishing sign regularity of its underlying Markovian dynamics. Our theoretical results lead to a fast algorithm for computing the exact jointly optimal auditing/restocking policy over the problem’s entire state space. This enables comparative statics analysis, which allows us to determine how inventory record inaccuracy affects the economic significance of various cost drivers. This, in turn, allows us to determine when or, better, under what conditions auditing can be an effective tool for reducing the total cost.

Design, one-pot novel synthesis of substituted acridine derivatives: DFT, structural characterisation, ADME and anticancer DNA polymerase epsilon molecular docking studies

A novel type of reaction synthesis of an acridine derivative alkaloid of 9-chloro-1-methylacridine-4-carboxylic acid (CMAC) and structurally characterised. FT-IR, 1H NMR, 13C NMR, and GC-mass spectrometry were used. Density functional theory calculations were performed to understand the electronic properties of the molecular structures, including the frontier molecular orbital (FMO), molecular electrostatic potentials (MEP), NLO material properties, RDG studies, and global chemical reactivity descriptors. Furthermore, Theoretical IR, a vibrational wavenumber was obtained for the title compound by simulation and compared with the experimental wavenumbers. Vibrational energy distribution analysis (VEDA) software was used for potential energy decomposition (PED) analysis. Finally, the bioavailability of the title compound was examined by (ADME/Tox) absorption, distribution, metabolism, and excretion properties. DNA polymerase epsilon, which carries a P301R substitution (PDB ID: 6g0a), was used as the receptor for employing an in silico molecular docking process. The docking study revealed the significant interactions between the receptor active sites and the CMAC ligand.

Revisiting the scattering regime map based on transport scattering coefficient for dielectric particulate medium

The independent scattering assumption is frequently employed in radiative transfer, as it is applicable to numerous scientific and practical scenarios involving sparsely distributed scatterers. However, dependent scattering effects must be considered if the particle distribution is not sparse, which requires a relatively more rigorous analysis. A scattering regime map that summarizes the conditions where the independent scattering assumption can be used safely was established in the 1980s. The validity of this regime map and corresponding transition criteria has been questioned due to revealed inaccuracies in certain portions of the map based on the recent experimental studies. This study aims to reevaluate the regime map for dielectric particulate medium through numerical simulations utilizing dense medium radiative transfer theory relying on static structure factor for incorporating the effects of dependent scattering. The transport scattering coefficient, encompassing both the scattering coefficient and the asymmetry parameter, is employed as the metric of evaluation as it accounts for both the quantitative and directional behavior of the scattering. Besides, it also reflects the behavior of reflectance/transmittance closely, which is presented by comparing the regime maps based on transport scattering coefficient and reflectance. While the resulting modified regime map agrees mostly with the established map, it corrects the parts where discrepancies were observed so that the modified map is in agreement with all available data. Moreover, the effects of particle size distribution and material properties are also investigated and it was found that a regime map for lower relative refractive index miss-match between particle and medium produces a demarcation line that is more conservative.

Evaluation of Joint Strength for CFRPs and Aluminum Alloys by Friction Stir Spot Welding Using Multi-Stage Heating

To reduce car body weight, multi-material structures with lightweight materials such as carbon-fiber-reinforced plastics (CFRPs) and aluminum alloys (Als) are used to replace parts of steel components, and joining technologies for such dissimilar materials are essential. Friction stir spot welding (FSSW) is one of the technologies used to rapidly and strongly join dissimilar materials. FSSW for carbon-fiber-reinforced thermosetting resin (CFRTS) and Als has been developed using composite laminates with integrally molded thermoplastic resin in the outermost layer. To suppress excessive heating under the tool, this study investigated whether multi-stage heating with a non-heating time during joining affects the heat distribution and strength properties of the joint. Due to heat diffusion in Al during the non-heating time, multi-stage heating can suppress excessive heating under the tool compared to continuous heating, resulting in up to 27% larger welded area, up to 37% smaller decomposed area, and up to 6% lower maximum temperature. The use of multi-stage heating results in up to 5% higher tensile shear strength and 210% longer fatigue life by reducing the thermal decomposition of CFRP matrix resin and PA12 resin.

Fast Impedance Spectrum Construction for Lithium-Ion Batteries Using a Multi-Density Clustering Algorithm

Effectively extracting a lithium-ion battery’s impedance is of great importance for various onboard applications, which requires consideration of both the time consumption and accuracy of the measurement process. Although the pseudorandom binary sequence (PRBS) excitation signal can inject the superposition frequencies with high time efficiency and an easily implementable device, processing the data of the battery’s impedance measurement is still a challenge at present. This study proposes a fast impedance spectrum construction method for lithium-ion batteries, where a multi-density clustering algorithm was designed to effectively extract the useful impedance after PRBS injection. According to the distribution properties of the measurement points by PRBS, a density-based spatial clustering of applications with noise (DBSCAN) was used for processing the data of the lithium-ion battery’s impedance. The two key parameters of the DBSCAN were adjusted by a delicate workflow according to the frequency range. The validation of the proposed method was proved on a 3 Ah lithium-ion battery under nine different test conditions, considering both the SOC and temperature variations.

Crystal structure, intermolecular interactions, charge-density distribution and ADME properties of the acridinium 4-nitrobenzoate and 2-amino-3-methylpyridinium 4-nitrobenzoate salts: a combined experimental and theoretical study.

Acridines are a class of bioactive agents which exhibit high biological stability and the ability to intercalate with DNA; they have a wide range of applications. Pyridine derivatives have a wide range of biological activities. To enhance the properties of acridine and 2-amino-3-methylpyridine as the active pharmaceutical ingredient (API), 4-nitrobenzoic acid was chosen as a coformer. In the present study, a mixture of acridine and 4-nitrobenzoic acid forms the salt acridinium 4-nitrobenzoate, C13H10N+·C7H4NO4- (I), whereas a mixture of 2-amino-3-methylpyridine and 4-nitrobenzoic acid forms the salt 2-amino-3-methylpyridinium 4-nitrobenzoate, C6H9N2+·C7H4NO4- (II). In both salts, protonation takes place at the ring N atom. The crystal structure of both salts is predominantly governed by hydrogen-bond interactions. In salt I, C-H...O and N-H...O interactions form an infinite chain in the crystal, whereas in salt II, intermolecular N-H...O interactions form an eight-membered R22(8) ring motif. A theoretical charge-density analysis reveals the charge-density distribution of the inter- and intramolecular interactions of both salts. An in-silico ADME analysis predicts the druglikeness properties of both salts and the results confirm that both salts are potential drug candidates with good bioavailability scores and there is no violation of the Lipinski rules, which supports the druglikeness properties of both salts. However, although both salts exhibit drug-like properties, salt I has higher gastrointestinal absorption than salt II and hence it may be considered a potential drug candidate.

Numerical Simulation on Dispersion of Hydrogen Leaked in Particle Layers of Glass Beads and Soil

In order to understand the dispersion of hydrogen (H2) leaked in packed beds of nonporous/porous particles in a partially open space practically, the dispersion of H2 in the particle layers of glass beads and soil was analytically studied using a computational fluid dynamics code to be compared with the experiments and to elucidate the effects of the particle layer. The packed beds in the partially open space can be considered as a basic model for all processes of transfer, treatment, storage, and disposal of radioactive materials containing fuel debris in the decommissioning of nuclear facilities after a severe accident. The H2 flowing out from a single leak point in the particle layer of nonporous glass beads was affected by buoyancy around the leak point and diffused directly above the leak point in an elliptical shape faster than in the horizontal direction. After that, when it reached the air layer in the head space above the particle layer, the H2 spread horizontally, formed a large concentration gradient near the boundary between the particle layer and the air layer, and further diffused in the air layer until the H2 concentration became about 1/3 or less of the concentration near the surface of the particle layer. When the particle diameters were 512 μm and 1200 μm, this tendency was more pronounced when the porosity was the same and the particle diameter was smaller. The calculations largely reproduced the experimental concentration distributions. When the particle layer was porous decomposed granite soil, the diffusion behavior of H2 in the particle layer proceeded in the same manner as in the case of the glass beads. However, a large concentration gradient was formed near the boundary between the particle layer and the air layer, and then H2 diffused in the air layer until the H2 concentration became below the lower combustion limit. It was suggested through sensitivity analysis that the air permeability coefficient had a large effect on the time course of the H2 concentration distribution. Based on this information, we further simulated H2 behavior in the vessel containing the H2 leaked particle layer. By inserting multiple vent pipes without considering H2 generation distribution and particle properties in the particle layer, H2 accumulated from one pipe was discharged by buoyancy without depending on the H2 generation distribution and particle properties in the particle layer and air flowed in from the other pipe. It was suggested that such a natural ventilation process would reduce the H2 concentration in the container.

Consistency of the Bayes method for the inverse scattering problem

In this work, we consider the inverse scattering problem of determining an unknown refractive index from the far-field measurements using the nonparametric Bayesian approach. We use a collection of large ‘samples’, which are noisy discrete measurements taking from the scattering amplitude. We will study the frequentist property of the posterior distribution as the sample size tends to infinity. Our aim is to establish the consistency of the posterior distribution with an explicit contraction rate in terms of the sample size. We will consider two different priors on the space of parameters. The proof relies on the stability estimates of the forward and inverse problems. Due to the ill-posedness of the inverse scattering problem, the contraction rate is of a logarithmic type. We also show that such contraction rate is optimal in the statistical minimax sense.

Unveiling Mechanobiology: A Compact Device for Uniaxial Mechanical Stimulation on Nanofiber Substrates and Its Impact on Cellular Behavior and Nanoparticle Distribution.

Biotechnology and its allied sectors, such as tissue culture, regenerative medicine, and personalized medicine, primarily rely upon extensive studies on cellular behavior and their molecular pathways for generating essential knowledge and innovative strategies for human survival. Most such studies are performed on flat, adherent, plastic-based surfaces and use nanofiber and hydrogel-like soft matrices from the past few decades. However, such static culture conditions cannot mimic the immediate cellular microenvironment, where they perceive or generate a myriad of different mechanical forces that substantially affect their downstream molecular pathways. Including such mechanical forces, still limited to specialized laboratories, using a few commercially available or noncommercial technologies are gathering increasing attention worldwide. However, large-scale consideration and adaptation by developing nations have yet to be achieved due to the lack of a cost-effective, reliable, and accessible solution. Moreover, investigations on cellular response upon uniaxial mechanical stretch cycles under more in vivo mimetic conditions are yet to be studied comprehensively. In order to tackle these obstacles, we have prepared a compact, 3D-printed device using a microcontroller, batteries, sensors, and a stepper motor assembly that operates wirelessly and provides cyclic mechanical attrition to any thin substrate. We have fabricated water-stable and stretchable nanofiber substrates with different fiber orientations by using the electrospinning technique to investigate the impact of mechanical stretch cycles on the morphology and orientation of C2C12 myoblast-like cells. Additionally, we have examined the uptake and distribution properties of BSA-epirubicin nanoparticles within cells under mechanical stimulation, which could act as fluorescently active drug-delivery agents for future therapeutic applications. Consequently, our research offers a comprehensive analysis of cellular behavior when cells are subjected to uniaxial stretching on various nanofiber mat architectures. Furthermore, we present a cost-effective alternative solution that addresses the long-standing requirement for a compact, user-friendly, and tunable device, enabling more insightful outcomes in mechanobiology.

Unravelling the impact of soil types on zinc, iron, and selenium concentrations in grains and straw of wheat/Amblyopyrum muticum and wheat/Triticum urartu doubled haploid lines

The concentration of mineral nutrients in plants is associated with bioavailabilities of soil mineral nutrients, which are regulated by various soil physio-chemical properties. A pot experiment was conducted to investigate the effects of soil type on grain and straw zinc (Zn), iron (Fe) and selenium (Se) concentrations of wheat/Amblyopyrum muticum and wheat/Triticum urartu doubled haploid lines. A set of 42 treatments in a factorial combination with 21 genotypes and two soil types collected from Ngabu and Chitedze Research Stations in Malawi was laid in a randomised complete block design (RCBD) in three replicates. Pre-experiment soil Zn and Fe were extracted using DTPA extraction method followed by analysis with inductively coupled plasma-mass spectrometry (ICP-MS). Aqua-regia hotplate acid digestion was used to extract soil Se and analysis was done using ICPM-MS. Grain and straw samples were digested using nitric acid digestion (HNO3) and analysed using ICP-MS. Soil analysis results showed that the two soils had the same textural class (Sandy clay loam), but different mineral concentrations, pH levels and percentage organic matter. Analysis of variance revealed a ~two-fold higher Zn concentration in grains grown in low pH, high Zn soils (Chitedze soils) compared to grains grown in high pH, low Zn soils (Ngabu soils). Variation in grain Zn concentration was associated with the genotypes (p = 0002), soil type (p = <0.0001), and their interaction (p = 0.035). Grain Fe was 1.3-fold higher in low pH than in high pH soils, and it was influenced by genotypes (p = < 0.0001) and soil type (p = <0.0001). Grain Se was highly associated with soil type (p = <0.0001), and it was 30-fold higher in high pH than in low pH soils. Straw Zn was generally higher in plants grown in Chitedze soils than Ngabu soils, whilst straw Se was higher in plants grown in Ngabu soils than Chitedze soils. The findings demonstrate the significance of soil physio-chemical properties for mineral accumulation and distribution to plant parts, thus informing future breeding programs on important considerations on crop genetic biofortification with the three mineral elements.

Design, Synthesis, Cytotoxic Evaluation, and Molecular Docking of New Alkyl Triphenylphosphonium Curcumin Derivatives

AbstractDespite the previous anticancer effects of curcumin against various cancer cell lines, in vitro, pre–clinical, and clinical studies have faced constraints, particularly at high doses. Therefore, the mitochondria–targeted approach represents a promising trend in cancer drug development. This study successfully synthesized three new alkyl triphenylphosphonium ester curcumin derivatives (1–3) with good yield. They demonstrated cytotoxicity against MCF‐7 cells with IC50 values of 49.72, 62.57, and 91.73 μM, respectively. These values indicated higher potency than free curcumin (IC50>100 μM). Molecular docking studies of curcumin and three derivatives 1–3 with two estrogen receptor α (ERα) ligand binding domains, 3ERT (antagonist recognition and antiproliferative function), and 1GWR (agonist recognition and pro–proliferative function), were carried out. These domains are important targets in hormone–dependent anticancer strategies. The favourable docking scores and key residue interactions suggested that these derivatives could be the potential antagonists. Three synthesized alkyl–TPP+ curcumin ester derivatives (1–3) demonstrated more potent cytotoxic efficacy than curcumin, particularly against the human MCF‐7 breast cancer cell line. In addition, molecular docking studies suggested their potential as antagonists of ERα. The in silico ADMET data of three derivatives (1–3) showed compliance with the Lipinski rule and demonstrated their absorption, distribution, metabolism, and excretion properties.

A generating family of unit-Garima distribution: Properties, likelihood inference, and application

This article proposes the unit Garima (UGa) distribution for analysing proportion data. Some statistical properties of the UGa distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measure. Next, a new family of continuous distributions, called the unit Garima-generated (UGa-G) family of distributions, is studied. The UGa-G family of distributions has the feature to use the UGa distribution as the main generator and the concept of the T-X family of distributions. Some UGa-G family sub-models are provided, such as the UGa-Beta, UGa-Weibull, and UGa-normal distributions. The maximum likelihood method is used to estimate the model parameters for the statistical aspect. A Monte Carlo simulation for the percentile bootstrap confidence intervals for each parameter of the proposed distributions is provided. Applications to eight practical data sets are given to demonstrate the usefulness of the proposed distributions.

Machine Learning Modeling of Wheel and Non-Wheel Path Longitudinal Cracking

Roads degrade over time due to various factors such as traffic loads, environmental conditions, and the quality of materials used. Significant investments have been poured into road construction globally, necessitating regular evaluations and the implementation of maintenance and rehabilitation (M&R) strategies to keep the infrastructure performing at a satisfactory level. The development and refinement of performance prediction models are essential for forecasting the condition of pavements, especially to address longitudinal cracking distress, a major issue in thick asphalt pavements. This research leverages multiple machine learning methods to create models predicting non-wheel path (NWP) and wheel path (WP) longitudinal cracking using data from the Long-Term Pavement Performance (LTPP) program. This study highlights the marked differences in distress conditions between WP and NWP, underscoring the importance of precise models that cater to their unique features. Aging trends for both types of cracking were identified through correlation analysis, showing an increase in WP cracking with age and a higher initial International Roughness Index (IRI) linked to NWP cracking. Factors such as material characteristics, kinematic viscosity, pavement thickness, air voids, particle size distribution, temperature, KESAL, and asphalt properties were found to significantly influence both WP and NWP cracking. The Exponential Gaussian Process Regression (GPR) emerged as the best model for NWP cracking, showcasing exceptional accuracy with the lowest RMSE of 89.11, MSE of 7940.72, and an impressive R-Squared of 0.63. For WP cracking, the Squared Exponential GPR model was most effective, with the lowest RMSE of 12.00, MSE of 143.93, and a high R-Squared of 0.62. The GPR models, with specific kernels for each cracking type, proved their adaptability and efficiency in various pavement scenarios. A comparative analysis highlighted the superiority of our new machine learning model, which achieved an R2 of 0.767, outperforming previous empirical models, demonstrating the strength and precision of our machine learning approach in predicting longitudinal cracking.

D-Glucosamine is a Potential Urease Inhibitor from Middle Eastern Medicinal Plants for Combatting Helicobacter Pylori Infections; a Molecular Docking and Simulation Approach.

Helicobacter pylori stands as a significant risk factor for both peptic and stomach ulcers. Their resistance to the highly acidic host environment primarily stems from their capability to produce urease, an enzyme that rapidly converts urea into NH3 and CO2. These byproducts are crucial for the bacterium's survival under such harsh conditions. Given the pivotal role of medicinal plants in treating various ailments with minimal side effects, there is an urgent need for a natural drug that can effectively eliminate H. pylori by inhibiting urease. Hence, the current study aims to identify the most potent urease inhibitor among the natural compounds found in Middle Eastern medicinal plants, taking into consideration factors such as optimal affinity, drug-like properties, pharmacokinetic characteristics, and thermodynamic attributes. In total, 5599 ligand conformers from 151 medicinal plants were subjected to docking against the urease's active site. The top-ranking natural compounds, as determined by their high docking scores, were selected for further analysis. Among these compounds, D-glucosamine (PubChem code 439,213) exhibited the most interactions with the crucial amino acid residues in the urease's active site. Furthermore, D-glucosamine demonstrated superior absorption, distribution, metabolism, excretion, and toxicity properties compared to other top-ranked candidates. Molecular dynamics simulations conducted over 100 nanoseconds revealed stable root mean square deviations and fluctuations of the protein upon complexation with D-glucosamine. Additionally, the radius of gyration and solvent-accessible surface area values for the D-glucosamine-urease complex were notably lower than those observed in other typical urease-inhibitor complexes. In conclusion, this study provides valuable insights into the potential development of D-glucosamine as a novel urease inhibitor. This promising compound holds the potential to serve as an effective drug for combating H. pylori infections in the near future.

Vibration response analysis of rotor system coupled with a novel 4-DOF SFD hydrodynamic model considering the influence of rotational displacement

As a damping structure, squeeze film dampers (SFDs) are commonly employed in turbomachinery. Aiming at the problem of hydrodynamic modeling and solution, this paper presents a four-degree-of-freedom (4-DOF) hydrodynamics model of SFD, which not only considers the influence of radial displacement on oil film clearance but also the influence of rotational displacement. The Reynolds equation of the SFD is solved utilizing the finite difference method (FDM). The oil film gap distribution and static properties of the SFD under different rotational displacements and journal eccentricity are analyzed. Then, the hydrodynamic model of the 4-DOF SFD is coupled with the rotor system, and the vibration characteristics of the SFD-rotor system are analyzed. Finally, the experimental verification is carried out. The analysis results reveal that the rotational displacement has little influence on the vibration response of the SFD-rotor system at the non-critical speed. However, near the critical speed, the occurrence of rotational displacement of the SFD is more beneficial to the vibration reduction effect. Moreover, the analysis results of the hydrodynamic characteristics of the SFD show that when the eccentricity is less than 0.4, the rotational displacement has little effect on the oil film gap distribution, load moment, and oil film reaction force. When the eccentricity exceeds 0.4, the rotational displacement has a great influence on the gap distribution, load moment, and oil film reaction force of SFD.

Searching for Intermediate-mass Black Holes in Globular Clusters through Tidal Disruption Events

Intermediate-mass black holes (IMBHs) may be the link between stellar mass holes and the supermassive variety in the nuclei of galaxies, and globular clusters (GCs) may be one of the most promising environments for their formation. Here, we carry out a pilot study of the observability of tidal disruption events (TDEs) from 103 M ⊙ < M • < 105 M ⊙ IMBHs embedded in stellar cusps at the center of GCs. We model the long super-Eddington accretion phase and ensuing optical flare, and derive the disruption rate of main-sequence stars as a function of black hole mass and GC properties with the help of a 1D Fokker–Planck approach. The photospheric emission of the adiabatically expanding outflow dominates the observable radiation and peaks in the near-ultraviolet/optical bands, outshining the brightness of the (old) stellar population of GCs in Virgo for a period of months to years. A search for TDE events in a sample of nearly 4000 GCs observed at multiple epochs by the Next Generation Virgo Cluster Survey yields null results. Given our model predictions, this sample is too small to set stringent constraints on the present-day occupation fraction of GCs hosting IMBHs. Naturally, better simulations of the properties of the cluster central stellar distribution, TDE light curves, and rates, together with larger surveys of GCs are all needed to gain deeper insights into the presence of IMBHs in GCs.