Coseismic deformation and fault slip distribution of the 2023 M_(W)7.8 and M_(W)7.6 earthquakes in Türkiye

On February 6,2023,a devastating earthquake with a moment magnitude of M_(W)7.8 struck the town of Pazarcik in south-central Türkiye,followed by another powerful earthquake with a moment magnitude of M_(W)7.6 that struck the nearby city of Elbistan 9 h later.To study the characteristics of surface deformation caused by this event and the influence of fault rupture,this study calculated the static coseismic deformation of 56 stations and dynamic displacement waveforms of 15 stations using data from the Turkish national fixed global navigation satellite system(GNSS)network.A maximum static coseismic displacement of 0.38 m for the M_(W)7.8 Kahramanmaras earthquake was observed at station ANTE,36 km from the epicenter,and a maximum dynamic coseismic displacement of 4.4 m for the M_(W)7.6 Elbistan earthquake was observed at station EKZ1,5 km from the epicenter.The rupture-slip distributions of the two earthquakes were inverted using GNSS coseismic deformation as a constraint.The results showed that the Kahramanmaras earthquake rupture segment was distinct and exposed on the ground,resulting in significant rupture slip along the Amanos and Pazarcik fault segments of the East Anatolian Fault.The maximum slip in the Pazarcik fault segment was 10.7 m,and rupture occurred at depths of 0–15 km.In the Cardak fault region,the Elbistan earthquake caused significant ruptures at depths of 0–12 km,with the largest amount of slip reaching 11.6 m.The Coulomb stress change caused by the Kahramanmaras earthquake rupture along the Cardak fault segment was approximately 2 bars,and the area of increased Coulomb stress corresponded to the subsequent rupture region of the M_(W)7.6 earthquake.Thus,it is likely that the M_(W)7.8 earthquake triggered or promoted the M_(W)7.6 earthquake.Based on the cumulative stress impact of the M_(W)7.8 and M_(W)7.6 events,the southwestern segment of the East Anatolian Fault,specifically the Amanos fault segment,experienced a Coulomb rupture stress change exceeding 2 bars,warranting further attention to assess its future seismic hazard risk.

Effects of surface chlorine atoms on charge distribution and reaction barriers for photocatalytic CO_(2)reduction

Photocatalytic CO_(2)reduction to produce high value-added carbon-based fuel has been proposed as a promising approach to mitigate global warming issues.However,the conversion efficiency and product selectivity are still low due to the sluggish dynamics of transfer processes involved in proton-assisted multi-electron reactions.Lowering the formation energy barriers of intermediate products is an effective method to enhance the selectivity and productivity of final products.In this study,we aim to regulate the surface electronic structure of Bi_(2)WO_(6)by doping surface chlorine atoms to achieve effective photocatalytic CO_(2)reduction.Surface Cl atoms can enhance the absorption ability of light,affect its energy band structure and promote charge separation.Combined with DFT calculations,it is revealed that surface Cl atoms can not only change the surface charge distribution which affects the competitive adsorption of H_(2)O and CO_(2),but also lower the formation energy barrier of intermediate products to generate more intermediate*COOH,thus facilitating CO production.Overall,this study demonstrates a promising surface halogenation strategy to enhance the photocatalytic CO_(2)reduction activity of a layered structure Bi-based catalyst.

Designing ultrastable P2/O3-type layered oxides for sodium ion batteries by regulating Na distribution and oxygen redox chemistry

P2/O3-type Ni/Mn-based layered oxides are promising cathode materials for sodium-ion batteries(SIBs)owing to their high energy density.However,exploring effective ways to enhance the synergy between the P2 and 03 phases remains a necessity.Herein,we design a P2/O3-type Na_(0.76)Ni_(0.31)Zn_(0.07)Mn_(0.50)Ti_(0.12)0_(2)(NNZMT)with high chemical/electrochemical stability by enhancing the coupling between the two phases.For the first time,a unique Na*extraction is observed from a Na-rich O3 phase by a Na-poor P2 phase and systematically investigated.This process is facilitated by Zn^(2+)/Ti^(4+)dual doping and calcination condition regulation,allowing a higher Na*content in the P2 phase with larger Na^(+)transport channels and enhancing Na transport kinetics.Because of reduced Na^(+)in the O3 phase,which increases the difficulty of H^(+)/Na^(+) exchange,the hydrostability of the O3 phase in NNZMT is considerably improved.Furthermore,Zn^(2+)/Ti^(4+)presence in NNZMT synergistically regulates oxygen redox chemistry,which effectively suppresses O_(2)/CO_(2) gas release and electrolyte decomposition,and completely inhibits phase transitions above 4.0 V.As a result,NNZMT achieves a high discharge capacity of 144.8 mA h g^(-1) with a median voltage of 3.42 V at 20 mA g^(-1) and exhibits excellent cycling performance with a capacity retention of 77.3% for 1000 cycles at 2000 mA g^(-1).This study provides an effective strategy and new insights into the design of high-performance layered-oxide cathode materials with enhanced structure/interface stability forSIBs.

Spatial distribution of shallow landslides caused by Typhoon Lekima in 2019 in Zhejiang Province, China

In recent years, the coastal region of Southeast China has witnessed a significant increase in the frequency and intensity of extreme rainfall events associated with landfalling typhoons. The hilly and mountainous terrain of this area, combined with rapid rainfall accumulation, has led to a surge in flash floods and severe geological hazards. On August 10, 2019, Typhoon Lekima made landfall in Zhejiang Province, China, and its torrential rainfall triggered extensive landslides, resulting in substantial damage and economic losses. Utilizing high-resolution satellite images, we compiled a landslide inventory of the affected area, which comprises a total of 2,774 rainfallinduced landslides over an area of 2965 km2. The majority of these landslides were small to mediumsized and exhibited elongated, clustered patterns. Some landslides displayed characteristics of high-level initiation, obstructing or partially blocking rivers, leading to the formation of debris dams. We used the inventory to analyze the distribution pattern of the landslides and their relationship with topographical, geological, and hydrological factors. The results showed that landslide abundance was closely related to elevation, slope angle, faults, and road density. The landslides were predominantly located in hilly and low mountainous areas, with elevations ranging from 150 to 300 m, slopes of 20 to 30 degrees, and a NE-SE aspect. Notably, we observed the highest Landslide Number Density(LND) and Landslide Area Percentage(LAP) in the rhyolite region. Landslides were concentrated within approximately 4 km on either side of fault zones, with their size and frequency negatively correlated with distances to faults, roads, and river systems. Furthermore, under the influence of typhoons, regions with denser vegetation cover exhibited higher landslide density, reaching maximum values in shrubland areas. In areas experiencing significantly increased concentrated rainfall, landslide density also showed a corresponding rise. In terms of spatial distribution, the rainfall-triggered landslides primarily occurred in the northeastern part of the study area, particularly in regions characterized by complex topography such as Shanzao Village in Yantan Town, Xixia Township, and Shangzhang Township. The research findings offer crucial data on the rainfallinduced landslides triggered by Typhoon Lekima, shedding light on their spatial distribution patterns. These findings provide valuable references for mitigating risks and planning reconstruction in typhoon-affected area.

Resurvey After 20 Years:Updating the Distribution,Population,and Potential Threats of the Chinting Alpine Toad

Considering the increased anthropogenic impacts,species with a limited range and low detectability often lack fundamental information and conservation actions,placing them at a high risk of endangerment.The Chinting alpine toad Scutiger chintingensis is a rare mountain amphibian endemic to the eastern margin of the Qinghai-Xizang Plateau in China.Within its whole distribution range,only three known populations(Wolong,Emei,and Wawu)exist and no recent population status report has been documented for this species over the past two decades.From 2020 to 2023,we investigated the species distribution,and assessed the risk factors for the main populations.We recorded this species in all distribution areas,and updated a new distribution site with a lower elevation limit.The relative population density was 0.024±0.012 ind./m^(2)on Mount Emei,whereas only 0.008±0.017 ind./m^(2)on Mount Wawu.No significant difference was observed in the number of individuals between the two populations;however,the relative population density was significantly different.Sewage and waste discharge resulting from the construction of scenic areas,as well as disturbances from tourism,were the primary anthropogenic factors that influenced the survival of this species.Our results provide the updated information on the distribution and population status of the Chinting alpine toad,and suggest that unrecorded populations,as well as a wider elevation range,may exist for this species.Our findings emphasise the importance of timely updates of species distribution and population information and offer a basis for the future conservation of endangered amphibians.

The changes in the annual distribution of mountain runoff during the period of 1965-2018 in Hexi Corridor,Northwest China

The annual distribution characteristics of river runoff in arid regions have significant implications for water resource stability and management.Based on the mountain runoff data from 1965 to 2018,this study examines the annual change characteristics of monthly runoff of the Shiyang River Basin,Heihe River Basin,and Shule River Basin in the Hexi Corridor,Northwest China.Many indexes are used and analyzed,including the coefficient of variance,the complete regulation coefficient,the concentration degree and concentration period,the magnitude of change,the skewness coefficient,and the kurtosis coefficient of the annual distribution curves.The results reveal the following:(1)The inhomogeneity of annual runoff distribution in the Taolai River and the rivers to the west of it,except the Shiyou River,show an increasing trend.Conversely,the inhomogeneity of the rivers to the east of the Taolai River generally show a downward trend,but the coefficient of variance value is still very high.(2)In the Shiyang River Basin,the annual distribution of the concentration period is characterized by a relatively discrete pattern.Conversely,the Heihe River Basin exhibits a relatively concentrated pattern,and the distribution pattern of the Shule River Basin is quite different.Notably,all concentration periods in the three basins have shifted backward after the 2000s.(3)The Shiyang River Basin exhibits disordered annual distribution curves of runoff in different years.In contrast,the Heihe River Basin presents a typical‘single-peak’pattern with a prominent right-skewed.The Shule River Basin has regular distribution curves,with a gradually significant‘double-peak’pattern from east to west.Overall,there has been a slight change in runoff in the Shiyang River Basin,while the Heihe River Basin and Shule River Basin have experienced significant increases in runoff.The annual distribution curves of runoff in the Liyuan River and the rivers to the east of it exhibit a gentle peak pattern,and the appearance probability of extreme runoff during the year is low.Conversely,the rivers to the west of the Liyuan River,excluding the Danghe River,display a sharp peak and thick tail pattern,indicating that the appearance probability of extreme runoff during the year is high.These findings have practical implications for the planning and management of water resources in the Hexi Corridor.Moreover,they provide a solid foundation for predicting future changes in regional water resources.

Distribution and Formation Causes of PM_(2.5) and O_(3) Double High Pollution Events in China during 2013–20

Fine particulate matter(PM_(2.5))and ozone(O_(3))double high pollution(DHP)events have occurred frequently over China in recent years,but their causes are not completely clear.In this study,the spatiotemporal distribution of DHP events in China during 2013–20 is analyzed.The synoptic types affecting DHP events are identified with the Lamb–Jenkinson circulation classification method.The meteorological and chemical causes of DHP events controlled by the main synoptic types are further investigated.Results show that DHP events(1655 in total for China during 2013–20)mainly occur over the North China Plain,Yangtze River Delta,Pearl River Delta,Sichuan Basin,and Central China.The occurrence frequency increases by 5.1%during 2013–15,and then decreases by 56.1%during 2015–20.The main circulation types of DHP events are“cyclone”and“anticyclone”,accounting for over 40%of all DHP events over five main polluted regions in China,followed by southerly or easterly flat airflow types,like“southeast”,“southwest”,and“east”.Compared with non-DHP events,DHP events are characterized by static or weak wind,high temperature(20.9℃ versus 23.1℃)and low humidity(70.0%versus 64.9%).The diurnal cycles of meteorological conditions cause PM_(2.5)(0300–1200 LST,Local Standard Time=UTC+8 hours)and O_(3)(1500–2100 LST)to exceed the national standards at different periods of the DHP day.Three pollutant conversion indices further indicate the rapid secondary conversions during DHP events,and thus the concentrations of NO_(2),SO_(2) and volatile organic compounds decrease by 13.1%,4.7%and 4.4%,respectively.The results of this study can be informative for future decisions on the management of DHP events.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

The relationship between the distribution of HBcAg in liver cells and the pathological manifestations of the liver in 429 HBeAg-positive chronic HBV-infected individuals

Background:The natural history of chronic HBV infection is typically characterized by four stages:the immune tolerance period,the immune clearance period,the immune control period,and the immune escape period.These stages are associated with the distribution of HBcAg in liver cells;however,this relationship remains a topic of broad debate within the field of liver disease.To objectively and quantitatively measure the intracellular distribution of HBcAg,this paper aims to design a method referred to as the“layered evaluation method”and to examine its validation.Methods:The distribution of HBcAg in liver cells is assessed using Image Pro Plus image processing software,along with calculations of cytoplasmic and nuclear positive staining rates.Results:The findings indicate that the highest proportion of patients exhibited a positive cytoplasmic expression rate ranging from 0-2.5%.More than 40% of the total sample was categorized within the 0-2.5% positive nuclear expression range.The HBcAg cytoplasmic positive staining rates were classified into five levels:a cytoplasmic HBcAg positive staining rate of less than 0.05% is designated as level 0,indicating negative expression;a staining rate between 0.05% and 5% is classified as level 1;a rate from 5% to less than 10% is classified as level 2;a rate from 10% to less than 20% is classified as level 3;and a nuclear positivity rate exceeding 20% is classified as level 4.Conclusion:The inflammatory activity grade in these patients was positively correlated with the cytoplasmic distribution of HBcAg.Furthermore,the nuclear distribution rate of HBcAg was significantly higher in the G3 group compared to the other groups.

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Extended wet sieving method for determination of complete particle size distribution of general soils

The traditional standard wet sieving method uses steel sieves with aperture?0.063 mm and can only determine the particle size distribution(PSD)of gravel and sand in general soil.This paper extends the traditional method and presents an extended wet sieving method.The extended method uses both the steel sieves and the nylon filter cloth sieves.The apertures of the cloth sieves are smaller than 0.063 mm and equal 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,0.003 mm,0.002 mm,and 0.001 mm,respectively.The extended method uses five steps to separate the general soil into many material sub-groups of gravel,sand,silt and clay with known particle size ranges.The complete PSD of the general soil is then calculated from the dry masses of the individual material sub-groups.The extended method is demonstrated with a general soil of completely decomposed granite(CDG)in Hong Kong,China.The silt and clay materials with different particle size ranges are further examined,checked and verified using stereomicroscopic observation,physical and chemical property tests.The results further confirm the correctness of the extended wet sieving method.

Integrative biogeography: Validating hypotheses of species distribution

DEAR EDITOR,Biogeography is a scientific field dedicated to the investigation of the origins and distribution patterns of organisms,as well as predicting future alterations in their geographical distributions(Cox&Moore,2005).However,the majority of conclusions drawn within the field of biogeography are hypothetical.Rigorous testing of these biogeographic hypotheses remains a considerable challenge.This paper presents the concept of“integrative biogeography”,which emphasizes the experimental testing of biogeographic hypotheses through studies on geological history,as well as biotic and abiotic factors(Figure 1).

Influence of Topography on the Distribution and Structure of Woody Plants in the Senegalese Sahel (Sandy Ferlo)

This study describes the floristic composition and structure of a woody stand in the Senegalese Sahel, paying particular attention to the edaphic factors of its floristic composition. A stratified inventory considering the different relief units was adopted. Woody vegetation was surveyed using a dendrometric approach. The results obtained show that the flora is dominated by a few species adapted to drought, such as Balanites aegyptiaca (L.) Del., Calotropis procera Ait. and Boscia senegalensis (Pers.). The distribution of this flora and the structure of the ligneous plants are linked to the topography. In the lowlands, the flora is more diversified and the ligneous plants reach their optimum level of development compared with the higher relief areas. In the lowlands, there are a few woody species which, in the past, were indicative of better climatic conditions. These are Anogeissus leiocarpus (DC.), Commiphora africana (A. Rich.), Feretia apodanthera Del., Loeseneriella africana (A. Smith), Mitragyna inermis (Willd.) and Sclerocarya birrea (A. Rich). It is important that their reintroduction into reforestation projects takes account of their edaphic preference.

Neural stem cell-derived exosomes promote mitochondrial biogenesis and restore abnormal protein distribution in a mouse model of Alzheimer's disease

Mitochondrial dysfunction is a hallmark of Alzheimer’s disease.We previously showed that neural stem cell-derived extracellular vesicles improved mitochondrial function in the cortex of AP P/PS1 mice.Because Alzheimer’s disease affects the entire brain,further research is needed to elucidate alterations in mitochondrial metabolism in the brain as a whole.Here,we investigated the expression of several important mitochondrial biogenesis-related cytokines in multiple brain regions after treatment with neural stem cell-derived exosomes and used a combination of whole brain clearing,immunostaining,and lightsheet imaging to clarify their spatial distribution.Additionally,to clarify whether the sirtuin 1(SIRT1)-related pathway plays a regulatory role in neural stem cell-de rived exosomes interfering with mitochondrial functional changes,we generated a novel nervous system-SIRT1 conditional knoc kout AP P/PS1mouse model.Our findings demonstrate that neural stem cell-de rived exosomes significantly increase SIRT1 levels,enhance the production of mitochondrial biogenesis-related fa ctors,and inhibit astrocyte activation,but do not suppress amyloid-βproduction.Thus,neural stem cell-derived exosomes may be a useful therapeutic strategy for Alzheimer’s disease that activates the SIRT1-PGC1αsignaling pathway and increases NRF1 and COXIV synthesis to improve mitochondrial biogenesis.In addition,we showed that the spatial distribution of mitochondrial biogenesis-related factors is disrupted in Alzheimer’s disease,and that neural stem cell-derived exosome treatment can reverse this effect,indicating that neural stem cell-derived exosomes promote mitochondrial biogenesis.

Diversity of Orchids in Terms of Their Distribution, Uses and Conservation in Annapurna Conservation Area of Nepal

The Annapurna Conservation Area (ACA), the first conservation area and the largest protected area (PA) in Nepal, is incredibly rich in biodiversity. Notwithstanding this, orchids in the ACA have not been explored enough yet thus making the need for ambitious research to be carried out. Previous study only included 81 species of orchids within ACA. This study aims to update the record of species and genera richness in the ACA. In total 198 species of orchids, belonging to 67 genera (40% and 62% of the total recorded orchid species and genera in Nepal) has been recorded in ACA. This represents an increase of 144% in species and 56% in genera over the previous data. Out of the 198 species, 99 were epiphytes, 6 were holomycotrophic and 93 were terrestrial. Among the 67 genera, Bulbophyllum (17) species were dominant, followed by Dendrobium (16), Herminium (10), Coelogyne, Plantanthera (9 each), Eria, Habenaria, Oberonia (8 each), Calanthe (7), and Liparis (6). Fifty-six species were found to be ornamentally significant and 85 species medicinally significant.

Boosting Adversarial Training with Learnable Distribution

In recent years,various adversarial defense methods have been proposed to improve the robustness of deep neural networks.Adversarial training is one of the most potent methods to defend against adversarial attacks.However,the difference in the feature space between natural and adversarial examples hinders the accuracy and robustness of the model in adversarial training.This paper proposes a learnable distribution adversarial training method,aiming to construct the same distribution for training data utilizing the Gaussian mixture model.The distribution centroid is built to classify samples and constrain the distribution of the sample features.The natural and adversarial examples are pushed to the same distribution centroid to improve the accuracy and robustness of the model.The proposed method generates adversarial examples to close the distribution gap between the natural and adversarial examples through an attack algorithm explicitly designed for adversarial training.This algorithm gradually increases the accuracy and robustness of the model by scaling perturbation.Finally,the proposed method outputs the predicted labels and the distance between the sample and the distribution centroid.The distribution characteristics of the samples can be utilized to detect adversarial cases that can potentially evade the model defense.The effectiveness of the proposed method is demonstrated through comprehensive experiments.

Application of neutrophil-lymphocyte ratio and red blood cell distribution width in diabetes mellitus complicated with heart failure

BACKGROUND Accumulating clinical evidence has shown that diabetes mellitus(DM)is a serious risk factor for cardiovascular disorders and an important factor for adverse cardiovascular events.AIM To explore the value of the combined determination of the neutrophil-lymphocyte ratio(NLR)and red blood cell distribution width(RDW)in the early diagnosis and prognosis evaluation of DM complicated with heart failure(HF).METHODS We retrospectively analyzed clinical data on 65 patients with type 2 DM(T2DM)complicated with HF(research group,Res)and 60 concurrent patients with uncomplicated T2DM(control group,Con)diagnosed at Zhejiang Provincial People’s Hospital between January 2019 and December 2021.The NLR and RDW values were determined and comparatively analyzed,and their levels in T2DM+HF patients with different cardiac function grades were recorded.The receiver operating characteristic(ROC)curves were plotted to determine the NLR and RDW values(alone and in combination)for the early diagnosis of HF.The correlation between NLR and RDW with the presence or absence of cardiac events was also investigated.RESULTS Higher NLR and RDW levels were identified in the Res vs the Con groups(P<0.05).The NLR and RDW increased gradually and synchronously with the deterioration of cardiac function in the Res group,with marked differences in their levels among patients with grade II,III,and IV HF(P<0.05).ROC curve analysis revealed that NLR combined with RDW detection had an area under the curve of 0.915,a sensitivity of 76.9%,and a specificity of 100%for the early diagnosis of HF.Furthermore,HF patients with cardiac events showed higher NLR and RDW values compared with HF patients without cardiac events.CONCLUSION NLR and RDW were useful laboratory indicators for the early diagnosis of DM complicated with HF,and their joint detection was beneficial for improving diagnostic efficiency.Additionally,NLR and RDW values were directly proportional to patient outcomes.

Effect of distribution of fines on evolution of cooperation in spatial public goods game

In the realm of public goods game,punishment,as a potent tool,stands out for fostering cooperation.While it effectively addresses the first-order free-rider problem,the associated costs can be substantial.Punishers incur expenses in imposing sanctions,while defectors face fines.Unfortunately,these monetary elements seemingly vanish into thin air,representing a loss to the system itself.However,by virtue of the redistribution of fines to cooperators and punishers,not only can we mitigate this loss,but the rewards for these cooperative individuals can be enhanced.Based upon this premise,this paper introduces a fine distribution mechanism to the traditional pool punishment model.Under identical parameter settings,by conducting a comparative experiment with the conventional punishment model,the paper aims to investigate the impact of fine distribution on the evolution of cooperation in spatial public goods game.The experimental results clearly demonstrate that,in instances where the punishment cost is prohibitively high,the cooperative strategies of the traditional pool punishment model may completely collapse.However,the model enriched with fine distribution manages to sustain a considerable number of cooperative strategies,thus highlighting its effectiveness in promoting and preserving cooperation,even in the face of substantial punishment cost.

Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function

Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting according to the consistency between the characteristics of Fuzzy distribution function and the distribution series of cumulative percentage of stand base diameter, and the fitting precision and effect of Fuzzy distribution function were discussed. The root mean square error RMSE and determination coefficient R2 values showed that Fuzzy-Γ1, Fuzzy-Γ2, Fuzzy-Γ3, Fuzzy-Γ4 had good fitting performance, among which Fuzzy-Γ1 had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ2 distribution function was the second, and Fuzzy-Γ4 distribution function had the worst fitting effect. By introducing a parameter c from the similarity of four distribution function formulas, a generalized Fuzzy distribution function Fuzzy-Γ5 is obtained. This function shows the highest fitting accuracy. Most of the values of parameter c are near 1 or 2, which shows that the diameter distribution is mainly approximate to Fuzzy-Γ1 and Fuzzy-Γ2.

Approximating the Radial Distribution Function of the Electron in a Hydrogen Atom by a Normal Distribution Suggests That Magnetic Confinement Fusion Would Be Less Energy Efficient than Inertial Confinement Fusion

Since the position of the electron in a hydrogen atom cannot be determined, the region in which it resides is said to be determined stochastically and forms an electron cloud. The probability density function of the single electron in 1s orbit is expressed as φ2, a function of distance from the nucleus. However, the probability of existence of the electron is expressed as a radial distribution function at an arbitrary distance from the nucleus, so it is estimated as the probability of the entire spherical shape of that radius. In this study, it has been found that the electron existence probability approximates the radial distribution function by assuming that the probability of existence of the electron being in the vicinity of the nucleus follows a normal distribution for arbitrary x-, y-, and z-axis directions. This implies that the probability of existence of the electron, which has been known only from the distance information, would follow a normal distribution independently in the three directions. When the electrons’ motion is extremely restricted in a certain direction by the magnetic field of both tokamak and helical fusion reactors, the probability of existence of the electron increases with proximity to the nucleus, and as a result, it is less likely to be liberated from the nucleus. Therefore, more and more energy is required to free the nucleus from the electron in order to generate plasma.