Representation of three-dimensional mass distribution of the Earth's interior by biorthogonal series and its use for studying internal structure of the planet

This paper utilizes the mathematical concept of approximation within an ellipsoid from a single viewpoint to present the spatial mass distribution function of the Earth's interior and its internal potential.The primary focus lies in constructing the volume distribution of masses in the planet's interior, with the expansion coefficients being linear combinations of the Stokes constants. Several possible approaches are suggested for determining accurately these coefficients employing three-dimensional(biorthogonal)polynomials. By expressing the mass distribution function of the Earth's interior and its internal potential as a series, an algorithm is introduced for the calculation of gravitational energy. It allows us to estimate fluctuations in gravitational energy. The implementation of this algorithm offers the means of establishing the extent to which the Earth deviates from a state of hydrostatic equilibrium as a celestial body.Due to the aforementioned method, calculations have been conducted to validate its effectiveness and reliability. This example is given as an illustration of a given method for studying the internal structure of planets.

Pairing effects on the fragment mass distribution of Th,U,Pu,and Cm isotopes

In this article,a comprehensive study of the fission process of Th,U,Pu,and Cm isotopes using a Yukawa-folded meanfield plus standard pairing model is presented.The study focused on analyzing the effects of the pairing interaction on the fragment mass distribution and its dependence on nuclear elongation.The significant role of pairing interactions in the fragment mass distributions of^(230)Th,^(234)U,^(240)Pu,and^(246)Cm was demonstrated.Numerical analysis revealed that increasing the pairing interaction strength decreased the asymmetric fragment mass distribution and increased the symmetric distribution.Furthermore,the odd-even mass differences at symmetric and asymmetric fission points were examined,highlighting their sensitivity to changes in the pairing interaction strength.Systematic analysis of the Th,U,Pu,and Cm isotope fragment mass distributions demonstrated the effectiveness of the model in reproducing the experimental data.In addition,the effects of the zero-point energy and half-width parameter on the fragment mass distribution for^(240)Pu were explored.Thus,this study provides valuable insights into the fission process by emphasizing the importance of pairing interactions and their relationship with nuclear elongation.

Seasonal Variations of Number Size Distributions and Mass Concentrations of Atmospheric Particles in Beijing

Particle number and mass concentrations were measured in Beijing during the winter and summer periods in 2003, together with some other parameters including black carbon (BC) and meteorological conditions. Particle mass concentrations exhibited low seasonality, and the ratio of PM2.5/PM10 in winter was higher than that in summer. Particle number size distribution (PSD) was characterized by four modes and exhibited low seasonality. BC was well correlated with the number and mass concentrations of accumulation and coarse particles, indicating these size particles are related to anthropogenic activities. Particle mass and number concentrations (except ultra-fine and nucleation particles) followed well the trends of BC concentration for the majority of the day, indicating that most particles were associated with primary emissions. The diurnal number distributions of accumulation and coarse mode particles were characterized by two peaks.

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

Vertical distribution characteristics of dust aerosol mass concentration in the Taklimakan Desert hinterland

The different height mass concentrations of dust aerosol data from the atmosphere environment observation station （Ta- zhong Station） was continuously observed by instruments of Grimm 1.108, Thermo RP 1400a and TSP from January of 2009 to February of 2010 in the Taklimakan Desert hinterland. Results show that： （1） The mass concentration value of 80 m PMl0 was higher, but PM2.5 and PM1.0 concentrations at 80 m was obviously lower than 4 m PMl0, and the value of 80 m PM1.0 mass concentration was the lowest. （2） The PM mass concentrations gradually decreased from night to sunrise, with the lowest concentration at 08：00, with the mass concentration gradually increased, up to the highest concentration around 18：00, and then decreased again. It was exactly the same with the changes of wind speed. （3） The high monthly average mass concentration of TSP mainly appeared from March to September, and the highest concentration was in April and May, subsequently gradually decreased. Also, March-September was a period with high value area of PM monthly average mass concentration, with the highest monthly average mass concentration of 846.0 p.g/m3 for 4 m PM^0 appeared in May. The concentration of PM10 was much higher than those of PM2.5 and PM1.0 at 80 m. There is a small difference between the concentration of PM2.5 and PM~ 0. Dust weather was the main factor which influenced the concentration content of the different diameter dust aerosol, and the more dust weather days, the higher content of coarse particle, conversely, fine particle was more. （4） The mass concentration of different diameter aerosols had the following sequence during dust weather： clear day 〈 blowing dust 〈 floating and blowing dust 〈 sandstorm. In different dust weather, the value of PM^o/TSP in fine weather was higher than that in floating weather, and much higher than those in blowing dust and sandstorm weather. （5） During the dust weather process, dust aerosol concentration gradually decreased with particle size decreasing. The dust aerosol mass concentration at different heights and diameter would have a peak value area every 3-4 days according to the strengthening process of dust weather.

Molar Mass Distribution and Chain Conformation of Polysaccharides from Fortunella margarita(Lour.) Swingle

In order to study the effects of different extraction methods on the molar mass distribution and chain conformation of Fortunella margarita （Lour.） Swingle polysaccharides （FP）, we used extraction by hot water （WFP）, ultrasonic-assisted treatment （UFP）, microwave-assisted treatment （MFP） and ultrasonic/microwave-assisted treatment （UMFP）, and then Fourier transform infrared （FT-IR） spectroscopy as well as 1H and 13C nuclear magnetic resonance （NMR） spectroscopy to characterize the structural properties of FP extracted. The molar weight （Mw）, polydispersity index （Mw/Mn）, root-mean-square （RMS） turning radius （Rg）, molar mass distribution and chain conformation of FP were studied systematically using size-exclusion chromatography （SEC）, multi-angle laser light-scattering （MALLS） and refractive index （RI）. WFP, UFP, MFP and UMFP are all typical carbohydrates according to 1H NMR, laC NMR and FT-IR measurements. The type of glycosidic linkage is mainly a fl-glycosidic bond with a small amount of a-glycosidic bond. The results obtained by the SEC-MALLS-RI system showed the molar masses of WFP and UMFP were distributed mainly in the range of 5.0x10^6-1.0x10^7 g-mo1-1 and they accounted for 57.80% and 56.84% of total FP, respectively. The molar masses of UFP and MFP were distributed mainly in the 1.0x10^6-5.0x10^6 g.mol-1 range, which accounted for 38.24% and 52.39% of FP, respectively. WFP and UMFP in water were uniform spherical polymers; UFP and MFP were typical highly branched polymers and the degree of branching for MFP was higher compared to UFP. These results indicated the ultrasonic- and microwave-assisted extraction methods caused a significant decrease of the molar mass of FP but the ultrasonic/microwave synergistic extraction method had no effect.

Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

Mechanical property and deformation mechanism of gold nanowire with non-uniform distribution of twinned boundaries:A molecular dynamics simulation study

The mechanical property and deformation mechanism of twinned gold nanowire with non-uniform distribution of twinned boundaries(TBs)are studied by the molecular dynamics(MD)method.It is found that the twin boundary spacing(TBS)has a great effect on the strength and plasticity of the nanowires with uniform distribution of TBs.And the strength enhances with the decrease of TBS,while its plasticity declines.For the nanowires with non-uniform distribution of TBs,the differences in distribution among different TBSs have little effect on the Young's modulus or strength,and the compromise in strength appears.But the differences have a remarkable effect on the plasticity of twinned gold nanowire.The twinned gold nanowire with higher local symmetry ratio has better plasticity.The initial dislocations always form in the largest TBS and the fracture always appears at or near the twin boundaries adjacent to the smallest TBS.Some simulation results are consistent with the experimental results.

Hospital-Based Phenotypic Features and Treatment Outcomes of Chinese Women with Polycystic Ovary Syndrome: The Effect of Body Mass Index and Geographic Distribution

Genetic,lifestyle,and environmental factors contribute to the etiology of polycystic ovary syndrome(PCOS).Increased body mass index(BMI)exacerbates the reproductive and metabolic parameters and reduces the fecundity of women with PCOS.This is a secondary analysis of a large-sample,multicenter,randomized controlled trial conducted at 21 sites in Chinese mainland.A total of 1000 women diagnosed with PCOS were enrolled in this trial.Of these,998 women with PCOS were included in the analysis.Increased BMI was associated with more severe menstrual irregularities,elevated testosterone level,higher prevalence of metabolic syndrome,and poorer quality of life.The rates of ovulation per woman for the normal,overweight,and obese BMI groups were 83.0%,78.2%,and 63.6%,respectively(P<0.001),and the rates of live birth were 23.6%,18.1%,and 15.3%(P=0.030).Northern PCOS patients showed more severe reproductive,glucose,and lipid profiles;less exercise;and lower total ovulation rates compared with PCOS patients from Southern China(74.8%vs 81.2%,absolute difference 6.4%,95%confidence interval 1.2%–11.5%).The results show the typical phenotypic features of Han women with PCOS in Northern and Southern China.The women living in Northern China showed a higher BMI,more severe glycolipid metabolism profiles,and subsequently worse clinical outcomes by the same interventions than those living in Southern China.The difference in phenotypic features can be explained mostly by differences in BMI and the resulting difference in ovulation.

Applicability of law of mass action to distribution of manganese between slag melts and liquid iron

According to the law of mass action and the coexistence theory of slag structure, the distribution of manganese between MnO FeO SiO 2 and MgO MnO FeO SiO 2 slag melts as well as liquid iron was analyzed. It is shown that K ′ Mn and K MnO are only dependent on temperature and don’t change with basicities and compositions of slag melts. So the distribution of manganese between the above mentioned slag melts and molten iron obeys the law of mass action. But analysis of experimental results from other sources shows that K ′ Mn and K MnO really change with basicities of slag, which is probably arisen from not approaching equilibrium under low basicity slag melts.

Preliminary analysis of distribution and variation of perennialmonthly mean water masses in the Bohai Sea,the Huanghai Sea and the East China Sea

On the basis of perennial monthly mean temperature and salinity data, the classification of monthly water masses at the surface and the bottom in the Bohai Sea, the Huanghai Sea and the East China Sea, has been made by using the method of fuzzy cluster from the modified characteristic of water masses in the shallow water area. In this paper, the basic features, growth and decline patterns of water masses in relation to fishing grounds in the whole shelves of the Bohai Sea, the Huanghai Sea and the East China Sea are discussed with emphasis.

Exact Statistical Distribution of the Body Mass Index (BMI): Analysis and Experimental Confirmation

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of the associated height (in meters), is one of the most widely discussed and utilized risk factors in medicine and public health, given the increasing obesity worldwide and its relation to metabolic disease. Statistically, BMI is a composite random variable, since human weight (converted to mass) and height are themselves random variables. Much effort over the years has gone into attempts to model or approximate the BMI distribution function. This paper derives the mathematically exact BMI probability density function (PDF), as well as the exact bivariate PDF for human weight and height. Taken together, weight and height are shown to be correlated bivariate lognormal variables whose marginal distributions are each lognormal in form. The mean and variance of each marginal distribution, together with the linear correlation coefficient of the two distributions, provide 5 nonadjustable parameters for a given population that uniquely determine the corresponding BMI distribution, which is also shown to be lognormal in form. The theoretical analysis is tested experimentally by gender against a large anthropometric data base, and found to predict with near perfection the profile of the empirical BMI distribution and, to great accuracy, individual statistics including mean, variance, skewness, kurtosis, and correlation. Beyond solving a longstanding statistical problem, the significance of these findings is that, with knowledge of the exact BMI distribution functions for diverse populations, medical and public health professionals can then make better informed statistical inferences regarding BMI and public health policies to reduce obesity.

Connection Between Liquid Distribution and Gas-Liquid Mass Transfer in Monolithic Bed

与在在在泰勒流动政体的整体的床上的液体流动分发和煤气液体的集体转移之间的连接的一个特别焦点，水动力学和煤气液体的集体转移实验与二个不同经销商(嘴和包装的床经销商)一起与 50 cpsi 的房间密度的一张整体的床在列被执行。在单个隧道的液体浸透被使用白手起家的测量微传导性的探针。一个 mal 分发因素被用来在独块巨石评估阶段分发的一致的度。全面的床压力落下和集体转移系数被测量。为液体流动分发和煤气液体的集体转移，表面的液体速度是一个关键因素，包装的床分发者比嘴分发者好，这被发现。用单个隧道模型的半理论的分析证明包装的床分发者总是与嘴分发者相比产出更短、一致地分布式的液体蛞蝓，它接着保证更好集体的转移表演。一个床规模团转移模型被在单个隧道雇用单个隧道模特儿并且沿着床剖面图合并不一致的液体分发的效果建议。

CORRELATION BETWEEN HYSTERESIS OF GAS-LIQUID MASS TRANSFER AND LIQUID DISTRIBUTION IN A TRICKLE BED

The hysteresis of gas-liquid mass transfer rate and the corresponding radial liquiddistribution in a trickle bed reactor are measured to provide evidence for the correlation between thesetwo behaviors.Experimental results indicate that the hysteresis of gas-liquid mass transfer originatesfrom the nonuniformity of the hydrodynamic state of gas-liquid flow and the radial maldistributionof local kgia corresponds very well to the radial maldistribution of liquid flow in the bed.The localliquid flow rate is also found to be nonuniform in the azimuthal direction.In view of maldistributedliquid flow even in the pulsing flow regime,the conventional plug flow model seems oversimplifiedfor describing the behavior of a trickle bed.

Contrasting vertical distribution between prokaryotes and fungi in different water masses on the Ninety-East Ridge, Southern Indian Ocean

Although the microbial diversity of the Indian Ocean has been extensively investigated,little is known about the community composition of microbes in the Southern Indian Ocean.In the present study,we divided 60 water column samples on the Ninety-East Ridge(NER)into fi ve water masses according to the temperature-salinity curves.We presented,for the fi rst time,a full description of the microbial biodiversity on NER through high-throughput amplicon sequencing approach,including bacteria,archaea,and fungi.We found that bacteria exhibited higher richness and diversity than archaea and fungi across the water masses on NER.More importantly,each water mass on NER featured distinct prokaryotic microbial communities,as indicated by the results of non-metric multidimensional scaling.In contrast,fungi were eurybathic across the water masses.Redundancy analysis results demonstrated that environmental factors might play a pivotal role in the formation and stability of prokaryotic communities in each water mass,especially that of archaea.In addition,indicator species might be used as fi ngerprints to identify corresponding water masses on NER.These results provide new insights into the vertical distribution,structure,and diversity of microorganisms on NER from the perspective of water mass.

Distribution of Mass and Energy in Five General Cosmic Models

Distributions of the universe horizon distance and universe horizon volume were investigated in the light of five general cosmic models which were constructed in a previous study. Both distributions increase so slowly up to t ≈ 21.5444 Myr, then they start raising very fast up to t ≈ 60 Gyr. Afterwards, they increase again very slowly until t ≈ 124 Gyr. Distributions of mass of radiation, matter and dark energy within the horizon volume of the universe were also studied in the five general cosmic models. The masses of both radiation and matter decrease gradually with time while the mass of dark energy increases. The mass of radiation prevailed in the early universe up to t ≈ 34627.5 - 55916.2 yr, where it becomes equal to the mass of matter. Then the mass of matter dominated until t ≈ 9.4525 - 10.0632 Gyr, where it becomes equal to the mass of dark energy. Thenceforward, the mass of dark energy prevails the universe. The cosmic space becomes approximately matter empty in the so far future of the universe.

UHAS-MIDA Software Package: Mass Isotopomer Distribution Analysis-Applying the Inverse Matrix for the Determination of Stable Isotopes of Chromium Distribution during Red Blood Cell Labelling

Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (53Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (50Cr, 52Cr, 53Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida

Study of the Non-Uniform Distribution of Earthquake Risk Within Potential Sources

Potential sources are aggregates of probable future epicenters.In this area,for source models currently,in common use for seismic risk analysis in China,the mean area of each potential source is about 3000-4000 km2.It is assumed that seismic risk has a uniform distribution within the range of each potential source,but studies have shown that the uniform distribution model to a large extent may give an underestimation of the seismic risk.In this paper,the relative distribution of historical epicenters in space within potential sources is discussed,a method is proposed to quantitatively describe the non-uniform distribution of strong earthquakes within potential sources,and some preliminary results are given.By using the results of this paper,seismic risk analysis and seismic zonation can be made more scientific and more reasonable.

Mass Yield Distribution in Intermediate Energy Heavy Ion Reactions

The production cross sections of the target residues were measured for the 40 MeV/u40Ar+Cu reaction by γ-ray spectroscopic technique and the mass yield distribution was deduced.The ex-perimental data were compared with the theoretical results from both the GEMINI code based on the statis-tical binary decay model and the McFRAG code based on the fusion-fragmentation model.

Surface distribution of alkalinity and specific alkalinity and their application to water mass tracing in Kuroshio area of the East China Sea

Surface distribution and seasonal variation of alkalinity and specific alkalinity in Kuroshio area of the East ChinaSea and their application to the water mass tracing are discussed in this paper. Results show a distinct seasonal variation of the alkalinity, which is concerned with the process of vertical mixing. Different specific alkalinity in various water masses has been found. On the basis of the difference of the specific alkalinity and the distribution of alkalinity, two water fronts in summer season, located at 27°-30°N and 124°-1 27°E, (Ⅰ), and at the northern waters about one latitude from the Taiwan Island, (Ⅱ); one in winter season at about one longitude from coast of mainland of China and 26°-30°N were found. In summer season, about 1-2 longitudes eastward shift of front (Ⅰ) is found by comparison of data in May and August. And the high alkalinity of the northern East China Sea in summer season may be caused by the Huanghe River runoff flowing southward along with the Huanghai Sea Coastal Current.