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.

Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load

Compared with the moving concentrated load model,it is more realistic and proper to use the moving distributed mass and load model to simulate the dynamics of a train moving along a railway track.In the problem of a moving concentrated load,there is only one critical velocity,which divides the load moving velocity into two categories:subcritical and supercritical.The locus of a concentrated load demarcates the space into two parts:the waves in these two domains are called the front and rear waves,respectively.In comparison,in the problem of moving distributed mass and load,there are two critical velocities,which results in three categories of the distributed mass moving velocity.Due to the presence of the distributed mass and load,the space is divided into three domains,in which three different waves exist.Much richer and different variation patterns of wave shapes arise in the problem of the moving distributed mass and load.The mechanisms responsible for these variation patterns are systematically studied.A semi-analytical solution to the steady-state is also obtained,which recovers that of the classical problem of a moving concentrated load when the length of the distributed mass and load approaches zero.

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.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed.This study investigated the fragmentation performance of a new high-carbon silicon-manganese(HCSiMn)steel cylindrical shell through fragment recovery experiments.Compared with the conventional 45Cr steel shell,the number of small mass fragments produced by the HCSi Mn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model.The fragmentation process of the HCSi Mn shell exhibited more brittle tensile fracture characteristics,with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation.On the one hand,the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite,so that microscopic intergranular fracture reduces the characteristic mass of the fragments;on the other hand,the distribution of alloy carbides can exert a"pinning"effect on the substrate grains,causing more initial cracks to form and propagate along the brittle carbides,further improving the shell fragmentation.Although the killing power radius for light armored vehicles was slightly reduced by about 6%,the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26%based on theoretical assessment.These results provided an experimental basis for high fragmentation warhead design,and to some extent,revealed the correlation mechanism between metallographic structure and shell fragmentation.

Recent progress on impact induced reaction mechanism of reactive alloys

In recent years,in order to improve the destructive effectiveness of munitions,the use of new types of destructive elements is an important way to improve destructive effectiveness.As a new type of reactive material,reactive alloy contains a large portion of reactive metal elements(Al,Mg,Ti,Zr,etc.),which breaks up under high-velocity impact conditions,generating a large number of high-temperature combustible fragments,which undergo a violent combustion reaction with air.Compared with traditional metal polymers(Al-PTFE)and other reactive composites,it has higher density and strength,excellent mechanical properties and broader application prospects.Currently,researchers have mainly investigated the impact energy release mechanism of reactive alloys through impact tests,and found that there are several important stages in the process of the material from fragmentation to reaction,i.e.,impact fragmentation of the material,rapid heating and combustion reaction.This paper focuses on three problems that need to be solved in the impact-induced energy release process of reactive alloys,namely:the fragmentation mechanism and size distribution law of the fragments produced by the impact of the material on the target,the relationship between the transient temperatures and the size of the fragments,and the reaction temperatures and size thresholds of the fragments to undergo the chemical reaction.The current status of the research of the above problems is reviewed,some potential directions to reveal the impact induced reaction mechanism of reactive alloy is discussed.

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.

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.

Cage and ladder structures of silsesquioxanes characterized by UV-MALDI-TOF mass spectrometry

The molar mass distribution of SSO in the first generation derived from the hydrolytic condensation oftwo trialkoxysilanes, [ 3- ( Methacryloxy ) propyl ] trimethoxysilane ( MPMS ) and vinyltrimethoxysilane ( VMS ) ,are determined by UV-MALDI-TOF MS. The comparisons of theoretical masses with experimental masses arecalculated using the proposed compounds, which are assigned to formulas Tn (OH)m, Tn (OMe)y orTn(OH)x(OMe)y[T=RSiO1.5 (x+y)/2n, R=--(CH2)3OOCCH(CH3)CH2 and--CHCH2]. Both theproposed cage and ladder structures of SSO derived from similar sol-gel process of monomers are illustrated. Thecauses for the difference in structures between SSO M and SSO V is discussed as well.

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.

Approximate energies and thermal properties of a position-dependent mass charged particle under external magnetic fields

We solve the Schrodinger equation with a position-dependent mass（PDM） charged particle interacted via the superposition of the Morse-plus-Coulomb potentials and is under the influence of external magnetic and Aharonov–Bohm（AB） flux fields. The nonrelativistic bound state energies together with their wave functions are calculated for two spatially-dependent mass distribution functions. We also study the thermal quantities of such a system. Further, the canonical formalism is used to compute various thermodynamic variables for second choosing mass by using the Gibbs formalism. We give plots for energy states as a function of various physical parameters. The behavior of the internal energy, specific heat, and entropy as functions of temperature and mass density parameter in the inverse-square mass case for different values of magnetic field are shown.

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

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.

磷酸化肽段质量数的分布特征

基于双向电泳和液相色谱的蛋白质鉴定是蛋白质组最常用的技术,质谱谱图的好坏对鉴定的成功率起决定性作用.其中,某些不确定的修饰和非蛋白污染物是影响谱图质量的难以忽略的因素.……

Enzymatic Hydrolysis of Cellulose with Different Crystallinities Studied by Means of SEC-MALLS

The reactions of exo-cellulase （cellobiohydrolase, CBH） and endo-cellulase （endoglucanase, EG） were investigated by analyzing the insoluble residues of microcrystalline cellulose （MCC） and filter paper cellulose （FPC） during enzymatic hydrolysis. Molecular parameters including molecular weight and its distribution, degree of polymerization, and radii of gyration were measured by size exclusion chromatography coupled with multi-angle laser light scattering. No significant change in MCC chains was found during the whole reaction period, indicating that CBH digestion follows a layer-by-layer solubilization manner. This reaction mode might be the major reason for slow enzymatic hydrolysis of cellulose. On the other hand, the degree of polymerization of FPC chains decreases rapidly in the initial reaction, indicating that EG digestion follows a random scission manner, which may create new ends for CBH easily. The slopes of the conformation plots for MCC and FPC increase gradually, indicating stronger chain stiffness of cellulose during hvdrolvsis

Long-term gravity changes in Chinese mainland from GRACE and ground-based gravity measurements

A long-term （9 years） gravity change in Chinese mainland is obtained on the basis of observation of the ground-based national gravity network. The result shows several features that may be related to sore, large-scale groundwater pumping in North China, glacier-water flow and storage in Tianshan region, and pre seismic gravity changes of the 2008 MsS. 0 Wenchuan earthquake, which are spatially similar to co-seismi, changes but reversed in sign. These features are also shown in the result of the satellite-based GRACE obser vation, after a height effect is corrected with GPS data.

Fermion or Boson Dark Matter?

We measure properties of dark matter in four well motivated scenarios: fermions with ultra-relativistic thermal equilibrium (URTE), bosons with URTE, fermions with non-relativistic thermal equilibrium (NRTE), and bosons with NRTE. We attempt to discriminate between these four scenarios with studies of spiral galaxy rotation curves, and galaxy stellar mass distributions. The measurements show evidence for boson dark matter with a significance of 3.5σ, and obtain no significant discrimination between URTE and NRTE.

Calculation of flow distribution in air reverse circulation bit interior fluid field by simplifying air flow model

By simplifying the characters in the air reverse circulation bit interior fluid field, the authors used air dynamics and fluid mechanics to calculate the air distribution in the bit and obtained an equation of flow distribution with a unique resolution. This study will provide help for making certain the bit parameters of the bit structure effectively and study the air reverse circulation bit interior fluid field character deeply.

Comments on Warm Dark Matter Measurements and Limits

Observed spiral galaxy rotation curves allow a measurement of the warm dark matter particle velocity dispersion and mass. The measured thermal relic mass mh ≈100 eV is in disagreement with limits, typically in the range 1 to 4 keV. We review the measurements, update the no freeze-in and no freeze-out scenario of warm dark matter, and try to identify the cause of the discrepancies between measurements and limits.

Upper Bound and Lower Bound Estimate of Monotone Increasing Fractal Function

Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f（x）（it is a monotone increasing fractal function） and its some applications.

Electrophoresis(SDS-PAGE)as a Method for Screening Species of Passiflora Using Seed Proteins as Molecular Markers

Brazil is the center of diversity and dispersion of species of the genus Passiflora.Two species of passion fruit Passiflora tenuifila BRS VT(passiflora garlic)and another of Passiflora setacea BRS PC were used in this study.The plants were grown on the Embrapa Cerrados experimental farm.The fruits were washed,minimally cut and their constituents separated.Both species differed in the proportion of wet mass between husk,seed,and pulp.As expected,both species had a higher proportion of husks and seeds and a lower amount of pulp.A semi-purification procedure for the proteins present in the seeds and husks was described and the molecular aspects were analyzed by polyacrylamide gel electrophoresis(SDS-PAGE).The quantification of soluble proteins was performed using the Bradford method.The analysis of the soluble protein extracted from the seeds and husks showed that these values are up to 70 times higher for the seeds of P.tenuifila and 28.5 times for P.setacea,in the husks.It was verified that both species present a similar protein profile,observed by the intense and diverse bands found in the polyacrylamide gel,mainly in the range of 32 to 19 kDa.This work opens up an unexplored field of tracking bioactive proteins and/or peptides including forms of nanostructure systems that protect other bioactive molecules.The objective of this work was to present an analytical procedure to semi-purify seed proteins of two Passiflora species and use electrophoresis as an analysis tool for further screening of their protein profiles and selection of a molecular marker to differentiate them.