A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a gre...A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a great number of rotational spectra of even-even nu-clei in rare-earth and actinides region show that the formula is the best one among all two-pa-rameter formulas. It is pointed out that this formula can be applied to the spin assignment forsuperdeformed band.展开更多
The two-parameter formulae, i.e. the nuclear softness formula and the power index formula, have been used to obtain the band head spin （I0） of the triaxial superdeformed （SD） bands in ^163Lu（1,2,3,4）, ^164Lu（1,...The two-parameter formulae, i.e. the nuclear softness formula and the power index formula, have been used to obtain the band head spin （I0） of the triaxial superdeformed （SD） bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3）, in the A - 160 mass region. The least squares fitting approach is used. The values of the root mean square （RMS） deviation among the computed and the measured experimental transition energies are obtained by calculating the model parameters. Whenever accurate spins are available, superb agreement is shown between the determined and the measured experimental transition energies. In comparison to the power index formula, the values of band head spin （I0） of the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） obtained by the nuclear softness formula are closer to the experimental data. The lowest RMS deviation is also achieved by the nuclear softness formula. Hence, the nuclear softness formula works well for obtaining the band head spin （I0） for the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） in the A-160 mass region. The dynamic moment of inertia against hω is also studied.展开更多
Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must ad...Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.展开更多
In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's...In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.展开更多
In the references[4,11,12],the authors gave some modular forms overΓ^(0)(2).In this note,we proceed with the study of cancellation formulas relating to the modular forms.
OBJECTIVE: To explore whether Soufeng Yuchuan(搜风愈喘, SFYC) formula alleviates asthma by promoting ferroptosis of airway epithelial cells. METHODS: A chronic asthma rat model was established using ovalbumin(OVA) com...OBJECTIVE: To explore whether Soufeng Yuchuan(搜风愈喘, SFYC) formula alleviates asthma by promoting ferroptosis of airway epithelial cells. METHODS: A chronic asthma rat model was established using ovalbumin(OVA) combined with aluminum hydroxide sensitization and OVA nebulization stimulation. Lung tissue pathology was assessed via hematoxylin and eosin staining and periodic acid-Schiff staining. Lung tissue ultrastructure was observed using transmission electron microscopy. Serum cytokine levels were measured by enzyme-linked immunosorbent assay. Malondialdehyde(MDA), glutathione, and tissue ferrous ion content in rat lung tissues and cells were detected using commercial kits. Immunohistochemical staining was used to determine the expression levels of interleukin-13(IL-13) and interleukin-6(IL-6) in lung tissue. Western blotting was employed to detect the expression levels of transferrin receptor 1(TFR1), transferrin receptor 2(TFR2), acyl-Co A synthetase longchain family member 4(ACSL4), glutathione peroxidase 4(GPX4), and solute carrier family 7 member 11(SLC7A11). Cell proliferation, apoptosis and reactive oxygen species(ROS) were evaluated using a cell counting kit-8 assay and flow cytometry. Intracellular lipid peroxidation was detected using a C11-BODIPY 581/591(C11-BODIPY) probe. RESULTS: SFYC formula effectively alleviates airway inflammation in asthmatic rats in a dose-dependent manner. It improves airway epithelial cell integrity, reduces alveolar wall thickening and expansion, inhibits goblet cell proliferation and mucus secretion, and decreases the expression of IL-6 and IL-13 in lung tissue, as well as the serum levels of IL-6, IL-13, interleukin-4(IL-4), and immunoglobulin E(Ig E). SFYC formula mitigates ferroptosis in lung tissue of asthmatic rats. At the cellular level, it promotes proliferation of rat airway epithelial cells, inhibits cell apoptosis, suppresses ROS, MDA, and lipid accumulation, reduces the expression of TFR1, TFR2, and ASCL4, and increases the expression of GPX4 and SLC7A11 to mitigate ferroptosis. CONCLUSION: SFYC formula alleviates asthma airway inflammation by inhibiting ferroptosis in airway epithelial cells, providing new insights and potential therapeutic targets for the development of new asthma treatment drugs.展开更多
A Cu-1.9Ni-1.9Co-0.9Si(mass fraction,%)alloy with high strength and electrical conductivity was designed by cluster formula approach.The microstructure evolution of the alloy during thermomechanical treatment was syst...A Cu-1.9Ni-1.9Co-0.9Si(mass fraction,%)alloy with high strength and electrical conductivity was designed by cluster formula approach.The microstructure evolution of the alloy during thermomechanical treatment was systematically investigated.The strengthening mechanism and electrical conductivity of the alloy were discussed in detail.The optimal thermomechanical treatment process was as follows:solid solution→80%cold rolling→(450℃,4 h)aging→50%cold rolling→(400℃,4 h)aging.The designed alloy achieved excellent comprehensive properties with a microhardness of HV 260,a yield strength of 843 MPa,a tensile strength of 884 MPa,and an electrical conductivity of 42.6%(IACS).Compared to direct aging treatment,the designed alloy subjected to multi-stage thermomechanical treatment had refined grains,high density of dislocations,and accelerated of precipitation of(Ni,Co)_(2)Si precipitates.High strength was mainly attributed to the combined effect of dislocation strengthening,work hardening and sub-grain strengthening,while good electrical conductivity was maintained through the precipitation of the large number of nanoparticles.展开更多
Background:Hua-Yi-Jie-Du formula(HYJD)is a traditional Chinese medicine that has proven effective against viral pneumonia and was extensively used during the COVID-19 pandemic.This study investigates how HYJD influenc...Background:Hua-Yi-Jie-Du formula(HYJD)is a traditional Chinese medicine that has proven effective against viral pneumonia and was extensively used during the COVID-19 pandemic.This study investigates how HYJD influences group 2 innate lymphoid cell(ILC2)and nucleotide oligomerization domain(NOD)-like receptor protein 3(NLRP3)inflammasome activation in a mouse model of viral pneumonia.Methods:A mouse model of viral pneumonia was established through the administration of polyinosinic-polycytidylic acid(poly(I:C))via nasal drops.Histopathological analysis of lung tissue was conducted,alongside enzyme-linked immunosorbent assay to quantify cytokine levels in serum and bronchoalveolar lavage fluid(BALF).Flow cytometry was employed to detect ILC2 cells in lung tissue and spleen,while immunofluorescence techniques were utilized to visualize ILC2 cells in lung tissue.Transcriptomic sequencing was performed,and the results were validated using qRT-PCR and western blot analysis.Results:HYJD significantly ameliorated inflammatory infiltration in lung tissue,decreased mucus protein secretion,and reduced the serum levels of inflammatory cytokines interleukin(IL)-1β,IL-6,and tumor necrosis factor-alpha(TNF-α).Additionally,it lowered the expression of cytokines IL-4,IL-5,IL-13,IL-25,thymic stromal lymphopoietin(TSLP),and IL-33 in BALF,and reduced the differentiation of ILC2 cells in both lung tissue and spleen.Transcriptomic analysis and experimental validation revealed that HYJD downregulated the expression of NLRP3 related genes and proteins within the NOD-like receptor signaling pathway.Conclusion:The mechanism by which HYJD intervenes in acute lung injury associated with viral pneumonia may involve the reduction of ILC2 cells differentiation and the inhibition of NLRP3 activation.展开更多
Chronic heart failure(CHF)impairs cognitive function.Xijiaqi Formula(XJQ),a traditional Chinese medicine(TCM)used clinically to treat CHF,demonstrates potential for improving cognition in CHF patients.However,its prec...Chronic heart failure(CHF)impairs cognitive function.Xijiaqi Formula(XJQ),a traditional Chinese medicine(TCM)used clinically to treat CHF,demonstrates potential for improving cognition in CHF patients.However,its precise mechanism in treating post-CHF cognitive dysfunction remains unclear.This study systematically investigates XJQ’s effects on post-CHF cognitive dysfunction and the underlying mechanisms.The components of XJQ were identified through liquid chromatography-mass spectrometry.CHF was induced in rats via ligation of the left anterior descending coronary artery,followed by six weeks of XJQ treatment.Cardiac function was evaluated through echocardiography and hemodynamic parameters,while cognitive function was assessed using Morris water maze(MWM)and open field tests(OFT).XJQ treatment enhanced both cardiac and cognitive functions in CHF rats.Network pharmacology identified 12 core active components of XJQ and indicated its effect on cognitive dysfunction involved regulating synapses,inflammation,and phosphodiesterase 4(PDE4)-dependent cyclic adenosine monophosphate(cAMP)signaling.XJQ inhibited microglial and astrocyte activation,decreased proinflammatory cytokines,and mitigated neuronal damage.Notably,XJQ promoted synaptic repair and dendritic growth by downregulating PDE4 and upregulating cAMP,protein kinase A(PKA),cAMP-response element binding protein(CREB),brain-derived neurotrophic factor(BDNF),PSD95,and synapsin I levels.Molecular docking and Bio-layer interferometry assays confirmed direct binding of quercetin,kaempferol,isorhamnetin,and darutoside to PDE4.In conclusion,XJQ alleviates neuroinflammation and enhances synaptic plasticity to improve cognitive dysfunction in CHF rats via the PDE4/cAMP/PKA/CREB signaling pathway.These findings provide valuable insight into the heart-brain axis.展开更多
BACKGROUND Perimenopausal women are prone to anxiety and depression due to fluctuating hormone levels,which significantly impair their quality of life.The current treatments have certain limitations.In traditional Chi...BACKGROUND Perimenopausal women are prone to anxiety and depression due to fluctuating hormone levels,which significantly impair their quality of life.The current treatments have certain limitations.In traditional Chinese medicine,liver-soothing formulas are commonly prescribed for mood-related disorders,but their overall efficacy in perimenopausal anxiety and depression remains uncertain and requires verification through meta-analysis.AIM To provide evidence-based support for clinical decision-making and research,a meta-analysis was conducted to evaluate the effectiveness of liver-soothing formulas in treating perimenopausal anxiety and depression.METHODS Relevant studies published up to April 2025 were retrieved from ClinicalTrials.gov,PubMed,Web of Science,EMBASE,and the Cochrane Library.Eligible studies were screened according to predefined inclusion and exclusion criteria.Data were extracted and analyzed using the Stata 12.0 software.RESULTS After searching and screening,12 articles involving 1798 patients(922 in the treatment group and 876 in the control group)were included in the analysis.Meta-analysis showed that the standardized scores for anxiety[standardized mean difference(SMD)=-0.71,95%confidence interval(95%CI):-1.06 to-0.36]and depression(SMD=-0.67,95%CI:-1.06 to-0.27)of the treatment group were lower than those of the control group.Subgroup analysis results revealed that for anxiety,liver-soothing formulas used alone(SMD=-0.34,95%CI:-0.50 to-0.18)or in combination(SMD=-0.88,95%CI:-1.43 to-0.34)both significantly reduced scores compared with the control group.For depression,monotherapy of liversoothing formulas showed no significant statistical difference between the treatment and control groups(SMD=-0.47,95%CI:-1.11 to 0.17),whereas combination therapy produced significantly lower standardized scale scores in the treatment group than in the control group,with a statistically significant difference(SMD=-0.83,95%CI:-1.39 to-0.28).Regarding Greene scores,no statistically significant difference was observed with monotherapy(SMD=0.87,95%CI:-0.32 to 2.06),whereas combination therapy had significantly lower Greene scores(SMD=-0.24,95%CI:-0.44 to-0.04).No statistically significant difference was found between the groups in the occurrence of adverse reactions(odds ratio=0.90,95%CI:0.57-1.43).However,liver-soothing formulas did not affect estrogen levels in perimenopausal women.CONCLUSION Compared with placebo,conventional Western medicine,or other interventions,the monotherapy of liver-soothing formulas demonstrates superior efficacy in treating perimenopausal anxiety.When used as an adjuvant,they exert a synergistic effect in alleviating negative emotions and improving overall perimenopausal symptoms.展开更多
Triacylglycerol(TAG)components in human milk,infant formulas with different fat sources,and plant oils(palm oil,flaxseed oil,sunflower oil,corn oil,soybean oil,coconut oil,low erucic acid rapeseed oil,and high oleic a...Triacylglycerol(TAG)components in human milk,infant formulas with different fat sources,and plant oils(palm oil,flaxseed oil,sunflower oil,corn oil,soybean oil,coconut oil,low erucic acid rapeseed oil,and high oleic acid rapeseed oil)were analyzed and compared using ultraperformance supercritical fluid chromatography coupled with quadrupole time-of-flight mass spectrometry(UPSFC-Q-TOF-MS).Distinct TAG profiles were identified by lipidomics,principal component analysis(PCA),and heatmap visualization.Human milk was characterized by a high abundance of medium-and long-chain triacylglycerols(MLCTs),saturated-unsaturated-unsaturated(SUU)-type TAGs(sn-2 palmitic acid).In contrast,plant oils lacked MLCTs and SUU-type TAGs,containing mainly TAGs esterified long-chain polyunsaturated fatty acid.Breast milk contains about 27%MLCT,about 50%SUU-type triacylglycerols(which contain about 34%UPU-type triacylglycerols),which is significantly different from plant oils,structured fats and infant formulas.These findings provide a clear basis for optimizing the fat blend in infant formula to better mimic the unique TAG profile of human milk,thereby improving energy delivery and nutrient absorption for infants.展开更多
OBJECTIVE:To investigate the pharmacological effects and underlying mechanisms of Pinggan Yuyin Qingre formula(平肝育阴清热方,PGYYQR)in the treatment of meibomian gland dysfunction(MGD)through network pharmacology and...OBJECTIVE:To investigate the pharmacological effects and underlying mechanisms of Pinggan Yuyin Qingre formula(平肝育阴清热方,PGYYQR)in the treatment of meibomian gland dysfunction(MGD)through network pharmacology and in vivo validation.METHODS:A mouse model of MGD was induced using the stearoyl-coenzyme a desaturase 1 inhibitor,followed by PGYYQR treatment for 2 weeks.MGD sign scoring,hematoxylin and eosin(HE)staining,oil red o(ORO)staining,and serum inflammatory cytokine analysis were conducted to assess the effects of PGYYQR on meibomian gland(MG)function,histopathology,and associated inflammation.Network pharmacology was employed to identify the active compounds and potential targets of PGYYQR.Molecular mechanisms were further investigated using Western blotting,reverse transcription quantitative real-time polymerase chain reaction,and reactive oxygen species(ROS)assays.RESULTS:PGYYQR treatment significantly reduced the scores of MG orifice obstruction and meibum quality in MGD mice.HE and ORO staining further demonstrated that PGYYQR ameliorated glandular damage and lipid dysfunction.Enzyme-linked immunosorbent assay results revealed that PGYYQR markedly decreased the serum levels of key inflammatory cytokines,including interleukin(IL)-1β,IL-6,and tumor necrosis factor-α.Network pharmacology identified 162 active compounds and 598 target genes in PGYYQR.Among these,IL-6,IL-1β,matrix metalloproteinase-9,and C-X-C motif chemokine ligand 8 were recognized as core targets related to MGD and were mainly enriched in the IL-17/nuclear factor kappa B(NF-κB)signaling pathway.Further molecular analyses confirmed that PGYYQR significantly inhibited the IL-17/NF-κB axis by downregulating IL-17 expression and reducing phosphorylated NF-κB p65 levels at both the protein and m RNA levels in MG tissues.PGYYQR also effectively reduced ROS levels in the conjunctival tissues of MGD mice.CONCLUSION:PGYYQR effectively improves MG function and preserves local tissue morphology in MGD model mice,primarily by suppressing the inflammatory response through coordinated modulation of the IL-17/NF-κB signaling pathway and oxidative stress.展开更多
OBJECTIVE:To explore the bioactive constituents,key targets,signalling pathways,and molecular mechanisms of Lianshi Jianpi formula(莲实健脾方,LSJPF)in the treatment of impaired glucose tolerance(IGT)through network ph...OBJECTIVE:To explore the bioactive constituents,key targets,signalling pathways,and molecular mechanisms of Lianshi Jianpi formula(莲实健脾方,LSJPF)in the treatment of impaired glucose tolerance(IGT)through network pharmacology,molecular docking,and in vivo experiments.METHODS:The active ingredients and targets of LSJPF were identified using the Traditional Chinese Medicine Systems Pharmacology and HERB databases,whereas the IGT-related targets were sourced from Gene Cards,Dis Ge NET,and Pub Med.The overlap analysis identified potential targets of LSJPF.Protein-protein interaction networks and core targets were evaluated using the Search Tool for the Retrieval of Interacting Genes/Proteins and Cytoscape,and molecular docking confirmed the binding affinities.Gene Ontology and Kyoto Encyclopedia of Genes and Genomes pathway enrichment analyses were performed using Metascape.The therapeutic mechanisms were validated in an animal IGT model.RESULTS:LSJPF contained 229 compounds,with 15 active compounds and 77 potential target proteins.The phosphatidylinositol-3-kinase(PI3K)-protein kinase B(AKT)signalling pathway emerged as a key IGT pathway.The KEGG enrichment analysis revealed the pivotal genes RAC-alpha serine/threonine-protein kinase(AKT1),heat shock protein 90 k Da alpha B1,and B-cell lymphoma 2 family protein,which predominantly interact with beta-sitosterol and beta-carotene,the major constituents of Semen Euryales,Semen lablab Album,Semen sojae Atricolor in LSJPF.Molecular docking revealed strong binding affinities between LSJPF and IGT-related targets.In an animal IGT model,LSJPF treatment prevented weight loss;reduced food and water intake;decreased blood glucose levels;improved insulin resistance;decreased serum triglyceride,cholesterol,and low-density lipoprotein cholesterol levels;alleviated liver pathology;and significantly increased the levels of phosphorylated adenosine 5'-monophosphate-activated protein kinase(AMPK),PI3K,and AKT,suggesting its potential role in regulating glucose and lipid metabolism.CONCLUSIONS:These findings reveal the potential of LSJPF as an IGT intervention that targets the AMPK/PI3K/AKT cascade,validating network pharmacology predictions and highlighting the role of multipathway mechanisms in metabolic diseases.展开更多
Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time mi...Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.展开更多
In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic found...The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.展开更多
<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensio...<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>展开更多
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement wi...The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.展开更多
基金The project supported by the National Natural Scicnce Foundation of China CCAST (World Lab)
文摘A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a great number of rotational spectra of even-even nu-clei in rare-earth and actinides region show that the formula is the best one among all two-pa-rameter formulas. It is pointed out that this formula can be applied to the spin assignment forsuperdeformed band.
文摘The two-parameter formulae, i.e. the nuclear softness formula and the power index formula, have been used to obtain the band head spin （I0） of the triaxial superdeformed （SD） bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3）, in the A - 160 mass region. The least squares fitting approach is used. The values of the root mean square （RMS） deviation among the computed and the measured experimental transition energies are obtained by calculating the model parameters. Whenever accurate spins are available, superb agreement is shown between the determined and the measured experimental transition energies. In comparison to the power index formula, the values of band head spin （I0） of the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） obtained by the nuclear softness formula are closer to the experimental data. The lowest RMS deviation is also achieved by the nuclear softness formula. Hence, the nuclear softness formula works well for obtaining the band head spin （I0） for the triaxial SD bands in ^163Lu（1,2,3,4）, ^164Lu（1,2,3） and ^165Lu（1,2,3） in the A-160 mass region. The dynamic moment of inertia against hω is also studied.
基金Project supported by the National Natural Science Foundation of China(No.12525202)。
文摘Transcritical and supercritical fluids widely exist in aerospace propulsion systems,such as the coolant flow in the regenerative cooling channels of scramjet engines.To numerically simulate the coolant flow,we must address the challenges in solving Riemann problems(RPs)for real fluids under complex flow conditions.In this study,an exact numerical solution for the one-dimensional RP of two-parameter fluids is developed.Due to the comprehensive resolution of fluid thermodynamics,the proposed solution framework is suitable for all forms of the two-parameter equation of state(EoS).The pressure splitting method is introduced to enable parallel calculation of RPs across multiple grid points.Theoretical analysis demonstrates the isentropic nature of weak waves in two-parameter fluids,ensuring that the same mathematical properties as ideal gas could be applied in Newton's iteration.A series of numerical cases validate the effectiveness of the proposed method.A comparative analysis is conducted on the exact Riemann solutions for the real fluid EoS,the ideal gas EoS,and the improved ideal gas EoS under supercritical and transcritical conditions.The results indicate that the improved one produces smaller errors in the calculation of momentum and energy fluxes.
基金Supported by the Natural Science Foundation of Sichuan Province(No.2023NSFSC0065)。
文摘In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.
文摘In the references[4,11,12],the authors gave some modular forms overΓ^(0)(2).In this note,we proceed with the study of cancellation formulas relating to the modular forms.
基金Supported by Natural Science Foundation-funded Project:the Study on the Mechanism of Soufeng Yuchuan Formula in Regulating Airway Remodeling in Asthmatic Rats Based on Epithelial-Mesenchymal Transition(No. 82174438)。
文摘OBJECTIVE: To explore whether Soufeng Yuchuan(搜风愈喘, SFYC) formula alleviates asthma by promoting ferroptosis of airway epithelial cells. METHODS: A chronic asthma rat model was established using ovalbumin(OVA) combined with aluminum hydroxide sensitization and OVA nebulization stimulation. Lung tissue pathology was assessed via hematoxylin and eosin staining and periodic acid-Schiff staining. Lung tissue ultrastructure was observed using transmission electron microscopy. Serum cytokine levels were measured by enzyme-linked immunosorbent assay. Malondialdehyde(MDA), glutathione, and tissue ferrous ion content in rat lung tissues and cells were detected using commercial kits. Immunohistochemical staining was used to determine the expression levels of interleukin-13(IL-13) and interleukin-6(IL-6) in lung tissue. Western blotting was employed to detect the expression levels of transferrin receptor 1(TFR1), transferrin receptor 2(TFR2), acyl-Co A synthetase longchain family member 4(ACSL4), glutathione peroxidase 4(GPX4), and solute carrier family 7 member 11(SLC7A11). Cell proliferation, apoptosis and reactive oxygen species(ROS) were evaluated using a cell counting kit-8 assay and flow cytometry. Intracellular lipid peroxidation was detected using a C11-BODIPY 581/591(C11-BODIPY) probe. RESULTS: SFYC formula effectively alleviates airway inflammation in asthmatic rats in a dose-dependent manner. It improves airway epithelial cell integrity, reduces alveolar wall thickening and expansion, inhibits goblet cell proliferation and mucus secretion, and decreases the expression of IL-6 and IL-13 in lung tissue, as well as the serum levels of IL-6, IL-13, interleukin-4(IL-4), and immunoglobulin E(Ig E). SFYC formula mitigates ferroptosis in lung tissue of asthmatic rats. At the cellular level, it promotes proliferation of rat airway epithelial cells, inhibits cell apoptosis, suppresses ROS, MDA, and lipid accumulation, reduces the expression of TFR1, TFR2, and ASCL4, and increases the expression of GPX4 and SLC7A11 to mitigate ferroptosis. CONCLUSION: SFYC formula alleviates asthma airway inflammation by inhibiting ferroptosis in airway epithelial cells, providing new insights and potential therapeutic targets for the development of new asthma treatment drugs.
基金the financial support by the National Natural Science Foundation of China(No.U2202255)the Hunan Provincial Natural Science Foundation of China(No.2024JJ2076)the Key Research and Development Program of Ningbo,China(No.2023Z092)。
文摘A Cu-1.9Ni-1.9Co-0.9Si(mass fraction,%)alloy with high strength and electrical conductivity was designed by cluster formula approach.The microstructure evolution of the alloy during thermomechanical treatment was systematically investigated.The strengthening mechanism and electrical conductivity of the alloy were discussed in detail.The optimal thermomechanical treatment process was as follows:solid solution→80%cold rolling→(450℃,4 h)aging→50%cold rolling→(400℃,4 h)aging.The designed alloy achieved excellent comprehensive properties with a microhardness of HV 260,a yield strength of 843 MPa,a tensile strength of 884 MPa,and an electrical conductivity of 42.6%(IACS).Compared to direct aging treatment,the designed alloy subjected to multi-stage thermomechanical treatment had refined grains,high density of dislocations,and accelerated of precipitation of(Ni,Co)_(2)Si precipitates.High strength was mainly attributed to the combined effect of dislocation strengthening,work hardening and sub-grain strengthening,while good electrical conductivity was maintained through the precipitation of the large number of nanoparticles.
基金supported by Yunnan Provincial Major Science and Technology Special Program(No.202402AA310035)Yunnan Key Laboratory of Dai and Yi Medicines(Yunnan University of Chinese Medicine)(No.2024JS2404)Research Foundation of Chuxiong Medical College(No.2024YYXM38).
文摘Background:Hua-Yi-Jie-Du formula(HYJD)is a traditional Chinese medicine that has proven effective against viral pneumonia and was extensively used during the COVID-19 pandemic.This study investigates how HYJD influences group 2 innate lymphoid cell(ILC2)and nucleotide oligomerization domain(NOD)-like receptor protein 3(NLRP3)inflammasome activation in a mouse model of viral pneumonia.Methods:A mouse model of viral pneumonia was established through the administration of polyinosinic-polycytidylic acid(poly(I:C))via nasal drops.Histopathological analysis of lung tissue was conducted,alongside enzyme-linked immunosorbent assay to quantify cytokine levels in serum and bronchoalveolar lavage fluid(BALF).Flow cytometry was employed to detect ILC2 cells in lung tissue and spleen,while immunofluorescence techniques were utilized to visualize ILC2 cells in lung tissue.Transcriptomic sequencing was performed,and the results were validated using qRT-PCR and western blot analysis.Results:HYJD significantly ameliorated inflammatory infiltration in lung tissue,decreased mucus protein secretion,and reduced the serum levels of inflammatory cytokines interleukin(IL)-1β,IL-6,and tumor necrosis factor-alpha(TNF-α).Additionally,it lowered the expression of cytokines IL-4,IL-5,IL-13,IL-25,thymic stromal lymphopoietin(TSLP),and IL-33 in BALF,and reduced the differentiation of ILC2 cells in both lung tissue and spleen.Transcriptomic analysis and experimental validation revealed that HYJD downregulated the expression of NLRP3 related genes and proteins within the NOD-like receptor signaling pathway.Conclusion:The mechanism by which HYJD intervenes in acute lung injury associated with viral pneumonia may involve the reduction of ILC2 cells differentiation and the inhibition of NLRP3 activation.
基金supported by the National Natural Science Foundation of China(Nos.82430116 and 82574622)the Special Fund of Central Committee High Level Chinese Medicine Hospital(Nos.DZMG-LJRC-0014,DZMG-ZJXY-23013)+1 种基金Chinese Medicine Inheritance and Innovation“Thousand Million”Talents Project(Qihuang Project 2021)Qihuang Scholarsthe Medical and Health Industry Development Project of Tongzhou District(2023).
文摘Chronic heart failure(CHF)impairs cognitive function.Xijiaqi Formula(XJQ),a traditional Chinese medicine(TCM)used clinically to treat CHF,demonstrates potential for improving cognition in CHF patients.However,its precise mechanism in treating post-CHF cognitive dysfunction remains unclear.This study systematically investigates XJQ’s effects on post-CHF cognitive dysfunction and the underlying mechanisms.The components of XJQ were identified through liquid chromatography-mass spectrometry.CHF was induced in rats via ligation of the left anterior descending coronary artery,followed by six weeks of XJQ treatment.Cardiac function was evaluated through echocardiography and hemodynamic parameters,while cognitive function was assessed using Morris water maze(MWM)and open field tests(OFT).XJQ treatment enhanced both cardiac and cognitive functions in CHF rats.Network pharmacology identified 12 core active components of XJQ and indicated its effect on cognitive dysfunction involved regulating synapses,inflammation,and phosphodiesterase 4(PDE4)-dependent cyclic adenosine monophosphate(cAMP)signaling.XJQ inhibited microglial and astrocyte activation,decreased proinflammatory cytokines,and mitigated neuronal damage.Notably,XJQ promoted synaptic repair and dendritic growth by downregulating PDE4 and upregulating cAMP,protein kinase A(PKA),cAMP-response element binding protein(CREB),brain-derived neurotrophic factor(BDNF),PSD95,and synapsin I levels.Molecular docking and Bio-layer interferometry assays confirmed direct binding of quercetin,kaempferol,isorhamnetin,and darutoside to PDE4.In conclusion,XJQ alleviates neuroinflammation and enhances synaptic plasticity to improve cognitive dysfunction in CHF rats via the PDE4/cAMP/PKA/CREB signaling pathway.These findings provide valuable insight into the heart-brain axis.
文摘BACKGROUND Perimenopausal women are prone to anxiety and depression due to fluctuating hormone levels,which significantly impair their quality of life.The current treatments have certain limitations.In traditional Chinese medicine,liver-soothing formulas are commonly prescribed for mood-related disorders,but their overall efficacy in perimenopausal anxiety and depression remains uncertain and requires verification through meta-analysis.AIM To provide evidence-based support for clinical decision-making and research,a meta-analysis was conducted to evaluate the effectiveness of liver-soothing formulas in treating perimenopausal anxiety and depression.METHODS Relevant studies published up to April 2025 were retrieved from ClinicalTrials.gov,PubMed,Web of Science,EMBASE,and the Cochrane Library.Eligible studies were screened according to predefined inclusion and exclusion criteria.Data were extracted and analyzed using the Stata 12.0 software.RESULTS After searching and screening,12 articles involving 1798 patients(922 in the treatment group and 876 in the control group)were included in the analysis.Meta-analysis showed that the standardized scores for anxiety[standardized mean difference(SMD)=-0.71,95%confidence interval(95%CI):-1.06 to-0.36]and depression(SMD=-0.67,95%CI:-1.06 to-0.27)of the treatment group were lower than those of the control group.Subgroup analysis results revealed that for anxiety,liver-soothing formulas used alone(SMD=-0.34,95%CI:-0.50 to-0.18)or in combination(SMD=-0.88,95%CI:-1.43 to-0.34)both significantly reduced scores compared with the control group.For depression,monotherapy of liversoothing formulas showed no significant statistical difference between the treatment and control groups(SMD=-0.47,95%CI:-1.11 to 0.17),whereas combination therapy produced significantly lower standardized scale scores in the treatment group than in the control group,with a statistically significant difference(SMD=-0.83,95%CI:-1.39 to-0.28).Regarding Greene scores,no statistically significant difference was observed with monotherapy(SMD=0.87,95%CI:-0.32 to 2.06),whereas combination therapy had significantly lower Greene scores(SMD=-0.24,95%CI:-0.44 to-0.04).No statistically significant difference was found between the groups in the occurrence of adverse reactions(odds ratio=0.90,95%CI:0.57-1.43).However,liver-soothing formulas did not affect estrogen levels in perimenopausal women.CONCLUSION Compared with placebo,conventional Western medicine,or other interventions,the monotherapy of liver-soothing formulas demonstrates superior efficacy in treating perimenopausal anxiety.When used as an adjuvant,they exert a synergistic effect in alleviating negative emotions and improving overall perimenopausal symptoms.
基金supported by the National Key Research and Development Program of China(2021YFD2100700).
文摘Triacylglycerol(TAG)components in human milk,infant formulas with different fat sources,and plant oils(palm oil,flaxseed oil,sunflower oil,corn oil,soybean oil,coconut oil,low erucic acid rapeseed oil,and high oleic acid rapeseed oil)were analyzed and compared using ultraperformance supercritical fluid chromatography coupled with quadrupole time-of-flight mass spectrometry(UPSFC-Q-TOF-MS).Distinct TAG profiles were identified by lipidomics,principal component analysis(PCA),and heatmap visualization.Human milk was characterized by a high abundance of medium-and long-chain triacylglycerols(MLCTs),saturated-unsaturated-unsaturated(SUU)-type TAGs(sn-2 palmitic acid).In contrast,plant oils lacked MLCTs and SUU-type TAGs,containing mainly TAGs esterified long-chain polyunsaturated fatty acid.Breast milk contains about 27%MLCT,about 50%SUU-type triacylglycerols(which contain about 34%UPU-type triacylglycerols),which is significantly different from plant oils,structured fats and infant formulas.These findings provide a clear basis for optimizing the fat blend in infant formula to better mimic the unique TAG profile of human milk,thereby improving energy delivery and nutrient absorption for infants.
基金Supported by National Famous and Senior Chinese Medicine Expert Heritage Studio Construction Project:Zhi Nan Heritage Studio(No.75[2022])Beijing Municipal Key Traditional Chinese Medicine Specialty Development Project during the 14th Five-Year Plan Period(No.BJZKBC0029)。
文摘OBJECTIVE:To investigate the pharmacological effects and underlying mechanisms of Pinggan Yuyin Qingre formula(平肝育阴清热方,PGYYQR)in the treatment of meibomian gland dysfunction(MGD)through network pharmacology and in vivo validation.METHODS:A mouse model of MGD was induced using the stearoyl-coenzyme a desaturase 1 inhibitor,followed by PGYYQR treatment for 2 weeks.MGD sign scoring,hematoxylin and eosin(HE)staining,oil red o(ORO)staining,and serum inflammatory cytokine analysis were conducted to assess the effects of PGYYQR on meibomian gland(MG)function,histopathology,and associated inflammation.Network pharmacology was employed to identify the active compounds and potential targets of PGYYQR.Molecular mechanisms were further investigated using Western blotting,reverse transcription quantitative real-time polymerase chain reaction,and reactive oxygen species(ROS)assays.RESULTS:PGYYQR treatment significantly reduced the scores of MG orifice obstruction and meibum quality in MGD mice.HE and ORO staining further demonstrated that PGYYQR ameliorated glandular damage and lipid dysfunction.Enzyme-linked immunosorbent assay results revealed that PGYYQR markedly decreased the serum levels of key inflammatory cytokines,including interleukin(IL)-1β,IL-6,and tumor necrosis factor-α.Network pharmacology identified 162 active compounds and 598 target genes in PGYYQR.Among these,IL-6,IL-1β,matrix metalloproteinase-9,and C-X-C motif chemokine ligand 8 were recognized as core targets related to MGD and were mainly enriched in the IL-17/nuclear factor kappa B(NF-κB)signaling pathway.Further molecular analyses confirmed that PGYYQR significantly inhibited the IL-17/NF-κB axis by downregulating IL-17 expression and reducing phosphorylated NF-κB p65 levels at both the protein and m RNA levels in MG tissues.PGYYQR also effectively reduced ROS levels in the conjunctival tissues of MGD mice.CONCLUSION:PGYYQR effectively improves MG function and preserves local tissue morphology in MGD model mice,primarily by suppressing the inflammatory response through coordinated modulation of the IL-17/NF-κB signaling pathway and oxidative stress.
基金Supported by Natural Science Foundation of Fujian Province Project:To Investigate the Mechanism of Lianshi Jianpi Formula In Improving Impaired Glucose Tolerance via the Fibroblast Growth Factor 21-Mediated Adenosine 5‘-monophosphate-Activated Protein Kinases Energy Metabolism Pathway(No. 2023J01841)ZHOU Guoying Fujian Province Famous Traditional Chinese Medicine Inheritance Workstation Construction Project(Min Zhong Yi[2023] No. 56)。
文摘OBJECTIVE:To explore the bioactive constituents,key targets,signalling pathways,and molecular mechanisms of Lianshi Jianpi formula(莲实健脾方,LSJPF)in the treatment of impaired glucose tolerance(IGT)through network pharmacology,molecular docking,and in vivo experiments.METHODS:The active ingredients and targets of LSJPF were identified using the Traditional Chinese Medicine Systems Pharmacology and HERB databases,whereas the IGT-related targets were sourced from Gene Cards,Dis Ge NET,and Pub Med.The overlap analysis identified potential targets of LSJPF.Protein-protein interaction networks and core targets were evaluated using the Search Tool for the Retrieval of Interacting Genes/Proteins and Cytoscape,and molecular docking confirmed the binding affinities.Gene Ontology and Kyoto Encyclopedia of Genes and Genomes pathway enrichment analyses were performed using Metascape.The therapeutic mechanisms were validated in an animal IGT model.RESULTS:LSJPF contained 229 compounds,with 15 active compounds and 77 potential target proteins.The phosphatidylinositol-3-kinase(PI3K)-protein kinase B(AKT)signalling pathway emerged as a key IGT pathway.The KEGG enrichment analysis revealed the pivotal genes RAC-alpha serine/threonine-protein kinase(AKT1),heat shock protein 90 k Da alpha B1,and B-cell lymphoma 2 family protein,which predominantly interact with beta-sitosterol and beta-carotene,the major constituents of Semen Euryales,Semen lablab Album,Semen sojae Atricolor in LSJPF.Molecular docking revealed strong binding affinities between LSJPF and IGT-related targets.In an animal IGT model,LSJPF treatment prevented weight loss;reduced food and water intake;decreased blood glucose levels;improved insulin resistance;decreased serum triglyceride,cholesterol,and low-density lipoprotein cholesterol levels;alleviated liver pathology;and significantly increased the levels of phosphorylated adenosine 5'-monophosphate-activated protein kinase(AMPK),PI3K,and AKT,suggesting its potential role in regulating glucose and lipid metabolism.CONCLUSIONS:These findings reveal the potential of LSJPF as an IGT intervention that targets the AMPK/PI3K/AKT cascade,validating network pharmacology predictions and highlighting the role of multipathway mechanisms in metabolic diseases.
基金supported by the Important National Science&Technology Specific Projects(No.2011ZX05019-003)the New Method and Technology Research Project of Geophysical Exploration of CNPC(No.2014A-3612)
文摘Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
文摘The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.
文摘<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
文摘The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.
