The neutrophil–osteogenic cell axis promotes bone destruction in periodontitis

The immune-stromal cell interactions play a key role in health and diseases. In periodontitis, the most prevalent infectious disease in humans, immune cells accumulate in the oral mucosa and promote bone destruction by inducing receptor activator of nuclear factor-κB ligand (RANKL) expression in osteogenic cells such as osteoblasts and periodontal ligament cells. However, the detailed mechanism underlying immune–bone cell interactions in periodontitis is not fully understood. Here, we performed single-cell RNAsequencing analysis on mouse periodontal lesions and showed that neutrophil–osteogenic cell crosstalk is involved in periodontitis-induced bone loss. The periodontal lesions displayed marked infiltration of neutrophils, and in silico analyses suggested that the neutrophils interacted with osteogenic cells through cytokine production. Among the cytokines expressed in the periodontal neutrophils, oncostatin M (OSM) potently induced RANKL expression in the primary osteoblasts, and deletion of the OSM receptor in osteogenic cells significantly ameliorated periodontitis-induced bone loss. Epigenomic data analyses identified the OSM-regulated RANKL enhancer region in osteogenic cells, and mice lacking this enhancer showed decreased periodontal bone loss while maintaining physiological bone metabolism. These findings shed light on the role of neutrophils in bone regulation during bacterial infection, highlighting the novel mechanism underlying osteoimmune crosstalk.

Tuning Second Chern Number in a Four-Dimensional Topological Insulator by High-Frequency Time-Periodic Driving

Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions.We investigate the effects of high-frequency time-periodic driving in a four-dimensional(4D)topological insulator,focusing on topological phase transitions at the off-resonant quasienergy gap.The 4D topological insulator hosts gapless three-dimensional boundary states,characterized by the second Chern number C_(2).We demonstrate that the second Chern number of 4D topological insulators can be modulated by tuning the amplitude of time-periodic driving.This includes transitions from a topological phase with C_(2)=±3 to another topological phase with C_(2)=±1,or to a topological phase with an even second Chern number C_(2)=±2,which is absent in the 4D static system.Finally,the approximation theory in the high-frequency limit further confirms the numerical conclusions.

Repeated inoculation with rumen fluid accelerates the rumen bacterial transition with no benefit on production performance in postpartum Holstein dairy cows

Background The dairy cow’s postpartum period is characterized by dramatic physiological changes,therefore imposing severe challenges on the animal for maintaining health and milk output.The dynamics of the ruminal microbiota are also tremendous and may play a crucial role in lactation launch.We aim to investigate the potential benefits of early microbial intervention by fresh rumen microbiota transplantation(RMT)and sterile RMT in postpartum dairy cows.Twelve fistulated peak-lactation dairy cows were selected to be the donors for rumen fluid collection.Thirty postpartum cows were divided into 3 groups as the transplantation receptors respectively receiving 10 L fresh rumen fluid(FR),10 L sterile rumen fluid(SR),or 10 L saline(CON)during 3 d after calving.Results Production performance,plasma indices,plasma lipidome,ruminal microbiome,and liver transcriptome were recorded.After fresh and sterile RMT,we found that the molar proportion of propionic acid was increased on d 7 in the FR and SR groups and the bacterial composition was also significantly changed when compared with the CON group.A similarity analysis showed that the similarities between the CON group and FR or SR group on d 7 were 48.40%or 47.85%,whereas the similarities between microbiota on d 7 and 21 in the FR and SR groups were 68.34%or 66.85%.Dry matter intake and feed efficiency were not affected by treatments.Plasmaβ-hydroxybutyrate concentration in the FR group was decreased and significantly different lipids mainly included phosphatidylcholine and lysophosphatidylcholine containing polyunsaturated fatty acids.Hepatic transcriptomics analysis indicated acutephase response pathways were upregulated in the SR group.Conclusions Our study suggests that RMT can shorten the transition process of the ruminal microbiota of postpartum dairy cows with no benefit on dry matter intake or feed efficiency.Inoculation with rumen fluid may not be a useful approach to promote the recovery of postpartum dairy cows.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

Preweaning period is a critical window for rumen microbial regulation of average daily gain in Holstein heifer calves

Background Rumen bacterial groups can affect growth performance,such as average daily gain(ADG),feed intake,and efficiency.The study aimed to investigate the inter-relationship of rumen bacterial composition,rumen fermentation indicators,serum indicators,and growth performance of Holstein heifer calves with different ADG.Twelve calves were chosen from a trail with 60 calves and divided into higher ADG(HADG,high pre-and post-weaning ADG,n=6)and lower ADG(LADG,low pre-and post-weaning ADG,n=6)groups to investigate differences in bacterial composition and functions and host phenotype.Results During the preweaning period,the relative abundances of propionate producers,including g_norank_f_Butyricicoccaceae,g_Pyramidobacter,and g_norank_f_norank_o_Clostridia_vadin BB60_group,were higher in HADG calves(LDA>2,P<0.05).Enrichment of these bacteria resulted in increased levels of propionate,a gluconeogenic precursor,in preweaning HADG calves(adjusted P<0.05),which consequently raised serum glucose concentrations(adjusted P<0.05).In contrast,the relative abundances of rumen bacteria in post-weaning HADG calves did not exert this effect.Moreover,no significant differences were observed in rumen fermentation parameters and serum indices between the two groups.Conclusions The findings of this study revealed that the preweaning period is the window of opportunity for rumen bacteria to regulate the ADG of calves.

Effects of drive imbalance on the particle emission from a Bose-Einstein condensate in a one-dimensional lattice

Time-periodic driving has been an effective tool in the field of nonequilibrium quantum dynamics,which enables precise control of the particle interactions.We investigate the collective emission of particles from a Bose-Einstein condensate in a one-dimensional lattice with periodic drives that are separate in modulation amplitudes and relative phases.In addition to the enhancement of particle emission,we find that amplitude imbalances lead to energy shift and band broadening,while typical relative phases may give rise to similar gaps.These results offer insights into the specific manipulations of nonequilibrium quantum systems with tone-varying drives.

Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations

In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Shear resistance characteristics and influencing factors of root-soil composite on an alpine metal mine dump slope with different recovery periods

Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the Qinghai-Tibet Plateau,China.However,there are few reports on the dynamic changes and the influencing factors of the soil reinforcement effect of plant species after artificial vegetation restoration under different recovery periods.We selected dump areas of the Delni Copper Mine in Qinghai Province,China to study the relationship between the shear strength and the peak displacement of the root-soil composite on the slope during the recovery period,and the influence of the root traits and soil physical properties on the shear resistance characteristics of the root-soil composite via in situ direct shear tests.The results indicate that the shear strength and peak displacement of the rooted soil initially decreased and then increased with the increase of the recovery period.The shear strength of the rooted soil and the recovery period exhibited a quadratic function relationship.There is no significant function relationship between the peak displacement and the recovery period.Significant positive correlations(P<0.05)exists between the shear strength of the root-soil composite and the root biomass density,root volume density,and root area ratio,and they show significant linear correlations(P<0.05).There are no significant correlations(P>0.05)between the shear strength of the root-soil composite and the root length density,and the root volume ratio of the coarse roots to the fine roots.A significant negative linear correlation(P<0.05)exists between the peak displacement of the rooted soil and the coarse-grain content,but no significant correlations(P>0.05)with the root traits,other soil physical property indices(the moisture content and dry density of the soil),and slope gradient.The coarse-grain content is the main factor controlling the peak displacement of the rooted soil.

Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Impact of Alcian blue and periodic acid Schiff expression on the prognosis of gastric signet ring cell carcinoma

BACKGROUND The Alcian blue(AB)and periodic acid Schiff(PAS)stains are representative mucus markers in gastric signet ring cell carcinoma(SRCC).They are low-cost special staining methods used to detect acidic mucus and neutral mucus,respectively.However,the clinical importance of the special combined AB and PAS stain is unclear.AIM To investigate AB expression,PAS expression and the AB-to-PAS(A/P)ratio in gastric SRCC patients and to assess patient prognosis.METHODS Paraffin-embedded sections from 83 patients with gastric SRCC were stained with AB and PAS,and signet ring cell positivity was assessed quantitatively.Immuno-histochemical staining for Ki67,protein 53(P53)and human epidermal growth factor receptor 2(HER2)was performed simultaneously.The cancer-specific survival(CSS)rate was estimated via Kaplan-Meier analysis.Cox proportional hazards models were used for univariate and multivariate survival analyses.RESULTS Kaplan-Meier survival analysis revealed that the 3-year CSS rate was significantly greater in the high-PAS-expression subgroup than in the low-PAS-expression subgroup(P<0.001).The 3-year CSS rate in the A/P≤0.5 group was significantly greater than that in the A/P>0.5 group(P=0.042).Univariate Cox regression analysis revealed that the factors affecting prognosis included tumor diameter,lymph node metastasis,vessel carcinoma embolus,tumor stage,the A/P ratio and the expression of Ki67,P53 and the PAS.Cox multivariate regression analysis confirmed that low PAS expression[hazard ratio(HR)=3.809,95%confidence interval(CI):1.563-9.283,P=0.003]and large tumor diameter(HR=2.761,95%CI:1.086-7.020,P=0.033)were independent risk factors for poor prognosis.CONCLUSION A/P>0.5 is potentially a risk factor for prognosis,and low PAS expression is an independent risk factor in the prognosis of gastric SRCC.PAS expression and the A/P ratio could help in predicting the clinical prognosis of patients with SRCC.

DNBP-CCA:A Novel Approach to Enhancing Heterogeneous Data Traffic and Reliable Data Transmission for Body Area Network

The increased adoption of Internet of Medical Things (IoMT) technologies has resulted in the widespread use ofBody Area Networks (BANs) in medical and non-medical domains. However, the performance of IEEE 802.15.4-based BANs is impacted by challenges related to heterogeneous data traffic requirements among nodes, includingcontention during finite backoff periods, association delays, and traffic channel access through clear channelassessment (CCA) algorithms. These challenges lead to increased packet collisions, queuing delays, retransmissions,and the neglect of critical traffic, thereby hindering performance indicators such as throughput, packet deliveryratio, packet drop rate, and packet delay. Therefore, we propose Dynamic Next Backoff Period and Clear ChannelAssessment (DNBP-CCA) schemes to address these issues. The DNBP-CCA schemes leverage a combination ofthe Dynamic Next Backoff Period (DNBP) scheme and the Dynamic Next Clear Channel Assessment (DNCCA)scheme. The DNBP scheme employs a fuzzy Takagi, Sugeno, and Kang (TSK) model’s inference system toquantitatively analyze backoff exponent, channel clearance, collision ratio, and data rate as input parameters. Onthe other hand, the DNCCA scheme dynamically adapts the CCA process based on requested data transmission tothe coordinator, considering input parameters such as buffer status ratio and acknowledgement ratio. As a result,simulations demonstrate that our proposed schemes are better than some existing representative approaches andenhance data transmission, reduce node collisions, improve average throughput, and packet delivery ratio, anddecrease average packet drop rate and packet delay.

Postpartum depression and partner support during the period of lactation:Correlation research and its influencing factors

BACKGROUND Postpartum depression(PPD)not only affects the psychological and physiological aspects of maternal health but can also affect neonatal growth and development.Partners who are in close contact with parturient women play a key role in communication and emotional support.This study explores the PPD support relationship with partners and its influencing factors,which is believed to establish psychological well-being and improve maternal partner support.AIM To explore the correlation between PPD and partner support during breastfeeding and its influencing factors.METHODS Convenience sampling was used to select lactating women(200 women)who underwent postpartum examinations at the Huzhou Maternity and Child Health Care Hospital from July 2022 to December 2022.A cross-sectional survey was conducted on the basic information(general information questionnaire),depression level[edinburgh postnatal depression scale(EPDS)],and partner support score[dyadic coping inventory(DCI)]of the selected subjects.Pearson’s correlation analysis was used to analyze the correlation between PPD and DCI in lactating women.Factors affecting PPD levels during lactation were analyzed using multiple linear regression.RESULTS The total average score of EPDS in 200 lactating women was(9.52±1.53),and the total average score of DCI was(115.78±14.90).Dividing the EPDS,the dimension scores were:emotional loss(1.91±0.52),anxiety(3.84±1.05),and depression(3.76±0.96).Each dimension of the DCI was subdivided into:Pressure communication(26.79±6.71),mutual support(39.76±9.63),negative support(24.97±6.68),agent support(6.87±1.92),and joint support(17.39±4.19).Pearson’s correlation analysis demonstrated that the total mean score and individual dimension scores of EPDS during breastfeeding were inversely correlated with the total score of partner support,stress communication,mutual support,and cosupport(P<0.05).The total mean score of the EPDS and its dimensions were positively correlated with negative support(P<0.05).Multiple linear regression analysis showed that the main factors affecting PPD during breastfeeding were marital harmony,newborn health,stress communication,mutual support,negative support,cosupport,and the total score of partner support(P<0.05).CONCLUSION PPD during breastfeeding was associated with marital harmony,newborn health,stress communication,mutual support,negative support,joint support,and the total DCI score.

A Brief Introduction to the English Periodical of Contemporary Social Sciences

The English periodical of Contemporary Social Sciences is an English periodical founded by Sichuan Academy of Social Sciences and is published every two months.It was approved by the National Radio and Television Administration of the People’s Republic of China(formerly the State Administration of Press,Publication,Radio,Film and Television of the People’s Republic of China)in March 2016.

Ultrafast dynamics of femtosecond laser-induced high spatial frequency periodic structures on silicon surfaces

Femtosecond laser-induced periodic surface structures(LIPSS)have been extensively studied over the past few decades.In particular,the period and groove width of high-spatial-frequency LIPSS(HSFL)is much smaller than the diffraction limit,making it a useful method for efficient nanomanufacturing.However,compared with the low-spatial-frequency LIPSS(LSFL),the structure size of the HSFL is smaller,and it is more easily submerged.Therefore,the formation mechanism of HSFL is complex and has always been a research hotspot in this field.In this study,regular LSFL with a period of 760 nm was fabricated in advance on a silicon surface with two-beam interference using an 800 nm,50 fs femtosecond laser.The ultrafast dynamics of HSFL formation on the silicon surface of prefabricated LSFL under single femtosecond laser pulse irradiation were observed and analyzed for the first time using collinear pump-probe imaging method.In general,the evolution of the surface structure undergoes five sequential stages:the LSFL begins to split,becomes uniform HSFL,degenerates into an irregular LSFL,undergoes secondary splitting into a weakly uniform HSFL,and evolves into an irregular LSFL or is submerged.The results indicate that the local enhancement of the submerged nanocavity,or the nanoplasma,in the prefabricated LSFL ridge led to the splitting of the LSFL,and the thermodynamic effect drove the homogenization of the splitting LSFL,which evolved into HSFL.

Hepatic and renal effects of oral stingless bee honey in a streptozotocin-induced diabetic rat model

BACKGROUND Diabetes is known damage the liver and kidney,leading to hepatic dysfunction and kidney failure.Honey is believed to help in lowering the blood glucose levels of diabetic patients and reducing diabetic complications.However,the effect of stingless bee honey(SBH)administration in relieving liver and kidney damage in diabetes has not been well-studied.AIM To investigate the effect of SBH administration on the kidney and liver of streptozotocin-induced(STZ;55 mg/kg)diabetic Sprague Dawley rats.METHODS The rats were grouped as follows(n=6 per group):non-diabetic(ND),untreated diabetic(UNT),metformin-treated(MET),and SBH+metformin-treated(SBME)groups.After successful diabetic induction,ND and UNT rats were given normal saline,whereas the treatment groups received SBH(2.0 g/kg and/or metformin(250 mg/kg)for 12 d.Serum biochemical parameters and histological changes using hematoxylin and eosin(H&E)and periodic acid–Schiff(PAS)staining were evaluated.RESULTS On H&E and PAS staining,the ND group showed normal architecture and cellularity of Bowman’s capsule and tubules,whereas the UNT and MET groups had an increased glomerular cellularity and thickened basement membrane.The SBH-treated group showed a decrease in hydropic changes and mild cellularity of the glomerulus vs the ND group based on H&E staining,but the two were similar on PAS staining.Likewise,the SBME-treated group had an increase in cellularity of the glomerulus on H&E staining,but it was comparable to the SBH and ND groups on PAS staining.UNT diabetic rats had tubular hydropic tubules,which were smaller than other groups.Reduced fatty vacuole formation and dilated blood sinusoids in liver tissue were seen in the SBH group.Conversely,the UNT group had high glucose levels,which subsequently increased MDA levels,ultimately leading to liver damage.SBH treatment reduced this damage,as evidenced by having the lowest fasting glucose,serum alanine transaminase,aspartate transaminase,and alkaline phosphatase levels compared to other groups,although the levels of liver enzymes were not statistically significant.CONCLUSION The cellularity of the Bowman’s capsule,as well as histological alteration of kidney tubules,glomerular membranes,and liver tissues in diabetic rats after oral SBH resembled those of ND rats.Therefore,SBH exhibited a protective hepatorenal effect in a diabetic rat model.

Practice of Perioperative Rational Use of Antibacterial Drugs Based on Drug Pathway

[Objectives]To establish a new management model for rational use of perioperative antibacterial drugs in surgical departments.[Methods]Based on evidence-based medicine,the department s drug pathway was formulated,and the new mode of rational drug use control was established by using fine pharmaceutical technology intervention,and the intervention effect was evaluated by the intensity of antibacterial drug use,per capita drug costs and the proportion of drugs.[Results]After adopting drug pathway in departments,the intensity of antibacterial drug use,per capita drug costs and the proportion of drugs decreased significantly,and the effect of rational drug use control was remarkable.[Conclusions]The drug pathway provides a new management and control mode for the rational use of perioperative antibacterial drugs in surgical departments of hospitals.Thus,it is worthy of popularization and application.

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

This article gives a general model using specific periodic special functions, which is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS) at the centers of cells of the 3-Torus. Satisfying a divergence-free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term which is smooth and spatially periodic, the existence of solutions which have finite time singularities can occur starting with the first derivative and higher with respect to time. The existence of a subspace of the solution space where v3 is continuous and {C, y1, y12}, is linearly independent in the additive argument of the solution in terms of the Lambert W function, (y12=y2, C∈R) together with the condition v2=-2y1v1. On this subspace, the Biot Savart Law holds exactly [see Section 2 (Equation (13))]. Also on this subspace, an expression X (part of PNS equations) vanishes which contains all the expressions in derivatives of v1 and v2 and the forcing terms in the plane which are related as with the cancellation of all such terms in governing PDE. The y3 component forcing term is arbitrarily small in ε ball where Weierstrass P functions touch the center of the ball both for inviscid and viscous cases. As a result, a significant simplification occurs with a v3 only governing PDE resulting. With viscosity present as v changes from zero to the fully viscous case at v =1 the solution for v3 reaches a peak in the third component y3. Consequently, there exists a dipole which is not centered at the center of the cell of the Lattice. Hence since the dipole by definition has an equal in magnitude positive and negative peak in y3, then the dipole Riemann cut-off surface is covered by a closed surface which is the sphere and where a given cell of dimensions [-1, 1]3 is circumscribed on a sphere of radius 1. For such a closed surface containing a dipole it necessarily follows that the flux at the surface of the sphere of v3 wrt to surface normal n is zero including at the points where the surface of sphere touches the cube walls. At the finite time singularity on the sphere a rotation boundary condition is deduced. It is shown that v3 is spatially finite on the Riemann Sphere and the forcing is oscillatory in y3 component if the velocity v3 is. It is true that . A boundary condition on the sphere shows the rotation of a sphere of viscous fluid. Finally on the sphere a solution for v3 is obtained which is proven to be Hölder continuous and it is shown that it is possible to extend Hölder continuity on the sphere uniquely to all of the interior of the ball.

The Resilience and Flexibility of Asia-Pacific Regional Economic Cooperation in the Period of Worldwide Turbulent Changes

The world today is undergoing a new period of turbulent changes,with the post-war trade and economic system dominated by neo-liberalism facing complex challenges.The political and economic landscape of the Asia-Pacific region also fluctuates from time to time due to various factors.Meanwhile,the willingness of Asia-Pacific countries to promote regional economic cooperation remains strong,as the experience and lessons of"prosperity for all,loss for all"learned over the past few decades of development have convinced countries that continued strengthening of regional cooperation is the only right choice to ensure sustainable economic growth for their own countries.