The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

基于UHPLC-Q-Exactive Orbitrap HRMS技术结合化学计量学方法的不同干燥处理杜仲叶成分分析

采用基于液质联用的非靶向代谢组学技术结合化学计量学数据自动解析软件AntDAS-LCHRMS分析了4种不同干燥处理(冻干、热泵烘干、电热烘干、晒干)杜仲叶样本中的化合物。杜仲叶样本数据由超高效液相色谱-四极杆-静电场轨道阱高分辨质谱(UHPLC-Q-Exactive Orbitrap HRMS)分别在正、负离子模式下进行采集,经AntDAS-LCHRMS软件解析,共鉴定出71种差异性化合物,经标准品验证确定40种化合物,包括环烯醚萜类、有机酸类、黄酮类、氨基酸类、核苷类、维生素类等9类物质。其中,正、负离子模式下均可识别并验证的化合物有车叶草苷、绿原酸、芦丁、异槲皮苷、车叶草苷酸、京尼平苷等25种化合物。层次聚类分析(HCA)及主成分分析(PCA)结果均显示,相同处理的杜仲叶样本各自聚成一类,不同处理的杜仲叶样本可明显区分。热图分析进一步揭示了不同干燥处理杜仲叶样本中差异性化合物的含量变化。晒干处理样本中苯丙氨酸及色氨酸等氨基酸类物质的水平较高;冻干及热泵烘干处理样本中有机酸类、环烯醚萜类、糖类等含量较高;电热烘干样本中核苷类、黄酮类物质的含量较高;黄酮类物质在冻干、热泵烘干及晒干样本中差异较小。研究结果为不同干燥处理杜仲叶的成分分析、品质评价及其开发应用提供了科学依据,也可为其他复杂药用植物体系的化学成分分析提供参考。

基于UHPLC-Q-Exactive Orbitrap MS的芪龙壮儿口服液指纹图谱研究

目的:建立芪龙壮儿口服液UHPLC-Q-Exactive Orbitrap MS正、负离子两种检测模式下的指纹图谱,为该制剂的质量控制提供参考和依据。方法:采用Thermo Accucore aQ RP18(2.1 mm×150 mm,2.6μm)色谱柱进行色谱分离,加热电喷雾离子源正、负离子同时检测。根据一级准分子离子精确质荷比、二级质谱碎片离子信息、文献报道和对照品比对鉴定共有峰成分。结果:构建了芪龙壮儿口服液正、负离子模式下的指纹图谱共有模式并分别确认了24(正离子模式)和17(负离子模式)个共有指纹峰。10批芪龙壮儿口服液指纹图谱与对照指纹图谱的相似度分别大于0.986(正离子模式)和0.968(负离子模式)。在正离子模式下鉴定了15个共有峰,其中9个共有峰采用对照品确认;负离子模式下鉴定了12个共有峰,其中9个共有峰采用对照品确认。结论:所建立的芪龙壮儿口服液正、负离子两种模式下的指纹图谱,结合共有峰的高分辨质谱定性分析,从正、负两个维度较为全面地表征了该制剂的化学成分指纹特征,为芪龙壮儿口服液的质量评价提供了依据和方法。

Exact solutions of a time-fractional modified KdV equation via bifurcation analysis

The time-fractional modified Korteweg-de Vries(KdV)equation is committed to establish exact solutions by employing the bifurcation method.Firstly,the phase portraits and related qualitative analysis are comprehensively provided.Then,we give parametric expressions of different types of solutions matching with the corresponding orbits.Finally,solution profiles,3D and density plots of some solutions are presented with proper parametric choices.

参仙升脉口服液化学成分的UHPLC-Q Exactive Focus MS/MS快速分析

目的探究参仙升脉口服液的化学物质基础。方法利用超高效液相色谱-四极杆/静电场轨道阱高分辨质谱(UHPLC-Q Exactive Focus MS/MS)对参仙升脉口服液的化学成分进行整体、系统辨识。采用Thermo Accucore aQ C_(18)色谱柱(150 mm×2.1 mm,2.6μm),流动相0.1%甲酸水溶液(A)-甲醇(B)梯度洗脱,洗脱程序为0-13 min,5%-60%B;13-27 min,60%-95%B;27-30 min,95%B,流速0.3 mL·min^(-1),柱温30°C;质谱分析离子化方式为加热电喷雾离子化(H-ESI),扫描模式为正、负离子切换,扫描范围m/z 120-1800,碰撞能量30 eV、50 eV、70 eV。结果共鉴定出160个化学成分,包括29个黄酮类成分,24个有机酸类成分,21个生物碱类成分,19个萜类成分,15个苯丙素类成分,12个皂苷类成分和40个其他类成分;其中6个化学成分(芦丁、补骨脂苷、异补骨脂苷、补骨脂素、异补骨脂素和补骨脂酚)经对照品比对确认。结论该研究借助UHPLC-Q Exactive Focus MS/MS技术实现了参仙升脉口服液化学成分准确、快速、系统的分析和鉴定,为其化学物质基础的阐明和质量控制提供了重要依据。

Exact Traveling Wave Solutions to Phi-4 Equation and Joseph-Egri (TRLW) Equation and Calogro-Degasperis (CD) Equation by Modified (G'/G2)-Expansion Method

In this study, we will introduce the modified (G'/G2)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.

基于UHPLC-Q Exactive Orbitrap/MS结合多元统计方法分析不同基原淫羊藿化学成分的差异

目的:建立超高效液相色谱-四极杆-静电场轨道阱高分辨质谱联用(UHPLC-Q Exactive Orbitrap/MS)结合多元统计分析技术对5种不同基原淫羊藿化学成分差异分析的方法。方法:对5种基原30批淫羊藿样品的UHPLC-Q Exactive Orbitrap/MS全扫描数据进行多元统计分析。利用SIMCA软件进行主成分分析(PCA)和正交偏最小二乘法-判别分析(OPLS-DA)。结果:5种基原淫羊藿的化学成分具有差异性,根据相关参考文献及谱图信息,共鉴定出27种化学成分。所建立的OPLS-DA模型具有良好的数据描述能力和预测能力。柔毛淫羊藿化学成分具有显著性差异,而朝鲜淫羊藿与箭叶淫羊藿,淫羊藿与巫山淫羊藿之间的化学成分及含量具有相似性。经过筛选与分析,确定8种差异化学成分。结论:建立的方法可分析出5种基原淫羊藿化学成分的差异性,操作简便,方法准确,可为不同基原淫羊藿的质量控制及开发应用提供理论依据。

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

基于UPLC-Q-Exactive-Orbitrap-MS的胃康灵胶囊化学成分分析

目的 建立超高效液相色谱串联四极杆静电场轨道阱质谱(UPLC-Q-Exactive-OrbitrapMS)法准确、快速定性鉴别胃康灵胶囊中的化学成分。方法 采用Waters ACQUITY UPLC HSS T3 C18色谱柱(1.7μm,2.1 mm×150 mm),以0.1%甲酸水溶液(A)-乙腈(B)为流动相进行梯度洗脱,流速为0.3 mL·min^(-1),柱温40℃,进样量2μL,电喷雾电离源(ESI)在正、负离子两种模式下采集数据,扫描方式为全扫描/数据依赖二级扫描(Full MS/dd-MS~2)。结果 在胃康灵胶囊水提液中共鉴定出142个化学成分,包括三萜类58个、生物碱类32个、单萜类17个、黄酮类12个、多酚类10个、有机酸类6个,菲类3个、香豆素类1个、木脂素类1个、苯并吡喃类1个和氮苷类1个。结论 UPLC-Q-Exactive-Orbitrap-MS技术能够快速有效地对胃康灵胶囊中化学成分进行鉴定,为进一步明确其药效物质提供参考。

基于UPLC-Q-Exactive-Orbitrap-MS、网络药理学和实验验证探讨裸花紫珠抗H1N1活性成分及其作用机制

本实验首先对裸花紫珠的提取物进行萃取,得到不同的萃取部位,然后对各部位进行抗甲型流感病毒H1N1型(H1N1)活性筛选,确定裸花紫珠乙酸乙酯萃取部位(EACN)具有较好的体外抗H1N1的活性。采用超高效液相色谱-四级杆-静电场轨道阱联用(UPLC-Q-Exactive-Orbitrap-MS)技术对EACN进行定性分析。基于定性分析的结果,进一步使用数据挖掘和网络药理学,评估药物的活性成分、关键靶点和关键通路,最后使用H1N1感染BALB/c小鼠模型对预测结果进行验证。结果显示,在各个萃取部位中,乙酸乙酯部位体外抗H1N1效果最佳,半数抑制浓度(IC_(50))为51μg/mL,半数细胞毒浓度(CC_(50))为859.4μg/mL,选择指数(SI,CC_(50)/IC_(50))为16.85。从EACN中鉴定出34种化合物,在此基础上,利用网络药理学,筛选出和EACN抗H1N1相关的药物靶点67个,靶点共涉及生物过程491个,与抗H1N1相关的通路147个。H1N1感染BALB/c小鼠实验结果发现,EACN能改善H1N1感染引起的体重降低和肺指数的增加,降低小鼠肺组织的病毒载量,减轻小鼠肺组织的病理损伤,降低外周血血清中TNF-α、IFN-γ、IL-1β水平。实验结果提示EACN可能从直接抑制病毒、抗炎作用和免疫调节作用等多个途径发挥抗H1N1的作用。

UPLC-Q-Exactive-Orbitrap-MS法同时测定牛黄上清片中18种胆汁酸的含量

目的 建立超高效液相色谱-四极杆-静电场轨道阱高分辨质谱(UPLC-Q-Exactive-Orbitrap-MS)法同时测定牛黄上清片中牛磺胆酸、7-酮-3α,12-α-羟基胆烷酸、甘氨猪去氧胆酸、12-脱氢胆酸、甘氨胆酸、3-酮-7α,12α-二羟基-5β-胆烷酸、牛磺鹅去氧胆酸、3α-羟基-7-氧代-5β-胆烷酸、猪胆酸、牛磺脱氧胆酸钠、猪去氧胆酸、胆酸、甘氨鹅脱氧胆酸、甘氨脱氧胆酸、牛磺石胆酸钠、鹅去氧胆酸、去氧胆酸、石胆酸的含量。方法 分析采用Thermo Fisher Scientfic Bremen HYPERSIL GOLD色谱柱(2.1 mm×100 mm, 1.9μm);流动相0.1%甲酸-甲醇,梯度洗脱;体积流量0.2 mL/min;柱温40℃;加热电喷雾离子源;负离子扫描;平行反应监测模式。再进行化学模式识别。结果 18种胆汁酸在各自范围内线性关系良好(r≥0.999 5),平均加样回收率96.73%~104.07%,RSD 2.10%~4.07%。不同厂家样品中各胆汁酸在种类和含量上存在一定差异。结论 该方法灵敏可靠,专属性好,可用于牛黄上清片的质量控制。

基于UHPLC-Q-Exactive Orbitrap MS技术的静宁方入脑、入肠及粪便成分分析

目的基于UHPLC-Q-Exactive Orbitrap MS技术对静宁方给药后的大鼠入脑、入肠及粪便中的成分进行分析和鉴定。方法采用UHPLC-Q-Exactive Orbitrap MS,以0.1%甲酸-乙腈(A)和0.1%甲酸-水(B)为流动相进行梯度洗脱,流速0.2 mL·min^(-1),进样量5μL,加热电喷雾离子化源(HESI),正、负离子扫描。结合对照品比对、文献报道、数据库比对等方式对成分进行分析鉴定。结果共鉴定出42种成分,其中脑、回肠、结肠、粪便中分别鉴定出9、33、20、27种成分。结论本实验初步阐明静宁方入脑、入肠及粪便成分,为阐明其药效物质基础及作用机制提供了依据。

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schr?dinger equation

We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.

Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation

By using the fractional complex transform and the bifurcation theory to the generalized fractional differential mBBM equation, we first transform this fractional equation into a plane dynamic system, and then find its equilibrium points and first integral. Based on this, the phase portraits of the corresponding plane dynamic system are given. According to the phase diagram characteristics of the dynamic system, the periodic solution corresponds to the limit cycle or periodic closed orbit. Therefore, according to the phase portraits and the properties of elliptic functions, we obtain exact explicit parametric expressions of smooth periodic wave solutions. This method can also be applied to other fractional equations.

Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

基于UPLC-Q-Exactive MS技术3种核桃类种仁中甘油酯组成比较

基于超高效液相色谱-四级杆-轨道阱高分辨质谱联用(UPLC-Q-Exactive MS)技术比较分析了山核桃(Carya cathayensis Sarg.)、胡桃(Juglans regia Linn.)和薄壳山核桃〔Carya illinoinensis(Wangenh.)K.Koch〕3种木本油料作物种仁中甘油酯的组成及差异,结合LipidSearch软件和混合脂质内标对脂质分子进行定性及定量分析。结果显示:3种核桃类种仁中均鉴定到298个甘油酯,包括245个甘油三酯、38个甘油二酯、1个单半乳糖甘油二酯、9个双半乳糖甘油二酯和5个硫代异鼠李糖甘油二酯。偏最小二乘法判别分析得到104个变量投影重要度(VIP)大于1的脂质分子。山核桃和薄壳山核桃种仁中甘油三酯的主要脂肪酸为油酸,胡桃种仁中甘油三酯的主要脂肪酸为亚油酸。3种核桃类种仁中甘油二酯的主要脂肪酸均为亚油酸,其次为油酸。山核桃和薄壳山核桃种仁的甘油酯组成更为相近。UPLC-Q-Exactive MS可作为鉴别这3种木本油料作物种仁中甘油酯组成的有效方式。

基于UPLC-Q-Exactive Orbitrap-MS的经典名方温胆汤化学成分分析

[目的]采用超高效液相色谱-四极杆静电场轨道阱高分辨质谱法(UPLC-Q-Exactive Orbitrap-MS)对温胆汤的化学成分进行快速识别和鉴定。[方法]采用Waters Acquity BEH C18(2.1×100 mm,1.7μm),以0.1%甲酸水溶液(A)-乙腈(B)作为流动相进行梯度洗脱,流速为0.3 mL/min、柱温30℃;采用加热电喷雾离子源(HESI),正、负离子模式同时检测,扫描模式为Full MS/dd-MS2,扫描范围m/z 100~1500。[结果]通过与对照品比对、精确相对分子质量、多级质谱碎片信息并结合文献报道、质谱数据库信息等对化合物进行鉴别。从温胆汤中共鉴别了121个成分,包括70个黄酮类成分,18个香豆素类成分,9个皂苷类成分,10个生物碱成分,3个苯丙素类成分及其他类化合物11个。其中15个成分通过与对照品比对后确认。[结论]利用UPLC-Q-Exactive Orbitrap-MS技术较为系统地阐明了温胆汤的物质基础,可为该复方药效物质基础的深入研究和质量标准的合理制定奠定基础。