Kangfuxin solution alleviates esophageal stenosis after endoscopic submucosal dissection:A natural ingredient strategy

BACKGROUND Esophageal stricture ranks among the most significant complications following endoscopic submucosal dissection(ESD).Excessive fibrotic repair is a typical pathological feature leading to stenosis after ESD.AIM To examine the effectiveness and underlying mechanism of Kangfuxin solution(KFX)in mitigating excessive fibrotic repair of the esophagus post-ESD.METHODS Pigs received KFX at 0.74 mL/kg/d for 21 days after esophageal full circumferential ESD.Endoscopic examinations occurred on days 7 and 21 post-ESD.In vitro,recombinant transforming growth factor(TGF)-β1(5 ng/mL)induced a fibrotic microenvironment in primary esophageal fibroblasts(pEsF).After 24 hours of KFX treatment(at 1.5%,1%,and 0.5%),expression ofα-smooth muscle actin-2(ACTA2),fibronectin(FN),and type collagen I was assessed.Profibrotic signaling was analyzed,including TGF-β1,Smad2/3,and phosphor-smad2/3(p-Smad2/3).RESULTS Compared to the Control group,the groups treated with KFX and prednisolone exhibited reduced esophageal stenosis,lower weight loss rates,and improved food tolerance 21 d after ESD.After treatment,Masson staining revealed thinner and less dense collagen fibers in the submucosal layer.Additionally,the expression of fibrotic effector molecules was notably inhibited.Mechanistically,KFX downregulated the transduction levels of fibrotic functional molecules such as TGF-β1,Smad2/3,and p-Smad2/3.In vitro,pEsF exposed to TGF-β1-induced fibrotic microenvironment displayed increased fibrotic activity,which was reversed by KFX treatment,leading to reduced activation of ACTA2,FN,and collagen I.The 1.5%KFX treatment group showed decreased expression of p-Smad 2/3 in TGF-β1-activated pEsF.CONCLUSION KFX showed promise as a therapeutic option for post-full circumferential esophageal ESD strictures,potentially by suppressing fibroblast fibrotic activity through modulation of the TGF-β1/Smads signaling pathway.

Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.

The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions of n-Dimensional Incompressible Navier-Stokes Equations

We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.

Riemann-Hilbert Problem and Multiple High-order Poles Solutions of the Focusing mKdV Equation with Nonzero Boundary Conditions

The focusing modified Korteweg-de Vries(mKdV)equation with multiple high-order poles under the nonzero boundary conditions is first investigated via developing a Riemann-Hilbert(RH)approach.We begin with the asymptotic property,symmetry and analyticity of the Jost solutions,and successfully construct the RH problem of the focusing mKdV equation.We solve the RH problem when 1/S_(11)(k)has a single highorder pole and multiple high-order poles.Furthermore,we derive the soliton solutions of the focusing mKdV equation which corresponding with a single high-order pole and multiple high-order poles,respectively.Finally,the dynamics of one-and two-soliton solutions are graphically discussed.

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

Approximate Solution for Mechanism of Thermally and Wind-driven Ocean Circulation

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.

Classification and Approximate Solutions to Perturbed Nonlinear Diffusion-Convection Equations

This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry （A GCS）. Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate invariant solutions to the resulting equations can also be obtained.

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.

Approximate Analytical Solutions for Scattering States of D-dimensional Hulthen Potentials

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.

New approximate solution for time-fractional coupled KdV equations by generalised differential transform method

In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.

Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.

Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method

The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.

Approximate Relativistic Solutions for One-Dimensional Cylindrical Coaxial Diode

Two approximate analytical relativistic solutions for one-dimensional, space-charge- limited cylindrical coaxial diode are derived and utilized to compose best-fitting approximate solutions. Comparison of the best-fitting solutions with the numerical one demonstrates an error of about 11% for cathode-inside arrangement and 12% in the cathode-outside case for ratios of larger to smaller electrode radius from 1.2 to 10 and a voltage above 0.5 MV up to 5 MV. With these solutions the diode lengths for critical self-magnetic bending and for the condition under which the parapotential model validates are calculated to be longer than 1 cm up to more than 100 cm depending on voltage, radial dimensions and electrode arrangement. The influence of ion flow from the anode on the relativistic electron-only solution is numerically computed, indicating an enhancement factor of total diode current of 1.85 to 4.19 related to voltage, radial dimension and electrode arrangement.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.

Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto-Sivashinsky Equation

Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Approximate Solutions of Primary Resonance for Forced Duffing Equation by Means of the Homotopy Analysis Method

Nonlinear dynamic equation is a common engineering model.There is not precise analytical solution for most of nonlinear differential equations.These nonlinear differential equations should be solved by using approximate methods.Classical perturbation methods such as LP method,KBM method,multi-scale method and the averaging method on weakly nonlinear vibration system is effective,while the strongly nonlinear system is difficult to apply.Approximate solutions of primary resonance for forced Duffing equation is investigated by means of homotopy analysis method （HAM）.Different from other approximate computational method,the HAM is totally independent of small physical parameters,and thus is suitable for most nonlinear problems.The HAM provides a great freedom to choose base functions of solution series,so that a nonlinear problem may be approximated more effectively.The HAM provides us a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter and the auxiliary function.Therefore,HAM not only may solve the weakly non-linear problems but also may be suitable for the strong non-linear problem.Through the approximate solution of forced Duffing equation with cubic non-linearity,the HAM and fourth order Runge-Kutta method of numerical solution were compared,the results show that the HAM not only can solve the steady state solution,but also can calculate the unsteady state solution,and has the good computational accuracy.

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.