Effect of Shuanghuanglian Oral Solution on Liver Function in a Mouse Model of Non-alcoholic Steatohepatitis

[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Exact Solutions of Forced Schrödinger Equation and How to Choose the External Forces

Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.

Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained.

Effects of Kangfuxin Solution (康复新液) Combined with Low-level Laser on Cytokines and Immune Function in Patients with Radiation-induced Oral Mucositis

Objective:To investigate the effect of Kangfuxin Solution(康复新液)combined with low-level laser therapy(LLLT)on cytokines and immune function in patients with radiation-induced oral mucositis.Methods:There were 84 nasopharyngeal carcinoma patients with oral mucositis after intensity-modulated radiation therapy(IMRT)were randomly divided into the control group(CG)and the observation group(OG),with 42 cases in each group.The CG was given LLLT,and the OG was treated with Kangfuxin Solution in addition to LLLT for 10 consecutive days.The healing time of oral mucosa,mucositis grading,oral pain scores,cytokines(interleukin-6,interleukin-1βand tumor necrosis factor-α)and T lymphocyte subsets were compared between the 2 groups before and after treatment.Results:The healing time of oral mucosa in the OG was(6.8±1.4)d,which was significantly shorter than(8.6±1.9)d in the CG(t=4.943,P<0.01).After treatment,the grading of oral mucositis in the OG was better than that in the CG,with a statistically significant difference(Z=2.942,P<0.05).The oral pain scores of the OG was lower than that in the CG at different time points after treatment,and the difference was statistically significant(t=8.207,11.017,P<0.01).After treatment,the levels of IL-6,IL-1βand TNF-αin peripheral blood of the OG were significantly lower than those in the CG(t=5.217,2.775,4.053,P<0.01).There were statistically significant differences in CD4+,CD8+and CD4+/CD8+between the OG and the CG after treatment(t=5.692,6.093,3.658,P<0.01).Conclusion:Kangfuxin Solution combined with LLLT can significantly shorten the healing time of oral mucosal,reduce the grading of oral mucositis,relieve oral pain,reduce inflammatory response and improve the immune function of patients.

Molecular Dynamics Study on Configuration Energy and Radial Distribution Functions of Ammonium Dihydrogen Phosphates Solution

Molecular dynamics simulations were carried out to study the configuration energy and radial distribution functions of mmonium dihydrogen phosphate solution at different temperatures. The dihydrogen phosphate ion was treated as a seven-site model and the ammonium ion was regarded as a five-site model, while a simple-point-charge model for water molecule. An unusually local particle number density fluctuation was observed in the system at saturation temperature. It can be found that the potential energy increases slowly with the temperature from 373 K to 404 K, which indicates that the ammonium dihydrogen phosphate has partly decomposed. The radial distribution function between the hydrogen atom of ammonium cation and the oxygen atom of dihydrogen phosphate ion at three different temperatures shows obvious difference, which indicates that the average H-bond number changes obviously with the temperature. The temperature has an influence on the combination between hydrogen atoms and phosphorus atoms of dihydrogen phosphate ion and there are much more growth units at saturated solutions.

Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations

The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.

ESTIMATES OF N -FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.

Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function

Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.

ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS

In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].

HYBRID FEM WITH FUNDAMENTAL SOLUTIONS AS TRIAL FUNCTIONS FOR HEAT CONDUCTION SIMULATION

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.

EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].

REFLECTIVE FUNCTION AND PERIODIC SOLUTION OF DIFFERENTIAL SYSTEMS

This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.

A hyperbolic function approach to constructing exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice

Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.

Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation

Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k →1, these solutions reduce to the solitary wave solutions of the equation.

SOME PROBLEMS WITH THE METHOD OF FUNDAMENTAL SOLUTION USING RADIAL BASIS FUNCTIONS

The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.