New method of local adjuvant therapy with bicarbonate Ringer’s solution for tumoral calcinosis: A case report

BACKGROUND Tumoral calcinosis is a condition characterized by deposits of calcium phosphate crystals in extra-articular soft tissues,occurring in hemodialysis patients.Calcium phosphate crystals are mainly composed of hydroxyapatite,which is highly infilt-rative to tissues,thus making complete resection difficult.An adjuvant method to remove or resolve the residual crystals during the operation is necessary.CASE SUMMARY A bicarbonate Ringer’s solution with bicarbonate ions(28 mEq/L)was used as the adjuvant.After resecting calcium phosphate deposits of tumoral calcinosis as much as possible,while filling with the solution,residual calcium phosphate deposits at the pseudocyst wall can be gently scraped by fingers or gauze in the operative field.A 49-year-old female undergoing hemodialysis for 15 years had swelling with calcium deposition for 2 years in the shoulders,bilateral hip joints,and the right foot.A shoulder lesion was resected,but the calcification remained and early re-deposition was observed.Considering the difficulty of a complete rection,we devised a bicarbonate dissolution method and excised the foot lesion.After resection of the calcified material,the residual calcified material was washed away with bicarbonate Ringer’s solution.CONCLUSION The bicarbonate dissolution method is a new,simple,and effective treatment for tumoral calcinosis in hemodialysis patients.

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.

Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

2022年四川芦山M_(S)6.1地震前应力状态研究

为研究2022年6月1日四川芦山M_(S)6.1地震的孕育和发生过程,采用CAP方法反演了2013年芦山M_(S)7.0主震及M_(S)≥5.0余震的震源机制解,并基于应力张量方差与b值时空分布特征,探讨了芦山M_(S)6.1地震的力学机制和震源区的应力状态。结果表明:2022年芦山M_(S)6.1地震震源机制表现出与2013年芦山M_(S)7.0主震和5级余震相似的逆冲型破裂特征,压应力轴方位与龙门山断裂带南段区域应力场一致。2013年芦山M_(S)7.0地震后震中及附近的应力张量方差和b值长期处于低值状态,2022年芦山M_(S)6.1地震前震中及附近出现了应力张量方差和b值的低值异常,表明芦山余震区处于较高的应力水平。分析认为:巴颜喀拉块体持续东向运动受到华南块体的阻挡,震中所在区域长期受挤压逆冲作用,从而使芦山余震区长期处于应力积累的状态,芦山M_(S)6.1地震也是在这种动力学背景下发生的。

Wave packet solutions in a bounded equatorial ocean and its interannual and decadal variabilities

Linearized shallow water perturbation equations with approximation in an equatorial β plane are used to obtain the analytical solution of wave packet anomalies in the upper bounded equatorial ocean. The main results are as follows. The wave packet is a superposition of eastward travelling Kelvin waves and westward travelling Rossby waves with the slowest speed, and satisfies the boundary conditions of eastern and western coasts, respectively.The decay coefficient of this solution to the north and south sides of the equator is inversely proportional only to the phase velocity of Kelvin waves in the upper water. The oscillation frequency of the wave packet, which is also the natural frequency of the ocean, is proportional to its mode number and the phase velocity of Kelvin waves and is inversely proportional to the length of the equatorial ocean in the east-west direction. The flow anomalies of the wave packet of Mode 1 most of the time appear as zonal flows with the same direction. They reach the maximum at the center of the equatorial ocean and decay rapidly away from the equator, manifested as equatorially trapped waves. The flow anomalies of the wave packet of Mode 2 appear as the zonal flows with the same direction most of the time in half of the ocean, and are always 0 at the center of the entire ocean which indicates stagnation, while decaying away from the equator with the same speed as that of Mode 1. The spatial structure and oscillation period of the wave packet solution of Mode 1 and Mode 2 are consistent with the changing periods of the surface spatial field and time coefficient of the first and second modes of complex empirical orthogonal function(EOF)analysis of flow anomalies in the actual equatorial ocean. This indicates that the solution does exist in the real ocean, and that El Ni?o-Southern Oscillation(ENSO) and Indian Ocean dipole(IOD) are both related to Mode 2.After considering the Indonesian throughflow, we can obtain the length of bounded equatorial ocean by taking the sum of that of the tropical Indian Ocean and the tropical Pacific Ocean, thus this wave packet can also explain the decadal variability(about 20 a) of the equatorial Pacific and Indian Oceans.

基于Kelvin-Voigt模型的黏弹性岩体位移反分析唯一性研究

在岩土工程中,准确的岩体力学参数对于工程项目的建设和维护极为重要,相较于现场原位试验、实验室试验、数值模拟等获取参数的方法,岩体位移反分析方法具有方便操作、条件获取难度小、数据准确等特点,而反分析结果的唯一性是位移反分析能否成功的重要影响因素。为了研究位移反分析结果的唯一性问题,使用Laplace变换和蠕变柔量的方法,推导了在圆形巷道中符合Kelvin-Voigt模型的黏弹性岩体的位移解析解,并运用参数可辨识准则研究了已知参数对黏弹性岩体反分析唯一性的影响。研究结果表明,无论在任何条件下,都无法唯一地反演出所有6个参数,在至少有2个参数是已知的情况下,才可能唯一地反演出其他参数;地应力分量被唯一反演的概率最大,弹性模量、泊松比和黏滞系数根据控制条件的不同,其可辨识性存在差异,并随着已知参数数量的增加,参数可辨识性也随之增强;地应力是否为0对反演结果的唯一性有着显著的影响。工程算例表明,研究结果对于岩体参数的反分析计算具有重要的指导意义。

Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.

Dynamics of vascular volume and hemodilution of lactated Ringer’s solution in patients during induction of general and epidural anesthesia

Objective： To investigate the dynamics of vascular volume and the plasma dilution of lactated Ringer＇s solution in patients during the induction of general and epidural anesthesia. Methods： The hemodilution of i.v. infusion of 1000 ml of lactated Ringer＇s solution over 60 min was studied in patients undergoing general （n=31） and epidural （n= 22） anesthesia. Heart rate, arterial blood pressure and hemoglobin （Hb） concentration were measured every 5 rain during the study. Surgery was not started until the study period had been completed. Results： General anesthesia caused the greater decrease of mean arterial blood pressure （MAP） （mean 15% versus 9%; P〈0.01） and thereby followed by a more pronounced plasma dilution, blood volume expansion （VE） and blood volume expansion efficiency （VEE）. A strong linear correlation between hemodilution and the reduction in MAP （r=-0.50;P〈0.01） was found. At the end of infusion, patients undergoing general anesthesia retained 47% （SD 19%） of the infused fluid in the circulation, while epidural anesthesia retained 29% （SD 13%） （P〈0.001）. Correspondingly, a fewer urine output （mean 89 ml versus 156 ml; P〈0.05） and extravascular expansion （454 ml versus 551 ml; P〈0.05） were found during general anesthesia. Conclusion： We concluded that the induction of general anesthesia caused more hemodilution, volume expansion and volume expansion efficiency than epidural anesthesia, which was triggered only by the lower MAP.

Exact Solutions for Einstein＇s Hyperbolic Geometric Flow

In this paper we investigate the Einstein＇s hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein＇s hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.

HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS

By means of an extension of Mawhin＇s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential systems is studied, and then the homoclinic solutions are obtained as the limit points of a certain subsequence of the above set.

Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method

With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.

Symmetry Reductions and Group-Invariant Solutions of (2+1)-Dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.

ON MULTIPLE SOLUTIONS TO A LOW-SPECTRUM MODEL OF OCEANIC CURRENT DRIVEN BY THE BOUNDARY FORCE——THE BIMODALITY OF THE KUROSHIO SOUTH OF JAPAN

This low-spectrun medel study on the multiple solutions to a nonlinear quasi-geostrophic ocanic cur-rent equation shows that they depend on the combination of Ro, Re, λ and ε, that the bimedaity of theKuroshio depends strongly on the nonlinear effect represented by Ro and λ, and that its occurrenceprobability is reduced by the dissipation represented by Re and ε. The stability of solutions is discussed indetail with Hurwitz’s theory.

Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics

In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.

Prediction of Activity Coefficients for Mixed Aqueous Electrolyte Solutions from the Data of Their Binary Solutions

The simple equation relating the activity coefficient of each solute in mixed electrolyte solution to its value in binary solutions under isopiestic equilibrium was tested by comparison with the experimental data for the 18 electrolyte solutions consisting of 1：1, 1：2, and 1：3 electrolytes. The isopiestic measurements were made on the quaternary system BaCl2-NH4Br-NaI-H2O and its ternary subsystems NaI-NH4Br-H2O, NaI-BaCl2-H2O, and NH4Br-BaCl2-H2O at 298.15K. The results were used to test the applicability of the Zdanovskii＇s rule to the mixed electrolyte solutions which contain no common ions, and the agreement is excellent. The activity coefficients of the solutes in the above quaternary and ternary systems calculated from the above-mentioned simple equation are in good agreement with the Pitzer＇s equation.

Comprehensive form of solution for Lamb's dynamic problem expressed by Green's functions

By the analysis for the vectors of a wave field in the cylindrical coordinate and Sommerfeld＇s identity as well as Green＇s functions of Stokes＇ solution pertaining the conventional elastic dynamic equation, the results of Green＇s function in an infinite space of an axisymmetric coordinate are shown in this paper. After employing a supplementary influence field and the boundary conditions in the free surface of a senti-space, the authors obtain the solutions of Green＇s function for Lamb＇s dynamic problem. Besides, the vertical displacement uzz and the radial displacement urz can match Lamb＇s previous results, and the solutions of the linear expansion source u^r and the linear torsional source uee are also given in the paper. The authors reveal that Green＇s function of Stokes＇ solution in the semi-space is a comprehensive form of solution expressing the dynamic Lamb＇s problem for various situations. It may benefit the investigation of deepening and development of Lamb＇s problems and solution for pertinent dynamic problems conveniently.

Soliton Solutions for Nonisospectral AKNS Equation by Hirota＇s Method

Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions are obtained through Hirota＇s method.

Symmetry Groups and New Exact Solutions to （2＋1）-Dimensional Variable Coefficient Canonical Generalized KP Equation

In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.