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.

Effects of Lugol's iodine solution and formalin on cell volume of three bloom-forming dinoflagellates

Fixatives are traditionally used in marine ecosystem research. The bias introduced by fixatives on.the dimensions of plankton cells may lead to an overestimation or underestimation of the carbon biomass. To determine the impact of traditional fixatives on dinoflagellates during short- and long-term fixation, we analyzed the degree of change in three bloom-forming dinoflagellates （Prorocentrum rnicans, Scrippsiella trochoidea and Nocfiluca scintillans） brought about by Lugol＇s iodine solution （hereafter Lugol＇s） and formalin. The fixation effects were species-specific. P. micans cell volume showed no significant change following long-term preservation, and S. trochoidea swelled by approximately 8.06% in Lugol＇s and by 20.97% in formalin as a percentage of the live cell volume, respectively. N. scintillans shrank significantly in both fixatives. The volume change due to formalin in N. scintillans was not concentration-dependent, whereas the volume shrinkage ofN. scintillans cells fixed with Lugol＇s at a concentration of 2% was nearly six-fold that in cells fixed with Lugol＇s at a concentration of 0.6%-0.8%. To better estimate the volume of N. scintillans fixed in formalin at a concentration of 5%, we suggest that the conversion relationship was as follows： volume of live cell=volume of intact fixed cell/0.61. Apart from size change, damage induced by fixatives on N. scintillans was obvious. Lugol＇s is not a suitable fixative for N. scintillans due to high frequency of broken cells. Accurate carbon biomass estimate ofN. scintillans should be performed on live samples. These findings help to improve the estimate of phytoplankton cell volume and carbon biomass in marine ecosystem.

Temporal change of plankton size structure preserved by Lugol's solution:a FlowCAM study

Plankton size structure is crucial for understanding marine ecosystem dynamics and the associated biogeochemical processes.A fixation step by acid Lugol’s solution has been commonly employed to preserve plankton samples in the field.However,the acid Lugol’s solution can bias the estimation of size structure and the preserved plankton size structure can vary with time.Here,we explore the impact of sample storage time on the size-structure of the plankton community preserved by Lugol’s solution.Two short-term experiments and one long-term experiment were conducted to explore the change of plankton community size structure with the storage time:covering from a week to a month,and to nearly seven months based on particle-size data obtained by continuous Flow Cytometer and Microscope(FlowCAM)measurements.We found a linear change of plankton size with the storage time in short-term periods(less than 3 months)with a decrease of the slope but an increase of the intercept for the normalized biomass size spectrum(NBS S).However,there were opposite trends for NBSS with increasing slope but decreasing intercept after3 months.The potential causes of the distinct patterns of the NBSS parameters are addressed in terms of the interplay between particle aggregation and fragmentation.We found large changes in plankton biovolume and abundance among different size classes,which may indicate a distinct effect of acid Lugol’s solution on various plankton size classes.The mechanism driving temporal change in the size-structure of the Lugolfixed plankton community was further discussed in terms of particle aggregation and fragmentation.Finally,we emphasize that the effect of storage time should be taken into account when interpreting or comparing data of plankton community acquired from samples with various storage durations.

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.

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form. A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t ≥ 0 is obtained, and a sharp estimate of the life span for the classical solution is given.

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.

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.

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.

Exact solutions for the mixed AKNS equation： Hirota approach

The mixed AKNS nonlinear evolution equation in equation, which contains an isospectral term the AKNS system. So searching for its exact and a nonisospectral term, is an important solutions is vital both for the AKNS system and in mathematical sense. In this paper, the corresponding Lax pair was given, the bilinear forms of the mixed AKNS equation were obtained through introducing the transformation of dependent variables. By using Hirota＇s bilinear method, the N-soliton solutions were obtained.