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.

Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

Examining the Use of Scott’s Formula and Link Expiration Time Metric for Vehicular Clustering

Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

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.

FORMULA OF GLOBAL SMOOTH SOLUTION FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE

In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.

Euler Loading Formula of LargeDeflection and the Quick Solution for Large Deflection Equation of Beam and Column

This paper develops Euler ’loadlng formula of large deflection to be easy to measure in-situ and puts forward the differeuce quick iterative solution ror large deflection of beam and column, whick can solve the uon-linear equation like a kind of θ"+K(s)f(θ) =0.

ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.

A Formula of Solution for a Class of Homogeneous Recurrence of Variable Coefficients with Two Indices

In this paper, we obtain an explicit formula of general solution for a class of the homogeneous recurrence of variable coefficients with two indices.

A Formula of General Solution for a Class of Homogeneous Trinomial Recurrence of Variable Coefficients with Two Indices

In practice, it is very difficult to find the solution of recurrence relation by using the characteristic roots. By applying iteration and induction we present an explicit formula of general solution for a class of homogeneous trinomial recurrence of variable coefficients with two indices. It provides a concrete and applicable model to solve the relevant problem with computer.

A Formula of Solution for a Class of Linear Recurence with Two Indices

It is very difficult, sometimes impossible, to get a formula solution of recurrence relation, even for the case of homogeneous recurrence with one indite. In this paper, according to the principle of soluting algebraic equation, we present the formula of solution for a class of recurrnce relations with two indices by appling iteration and induction. It provides a concrete model to solve the concerning problems with modern computing tools.

Asymptotic Formulas of the Solutions and the Trace Formulas for the Polynomial Pencil of the Sturm-Liouville Operators

This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.

Solution of Cauchy's Problem for Wave Equations in Higher Space Dimensions by Means of D'Alembert's Formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.

SPECTRAL DECOMPOSITRION FORMULA FOR REGULARIZATION SOLUTION OF ILL-POSED EQUATION

This paper discusses the regularization solution of ill posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank deficient adjustment and the regularization solution of ill posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the secondnorm of estimated parameter’s total error.

基于全概率公式的M-APSK误码率分析模型

为有效评估加性白高斯噪声信道中M-APSK的性能,提出了一种基于全概率公式的理论误码率分析模型。首先根据星座点分布及其编码特点对星座平面进行区域划分,然后由接收符号落在相应区域的概率推导出各比特的判决错误概率表达式,最后得到理论误码率的精确闭式解。以16APSK和32APSK为例,推导出了其各类星座图的理论误码率计算公式,与Monte Carlo仿真结果非常吻合。模型具有通用性,PSK、QAM、PAM、APSK等调制方式均可利用该模型得到理论误码率的精确闭式解。相较于依赖大量数值计算的复杂二维概率积分方法,所提模型能够更方便地给出M-APSK的误码率性能。

On fundamental solution for powers of the sub-Laplacian on the Heisenberg group

We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.

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.

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.

Bushen Yizhi Formula regulates the IRE1αpathway to alleviate endoplasmic reticulum stress in an Alzheimer’s disease rat model

While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amyloid-beta peptide(Aβ)were used to treat rat pheochromocytoma cells(P12)and human neuroblastoma cells(SH-SY5Y).Cell morphological changes were observed to determine the in vitro cell damage.Cell Counting Kit(CCK)-8 assay and flow cytometry were employed to identify cell viability and apoptosis/cell cycle,respectively.Western blotting and immunohistochemistry were employed to measure the expressions of endoplasmic reticulum stress(ERS)-related proteins(GRP78 and CHOP),p-IRE1α,IRE1α,ASK1,p-JNK,JNK,Bax,Bcl-2,XBP-1,and Bim.Fura 2-acetoxymethyl ester(Fura-2/AM)was used to determine the intracellular calcium(Ca^(2+))concentration.Also,an AD model was constructed by injecting Aβinto the CA1 area of the hippocampus in Sprague Dawley rats.AD model rats were gavaged with different concentrations of Bushen Yizhi Formula for 14 consecutive days.The Morris water maze experiment was conducted to test the learning and memory of rats.Hematoxylin&Eosin(H&E)and Terminal-deoxynucleotidyl Transferase(TdT)-mediated dUTP Nick-End Labeling(TUNEL)staining were done to determine histopathological changes in the brain.Results:Bushen Yizhi Formula relieved the Aβ-induced effects including cell injury,decreased viability,increased apoptosis,G0/G1 phase cell cycle arrest,upregulation of GRP78,CHOP,p-IRE1α,p-JNK,Bax,XBP-1 and Bim,as well as down-regulation of Bcl-2.These results were also seen with IRE1αsilencing.While Aβsuppressed the learning and memory abilities of rats,the Bushen Yizhi Formula alleviated these effects of Aβ.Brain nerve cell injury induced by Aβcould also be treated with Bushen Yizhi Formula.Conclusion:Bushen Yizhi Formula could influence ERS through the IRE1αsignaling pathway to achieve its therapeutic effects on AD.