New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations

In this paper, we have modified fixed point method and have established two new iterative methods of order two and three. We have discussed their convergence analysis and comparison with some other existing iterative methods for solving nonlinear equations.

Does the Total Soil N Determined by Kjeldahl Method Include Fixed NH4^+?

Forty soils from top layer (0-20 cm) were sampled in different regions of China and Kjeldahl, HF-Kjeldahl and double treatment methods were used to determine total N, total N plus fixed ammonium, and total N and the residual fixed ammonium left in soil after determination of total N, respectively, to evaluate if Kjeldahl’s method could include the fixed N by soil minerals. The fixed N by soil minerals was measured by Silva-Bremner procedure to make comparison. Results showed that total N determined by Kjeldahl’s method averaged 1.622 g kg-1, while that by HF- Kjeldahl’s method 1.633 g kg-1, and that by double procedure 1.666 g kg-1. Obviously results obtained by the last two methods, particularly the double treatment method, were higher than Kjeldahl’s, showing that Kjeldahl’s method could not or not fully release N fixed by 2:1 minerals in soil, and therefore the determined results would not be the true “total N” for soils that contained large amount of the fixed N. The mineral fixedN averaged 166 mg kg-1, accounting for 10.1% of the total N while the residual fixed N amounted to 30.4 mg kg-1, equivalent to 1.9% of the total N or 18.3% of the total fixed N. The residual fixed N was correlated neither to organic matter nor to total N, but closely related to the total fixed N with a correlation coefficient of 0.598 (n=40), showing that the fixed N was the sole source of the residues. Soils having high residues of the fixed N were just those containing high fixed N, and soils containing high fixed N were just those containing high amount of 2:1 minerals. As a result, Kjeldahl’s method could not give a true value of the total N for such soils. However, for those containing small or little amount of 2:1 minerals, there was no significant difference in results measured by these methods.

VISCOSITY ITERATIVE METHODS FOR COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS WITHOUT COMMUTATIVITY ASSUMPTION IN HILBERT SPACES

In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].

A Modified Fixed Point Method for the Perona Malik Equation

In this work we present a new method to solve the Perona Malik equation for the image denoising. The method is based on a modified fixed point algorithm which is fast and stable. We discretize the equation using a finite volume method by integrating the equation using a fuzzy measure on the control volume. To make our algorithm move faster in time, we have used an optimized domain decomposition which generalize the wave relaxation method. Several test of noised images illustrate this approach and show the efficiency of the proposed new method.

The Influence of Feeding Method on Fluidization Behavior of Fixed Fluidized Bed

An experimental installation of cold model simulation was set up to study the bed pressure drop in different regions of fixed fluidized bed reactor during top feeding and bottom feeding, respectively, at various gas velocities with the fluidization image of solid particles monitored at the same time. By comparing the changes in bed density and operating gas velocity in different regions of fixed fluidized bed reactor, the influence of top feeding and bottom feeding patterns on fluidization behavior could be investigated. The results showed that the bed density in top feeding reactor responded more stably to the change in gas velocity along with the advantage of working in a wider range of operating gas velocities. Based on this study, it is concluded that existing bottom feeding reactor configurations cannot meet the fluidization requirements; and optimization of bottom feeding reactor will be needed.

Solving a Class of Brouwer Fixed-point Problems via a Modified Aggregate Constraint Homotopy Method

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method （proposed by Yu and Lin, Appl. Math. Comput., 74（1996）, 65）, the main adavantages of this method are as foUows： on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n （in this paper, we let Ω={x∈ R^n ： gi（x） ≤0, i= 1,... , m}）; on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.

Modified Homotopy Method for a Class of Brouwer Fixed-point Problems

In this paper, we modify the homotopy method （proposed by Yu and Lin, Appl. Math. Comput., 74（1996）, 65） and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonconvex subsets in Rn. In addition, a simple example is given to show the effectiveness of the modified method.

A Continuation Method for Solving Fixed Point Problems in Unbounded Convex Sets

In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

一种改进的Fixed-base Comb安全快速算法

本文从分析椭圆曲线上Fixed-baseComb算法出发,根据其特点,利用牺牲乘法操作以降低求逆操作的方法,分别用2kP、2P+Q的快速算法对Fixed-baseComb算法的预计算阶段和赋值阶段进行改进,极大地提高了计算效率:在素数域上预计算阶段提高70%～80%,而赋值阶段提高38%～43%,同时,改进算法通过对k的预处理,使得算法能够抵抗边际信道攻击.

ISOFIX固定装置的技术要求及试验方法对比

随着汽车技术的日益发展,儿童乘员数量也在不断地增多,世界上各个汽车制造厂商也对如何保护儿童安全乘车的问题不断地进行技术创新。为适应这种形势,欧美等国家就儿童约束系统出台了相应的法规和标准,并提出了具体的技术要求和试验方法。文章主要介绍了美国和欧洲儿童约束系统标准中有关ISOFIX固定装置的技术要求和试验方法,并结合我国情况,指出随着国家标准的不断完善和企业研发能力的加强,国内儿童乘员保护技术也将取得重大进步。

梅花针组穴叩刺法联合定点旋转复位法治疗神经根型颈椎病的临床研究

目的分析梅花针组穴叩刺法联合定点旋转复位法治疗神经根型颈椎病的效果及对患者疼痛、肌电图的影响。方法选取河南省洛阳正骨医院2021年4月至2024年4月103例神经根型颈椎病患者临床资料,按治疗方案分组,其中行旋转复位法治疗的34例为复位组,行梅花针组穴叩刺法治疗的34例为叩刺组,行旋转复位联合梅花针组穴叩刺治疗的35例为联合组。对比三组治疗效果、疾病相关评分[颈椎功能障碍指数(NDI)、颈椎病临床评价量表(CASCS)、视觉模拟评分法(VAS)评分]、肌电图指标、颈椎活动度。结果治疗4周后联合组治愈率为80.00%,高于复位组52.94%、叩刺组55.88%(P<0.05);治疗4周后联合组NDI、VAS评分低于复位组、叩刺组,CASCS评分高于复位组、叩刺组(P<0.05);治疗4周后联合组正中神经、腋神经的潜伏期均低于复位组、叩刺组,运动传导速度均高于复位组、叩刺组(P<0.05);治疗4周后颈椎侧屈、前屈、后伸活动度高于复位组、叩刺组(P<0.05)。结论神经根型颈椎病经梅花针组穴叩刺联合定点旋转复位治疗可提高治愈率,纠正颈椎功能,恢复颈椎活动度,改善神经传导功能,提高神经运动传导速度。

A FIXED POINT APPROACH TO THE STABILITY OF A GENERALIZED APOLLONIUS TYPE QUADRATIC FUNCTIONAL EQUATION

Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

Solving Large Scale Nonlinear Equations by a New ODE Numerical Integration Method

In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been significantly improved, so it is especially suitable for large scale systems. For Brown’s equations, an existing article reported that when the dimension of the equation N = 40, the subroutines they used could not give a solution, as compared with our method, we can easily solve this equation even when N = 100. Other two large equations have the dimension of N = 1000, all the existing available methods have great difficulties to handle them, however, our method proposed in this paper can deal with those tough equations without any difficulties. The sigularity and choosing initial values problems were also mentioned in this paper.

Analysis of Cavitation Performance of a 2-D Hydrofoil Based on Mixed-iterative Method

In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length （CSCL） iteration and cavity shape for fixed cavitation number （CSCN） iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.

Stability Control of Stretch-Twist-Fold Flow by Using Numerical Methods

In this study, the multistep method is applied to the STF system. This method has been tested on the STF system, which is a three-dimensional system of ODE with quadratic nonlinearities. A computer based Matlab program has been developed in order to solve the STF system. Stable and unstable position of the system has been analyzed graphically and finally a comparison as well as accuracy between two-step sizes with detail. Newton’s method has been applied to show the best convergence of this system.

STUDIES OF MELNIKOV METHOD AND TRANSVERSAL HOMOCLINIC ORBITS IN THE CIRCULAR PLANAR RESTRICTED THREE－BODY PROBLEM

Non-Hamiltonian systems containing degenerate fixed points obtained from twodegrees of freedom near-integrable Hamiltonian systems through non-canonicaltransformations are dealt with in this paper. Two criteria .for determining theexistence of transversal homoclinic and heteroclinic orbits are presented. By exploitingthese criteria the existence of the transversal homoclinic orbits and so, of thetransversal homoclinic tangle .phenomenon in the near-integrable circular planarrestricted three-body problem with sufficiently small mass ratio of the two primaries isproven. Under some assumptions, the existence of the transversal heleroclinic orbits isproven. The global qualitative phase diagram is also illustrated.

Fixed-node Quantum Monte Carlo: A Novel Approach

In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy. But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (0, 1 and 2) of the energies of 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O using this novel method. The results indicate that for 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.

巴马小型猪仰卧位的新型固定方法

目的 研究广西巴马小型猪仰卧位的固定方法以便于动物实验的开展。方法 选择行胸腔器官获取的广西巴马小型猪12头,接受全身麻醉后采用专用的固定装置进行仰卧位固定。结果 12头广西巴马小型猪在手术中体位得到很好的保持,未发生侧翻、移位等现象。结论 采用专用的固定装置对广西巴马小型猪进行仰卧位固定是一种简单有效的方法。