New Approach to Find Initial Basic Feasible Solution (IBFS) for Optimal Solution in Transportation Problem

Minimizing transportation time and getting optimal solutions are always considered as important factors while solving transportation problem. This paper shows a new approach for finding initial basic solution for transportation problem which reduces cost of transportation more than any transportation method such as LCM, northwest, Vogel’s approximation and so on. This method has been illustrated by taking an example;afterwards, it compares basic initial feasible solution with other methods IBF and optimal dictate solutions such as MODI and Steppingstone method.

Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches

In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.

An Effective Approach to Determine an Initial Basic Feasible Solution: A TOCM-MEDM Approach

Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. In this article, a new and effective algorithm is introduced for finding an initial basic feasible solution of a balanced transportation problem. Number of numerical illustration is introduced and optimality of the result is also checked. Comparison of findings obtained by the new heuristic and the existing heuristics show that the method presented herein gives a better result.

A Comparative Study of Initial Basic Feasible Solution by a Least Cost Mean Method (LCMM) of Transportation Problem

Transportation Problems (TP), as is known, are a basic network problem which can be formulated as a Linear Programming Problem (LPP). Transportation networks are built up in order to save transportation cost. In the solution procedure of a TP, finding an Initial Basic Feasible Solution (IBFS) is necessary to obtain the optimal solution. Optimality gives us the optimal route that prompts either most extreme benefit or least aggregate cost whichever is required. In this research paper, a new method named Least Cost Mean Method is proposed to obtain a better IBFS where row penalty and column penalty is brought out by the mean of lowest and next lowest cost of each row and each column of the cost matrix. The method is illustrated with numerical examples. To verify the performance of the proposed method, a comparative study is also carried out and observed that it is computationally easier and yielding comparatively better solution.

Analytical solution of basic equations set of atmospheric motion

On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.

New Procedure of Finding an Initial Basic Feasible Solution of the Time Minimizing Transportation Problems

Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.

Solution with Singularity of Order One for Singular Integral Equation with Hilbert Kernal

The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.

A New Understanding on the Problem That the Quintic Equation Has No Radical Solutions

It is proved in this paper that Abel’s and Galois’s proofs that the quintic equations have no radical solutions are invalid. Due to Abel’s and Galois’s work about two hundred years ago, it was generally accepted that general quintic equations had no radical solutions. However, Tang Jianer et al. recently prove that there are radical solutions for some quintic equations with special forms. The theories of Abel and Galois cannot explain these results. On the other hand, Gauss et al. proved the fundamental theorem of algebra. The theorem declared that there were n solutions for the n degree equations, including the radical and non-radical solutions. The theories of Abel and Galois contradicted with the fundamental theorem of algebra. Due to the reasons above, the proofs of Abel and Galois should be re-examined and re-evaluated. The author carefully analyzed the Abel’s original paper and found some serious mistakes. In order to prove that the general solution of algebraic equation he proposed was effective for the cubic equation, Abel took the known solutions of cubic equation as a premise to calculate the parameters of his equation. Therefore, Abel’s proof is a logical circular argument and invalid. Besides, Abel confused the variables with the coefficients (constants) of algebraic equations. An expansion with 14 terms was written as 7 terms, 7 terms were missing. We prefer to consider Galois’s theory as a hypothesis rather than a proof. Based on that permutation group S5 had no true normal subgroup, Galois concluded that the quintic equations had no radical solutions, but these two problems had no inevitable logic connection actually. In order to prove the effectiveness of radical extension group of automorphism mapping for the cubic and quartic equations, in the Galois’s theory, some algebraic relations among the roots of equations were used to replace the root itself. This violated the original definition of automorphism mapping group, led to the confusion of concepts and arbitrariness. For the general cubic and quartic algebraic equations, the actual solving processes do not satisfy the tower structure of Galois’s solvable group. The resolvents of cubic and quartic equations are proved to have no symmetries of Galois’s soluble group actually. It is invalid to use the solvable group theory to judge whether the high degree equation has a radical solution. The conclusion of this paper is that there is only the Sn symmetry for the n degree algebraic equations. The symmetry of Galois’s solvable group does not exist. Mathematicians should get rid of the constraints of Abel and Galois’s theories, keep looking for the radical solutions of high degree equations.

探讨线性方程组求解问题

对于线性方程组,只有在方程的个数等于未知量的个数,系数行列式不等于零的情况下,才可以使用克莱姆法则求得,也可以使用逆矩阵法求得。而对于一般的线性方程组,如何判定它是否有解、解是否唯一,以及在解不唯一的情况下,又该如何求出它的解。这个问题的解决,对理论和实际都具有十分重要的意义。以下以矩阵为工具,探求一般线性方程组解的情况和解的问题。

西帕依固龈液含漱联合牙周基础疗法在慢性牙周炎治疗中的应用效果分析

目的分析慢性牙周炎应用西帕依固龈液含漱+牙周基础疗法的临床效果。方法选取126例慢性牙周炎患者作为本次研究对象,按随机数字表法分为对照组和研究组,每组63例。对照组患者采用复方氯己定含漱液+牙周基础疗法,研究组患者采用西帕依固龈液含漱+牙周基础疗法。对比两组患者咀嚼功能指标(咬合力、咀嚼效率、出血指数评分、牙齿松动)、治疗效果。结果研究组患者咬合力(129.48±10.05)lbs、咀嚼效率(92.08±2.54)%高于对照组的(111.09±10.02)lbs、(75.73±2.46)%,出血指数评分(0.58±0.08)分、牙齿松动(0.57±0.26)mm小于对照组的(1.62±0.06)分、(1.33±0.81)mm,存在统计学意义(P<0.05)。研究组患者的治疗总有效率93.65%明显高于对照组的76.19%,存在统计学意义(P<0.05)。结论应用西帕依固龈液含漱+牙周基础疗法治疗慢性牙周炎,患者在治疗后各项咀嚼功能指标均恢复较好,具有显著的临床疗效。

石墨炉原子吸收标准加入法测定血液滤过置换基础液中的铝含量

目的:建立石墨炉原子吸收法测定血液滤过置换基础液中铝的含量。方法:采用石墨炉原子吸收标准加入法,加入基体改进剂,测定铝的含量。结果:铝在0~20μg·L^(-1)范围内线性关系良好,r=0.998;检出限浓度为0.91μg·L^(-1);平均回收率为96.5%。3批样品测定结果分别为3.299、1.232、2.431μg·L^(-1)。结论:本法可有效地测定血液滤过置换基础液产品中铝的含量,对产品的原料、生产和包装等可能引入污染的途径进行控制。建议企业重视血液滤过置换基础液中铝含量的检测,尽量减小污染风险,保证产品的质量。

用QBASIC语言计算溶液的pH值

利用计算机编写 QBASIC语言程序计算各种酸碱溶液的pH值,能快速、准确地给出结果。

大型专业基础课程中课程思政建设的关键问题与解决路径

分析大型专业基础课程中课程思政建设的关键问题,提出对应的解决路径。通过重塑思政融入的课程内容,明确课程思政建设目标要求和内容重点,找准育人的维度与角度;通过建立课程思政素材库与案例库,实现教师先思政,统一课程融合点与教师思想,引导教师树立新型育人观;再让教师基于OBE理念创新课堂教学模式,在实践中精准课程思政,实现学生快乐思政与提高学生综合能力的课程思政目标,同时提出一种思政考核方式。

白云石炼镁收尘灰制备碱式碳酸镁的碳化-热解法工艺研究

以白云石炼镁收尘灰作为原料,采用碳化-热解法制备碱式碳酸镁,通过单因素试验研究了碳化过程中温度、时间、CO_(2)流速对碱式碳酸镁产率的影响及热解过程中温度对碳酸氢镁水溶液(重镁水)分解率的影响,确定了碳化-热解法制备碱式碳酸镁的最佳工艺条件,并通过XRD、SEM和EDS对制备的样品进行表征.结果表明,在碳化时间为40 min、碳化温度为25~30℃、CO_(2)流速为0.4 L/min、碳化终止pH为8.0、碳酸氢镁水溶液热分解温度为90℃的条件下,采用碳化-热解法制备得到的碱式碳酸镁产率最高为84.72%.在最佳制备工艺条件下制备得到的片状碱式碳酸镁(4MgCO_(3)·Mg(OH)_(2)·4H_(2)O)杂质含量少、纯度高,达到了冶镁原料标准要求,实现了灰渣废弃物的高效回收利用.

具有垂直传播和时间周期的登革热模型的三次B样条拟插值法数值解

数学模型是理解和控制传染病传播的重要途径。利用三次B样条拟插值法求解一类具有垂直传播和时间周期的登革热数学模型,首先介绍三次B样条拟插值的基本知识,接着用拟插值的导数来逼近因变量的空间导数,再用修正的欧拉法逼近因变量的时间导数,得到数值算法。最后用该方法分别求得登革热模型的基本再生数大于1和小于1时的数值模拟图和数值解。

线性方程组的基础解系

本文研究了线性方程组的基础解系.

脉冲镀金工艺研究进展

金镀层具有良好的耐腐蚀性、抗氧化性、导电性及延展性,广泛应用于精密微纳元器件制造。电化学镀金是实现微纳元器件镀金的主要工艺之一,主要分为直流镀金工艺和脉冲镀金工艺。相较于直流镀金工艺,脉冲镀金工艺可通过控制脉冲波形、频率、占空比及电流密度等脉冲参数,改变金属离子电沉积过程中的电化学极化和浓差极化,灵活调控镀层的物理化学性能。近年来,国内外在微纳元器件脉冲镀金工艺领域开展了系列研究工作,并取得了不错的进展。综述了电化学脉冲镀金的基本原理,描述了电镀金试验中金由离子形态转化为金属的过程。此外,还综述了占空比、频率、电流密度、脉冲导通时间、脉冲关断时间等脉冲参数对金镀层形成的影响,以及镀层性能评价方式;另外,介绍了无氰和有氰两大典型镀液获得金镀层的基本情况,分析了它们各自的优缺点,主要表现为有氰镀液稳定性好,所得金镀层较均匀,而无氰镀液的突出优势为无毒,但其稳定性有待进一步提高。最后,展望了脉冲镀金工艺的发展方向,可为发展新型脉冲镀金工艺及应用拓展提供有益的参考和启示。

基于现代物流的中国铁路干线运输解决方案研究

我国铁路、公路、水路运输的货物周转量、港口货物吞吐量、快递业务量等主要指标连续多年位居世界前列,中国已成为世界上运输最繁忙的国家之一,但由于物流枢纽、集疏运体系以及新型货运装备、智能转接装卸设备存在短板,出现了多种运输方式之间衔接不畅、融合不足等问题。电商经济发展需求及国家政策规划指导对铁路干线运输提出了更高的要求,文章分析了我国近年来货运总量及多种运输方式的发展变化,研究了中美日运输成本,对比分析了中美货运种类。为更好地满足现代物流运输要求,提出了稳住大宗货物、吸引白货等方案优化货源组织,并提出了完善集装箱货场、加快智能化场站建设、加强堆场集疏运建设等方案,加强基础网络设施建设,通过研发新型货运装备、提升智能装备设备和技术装备以及加强先进信息技术等方案提升货运装备技术水平,建立以铁路为骨干的现代物流运输体系。

Cellulose conversion to polyols on supported Ru catalysts in aqueous basic solution

It is of great significance and challenge to achieve direct conversion of cellulose to specific polyols,e.g.,ethylene glycol and propylene glycol.For such selective conversion,a novel one-pot approach was studied by combination of alkaline hydrolysis and hydrogenation on supported Ru catalysts.A wide range of bases including solid bases,e.g.,Ca(OH)2 and La2O3,and phosphate buffers were examined in the cellulose reaction in water,and the cellulose conversions and polyol products depended largely on the basicity or pH values in the aqueous solutions.Ethylene glycol,1,2-propanediol,and especially 1,2,5-pentanetriol were obtained with selectivities of 15%,14% and 22%,respectively,at 38% cellulose conversion at pH 8 in phosphate buffer solution.These preliminary results provide potentials for efficient conversion of cellulose to targeted polyols by using the advantages of bases.

我国基层食品抽检工作存在的问题及解决方法探究

基层食品抽检工作是保证食品安全的重要手段,也是我国食品安全卫生管理的主要辅助措施。本文简要阐述了当前我国基层食品抽检工作基础成果,分析了我国基层食品抽检工作问题,从多个角度入手提出我国基层食品抽检问题的解决方法,以期能够为进一步完善基层食品抽检工作提供借鉴。