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 findin...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.展开更多
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 s...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.展开更多
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 thi...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.展开更多
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...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.展开更多
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 tran...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.展开更多
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 simplifi...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.展开更多
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 t...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 <i><span style="font-family:Verdana;font-size:12px;">et</span></i><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> 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 </span><i><span style="font-family:Verdana;font-size:12px;">et</span></i></span><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> proved the fundamental theorem of algebra. The theorem declared that there were </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> solutions for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> 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</span></span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">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.</span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">We prefer to consider Galois’s theory as a hypothesis rather than a proof. Based on that permutation group </span><i><span style="font-size:12px;font-family:Verdana;">S</span></i><sub><span style="font-size:12px;font-family:Verdana;">5</span></sub><span style="font-size:12px;font-family:Verdana;"> 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 </span><i><span style="font-size:10.0pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;">S</span><sub><span style="font-family:Verdana;font-size:12px;">n</span></sub></span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> symmetry for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> 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.</span></span>展开更多
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 dif...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.展开更多
Taking the Jiangsu Province as Zhenjiang Academy of Agricultural Sciences in Hilly Areas of an example, the paper elaborated the advanced practices of agricultural research institutes in agricultural science and techn...Taking the Jiangsu Province as Zhenjiang Academy of Agricultural Sciences in Hilly Areas of an example, the paper elaborated the advanced practices of agricultural research institutes in agricultural science and technology services and analyzed the difficulties and solutions in the services. process of science and technologyservices.展开更多
The Taishang-Shuiwangzhuang gold deposit is located in the southeastern margin of Linglong gold field in the northern part of the Zhaoping Fault metallogenic belt of the Jiaodong gold province-the world’s third-large...The Taishang-Shuiwangzhuang gold deposit is located in the southeastern margin of Linglong gold field in the northern part of the Zhaoping Fault metallogenic belt of the Jiaodong gold province-the world’s third-largest gold metallogenic area.Major prospecting breakthroughs have been made at the depth of 600‒2500 m in recent years,with cumulative proven gold resources exceeding 700 t.Based on a large number of exploration data,the main characteristics of the deposit are described in detail,and the spatial coupling relationship between ore-controlling fault and main orebodies is discussed.The main orebodies occur as regular large veins,exhibiting branching and combination,expansion and contraction,and pinch-out and reoccurrence.They extend in a gentle wave pattern along their strikes and dip directions and generally have a pitch direction of NEE and a plunge direction of NEE.As the ore-controlling fault,the Zhaoping Fault has the characteristics of wave-like fluctuation,with its dip angle presenting three steps of steep-slow transition within the depth range of 2500 m.The gold mineralization enrichment area is mainly distributed in the step parts where the fault plane changes from steeply to gently.The ore-forming age,ore-forming fluid and ore-forming material sources and the genesis of the ore deposit are analyzed based on the research results of ore deposit geochemistry.The ore-forming fluids were H_(2)O-CO_(2)-NaCl-type hydrothermal solutions with a medium-low temperature and medium-low salinity.The H-O isotopic characteristics indicate that the fluids in the early ore-forming stage were possibly formed by degassing of basic magma and that meteoric water gradually entered the ore-forming fluids in the late ore-forming stage.The S and Pb isotopes indicate that the ore-forming materials mainly originate from the lower crust and contain a small quantity of mantle-derived components.The comprehensive analysis shows that the Taishang-shuiwangzhuang gold deposit was a typical“Jiaodong type”gold deposit.The strong crust-mantle interactions,large-scale magmatism,and the material exchange arising from the transformation from the ancient lower crust to the juvenile lower crust during the Early Cretaceous provided abundant fluids and material sources for mineralization.Moreover,the detachment faults formed by the rapid magmatic uplift and the extensional tectonism created favorable temperature and pressure conditions and space for fluid accumulation and gold precipitation and mineralization.展开更多
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘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.
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China(19971064)Ziqiang Invention Foundation of Wuhan University(201990336)
文摘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.
文摘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 <i><span style="font-family:Verdana;font-size:12px;">et</span></i><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> 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 </span><i><span style="font-family:Verdana;font-size:12px;">et</span></i></span><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> proved the fundamental theorem of algebra. The theorem declared that there were </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> solutions for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> 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</span></span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">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.</span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">We prefer to consider Galois’s theory as a hypothesis rather than a proof. Based on that permutation group </span><i><span style="font-size:12px;font-family:Verdana;">S</span></i><sub><span style="font-size:12px;font-family:Verdana;">5</span></sub><span style="font-size:12px;font-family:Verdana;"> 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 </span><i><span style="font-size:10.0pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;">S</span><sub><span style="font-family:Verdana;font-size:12px;">n</span></sub></span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> symmetry for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> 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.</span></span>
文摘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.
文摘Taking the Jiangsu Province as Zhenjiang Academy of Agricultural Sciences in Hilly Areas of an example, the paper elaborated the advanced practices of agricultural research institutes in agricultural science and technology services and analyzed the difficulties and solutions in the services. process of science and technologyservices.
基金financially supported by the National Key Research and Development Program of China(Grant No.2023YFC2906900)Key Research and Development Program of Shandong Province(Grant No.2023CXGC011001)+2 种基金The Taishan Scholars Talent Project(TSTP 20240847)The Open Project of Technology Innovation Center for Deep Gold Resources Exploration and Mining,Ministry of Natural Resources(Grant No.SDK202211,SDK202214)Science and Technology Project of Shandong Bureau of Geology and Mineral Exploration and Development(Grant No.KY202208)。
文摘The Taishang-Shuiwangzhuang gold deposit is located in the southeastern margin of Linglong gold field in the northern part of the Zhaoping Fault metallogenic belt of the Jiaodong gold province-the world’s third-largest gold metallogenic area.Major prospecting breakthroughs have been made at the depth of 600‒2500 m in recent years,with cumulative proven gold resources exceeding 700 t.Based on a large number of exploration data,the main characteristics of the deposit are described in detail,and the spatial coupling relationship between ore-controlling fault and main orebodies is discussed.The main orebodies occur as regular large veins,exhibiting branching and combination,expansion and contraction,and pinch-out and reoccurrence.They extend in a gentle wave pattern along their strikes and dip directions and generally have a pitch direction of NEE and a plunge direction of NEE.As the ore-controlling fault,the Zhaoping Fault has the characteristics of wave-like fluctuation,with its dip angle presenting three steps of steep-slow transition within the depth range of 2500 m.The gold mineralization enrichment area is mainly distributed in the step parts where the fault plane changes from steeply to gently.The ore-forming age,ore-forming fluid and ore-forming material sources and the genesis of the ore deposit are analyzed based on the research results of ore deposit geochemistry.The ore-forming fluids were H_(2)O-CO_(2)-NaCl-type hydrothermal solutions with a medium-low temperature and medium-low salinity.The H-O isotopic characteristics indicate that the fluids in the early ore-forming stage were possibly formed by degassing of basic magma and that meteoric water gradually entered the ore-forming fluids in the late ore-forming stage.The S and Pb isotopes indicate that the ore-forming materials mainly originate from the lower crust and contain a small quantity of mantle-derived components.The comprehensive analysis shows that the Taishang-shuiwangzhuang gold deposit was a typical“Jiaodong type”gold deposit.The strong crust-mantle interactions,large-scale magmatism,and the material exchange arising from the transformation from the ancient lower crust to the juvenile lower crust during the Early Cretaceous provided abundant fluids and material sources for mineralization.Moreover,the detachment faults formed by the rapid magmatic uplift and the extensional tectonism created favorable temperature and pressure conditions and space for fluid accumulation and gold precipitation and mineralization.
