Four-color theorem has only been proved by computer since it was proposed, many people have proposed their mathematical proof of four-color theorem, but their proof is disputed then, what lead to a situation that the ...Four-color theorem has only been proved by computer since it was proposed, many people have proposed their mathematical proof of four-color theorem, but their proof is disputed then, what lead to a situation that the mathematical proof of four-color theorem has been lacking to this day. In this article, we have summarized some laws based on previous researches, and proposed a mathematical proof of four-color theorem by using these laws trough a recursive method.展开更多
This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral w...This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture.展开更多
Through discussing the color matching technology and its application in printing industry the conventional approaches commonly used in color matching, and the difficulties in color matching, a nonlinear color matching...Through discussing the color matching technology and its application in printing industry the conventional approaches commonly used in color matching, and the difficulties in color matching, a nonlinear color matching model based on two step learning is established by finding a linear model by learning pure color data first and then a nonlinear modification model by learning mixed color data. Nonlinear multiple regression is used to fit the parameters of the modification model. Nonlinear modification function is discovered by BACON system by learning mixture data. Experiment results indicate that nonlinear color conversion by two step learning can further improve the accuracy when it is used for straightforward conversion from RGB to CMYK. An improved separation model based on GCR concept is proposed to solve the problem of gray balance and it can be used for three to four color conversion as well. The method proposed has better learning ability and faster printing speed than other historical approaches when it is applied to four color ink jet printing.展开更多
Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points wi...Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points without a loop, and a maximum of four colors are used for points with a loop. A maximum of four colors are used to color all points. .展开更多
文摘Four-color theorem has only been proved by computer since it was proposed, many people have proposed their mathematical proof of four-color theorem, but their proof is disputed then, what lead to a situation that the mathematical proof of four-color theorem has been lacking to this day. In this article, we have summarized some laws based on previous researches, and proposed a mathematical proof of four-color theorem by using these laws trough a recursive method.
文摘This article attempts to successfully fill Kempe proof loophole, namely 4-staining of “staining dilemma configuration”. Our method is as follows: 1) Discovered and proved the existence theorem of the quadrilateral with four-color vertices and its properties theorems, namely theorems 1 and 2. From this, the non-10-fold symmetry transformation rule of the geometric structure of Errera configuration is generated, and using this rule, according to whether the “staining dilemma configuration” is 10-fold symmetry, they are divided into two categories;2) Using this rule, combining the different research results of several mathematicians on Errera graphs, and using four different classifications of propositional truth and falsehood, a new Theorem 3 is established;3) Using Theorem 3, the theoretical proof that the non-10-fold symmetric “ staining dilemma configuration” can be 4-staining;4) Through 4-staining of the four configurations of Errera, Obtained the Z-staining program (also called Theorem 4), and using this program and mathematical induction, gave the 10-fold symmetric “staining dilemma configuration” 4-staining proof. Completed the complete and concise manual proof of the four-color conjecture.
文摘Through discussing the color matching technology and its application in printing industry the conventional approaches commonly used in color matching, and the difficulties in color matching, a nonlinear color matching model based on two step learning is established by finding a linear model by learning pure color data first and then a nonlinear modification model by learning mixed color data. Nonlinear multiple regression is used to fit the parameters of the modification model. Nonlinear modification function is discovered by BACON system by learning mixture data. Experiment results indicate that nonlinear color conversion by two step learning can further improve the accuracy when it is used for straightforward conversion from RGB to CMYK. An improved separation model based on GCR concept is proposed to solve the problem of gray balance and it can be used for three to four color conversion as well. The method proposed has better learning ability and faster printing speed than other historical approaches when it is applied to four color ink jet printing.
文摘Different vertices are colored in a plan. Adjacent vertices are colored dif-ferently from nonadjacent vertices, which are colored the same color. One color is used for a single point, two colors are used for points without a loop, and a maximum of four colors are used for points with a loop. A maximum of four colors are used to color all points. .
