Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers...Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.展开更多
RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different co...RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different colors.The problem is that these two systems are hard to use for manipulating any operations involving combinations of colors,and they lack the capacity for inter-changeability or unification.Based on prime number theory and Goldbach's conjecture,this study presents a universal color system(C235)using a number-based structure to encode,compute and unify all colors on a color wheel.The proposed C235 system offers a unified representation for the efficient encoding and effective manipulation of color.It can be applied to designing a high-rate LCD system and colorizing objects with multiple attributes and DNA codons,opening the door to manipulating colors and lights for even broader applications.展开更多
Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are considered for the redundancy allocation problem with series-parallel structure. The max-min approach can formulate the problem as an int...Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are considered for the redundancy allocation problem with series-parallel structure. The max-min approach can formulate the problem as an integer linear programming problem instead of an integer nonlinear problem. This paper presents a comparison between those methods from the standpoint of solution quality and computational complexity. The experimental results show that the max-min approach is superior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems, but analysis of computational complexity shows that the max-min approach is inferior to other greedy heuristics.展开更多
文摘Over millennia, nobody has been able to predict where prime numbers sprout or how they spread. This study establishes the Periodic Table of Primes (PTP) using four prime numbers 2, 3, 5, and 7. We identify 48 integers out of a period 2×3×5×7=210 to be the roots of all primes as well as composites without factors of 2, 3, 5, and 7. Each prime, twin primes, or composite without factors of 2, 3, 5, and 7 is an offspring of the 48 integers uniquely allocated on the PTP. Three major establishments made in the article are the Formula of Primes, the Periodic Table of Primes, and the Counting Functions of Primes and Twin Primes.
文摘RGB and CYMK are two major coloring schemes currently available for light colors and pigment colors,respectively.Both systems use letter-based color codes that require a large range of values to represent different colors.The problem is that these two systems are hard to use for manipulating any operations involving combinations of colors,and they lack the capacity for inter-changeability or unification.Based on prime number theory and Goldbach's conjecture,this study presents a universal color system(C235)using a number-based structure to encode,compute and unify all colors on a color wheel.The proposed C235 system offers a unified representation for the efficient encoding and effective manipulation of color.It can be applied to designing a high-rate LCD system and colorizing objects with multiple attributes and DNA codons,opening the door to manipulating colors and lights for even broader applications.
文摘Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are considered for the redundancy allocation problem with series-parallel structure. The max-min approach can formulate the problem as an integer linear programming problem instead of an integer nonlinear problem. This paper presents a comparison between those methods from the standpoint of solution quality and computational complexity. The experimental results show that the max-min approach is superior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems, but analysis of computational complexity shows that the max-min approach is inferior to other greedy heuristics.
