Let K_(1,k)be a star of order k+1 and K_(n)■K_(1,k)the graph obtained from a complete graph K_(n)and an additional vertex v by joining v to k vertices of K_(n).For graphs G and H,the star-critical Ramsey number r_(*)...Let K_(1,k)be a star of order k+1 and K_(n)■K_(1,k)the graph obtained from a complete graph K_(n)and an additional vertex v by joining v to k vertices of K_(n).For graphs G and H,the star-critical Ramsey number r_(*)(G,H)is the minimum integer k such that any red/blue edge-coloring of K_(r-1)■K_(1,k)contains a red copy of G or a blue copy of H,where r is the classical Ramsey number R(G,H).Let C_(m)denote a cycle of order m and W_(n)a wheel of order n+1.Hook(2010)proved that r_(*)(W_(n),C_3)=n+3 for n≥6.In this paper,we show that r_(*)(W_(n),C_(m))=n+3 for m odd,m≥5 and n≥3(m-1)/2+2.展开更多
The performance of solar panels significantly degrades due to dust accumulation but cleaning too frequently will severely impact the financial benefits of the installation of solar panels. This paper assumes a realist...The performance of solar panels significantly degrades due to dust accumulation but cleaning too frequently will severely impact the financial benefits of the installation of solar panels. This paper assumes a realistic linear model for accumulation of dust on the solar panels and the resulting hourly average of absolute loss of efficiency in solar panels. This model accurately depicts the fact that energy production by solar panels occurs during sunshine hours only and also accounts for the degradation in the efficiency of solar panels due to dust accumulation throughout the entire day. Based on this, the optimal number of days for maximum financial profit and the critical number of days (above which there is no profit in installing solar panels) have been estimated. Furthermore, we have suggested a formalism to help estimate the finances for self-cleaning technology for PV system and also for calculating the minimum payback period for installing solar panels with the financial cost of the cleaning cycles properly considered. This research could be motivation for companies in developing self-cleaning mechanism for PV system.展开更多
用r种颜色对图G的所有边着色,记着第i色的边构成的子图为Gi,如果存在一种着色方法使得对所有的1≤i≤r都满足Hi Gi,则称图G对于(H1,H2,…,Hr)可r着色.R am sey数R(H1,H2,…,Hr)是使得完全图Kn对于(H1,H2,…,Hr)不可r着色的最小正整数n....用r种颜色对图G的所有边着色,记着第i色的边构成的子图为Gi,如果存在一种着色方法使得对所有的1≤i≤r都满足Hi Gi,则称图G对于(H1,H2,…,Hr)可r着色.R am sey数R(H1,H2,…,Hr)是使得完全图Kn对于(H1,H2,…,Hr)不可r着色的最小正整数n.令m1>m2≥m3,E r.do.s等给出了当m1足够大时R(Cm1,Cm2,Cm3)的值.通过对m1不是足够大的情况进行研究,证明了当m≥5时,R(Cm,C3,C3)=5m-4;并给出了当m1≤7时R(Cm1,Cm2,Cm3)的值.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11871270,12161141003,11931006)。
文摘Let K_(1,k)be a star of order k+1 and K_(n)■K_(1,k)the graph obtained from a complete graph K_(n)and an additional vertex v by joining v to k vertices of K_(n).For graphs G and H,the star-critical Ramsey number r_(*)(G,H)is the minimum integer k such that any red/blue edge-coloring of K_(r-1)■K_(1,k)contains a red copy of G or a blue copy of H,where r is the classical Ramsey number R(G,H).Let C_(m)denote a cycle of order m and W_(n)a wheel of order n+1.Hook(2010)proved that r_(*)(W_(n),C_3)=n+3 for n≥6.In this paper,we show that r_(*)(W_(n),C_(m))=n+3 for m odd,m≥5 and n≥3(m-1)/2+2.
文摘The performance of solar panels significantly degrades due to dust accumulation but cleaning too frequently will severely impact the financial benefits of the installation of solar panels. This paper assumes a realistic linear model for accumulation of dust on the solar panels and the resulting hourly average of absolute loss of efficiency in solar panels. This model accurately depicts the fact that energy production by solar panels occurs during sunshine hours only and also accounts for the degradation in the efficiency of solar panels due to dust accumulation throughout the entire day. Based on this, the optimal number of days for maximum financial profit and the critical number of days (above which there is no profit in installing solar panels) have been estimated. Furthermore, we have suggested a formalism to help estimate the finances for self-cleaning technology for PV system and also for calculating the minimum payback period for installing solar panels with the financial cost of the cleaning cycles properly considered. This research could be motivation for companies in developing self-cleaning mechanism for PV system.
文摘用r种颜色对图G的所有边着色,记着第i色的边构成的子图为Gi,如果存在一种着色方法使得对所有的1≤i≤r都满足Hi Gi,则称图G对于(H1,H2,…,Hr)可r着色.R am sey数R(H1,H2,…,Hr)是使得完全图Kn对于(H1,H2,…,Hr)不可r着色的最小正整数n.令m1>m2≥m3,E r.do.s等给出了当m1足够大时R(Cm1,Cm2,Cm3)的值.通过对m1不是足够大的情况进行研究,证明了当m≥5时,R(Cm,C3,C3)=5m-4;并给出了当m1≤7时R(Cm1,Cm2,Cm3)的值.
