Leaf area (LA) is a valuable key for plant physiological studies, therefore accurate and simple models for LA determination are important for many experimental comparisons. A greenhouse experiment was conducted from October 2009 to February 2010 in two basil cultivars (Purple Ruffles and Genovese) to estimate LA, leaf dry weight (DW), leaf fresh weight (DW) and leaf dimensions (width-W and leng...

Let C be the middle-third Cantor set. In this paper, we show that for every x∈[0,4], there exist x1,x2,x3,x4∈C such x=x12+x22+x32+x42, which was conjectured in Athreya et al. (2019) [1].

In [6], Murray Marshall proved that every f∈R[X,Y] non-negative on the strip [0,1]×R can be written as f=σ0+σ1X(1−X) with σ0,σ1 sums of squares in R[X,Y]. this work, we present a few results concerning representation particular cases. First, under assumption degY⁡f≤2, by characterizing extreme rays suitable cone, obtain degree bound for each term. Then, consider case f positive and non-vanishin...

The celebrated Four Squares Theorem of Lagrange states that every positive integer is the sum of four squares of integers. Interest in this Theorem has motivated a number of different demonstrations. While some of these demonstrations prove the existence of representations of an integer as a sum of four squares, others also produce the number of such representations. In one of these demonstrati...

In this paper, we prove some identities for the alternating sums of squares and cubes of the partial sum of the q-binomial coefficients. Our proof also leads to a q-analogue of the sum of the first n squares due to Schlosser.