To analyze filament-shaped versus dot-shaped aggregates, an aggregate with "Circularity" (4π×Area/Perimetre2) of 0 to 0.7 was considered a filament-shaped aggregate while an aggregate with "Circularity" of 0.7 to 1 was considered dot shaped.
First, we give proofs of Theorems 1 and 2, and in the last section, we provide x- and n- integrals for equations found in Theorems 1 and 2. In what follows, all calculations are done on the set of solutions of equation (1), that is, we consider (dots, t_{-1}, t_{0}, t_{1}, dots) and (t_{x}, t_{xx}, t_{xxx}, dots) as independent dynamical variables.
Round or oval tonsilloliths with a long diameter under 2 mm were considered dots, while those with a long: short diameter ratio of under 3 2 were considered round, those with a long: short diameter ratio of over 3 2 were considered oval, and those with shapes that were neither round nor oval were considered irregular.
They also tell us that no team has overcome a 3-0 Stanley Cup series deficit since the Toronto Maple Leafs did it during the FDR administration, which is a bit unfair considering T-Dot's location.
Cosine of the angle can be computed by the Euclidean dot product ω 1 T ω 2. When we consider the dot product of tangent vectors on S, we obtain ω ˜ 1 T ω 2 ˜ = ( J ω 1 ) T ( J ω 2 ) = ω 1 T ( J T J ) ω 2. Therefore, the matrix product J T J induces the metric on a surface on time scales.
Because we can consider each dot in Figure 2 to be a unique genotype table in the space of genotype tables with fixed control data and a fixed number of cases, those tables that lie on the same dashed line will have the same value of χ2 statistic.
Conversely, considering the black dot on the demand curve, we can see that the demand is higher than the volume of goods that the supplier can produce.
Andrew Shapiro: Thinking by analogy, or thinking historically by comparison, consider the dot-com boom 10 years ago and the bust that followed.
The box plots indicate the median (horizontal line); the interquartile range (box), not farther away than 1.5 times the interquartile range from the first and third quartiles (whiskers); and the values that are not in the range of whiskers and not considered outliers (dots).
Consider polka dots, geometric shapes, and floral prints.
Considering spherical quantum dots, as the nanoparticle size reduces (radius, R), the relative surface (S) to volume (V) ratio (S/V = 4πR2 / (4/3 πR3) = 3/R) is significantly increased leading to more surface defects.
