The surface-area-to-volume ratio, also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of an object or collection of objects. In chemical reactions involving a solid material, the surface area to volume ratio is an important factor for the reactivity, that is, the rate at which the chemical reaction will proceed.
For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is the sphere, a consequence of the isoperimetric inequality in 3 dimensions. By contrast, objects with tiny spikes...
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a...
The specific strength is a material's strength (force per unit area at failure) divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pa m3/kg, or N·m/kg, which is dimensionally equivalent to m2/s2, though the latter form is rarely used. Specific strength has the same units as specific energy, and is related to the maximum specific energy of rotation that an object can have without flying apart due to centrifugal force.
Another way...
I'm trying to understand the following. I'll denote by $X$ the set of all ordinals that are at most $\omega_1$, the first uncountable ordinal. To avoid confusion, they can be equal to $\omega_1$ as well. Equip $X$ with the order topology.
Then how come $\omega_1$ is an accumulation point of $X\...
I am working through these examples of computations on Bayesian networks and came across this claim (part of the last sample computation):
$$
P(E=e|A=a) = \sum_{c \in C} P(E=e, C=c | A=a)
$$
I am newly familiar with marginalization, but I thought that it was:
$$
P(A=a) = \sum_{b \in B} P(A=a,B...
Let $\{a_n\}$ be an unbounded, strictly increasing sequence of positive real numbers and let $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$. Which of the following statements is/are correct? (CSIR NET December 2014)
For all $n\geq m, \sum\limits^{n}_{k=m}x_k>1-\bf{\frac{a_m}{a_n}}$
There exist ...
