Q. What is double periodic phenomena?
Answers
Answer:Double pneumonia is a lung infection that affects both of your lungs. The infection inflames the air sacs in your lungs, or the alveoli, which fill with fluid or pus. This inflammation makes it hard to breathe.
The most common causes of pneumonia are bacteria and viruses. Infection from fungi or parasites can also cause pneumonia.
Pneumonia can also be categorized by the number of segments of the lobes in your lungs that are infected. If more segments are infected, whether in one lung or both lungs, the disease is likely to be more serious.
You can catch pneumonia by coming into contact with infectious viruses or breathing in infectious air droplets. If it’s not treated, any pneumonia can be life-threatening.
Explanation:
Explanation:
In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v are periods of a function ƒ means that
{\displaystyle f(z+u)=f(z+v)=f(z)\,}f(z+u)=f(z+v)=f(z)\,
for all values of the complex number z.
The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine. In the complex plane the exponential function ez is a singly periodic function, with period 2πi.
As an arbitrary mapping from pairs of reals (or complex numbers) to reals, a doubly periodic function can be constructed with little effort. For example, assume that the periods are 1 and i, so that the repeating lattice is the set of unit squares with vertices at the Gaussian integers. Values in the prototype square (i.e. x + iy where 0 ≤ x < 1 and 0 ≤ y < 1) can be assigned rather arbitrarily and then 'copied' to adjacent squares. This function will then be necessarily doubly periodic.
If the vectors 1 and i in this example are replaced by linearly independent vectors u and v, the prototype square becomes a prototype parallelogram that still tiles the plane. The "origin" of the lattice of parallelograms does not have to be the point 0: the lattice can start from any point. In other words, we can think of the plane and its associated functional values as remaining fixed, and mentally translate the lattice to gain insight into the function's characteristics.
If a doubly periodic function is also a complex function that satisfies the Cauchy–Riemann equations and provides an analytic function away from some set of isolated poles – in other words, a meromorphic function – then a lot of information about such a function can be obtained by applying some basic theorems from complex analysis. PLEASE FOLLOW &LIKE THE ANSWER