What is Polylogarithmic time?
In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., “it has polylogarithmic order”).
What is dilog function?
Dilogarithm Function for Numeric and Symbolic Arguments Depending on its arguments, dilog returns floating-point or exact symbolic results. Compute the dilogarithm function for these numbers. Because these numbers are not symbolic objects, dilog returns floating-point results.
What is Li math?
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance.
What does Poly N mean?
Abuse of notation or not, polylog(n) does mean “some polynomial in log(n)”, just as “poly(n)” can mean “some polynomial in n”. So O(polylog(n)) means “O((log n)k) for some k”. (See Wikipedia: Polylogarithmic, or, to see it in context, Prof.
What is n log n means?
O(nlogn) is known as loglinear complexity. O(nlogn) implies that logn operations will occur n times. O(nlogn) time is common in recursive sorting algorithms, sorting algorithms using a binary tree sort and most other types of sorts. The above quicksort algorithm runs in O(nlogn) time despite using O(logn) space.
What is Lcst of Pnipam?
Poly-N-isopropyl acrylamide (PNiPAM) is a well-known thermosensitive polymer that dissolves in cold water but collapses to a globule or phase separates when the temperature is increased beyond the lower critical solution temperature (LCST) of Tc ≈ 32 °C1,2.
What is Pnipam used for?
Poly(N-isopropylacrylamide) (PNIPAm) is widely used to fabricate cell sheet surfaces for cell culturing, however copolymer and interpenetrated polymer networks based on PNIPAm have been rarely explored in the context of tissue engineering.
What is gamma function formula?
To extend the factorial to any real number x > 0 (whether or not x is a whole number), the gamma function is defined as Γ(x) = Integral on the interval [0, ∞ ] of ∫ 0∞t x −1 e−t dt. Using techniques of integration, it can be shown that Γ(1) = 1.
How is gamma calculated?
Calculating Gamma Gamma is the difference in delta divided by the change in underlying price. You have an underlying futures contract at 200 and the strike is 200. The options delta is 50 and the options gamma is 3. If the futures price moves to 201, the options delta is changes to 53.
What is Ucst and LCST?
The critical temperature is called the upper critical solution temperature (UCST) when the phase separation occurs at temperatures below the critical temperature, and it is called the lower critical solution temperature (LCST) when the phase separation occurs at temperatures above the critical temperature, as shown in …
What is on * log n?
O(log N) basically means time goes up linearly while the n goes up exponentially. So if it takes 1 second to compute 10 elements, it will take 2 seconds to compute 100 elements, 3 seconds to compute 1000 elements, and so on. It is O(log n) when we do divide and conquer type of algorithms e.g binary search.
What is log base 2 of n?
What Is Log Base 2 In Algebra? The log base 2 to a number N in algebra is equal to the exponent value of 2 which gives the number N. The log base 2 is written in the logarithmic form as log2N=k l o g 2 N = k , and the same is written in exponential form as 2k = N.
What is polylogarithm in math?
In mathematics, the polylogarithm (also known as Jonquière’s function, for Alfred Jonquière) is a special function Li s ( z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function.
How do you find the O notation for polylogarithmic functions?
All polylogarithmic functions of n {\\displaystyle n} are o (n ε) {\\displaystyle o (n^ {\\varepsilon })} for every exponent ε > 0 (for the meaning of this symbol, see small o notation), that is, a polylogarithmic function grows more slowly than any positive exponent. This observation is the basis for the soft O notation Õ (n).
What are polylogarithms of positive integer order?
In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams . The polylogarithm function is equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent.
Is the polylogarithm a rational function of Z?
Accordingly the polylogarithm reduces to a ratio of polynomials in z, and is therefore a rational function of z, for all nonpositive integer orders. The general case may be expressed as a finite sum: