# As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and its sums of squares indicate the variance of each component of the decomposition ( or, equivalently, each set of terms of a linear model ).

# Closely related to the ANOVA is a linear model fit with coefficient estimates and standard errors.

# The accused person ( defendant ) is addressed by name ;

# The charge against the accused person is read, including the alleged date, time, and place of offense ; and,

# The accused person is asked formally how he or she pleads.

# Assume the first item is largest.

# Look at each of the remaining items in the list and if it is larger than the largest item so far, make a note of it.

# The last noted item is the largest in the list when the process is complete.

# The Lambeth Conference ( first held in 1867 ) is the oldest international consultation.

# The Primates ' Meeting ( first met in 1979 ) is the most recent manifestation of international consultation and deliberation, having been first convened by Archbishop Donald Coggan as a forum for " leisurely thought, prayer and deep consultation ".

# Deontological ethics, notions based on ' rules ' i. e. that there is an obligation to perform the ' right ' action, regardless of actual consequences ( epitomized by Kant's notion of the Categorical Imperative )

# A Murder is Announced ( 1950 )

# Civil aviation, held by Armavia national airline ( owned by Mikhail Baghdasarov, who is thought to be close to President Serge Sarkisian )

# There is always an integer number of electrons orbiting the nucleus.

# The Slater-type orbital ( STO ) is a form without radial nodes but decays from the nucleus as does the hydrogen-like orbital.

# A person who is skilled at some activity.

# unaided by the Holy Spirit, no person is able to respond to God ’ s will ;

# grace is resistible ; and

# Prior to being drawn and enabled, one is unable to believe … able only to resist.

# Having been drawn and enabled, but prior to regeneration, one is able to believe … able also to resist.

# After one believes, God then regenerates ; one is able to continue believing … able also to resist.

# Upon resisting to the point of unbelief, one is unable again to believe … able only to resist.

# The carbon-hydrogen ratio is high.

# It is easily harvested.

More formally, # P is the class of function problems of the form " compute ƒ ( x )," where ƒ is the number of accepting paths of a nondeterministic Turing machine running in polynomial time.

One consequence of Toda's theorem is that a polynomial-time machine with a # P oracle ( P < sup ># P </ sup >) can solve all problems in PH, the entire polynomial hierarchy.

Many # P-complete problems have a fully polynomial-time randomized approximation scheme, or " FPRAS ," which, informally, will produce with high probability an approximation to an arbitrary degree of accuracy, in time that is polynomial with respect to both the size of the problem and the degree of accuracy required.

Jerrum, Valiant, and Vazirani showed that every # P-complete problem either has an FPRAS, or is essentially impossible to approximate ; if there is any polynomial-time algorithm which consistently produces an approximation of a # P-complete problem which is within a polynomial ratio in the size of the input of the exact answer, then that algorithm can be used to construct an FPRAS.

# Test that F ≠ N, that F divides N ( time complexity O ( log N )), and that F is prime ( polynomial time ; see AKS primality test ).

# Using a mathematical expression, such as a polynomial or a trigonometric function, and a single point on the corresponding curve instead of storing or transmitting the entire graphic curve or a series of points on it.

# Find the characteristic polynomial p ( t ).

# r ( x ) is a polynomial

Thus, if the permanent can be computed in polynomial time by any method, then FP = # P, which is an even stronger statement than P = NP.

# In there are k terms in the product and each term contains one x, so L ( x ) ( which is a sum of these k-degree polynomials ) must also be a k-degree polynomial.

# In algebraic number theory, a " height function " is a measurement related to the minimal polynomial of an algebraic number ;

# REDIRECT homogeneous polynomial

# Pontryagin numbers of closed Riemannian manifold ( as well as Pontryagin classes ) can be calculated as integrals of certain polynomial from curvature tensor of Riemannian manifold.

If real computation were physically realizable, one could use it to solve NP-complete problems, and even # P-complete problems, in polynomial time.

# A ring R is Cohen – Macaulay if and only if the polynomial ring R is Cohen – Macaulay.

This counting problem is # P-complete, which implies that it is not solvable in polynomial time unless P = NP.

Moreover, there is no fully polynomial randomized approximation scheme for # 2SAT unless NP = RP and this even holds when the input is restricted to monotone 2-CNF formulas, i. e., 2-CNF formulas in which each literal is a positive occurrence of a variable.

# If k is a field and X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > d </ sub > are indeterminates, then X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > d </ sub > form a regular sequence of length d on the polynomial ring kX < sub > 2 </ sub >, ..., X < sub > d </ sub > and there are no longer R-sequences, so R has depth d, as does the formal power series ring in d indeterminates over any field.

# Redirect knot polynomial

# REDIRECT polynomial ring

# REDIRECT polynomial ring

# REDIRECT Gromov's theorem on groups of polynomial growth