SP are analogous to sums of squares (SS) in an anova and can be calculated from eqn (1): (1) where X and Y are the two traits, and X + Y is the sum of the two traits.
In individuals with multiple target lesions, SUVmax values from each ROI were summed to obtain a summed SUVmax, analogous to the RECIST summed longest diameter [ 10].
The main purpose of this paper is, using the properties of Gauss sums and the estimate for the generalized exponential sums, to study the upper bound estimate problem of one kind sums analogous to the high-dimensional Kloosterman sums and to give some interesting mean value formula and an upper bound estimate for it.
Now we define another sum analogous to Kloosterman sums as follows: S ( χ, q ) = ∑ ′ a = 1 q − 1 χ ( a + a ¯ ).
which is analogous to the sum relation on the classical Euler polynomials stated in [[25], Theorem 7].
In this paper, we introduce a new sum, analogous to Cochrane sums, and use elementary and analytic methods to study the hybrid mean value problem involving this sum and Kloosterman sums, and we give an interesting asymptotic formula for it.
Now for any odd prime p > 1 and integer h with ( h, q ) = 1, we define another sum analogous to the Cochrane sum as follows: C 1 ( h, p ) = ∑ a = 1 p − 1 2 ( ( a ¯ 2 p ) ) ( ( a 2 h p ) ).
The main purpose of this paper is, using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving the quadratic Gauss sums and a new sum analogous to Kloosterman sums, and to give an interesting hybrid mean value formula for it.
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of a new sum analogous to quadratic Gauss sums, and to give an interesting asymptotic formula for its 2k th power mean.
In this paper, we consider a sum analogous to the high-dimensional Kloosterman sums as follows: S ( c 1, c 2, …, c k, m, χ ; q ) = ∑ ′ a 1 = 1 q ⋯ ∑ ′ a k = 1 q χ ( c 1 a 1 + ⋯ + c k a k + m a ¯ 1 ⋯ a ¯ k ), (1.1).
In a way, the overall cardiovascular burden analysis is analogous to analyzing sum scores of symptoms using a symptom checklist as opposed to analyzing each symptom individually.
