Sentence examples for sum analogous to from inspiring English sources

Now we define another sum analogous to Kloosterman sums as follows: S ( χ, q ) = ∑ ′ a = 1 q − 1 χ ( a + a ¯ ).

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.

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.

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.

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 ) ).

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).

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.

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].

Their regularity is ruled by a sum law analogous to that describing the propagation of singularities in one dimension.

Second, we calculated the measure for effect size and we used the mean sum of squares (analogous to the effect size parameter evaluated in the F test), which was calculated as: (3) ∑ y ¯ i, j − y ¯ j 2 n where y ¯ i, j is the mean methylation of tissue i of CpG j, y ¯ i is the overall mean methylation of CpG j and n the number of tissues studied.

As further applications, we also give some new sum relations of products of the Frobenius-Euler polynomials by applying some summation transform techniques, which are analogous to some sum relations of products of the classical Euler polynomials and Frobenius-Euler polynomials stated in [9, 25].