Journal of Number TheoryD. Hensley, The sum of a αΩ(n) over integers n ≤ x with all factors between α and y, J. Number Theory 18 (1984), 206–212Hensley, D. (1984). The sum of \(\alpha ^{\Omega (n)}\) over integers \(n\le x\) with all prime factors between \(\...
Then for any positive sequence {rn}↗+∞, we have limninfx,y∈Cf(x)+g(y)+rn∣x-y∣2=infx∈Cf(x)+g(x). Proof Let us observe first that the limit in the formula exists since the sequence is increasing. Let us consider the function Fn(x,y)=f(x)+g(y)+rn∣x-y∣2, this...
These companies require suppliers to stop clearing all High Conservation Value (HCV) areas, High Carbon Stock (HCS) areas and carbon-‐rich peatlands, regardless of depth. In addition, ...
A positive integer can be represented as the sum of two squares iff each of its prime factors of the form occurs as an even power, as first established by Euler in 1738. In Lagrange's four-square theorem, Lagrange proved that every positive integer can be written as the sum of at most...
The sum of the square of a positive number and the square of {eq}3 {/eq} more than the number is {eq}185 {/eq}. What is the number? Quadratic equation: A quadratic equation is an equation with degree {eq}2 {/eq}. There are two ways...
1, if n has no square prime factors and an even number of prime factors; -1, if n has no square prime factors and an odd number of prime factors. Answer and Explanation: We attempt a proof by strong induction. Suppose f is multiplicative, and let n∈...
2 August 2024 / Accepted: 17 November 2024 / Published online: 21 December 2024 © The Author(s) 2024 Abstract In this work, we calculated the form factors of the weak decay process Λ0b →Λc(2595)+, where the final charm baryon represents an excited state with spin-parity 1 2 ...
The bias was also positive across all simulation scenarios. The standard (delete-1) jackknife approach performed the worst among all methods, producing inflated estimates of SE. The variance and RMSE of this estimator were high compared to other approaches. The SE was, in general, over-estimated...
Consumer spending and GDP have a strong positive correlation, and it is possible to predict a country's GDP based on consumer spending (CS). Using the formula for abest fit line, this relationship can be approximated as: GDP = 1.3232 x CS + 10447 ...
It is again natural to model it as being close to low rank, under the assumption that a much smaller number of (latent) factors about the interests of the user, the type of activity and the time period should contribute to the rating. How many entries of the tensor do we need to ...