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diff --git a/proofs_1.txt b/proofs_1.txt new file mode 100644 index 0000000..ba89f09 --- /dev/null +++ b/proofs_1.txt @@ -0,0 +1,172 @@ +1. Logarithmic notation is appropriate and shouldn't be modified. + +2. Unbolding all bold greek characters was wrong. Here is the exhaustive list of mistakes you have introduced to the manuscript: + + In equation (23) ω must be bold in its first appearance but not its second. + + On line 273 ω must be bold. + + In equation (24) ω must be bold in its first two appearances but not its third. + + In equation (25) ω must be bold in its first two appearances but not its third. + + On line 285 ω must be bold. + + On line 287 ω must be bold. + + In equation (26) all appearances of ω must be bold. + + In equation (27) all appearances of ω must be bold. + + In equation (28) all appearances of ω must be bold. + + In equation (31) all appearances of ω must be bold. + + In equation (34) all appearances of ω must be bold. + + In equation (36) all appearances of ω must be bold. + + In equation (37) all appearances of ω and η must be bold. + + On line 356 all appearances of η must be bold. + + In equation (40) all appearances of φ and η must be bold. + + In equation (41) all appearances of φ and ω must be bold. + + In equation (43) all appearances of φ and η must be bold. + + In equation (44) ω must be bold in its first appearance only. + + On line 409 φ must be bold. + + In equation (48) all appearances of η must be bold. + + In equation (49) all appearances of η must be bold. + + In equation (61) ω must be bold in its first appearance only. + + In equation (62) ω must be bold in its first appearance only. + + In equation (76) all appearances of φ must be bold. + + In equation (77) all appearances of φ must be bold. + + In equation (78) all appearances of φ must be bold. + + In equation (79) all appearances of φ must be bold. + + In equation (80) all appearances of φ must be bold. + + On line 768 all appearances of φ must be bold. + + On line 769 φ must be bold. + + In equation (A3) all appearances of φ and η must be bold. + + On line 937 all appearances of η must be bold + + On line 938 φ must be bold. + + On line 940 φ must be bold. + + In equation (A4) all appearances of φ and η must be bold. + + In equation (A5) all appearances of φ and η must be bold. + + In equation (A6) all appearances of φ and η must be bold. + + On line 950 φ must be bold. + + On line 951 all appearances of η must be bold. + + In equation (A7) all appearances of φ must be bold. + + On line 961 φ must be bold. + + In equation (A8) all appearances of φ must be bold. + + In equation (A10) all appearances of φ must be bold. + + In equation (B1) ω must be bold. + + On line 1010 all appearances of η must be bold. + + In equation (B2) all appearances of η and ε must be bold. + + On line 1012 all appearances of ε and η must be bold. + + On line 1013 all appearances of ε and η must be bold. + + On line 1015 ε must be bold. + + In equation (B3) all appearances of ε and η must be bold. + + In equation (B4) all appearances of η must be bold. + + In equation (B5) all appearances of η must be bold. + + In equation (B6) all appearances of η must be bold. + + In equation (C1) ω must be bold in its first appearance only. + + In equation (D1) all appearances of φ and η must be bold. + + In equation (D2) all appearances of φ must be bold. + + On line 1044 φ must be bold. + + In equation (D3) all appearances of φ must be bold. + + In equation (D4) all appearances of φ must be bold. + + In equation (D5) all appearances of φ must be bold. + + In equation (D6) all appearances of φ must be bold. + + On line 1049 all appearances of φ must be bold. + + In equation (D7) φ must be bold. + +3. The definition is correct. + +4. The use of the "multiplication sign" is correct and shouldn't be modified. + +5. Ok. + +6. The definition is correct. + +7. For Ref [1], World Scientific lists the following cities: New Jersey; London; Singapore; Beijing; Shanghai; Hong Kong; Taipei; Chennai; Tokyo. + + For Ref [9], North-Holland Publishing Company lists the following cities: Amsterdam; New York; Oxford. + + For Ref [15], Elsevier lists the following cities: Amsterdam; Oxford; New York; Tokyo. + + For Ref [54], IEEE list the following cities: Los Alamitos, California; Washington; Tokyo. + + For Ref [57], Clarendon Press lists Oxford. + + For Ref [58], Springer International Publishing lists Cham, Switzerland. + +8. None of the cited eprints have since been published. + +9. Ref [23] should be cited in the block of citations on line 131. + +FQ. The information is correct. + +Q. Ref [16] has DOI 10.1063/10.0034343 + Ref [28] can be found at https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-49/issue-4/On-the-average-number-of-real-roots-of-a-random/bams/1183505112.full + +Other corrections: + +Changes of the text at line 70 affect its scientific meaning. A more appropriate text reads "is independent of the energy and the gradient." + +In equation (39), Tr Hess H(x) should instead read Tr Hess H(x, ω) with a bold ω. + +In equation (60), L(x) should instead read L(x, ω) with a bold ω. + +In equation (D1), '\bar{θ}₁ θ₁ \hat{x}_a' should instead read 'i \hat{x}_a \bar{θ}₁ θ₁', similar to equation (40). + +On line 1051, 'RSBorder' should be replaced by 'RSB order'. + +References [21], [27], [39], [40], [50], and [51] have an empty set of parentheses that should be removed. |