[PDF] Top 20 Solving $X^{q+1}+X+a=0$ over Finite Fields

... including finite geometry, the inverse Galois problem [1], the construction of difference sets with Singer parameters [8], determining cross-correlation between m-sequences [11, 14] and to construct error- ... See full document

... In Theorem 2.3(ii) below we prove a sufficient condition for solvability: if every element of F can be written as a sum of nth powers of elements of F, then the equation in Problem A2 is always solvable for this particular ... See full document

... For q a prime power, let F q denote the finite field with q elements, F ∗ q = F q \ {0}, and F q [x] the ring of polynomials over F q ...F ... See full document

... p q ( 0 , 1 ) X − A X A B X ∗ − ∗ − B = I < p q < ...with 0 < p q , < 1 always has the unique positive definite ... See full document

... We are going to apply Arakelov theory to smooth projective geometrically connected curves X over number fields K . In [3] Arakelov defined an intersection theory on the arithmetic surfaces attached ... See full document

... p, q < 1 always has the unique positive definite ...equation X − A ∗ XA + B ∗ X −1 B = I (2) has been ...equations X − B ∗ X −1 B = I [5, 6] and X + B ∗ ... See full document

... (X, X (g, U) ). Especially, the Alaoglu-Bourbaki theorem for the pair (X, X (g, U) ) is ...(X, X ’ ) can be extended to (X, X (g, U) ... See full document

... In LW’s model, buyers choose cash holdings …rst and then sellers produce on demand. Their economy can then be described as a sequential game. In that economy buyers face a holdup problem due to their up-front investment ... See full document

... The Gibbs phenomenon is artificial oscillations near the discontinuities and aperiodic endpoints. They are numerical noise without any physical meaning, and should be elim- inated if possible. In [1], the Fourier ... See full document

... layers and the C-type AFM insulating ground state for x > 0.6 with polaronic conductivity along the one-dimen- sional (1D) FM coupling, i.e., MnO chains. 26­28) Further- more, above room temperature, the ... See full document

... Furthermore, we observe that, in R n , the existence of an approximate tangent for E implies that the projection of E onto a line with direction not perpendicular to the approximate tangent direction has positive ... See full document

... The coordination polyhedron of the La1 atoms is a 15-vertices polyhedron (CN=15). The nearest neighbours of La2 atoms form 14-vertices polyhedra with CN=14 (see Fig. 1a). The 10-vertices polyhedra around Pb3 can be seen ... See full document

... Sequencing of perA. Three overlapping DNA fragments, perA-1, perA-2, and perA-3, or perA-3 ⌬ R*, covering the whole perA or perA- ⌬ R* gene, was amplified using primer sets defined in Table S3 in the supple- mental ... See full document

... with 36% to the total DOS. It is necessary to underline, that we have projected only 6 out of 24 Carbon atoms, just to save time. This contribution appears in the band bellow the Fermi level, due to its semiconductor ... See full document

... Equations of this form often arise in applications of Newton’s second law of motion. For example, suppose y is the displacement of a moving object with mass m. It’s reasonable to think of two types of time-independent ... See full document

... 20) On lighting a rocket cracker, it gets projected in a parabolic path and reaches a maximum height of 4mts when it is 6 mts away from the point of projection. Finally, it reaches the g[r] ... See full document

... See § 746.6 for additional license requirements for export and reexports to the Crimea region of Ukraine and transfers (in-country) within the Crimea region of Ukraine for all items sub[r] ... See full document

... 2 0), (3 1 1), (4 0 0), (4 2 2), (5 1 1), (4 4 0) and (5 3 3) respectively are ...the X-ray diffraction pattern of Mg (x) Fe (1–x) O/SiO ... See full document

... of X. The number p = αg + k − 1 is called the algebraic genus of X, where α = 1 or 2, if the sign of σ ( Γ ) is “ − ” or “+”, ...= 0, then Γ is a Fuchsian ... See full document

... cdo over X in the following cases: X = G is an affine algebraic group; X = G/N or G/P, where N is a unipotent subgroup and P is a para- bolic subgroup and G is simple (the extension to the case ... See full document