Abstract We determine all permutation polynomials over of the form where, for some that is a power characteristic , we have and terms degrees in . use this classification to resolve eight conjectures open problems from literature, list 77 recent results literature follow immediately simplest special cases our result. Our proof makes novel geometric techniques situation where they previously did not seem applicable, namely understand arithmetic high‐degree rational functions small finite...

We determine all degree-$4$ rational functions $f(X)\in \mathbb {F}_q(X)$ which permute $\mathbb {P}^1(\mathbb {F}_q)$, and answer two questions of Ferraguti Micheli about the number such equivalence classes func

For each prime power [Formula: see text], we determine all text] for which permutes text].

considering the problem of uncertainty data in information gathering system, a multi-sensor fusion method based on fuzzy set and evidence theory (FS-DS) is proposed . The support probability uncertain defined by making using correlation function , Then it received credibility measured each sensor form membership function. And will confidence into basic Finally, sensors with higher measurement precision are identified D-S combination. can improve assignment difficult to be determined...

For each q of the form 4 k , we determine all a ∈ Fq for which X + 2q-1 aX 2 -q+1 permutes F .We also construct class permutation trinomials over in case ≡ 1 (mod 3) .

Abstract For each odd prime power $q$, we construct an infinite sequence of rational functions $f(X) \in{\mathbb{F}}_q(X)$, which is exceptional in the sense that for infinitely many $n$ map $c \mapsto f(c)$ induces a bijection ${\mathbb{P}}^1({\mathbb{F}}_{q^n})$. Moreover, our $f(X)$ indecomposable it cannot be written as composition lower-degree ${\mathbb{F}}_q(X)$. These are first known examples wildly ramified $f(X)$, other than linear changes polynomials. In case $q$ not $3$, these...

We determine the roots in F_{q^3} of polynomial X^{2q^k+1} + X c for each positive integer k and F_q, where q is a power 2. introduce new approach this type question, we obtain results which are more explicit than previous area. Our resolve an open problem conjecture Zheng, Kan, Zhang, Peng, Li.

We determine all permutations in two large classes of polynomials over finite fields, where the construction each class involves denominators a rational functions generalizing classical Redei functions. Our results generalize eight recent from literature, and our proofs more general are much shorter simpler than previous special cases.

For each odd prime power q, and integer k, we determine the sum of k-th powers all elements x in F_q for which both x+1 are squares F_q^*. We also solve analogous problem when one or is a nonsquare. use these results to image set f(F_q) f(X) F_q[X] form X^4+aX^2+b, resolves two conjectures by Finch-Smith, Harrington, Wong.

In this paper, some new results on the distribution of generalized singular value decomposition (GSVD) are presented.

For any nonconstant f,g∈C(x) such that the numerator H(x, y) of f(x)−g(y) is irreducible, we compute genus normalization curve H(x,y)=0. We also prove an analogous formula in arbitrary characteristic when f and g have no common wildly ramified branch points, generalize to (possibly reducible) fiber products morphisms curves f:A→D g:B→D.

We determine all permutation polynomials over F_{q^2} of the form X^r A(X^{q-1}) where, for some Q which is a power characteristic F_q, integer r congruent to Q+1 (mod q+1) and terms A(X) have degrees in {0, 1, Q, Q+1}. then use this classification resolve eight conjectures open problems from literature, we show that simplest special cases our result imply 58 recent results literature. Our proof makes novel geometric techniques situation where they previously did not seem applicable, namely...