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On factorization of q-difference equation for continuous q-Hermite polynomials
We argue that a customary q-difference equation for the continuous q-Hermite
polynomials H_n(x|q) can be written in the factorized form as (D_q^2 -
1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference
operator. This means that the polynomials H_n(x|q) are in fact governed by the
q-difference equation D_qH_n(x|q)=q^{-n/2}H_n(x|q), which is simpler than the
conventional one.Comment: 7 page
Fractional differentiability for solutions of nonlinear elliptic equations
We study nonlinear elliptic equations in divergence form
When
has linear growth in , and assuming that enjoys smoothness, local
well-posedness is found in for certain values of
and . In the particular case
, and ,
, we obtain for each
. Our main tool in the proof is a more general result, that
holds also if has growth in , , and
asserts local well-posedness in for each , provided that
satisfies a locally uniform condition
Target Mass Effects in Polarized Virtual Photon Structure Functions
We study target mass effects in the polarized virtual photon structure
functions , in the kinematic
region , where is the mass squared of
the probe (target) photon. We obtain the expressions for and in closed form by inverting the
Nachtmann moments for the twist-2 and twist-3 operators. Numerical analysis
shows that target mass effects appear at large and become sizable near
, the maximal value of , as the ratio
increases. Target mass effects for the sum rules of and
are also discussed.Comment: 24 pages, LaTeX, 9 eps figure
Determination of a Type of Permutation Trinomials over Finite Fields
Let . We find
explicit conditions on and that are necessary and sufficient for to
be a permutation polynomial of . This result allows us to solve a
related problem. Let (,
) be the polynomial defined by the functional equation
. We determine all
of the form , , for which
is a permutation polynomial of .Comment: 28 page
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