We study Darboux-type transformations associated with the focusing nonlinear Schrödinger equation (NLS−) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J -selfadjoint (but non-self-adjoint) Dirac-type differential expression of the form M(q) = i d dx −q −q − d dx , satisfying JM(q)J = M(q), where J is defined by J = 0 1 1 0 C, and C denotes the ...

Geometric puncturing is a method to construct new codes from a given [n, k, d]q code by deleting the coordinates corresponding to some geometric object in PG(k − 1, q). We construct [gq(4, d), 4, d]q and [gq(4, d)+1, 4, d]q codes for some d by geometric puncturing, where gq(k, d) = ∑k−1 i=0 ⌈

We classify all embeddings θ : PG(n, q) −→ PG(d, q), with d ≥ n(n+3) 2 , such that θ maps the set of points of each line to a set of coplanar points and such that the image of θ generates PG(d, q). It turns out that d = 1 2n(n+3) and all examples are related to the quadric Veronesean of PG(n, q) in PG(d, q) and its projections from subspaces of PG(d, q) generated by sub-Veroneseans (the point s...

We propose new formulas for extracting a difference of the polarized light sea–quark density, ∆d̄(x)−∆ū(x), from polarized deep–inelastic semi–inclusive data. We have estimated the value of it from the present experimental data measured by SMC and HERMES groups. Although the data might suggest a violation of polarized light flavor sea–quark symmetry, the precision of the present data is not enou...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...

where B and D are square blocks. We prove the following inequalities for the Schatten q-norm ||.||q , which are sharp when the blocks are of size at least 2× 2: ||A||q ≤ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 1 ≤ q ≤ 2, and ||A||q ≥ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 2 ≤ q. These bounds can be extended to symmetric partitionings into larger numbers of blocks, at the expense of no longer...

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Let $$T(q) = \sum\limits_{k 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors natural k. We present monotonicity properties functions defined in terms T. More specifically, we prove that $$H(q) T(q) - {{\log (1 q)} \over {\log (q)}}$$ is strictly increasing on (0, 1), while $$F(q) {{1 q} q}H(q)$$ decreasing 1). These results are then ap...