‎a $(p‎,‎q)$ graph $g$ is said to have a $k$-odd mean‎ ‎labeling $(k ge 1)$ if there exists an injection $f‎ : ‎v‎ ‎to {0‎, ‎1‎, ‎2‎, ‎ldots‎, ‎2k‎ + ‎2q‎ - ‎3}$ such that the‎ ‎induced map $f^*$ defined on $e$ by $f^*(uv) =‎ ‎leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a‎ ‎bijection from $e$ to ${2k - ‎‎‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3}$‎. ‎a graph that admits $k$...

We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...

Let K denote an algebraically closed field and let q denote a nonzero scalar in K that is not a root of unity. Let V denote a vector space over K with finite positive dimension and let A,A denote a tridiagonal pair on V . Let θ0, θ1, . . . , θd (resp. θ ∗ 0, θ ∗ 1, . . . , θ ∗ d) denote a standard ordering of the eigenvalues of A (resp. A). We assume there exist nonzero scalars a, a in K such t...

We obtain an explicit expression for the defining relation of the deformed WN algebra, DWA(ŝlN)q,t. Using this expression we can show that, in the q → 1 limit, DWA(ŝlN)q,t with t = e 2πi N q k+N N reduces to the slN -version of the Lepowsky-Wilson’s Z-algebra of level k, ZA(ŝlN)k . In other words DWA(ŝlN)q,t with t = e − 2πi N q k+N N can be considered as a q-deformation of ZA(ŝlN)k . In the ap...

AbsrructAn ( n, k, d) linear code over F = GF( q) is said to be ntcrximunt dktunce separable (MDS) if d = n k + 1. It is shown that an (II, k, FI k + 1) generalized Reed-Solomon code such that 2 I k 5 n 1 ((I 1)/2] (k + 3 if q is even) can be extended by one digit while preserving the MDS property if and only if the resulting extended code is also a generalized Reed-Solomon code. It follows tha...

We investigate small weight code words of the $p$-ary linear $\mathcal C_{j,k}(n,q)$ generated by incidence matrix $k$-spaces and $j$-spaces PG$(n,q)$ its dual, with $q$ a prime power $0 \leq j < k n$. Firstly, we prove that all up to $\left(3 - \mathcal{O}\left(\frac 1 q \right) \genfrac{[}{]}{0pt}{}{k+1}{j+1}_q$ are combinations at most two (i.e. rows matrix). As for dual C_{j,k}(n,q)^\perp$,...

High accuracy measurements in M\"ossbauer transitions open up the possibility to use them search for temporal and spatial variations of fine structure constant $\ensuremath{\alpha}$, quark mass ${m}_{q}$, dark matter field which may lead $\ensuremath{\alpha}$ ${m}_{q}$. We calculate sensitivity nuclear have high variation ${m}_{q}$ strong interaction scale ${\mathrm{\ensuremath{\Lambda}}}_{\mat...

The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...

Let q be a positive squarefree integer. A prime p is said to be q-admissible if the equation p = u2 + qv2 has rational solutions u, v. Equivalently, p is q-admissible if there is a positive integer k such that pk2 ∈ N , where N is the set of norms of algebraic integers in Q( √ −q). Let k(q) denote the smallest positive integer k such that pk2 ∈ N for all q-admissible primes p. It is shown that ...

For a k-graph F?[n]k, the clique number of F is defined to be maximum size subset Q [n] with Qk?F. In present paper, we determine edges in on matching at most s and least q for n?8k2s q?(s+1)k?l, n?(s+1)k+s/(3k)?l. Two special cases that q=(s+1)k?2 k=2 are solved completely.