A new method for designing a minimal order perfect functional observers for singular continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of the minimal order perfect functional observer are established. A procedure for computation of matrices of the observers is derived and illustrated by a numerical example. Key-Words: Design, existence, minimal or...

we use the recursive method of construction large sets of t-designs given by qiu-rong wu (a note on extending t-designs‎, ‎{em australas‎. ‎j‎. ‎combin.}‎, ‎{bf 4} (1991) 229--235.), and present a similar method for constructing $t$-subset-regular‎ ‎self-complementary $k$-uniform hypergraphs of order $v$‎. ‎as an‎ ‎application we show the existence of a new family of 2-subset-regular‎ ‎self-com...

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

Using the methods of Brown and Walsh, we get condition guaranteeing that, for an ideal I of sets in a perfect Polish space some (s 0) sets are not in I. A few examples and corollaries are given. 0. Introduction Papers Br], W1], W2] and C] made a signiicant progress in the studying of (s 0) sets introduced by Marczewski in Sz]. One of the main results states that there exists a nonmeasurable (s ...

TWO theorems nre proved on perfect codes. The first cne states tk.at Lloyd's theorem is true without tne assumption that the number of symbols in the alphabet is a prime power. The second thevrem asser?s the impossibility of perfect group codes over non-prime-pcwer-alphabets. IA V be a finite set, I VI = q > 2, and let 1 <_ e 2 ye be Ia:ional integers. We pu?iV= (1, 2,. .. . n). Forv=(Vi)~=l E ...

The complement of a graph G is denoted by G. χ(G) denotes the chromatic number and ω(G) the clique number of G. The cycles of odd length at least five are called odd holes and the complements of odd holes are called odd anti-holes. A graph G is called perfect if, for each induced subgraph G of G, χ(G) = ω(G). Classical examples of perfect graphs consist of bipartite graphs, chordal graphs and c...

Recent technologies for typing single nucleotide polymorphisms (SNPs) across a population are producing genome-wide genotype data for tens of thousands of SNP sites. The emergence of such large data sets underscores the importance of algorithms for large-scale haplotyping. Common haplotyping approaches first partition the SNPs into blocks of high linkage-disequilibrium, and then infer haplotype...

The Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conjectures in graph theory. During more than four decades, numerous attempts were made to solve it, by combinatorial methods, by linear algebraic methods, or by polyhedral methods. The rst of these three approaches yielded the rst (and to date only) proof of the SPGC; the other two remain promising to consider...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs....

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...