The strength of a homogeneous polynomial (or form) is the smallest length an additive decomposition expressing it whose summands are reducible forms. Using functors, we show that set forms with bounded not always Zariski-closed. More specifically, if ground field algebraically closed, prove quartics ≤3 Zariski-closed for large number variables.

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.

Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

In this paper we consider the Target Set Selection problem. The problem naturally arises in many fields like economy, sociology, medicine. one is given a graph G with function $${{\,\mathrm{thr}\,}}: V(G) \rightarrow {\mathbb {N}} \cup \{0\}$$ and two integers $$k, \ell $$ . goal of to activate at most k vertices initially so that end activation process there are least $$\ell activated vertices...

The state estimation of a quantized system (Q.S.) is a challenging problem for designing feedback control and model-based fault diagnosis algorithms. The core of a Q.S. is a continuous variable system whose inputs and outputs are represented by their corresponding quantized values. This paper concerns with state estimation of a Q.S. by a qualitative observer. The presented observer in this pape...