Jacobian Conjecture in characteristic p ≥ 0 [37] [41] [2] means that for any positive integer n, any jacobian 1 endomorphism of the algebra of polynomials in n indeterminates over a field of characteristic p is an automorphism, provided it induces a field extension of degree not a multiple of p. Dixmier Conjecture in characteristic p [26] means that, for any positive integer n, any endomorphism...

In [2], Faugére et al. shows that the decomposition problem of a point of elliptic curve over binary field F2n reduces to solving low degree equations system over F2 coming from Weil descent. Using this method, the discrete logarithm problem of elliptic curve over F2n reduces to linear constrains, i.e., solving equations system using linear algebra of monomial modulo field equations, and its co...

For a graph property P and a graph G, a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. A P-Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the set of all vertices with label 1 or 2 is a P-set. The P-Roman domination number γPR(G) of G is the minimum of Σv∈V (...

Weil descent methods have recently been applied to attack the Hidden Field Equation (HFE) public key systems and solve the elliptic curve discrete logarithm problem (ECDLP) in small characteristic. However the claims of quasi-polynomial time attacks on the HFE systems and the subexponential time algorithm for the ECDLP depend on various heuristic assumptions. In this paper we introduce the noti...

Up to two centuries ago patients were lucky to survive even minor surgical interventions without contracting life-endangering infections, and having to endure extreme distress. Such advances highlighted the importance of clean dressing and sterility. Lint, gauze and cotton rapidly replaced older types of dressings. Almost a century later another major advance occurred when Winter defined the ph...

Up to two centuries ago patients were lucky to survive even minor surgical interventions without contracting life-endangering infections, and having to endure extreme distress. Such advances highlighted the importance of clean dressing and sterility. Lint, gauze and cotton rapidly replaced older types of dressings. Almost a century later another major advance occurred when Winter defined the ph...

The paper discusses the questions of coincidence basic nil-radicals on classes algebraic Lie algebras and proves local finite-dimensionality with an adjoint representation bounded degree over fields sufficiently large positive characteristic.

In [2], Faugére et al. shows that the decomposition problem of a point of elliptic curve over binary field F2n reduces to solving low degree equations system over F2 coming from Weil descent. Using this method, the discrete logarithm problem of elliptic curve over F2n reduces to linear constrains, i.e., solving equations system using linear algebra of monomial modulo field equations, and its co...

Abstract The reliability and safety of any system is the most important qualitative characteristic of a system. This qualitative characteristic is of particular importance in systems whose functions are under various stresses, such as high temperature, high speed, high pressure, etc. A considerable point, which is rarely taken into account when calculating the reliability and safety of syst...