We prove that for every d ≥ 3 the homomorphism order of the class of line graphs of finite graphs with maximal degree d is universal. This means that every finite or countably infinite partially ordered set may be represented by line graphs of graphs with maximal degree d ordered by the existence of a homomorphism.

The classical degree function constructed earlier for pseudomonotone mappings has been used to develop a broader degree theory of classical type for the sum of a maximal monotone map from a reflexive Banach space to its dual together with a bounded pseudomonotone map. The proof uses the generalized Yosida approximation of the maximal monotone mapping.

It is recognized that Grover arrived at his original quantum search algorithm inspired by comprehension of the interference classical waves originating from an array antennas. also known quantum-mechanical characterization electromagnetic radiation isomorphic to treatment orientation a spin-$1/2$ particle. In this paper, motivated Grover's intuition and starting mathematical equivalence, we pre...

Consider the random walk on graphs such that, at each step, the next visited vertex is a neighbor of the current vertex, chosen with probability proportional to the inverse of the square root of its degree. On one hand, for every graph with n vertices, the maximal mean hitting time for this degree-biased random walk is asymptotically dominated by n. On the other hand, the maximal mean hitting t...

In [3] De Clerck, De Winter and Maes counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2), h 6= 7 and prime. In this article we will show that in PG(2, 2) a special class of Mathon maximal arcs of degree 8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then cou...

Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, B...

The warping degree of an oriented knot diagram is the minimal number crossings which we meet as under-crossing first when travel along from a fixed point. projection value for all alternating diagrams obtained projection. In this paper, consider maximal regions share no with crossing, and give lower bounds degree.