We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graph-theoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the nu...

In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not...

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid...

this paper aims to offer a critical reading of the contemporary english author ian mcewan’s fifth novel entitled black dogs (1992). i postulate that literary critics have frequently read his fiction for what it is not. as such, mcewan’s thought-provoking engagement with cultural questions has more often than not gone unexamined owing to a critical blueprint that, reducing his oeuvre to the topo...

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum s...

solvable graphs (also known as reachable graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). in this paper, the properties of solvable graphs are investigated, and a new concept in multi agent moti...

die direktreduktion von eisenerzen zu eisenschwamm mittels erdgas wird iiberall dort verwendet wo einmal die notwendtigen rohstoffe und besonders der metallurgische koks zu wirtschaftlischen bedingungen fehlen. andereseirs wiederum miissen erdgasrerven in geniigenden mengen und qualitat zu verfugung stehen, urn die direktredution mit gutem wirkungsgrad durchfuhren zu konnen. in dieser arbeit wi...