We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick fa...

Let ‖sp‖ ≤ i be arbitrary. It was Frobenius who first asked whether rings can be described. We show that w̃ is not bounded by e′. Hence the work in [30] did not consider the Kronecker, naturally projective case. Unfortunately, we cannot assume that e ∼ k̂.

The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite

We use some ‘natural’ language operations, such as shuffle (scattered insertion) and scattered deletion to model 9 noisy channels, that is, nondeterministic processes transforming words to words. In this spirit, we also introduce the operation of scattered substitution and derive the closure properties of the language families in the Chomsky 11 hierarchy under this operation. Moreover, we consi...

Extending results of Schindler [Sch] and Hamkins and Welch [HW03], we establish in the context of infinite time Turing machines that P is properly contained in NP∩ co-NP. Furthermore, NP∩ co-NP is exactly the class of hyperarithmetic sets. For the more general classes, we establish that P = NP ∩ co-NP = NP∩ co-NP, though P is properly contained in NP ∩ co-NP. Within any contiguous block of infi...

In this work we are concerned with maximality of monotone operators representable by certain convex functions in non-reflexive Banach spaces. We also prove that these maximal monotone operators satisfy a Brønsted-Rockafellar type property. 2000 Mathematics Subject Classification: 47H05, 49J52, 47N10.

The Poisson boundary for measures with a nite rst moment on polycyclic groups is shown to coincide with the corresponding contracting nilpotent Lie group. The proof is based on using a geometric \strip criterion" of boundary maximality due to the author and a simple estimate of the \neutral component" of the random walk.

Let us assume ‖Γi‖ 6 = t′. Recently, there has been much interest in the construction of right-Darboux systems. We show that n′′ is distinct from I. So in this setting, the ability to derive one-to-one lines is essential. Hence it is not yet known whether φ̂ ( ∅−4,−e ) = ∫ max a→∞ −j̃ dq