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Various questions posed by P. Nyikos concerning ultrafilters on $\omega$ and chains in the partial order $(\omega,<^*)$ are answered. The main tool is the oracle chain condition and variations of it.
Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effect obtained after all earlier tests have failed, and appends…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
High fidelity state transfer is an important ingredient of distributed quantum information processing. We present and analyse results on perfect and quasi-perfect state transfer with linear spin chains incorporating non-uniform on-site…
We show that the monoid of all injective and extensive partial transformations of a chain with three elements admits no finite basis of its identities. This completes solving of the finite basis problem for the monoids in the basic frame of…
We consider subordination chains of simply connected domains with smooth boundaries in the complex plane. Such chains admit Hamiltonian and Lagrangian interpretations through the Loewner-Kufarev evolution equations. The action functional is…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, or algebraic information about the embedded group. We discuss…
We recall some abstract connectivity concepts, and apply them to special chains in partially ordered sets, called veins, that are defined as order-convex chains that are contained in every maximal chain they meet. Veins enable us to define…
We discuss both simple and more subtle connections between the numbers of permutations and full cycles with some restrictions,in particular, between the numbers of permutations and full cycles with prescribed up-down structure.
We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate…
The monoid of all partial injections on a finite set (the symmetric inverse semigroup) is of particular interest because of the well-known Wagner-Preston Theorem. In this article, we step forward the study of a submonoid of the symmetric…
Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal…
An internal characterization of complete metric mappings (by means of Cauchy nets tied at a point) is given and a construction of the completion of a metric mapping is presented.
We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type.
A right amount of disorder in the form of refractive index variation has been introduced to achieve transverse localization of light 1D semi-infinite photonic lattices. Presence of longitudinally-invariant transverse disorder opens-up a new…
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…
This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips)…
In this paper, nil extensions of some special type of ordered semigroups, such as, simple regular ordered semigroups, left simple and right regular ordered semigroup. Moreover, we have characterized complete semilattice decomposition of all…