On slender 0L languages

AbstractWe give a complete proof of Theorem 3.1 in [2]. A pathological exception of Theorem 4.3 in [2] is exhibited and a condition to remove it is mentioned

Rewrite Closure and CF Hedge Automata

We introduce an extension of hedge automata called bidimensional context-free hedge automata. The class of unranked ordered tree languages they recognize is shown to be preserved by rewrite closure with inverse-monadic rules. We also extend the parameterized rewriting rules used for modeling the W3C XQuery Update Facility in previous works, by the possibility to insert a new parent node above a given node. We show that the rewrite closure of hedge automata languages with these extended rewriting systems are context-free hedge languages

Spectrum of bound fermion states on vortices in 3^3He-B

We study subgap spectra of fermions localized within vortex cores in $^3$He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular $o$ and $u$ vortices the anomalous branches are similar to the standard Caroli-de Gennes -Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the $v$, $w$ and $uvw$ vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.Comment: 6 pages, 1 figur

Motion of vortices in ferromagnetic spin-1 BEC

The paper investigates dynamics of nonsingular vortices in a ferromagnetic spin-1 BEC, where spin and mass superfluidity coexist in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based on hydrodynamics following from the Gross-Pitaevskii theory. Cores of nonsingular vortices are skyrmions with charge, which is tuned by uniaxial anisotropy and can have any fractal value between 0 and 1. There are circulations of mass and spin currents around these vortices. The results are compared with the equation of vortex motion derived earlier in the Landau-Lifshitz-Gilbert theory for magnetic vortices in easy-plane ferromagnetic insulators. In the both cases the transverse gyrotropic force (analog of the Magnus force in superfluid and classical hydrodynamics) is proportional to the charge of skyrmions in vortex cores.Comment: 19 pages, 2 figures, to be published in the special issue of Fizika Nizkikh Temperatur dedicated to A.M.Kosevich. arXiv admin note: substantial text overlap with arXiv:1801.0109

k-Spectra of weakly-c-Balanced Words

A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered factors of a given word w, called here $k$-spectrum and denoted \ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w) for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e., words over a two-letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has $c$-more occurrences than the other. In particular, we consider the question which cardinalities n= |\ScatFact_k(w)| are obtainable, for a positive integer $k$, when $w$ is either a strictly balanced binary word of length $2k$, or a $c$-balanced binary word of length $2k-c$. We also consider the problem of reconstructing words from their $k$-spectra

Quantum, Stochastic, and Pseudo Stochastic Languages with Few States

Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal. After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata. Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power.Comment: A new version with new results. Previous version: Arseny M. Shur, Abuzer Yakaryilmaz: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. UCNC 2014: 327-33

Additive decomposability of functions over abelian groups

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.Comment: 17 page

Currents on Superconducting Strings at Finite Chemical Potential and Temperature

We consider the model giving rise to Witten's superconducting cosmic strings at finite fermion chemical potential and temperature. We demonstrate how various symmetries of the hamiltonian can be used to exactly compute the fermion electric current in the string background. We show that the current along the string is not sensitive to the profiles of the string fields, and at fixed chemical potential and temperature depends only on the string winding number, the total gauge flux through the vortex and, possibly, the fermion mass at infinity.Comment: 9 page

The Need for Effective Early Behavioral Family Interventions for Children with Attention Deficit Hyperactivity Disorder (ADHD)

There is a pressing need for the development of effective early family intervention programs for children showing Attention Deficit Hyperactivity Disorder (ADHD) behaviours with Conduct Disorder (CD) or Oppositional Defiant Disorder (ODD) behaviours. Previous research has indicated that children with ADHD are at risk of developing comorbid CD or ODD behaviours. In addition, it has been shown that ODD or CD behaviours in childhood tend to persist and to have adverse effects on later social adjustment. However, ODD or CD behaviours are not necessary concomitants of ADHD, and it has been demonstrated that behavioural intervention can have both short- and long term beneficial effects for children showing early signs of ODD or CD behaviours. In short term, behavioural family interventions may be able to reduce oppositional behaviour, particularly in the preschool years. In the long term, early intervention has shown to reduce the incidence of later antisocial behaviour in children at risk for this developmental trajectory. In this paper, it will be argued that behavioural family interventions have not been effectively utilised or promulgated in the community for children with ADHD despite the demonstrated efficacy of these types of interventions. A model of a multilevel system of intervention that can be tailored to the individual family’s needs is presented

On the effect of variable identification on the essential arity of functions

We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variables. This is a generalization of a theorem of Salomaa on the essential variables of Boolean functions. We also strengthen Salomaa's theorem by characterizing all the Boolean functions f having a variable identification minor that has just one essential variable less than f.Comment: 10 page