Extensions of rich words

In [X. Droubay et al, Episturmian words and some constructions of de Luca and Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has at most |w|+1 many distinct palindromic factors, including the empty word. The unified study of words which achieve this limit was initiated in [A. Glen et al, Palindromic richness, Eur. Jour. of Comb. 30 (2009)]. They called these words rich (in palindromes). This article contains several results about rich words and especially extending them. We say that a rich word w can be extended richly with a word u if wu is rich. Some notions are also made about the infinite defect of a word, the number of rich words of length n and two-dimensional rich words.Comment: 19 pages, 3 figure

Junior Recital, Zhiqian Wu, piano

Junior RecitalZhiqian Wu, pianoFriday, March 29, 2019 at 7pmRecital Hall / James W. Black Music CenterThe presentation of this Junior Recital will fulfill in part the requirements for the Bachelor of Music degree in Performance. Zhiqian Wu studies piano with Dr. Sonia Vlahcevic and Dr. Yin Zheng

Higgs algebraic symmetry of screened system in a spherical geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(\dot{r}=0)$.Comment: 8 pages, 1 fi

Structures of W(2,2)W(2,2) Lie conformal algebra

The purpose of this paper is to study $W(2,2)$ Lie conformal algebra, which has a free $\mathbb{C}[\partial]$-basis $\{L, M\}$ such that $[L_\lambda L]=(\partial+2\lambda)L$, $[L_\lambda M]=(\partial+2\lambda)M$, $[M_\lambda M]=0$. In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1601.0691

Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug

Implementasi Metode Optimasi Particle Swarm Optimization (PSO) Untuk Tuning Pengendali Model Predictive Control (MPC) Pada Quadruple Tank

Pada penelitian ini telah dibangun mode kontrol Model Predictive Control (MPC) dengan metode optimasi Particle Swarm Optimization untuk mencari nilai terbaik pada parameter beban sinyal kontrol Wu dan sinyal control error W∆u yang kemudian diimplementasikan secara online pada rancang bangun system Quadruple Tank. Metode IMOPSO untuk MPC dengan nilai sinyal control Wu =0.0076 dan sinyal control error Wdu = 0.1221 menghasilkan respon system terbaik dengan maximum overshoot = 4% error steady state 1% settling time 55 detik dibandingkan MOPSO dengan nilai sinyal control Wu 0.0397 dan sinyal control error Wdu 0.1780 menghasilkan respon sistem dengan maksimum overshoot = 5% Error Steady State = 3 % settling time 65 detik. Selain itu, dibangun juga control PSO – PID yang digunakan sebagai pembanding dimana mode MOPSO menghasilkan nilai Kp = 3.0828 Ki = 0.4219 memiliki respon sistem dengan maksimum overshoot = 3 % Error Steady State = 2% dan settling time 250 detik. Sedangkan pada mode IMOPS nilai Kp = 2.9388 Ki = 0.2166 memiliki respon system dengan maksimum overshoot = 3 % Error Steady State 1.5% dan settling time 150 detik

Analysing development to shape the future

This article links theory and politics in a systematic way by proposing Is-Shall-Do as a didactical model for analysing a concrete conjuncture, relating it to the desired future in the form of a concrete utopia. Aware of structural limits and potential space of manoeuvre for political agency adequate practical steps to implement the concrete utopia are elaborated. The paper is divided in a first section which exposes three interwoven aspects of development: the the idea of a good life, the complexity and multi-dimensionality of development and the relationship of knowledge and power. Section two exposes the model of Is-Shall-Do abstractly, while section 3 exemplifies it by exposing the challenges for the European left. The analysis of conjuncture as a concrete analysis of a concrete situation is centred in Europe today on the topic of inequality produced by finance-based accumulation. As the concrete utopia of a good life , the authors propose the values of the French revolution, freedom, equality and solidarity which are unfulfilled promises of European development. The paper ends with a plea for organising democratic and egalitarian alternatives. (...) (authors' abstract)Series: SRE - Discussion Paper