Naturally graded quasi-filiform Leibniz algebras

AbstractThe classification of naturally graded quasi-filiform Lie algebras is known; they have the characteristic sequence (n−2,1,1) where n is the dimension of the algebra. In the present paper we deal with naturally graded quasi-filiform non-Lie–Leibniz algebras which are described by the characteristic sequence C(L)=(n−2,1,1) or C(L)=(n−2,2). The first case has been studied in [Camacho, L.M., Gómez, J.R., González, A.J., Omirov, B.A., 2006. Naturally graded 2-filiform Leibniz Algebra and its applications, preprint, MA1-04-XI06] and now, we complete the classification of naturally graded quasi-filiform Leibniz algebras. For this purpose we use the software Mathematica (the program used is explained in the last section)

Constant & time-varying hedge ratio for FBMKLCI stock index futures

This paper examines hedging strategy in stock index futures for Kuala Lumpur Composite Index futures of Malaysia. We employed two different econometric methods such as-vector error correction model (VECM) and bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models to estimate optimal hedge ratio by using daily data of KLCI index and KLCI futures for the period from January 2012 to June 2016 amounting to a total of 1107 observations. We found that VECM model provides better results with respect to estimating hedge ratio for spot month futures and one-month futures, while BGACH shows better for distance futures. While VECM estimates time invariant hedge ratio, the BGARCH shows that hedge ratio changes over time. As such, hedger should rebalance his/her position in futures contract time to time in order to reduce risk exposure

Cone-equivalent nilpotent groups with different Dehn functions

For every $k\geqslant 3$, we exhibit a simply connected $k$-nilpotent Lie group $N_k$ whose Dehn function behaves like $n^k$, while the Dehn function of its associated Carnot graded group $\mathsf{gr}(N_k)$ behaves like $n^{k+1}$. This property and its consequences allow us to reveal three new phenomena. First, since those groups have uniform lattices, this provides the first examples of pairs of finitely presented groups with bilipschitz asymptotic cones but with different Dehn functions. The second surprising feature of these groups is that for every even integer $k \geqslant 4$ the centralized Dehn function of $N_k$ behaves like $n^{k-1}$ and so has a different exponent than the Dehn function. This answers a question of Young. Finally, we turn our attention to sublinear bilipschitz equivalences (SBE). Introduced by Cornulier, these are maps between metric spaces inducing bi-Lipschitz homeomorphisms between their asymptotic cones. These can be seen as weakenings of quasiisometries where the additive error is replaced by a sublinearly growing function $v$. We show that a $v$-SBE between $N_k$ and $\mathsf{gr}(N_k)$ must satisfy $v(n)\succcurlyeq n^{1/(2k + 1)}$, strengthening the fact that those two groups are not quasiisometric. This is the first instance where an explicit lower bound is provided for a pair of SBE groups.Comment: 64 pages, v1->v2: Abstract and introduction partly rewritte

Pameran Reka Cipta, Penyelidikan dan Inovasi (PRPI) 2009

PRPI 2009 kini telah memasuki tahun penganjurannya yang ke-7. Pameran penyelidikan di UPM telah bermula sejak tahun 1997 semasa Exhibition & Seminar Harnessing for Industry Advantage. Pada tahun 2002, Pameran Reka Cipta dan Penyelidikan (PRP) buat pertama kali telah diadakan dengan menggunakan konsep pertandingan hasil projek penyelidikan yang telah dijalankan oleh para penyelidik UPM. Kejayaan penganjuran PRP 2002 telah merintis usaha untuk menjadikannya sebagai aktiviti tahunan UPM dan ianya terus berkembang sejajar dengan nama baharunya yang ditukar kepada Pameran Reka Cipta, Penyelidikan dan Inovasi yang bermula penganjurannya pada tahun 2005. Sebagai kesinambungan daripada kejayaan penganjuran PRPI 2006, 2007 dan 2008 yang lalu dan status UPM sebagai salah sebuah Universiti Penyelidikan, PRPI 2009 kali ini yang merupakan pameran penyelidikan yang terbesar di UPM terus dilaksanakan dengan aspirasi dan semangat yang lebih jitu. Pameran ini juga menjadi pelantar kepada para penyelidik untuk mengenengahkan hasil penyelidikan yang dijalankan dan penemuan baharu kepada umum. Di samping itu ianya juga menjadi penanda aras terhadap kualiti sesuatu projek penyelidikan bagi melayakkan para penyelidik UPM untuk menyertai pameran di peringkat kebangsaan dan seterusnya antarabangsa. Adalah diharapkan pelaksanaan PRPI 2009 ini akan dapat menyemarakkan budaya penyelidikan di kalangan staf dan juga pelajar UPM sekaligus menjadikan UPM sebagai Universiti Penyelidikan yang cemerlang di negara ini

2nd International Conference on Numerical and Symbolic Computation

The Organizing Committee of SYMCOMP2015 – 2nd International Conference on Numerical and Symbolic Computation: Developments and Applications welcomes all the participants and acknowledge the contribution of the authors to the success of this event. This Second International Conference on Numerical and Symbolic Computation, is promoted by APMTAC - Associação Portuguesa de Mecânica Teórica, Aplicada e Computacional and it was organized in the context of IDMEC/IST - Instituto de Engenharia Mecânica. With this ECCOMAS Thematic Conference it is intended to bring together academic and scientific communities that are involved with Numerical and Symbolic Computation in the most various scientific area

The physics and applications of strongly coupled plasmas levitated in electrodynamic traps

Charged (nano)particles confined in electrodynamic traps can evolve into strongly correlated Coulomb systems, which are the subject of current investigation. Exciting physical phenomena associated to Coulomb systems have been reported such as autowave generation, phase transitions, system self-locking at the ends of the linear Paul trap, self-organization in layers, or pattern formation and scaling. The dynamics of ordered structures consisting of highly nonideal similarly charged nanoparticles, with coupling parameter of the order $\Gamma = 10^8$ is investigated. This approach enables us to study the interaction of nanoparticle structures in presence and in absence of the neutralizing plasma background, as well as to investigate various types of phenomena and physical forces these structures experience. Applications of electrodynamic levitation for mass spectrometry, including containment and study of single aerosols and nanoparticles are reviewed, with an emphasis on state of the art experiments and techniques, as well as future trends. Late experimental data suggest that inelastic scattering can be successfully applied to the detection of biological particles such as pollen, bacteria, aerosols, traces of explosives or synthetic polymers. Brownian dynamics is used to characterize charged particle evolution in time and thus identify regions of stable trapping. An analytical model is used to explain the experimental results. Numerical simulations take into account the stochastic forces of random collisions with neutral particles, the viscosity of the gas medium, the regular forces produced by the a.c. trapping voltage, and the gravitational force. We show that microparticle dynamics is characterized by a stochastic Langevin differential equation. Laser plasma acceleration of charged particles is also discussed