Harmonic Analysis in One-Parameter Metabelian Nilmanifolds

Let $G$ be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that $G$ contains a discrete cocompact subgroup. Given a discrete cocompact subgroup $\Gamma$ of $G$, we define the quasi-regular representation $\tau = {\rm ind}_\Gamma^G 1$ of $G$. The basic problem considered in this paper concerns the decomposition of $\tau$ into irreducibles. We give an orbital description of the spectrum, the multiplicity function and we construct an explicit intertwining operator between $\tau$ and its desintegration without considering multiplicities. Finally, unlike the Moore inductive algorithm for multiplicities on nilmanifolds, we carry out here a direct computation to get the multiplicity formula

Content Delivery in Erasure Broadcast Channels with Cache and Feedback

We study a content delivery problem in a K-user erasure broadcast channel such that a content providing server wishes to deliver requested files to users, each equipped with a cache of a finite memory. Assuming that the transmitter has state feedback and user caches can be filled during off-peak hours reliably by the decentralized content placement, we characterize the achievable rate region as a function of the memory sizes and the erasure probabilities. The proposed delivery scheme, based on the broadcasting scheme by Wang and Gatzianas et al., exploits the receiver side information established during the placement phase. Our results can be extended to centralized content placement as well as multi-antenna broadcast channels with state feedback.Comment: 29 pages, 7 figures. A short version has been submitted to ISIT 201

Existence and uniqueness of traveling wave for accelerated Frenkel-Kontorova model

In this paper, we study the existence and uniqueness of traveling wave solution for the accelerated Frenkel-Kontorova model. This model consists in a system of ODE that describes the motion particles in interaction. The most important applications we have in mind is the motion of crystal defects called dislocations. For this model, we prove the existence of traveling wave solutions under very weak assumptions. The uniqueness of the velocity is also studied as well as the uniqueness of the profile which used different types of strong maximum principle. As far as we know, this is the first result concerning traveling waves for accelerated, spatially discrete system

Cache-Enabled Broadcast Packet Erasure Channels with State Feedback

We consider a cache-enabled K-user broadcast erasure packet channel in which a server with a library of N files wishes to deliver a requested file to each user who is equipped with a cache of a finite memory M. Assuming that the transmitter has state feedback and user caches can be filled during off-peak hours reliably by decentralized cache placement, we characterize the optimal rate region as a function of the memory size, the erasure probability. The proposed delivery scheme, based on the scheme proposed by Gatzianas et al., exploits the receiver side information established during the placement phase. Our results enable us to quantify the net benefits of decentralized coded caching in the presence of erasure. The role of state feedback is found useful especially when the erasure probability is large and/or the normalized memory size is small.Comment: 8 pages, 4 figures, to be presented at the 53rd Annual Allerton Conference on Communication, Control, and Computing, IL, US

Starost i rast glavoča travaša Zosterisessor ophiocephalus Pallas, 1811 u zaljevu Gabes (Tunis, središnji Mediteran)

Zosterisessor ophiocephalus is currently an important component of the eastern Mediterranean inshore fisheries. In Tunisia it was recorded for the first time in the Gulf of Gabes in 1993, where it is now an important fished species. In this study age and growth parameters were determined in the Gulf of Gabes (southeast of Tunisia) based on otolith analysis of 824 specimens caught between September 2006 and August 2007. Monthly changes in marginal increments, determined from alternation of macroscopic opaque and translucent bands, of Zosterisessor ophiocephalus sagittae were examined. These results allowed us the estimation of the approximate age to the appearance of each annulus. The observed age was 6 years old for both sexes. Von Bertalanffy parameters based on length at age data were TL∞ = 24.83 ± 1.69 cm, K = 0.19 ± 0.03 year-1 and t0 = - 0.91 ± 0.12 for males and TL∞ = 24.13 ± 1.17 cm, K = 0.20 ± 0.02 year-1 and t0 = - 0.80 ± 0.09 for females. The length-weight relationship for both sexes of Zosterisessor ophiocephalus is Wt = 0.021 TL 2.789. The size at which 50% of females and males matured was respectively 12.65 cm and 13.91 cm total length (TL). The age at which 50% of females and males matured was respectively 2.9 and 3.5 years.Zosterisessor ophiocephalus je trenutno važna komponenta priobalnog ribolova istočnog Mediterana. U Tunisu je prvi put zabilježen u zaljevu Gabes 1993. godine, gdje je sada važna ribolovna vrsta. U ovoj studiji određivani su parametri starosti i rasta u zaljevu Gabes (jugoistočno od Tunisa) na temelju analize otolita 824 primjerka, ulovljenih između rujna 2006. i kolovoza 2007. godine. Starost je utvrđena na temelju fosilnih naraštajnih prstenova na otolitima (sagitta) vrste Zosterisessor ophiocephalus. Ovi rezultati su nam omogućili procjenu približne starosti pojavom svakog prstena kruga /annulus. Utvrđene su najstarije jednike koje su imale 6 godina za oba spola. Von Bertalenffyjevi parametri zasnovani na podatcima o duljini pri određenoj starosti bili su; TL∞ = 24.83 ± 1.69 cm, K = 0.19 ± 0.03 godina-1 i t0 = - 0.91 ± 0.12 za mužjake i TL∞ = 24.13 ± 1.17 cm, K = 0.20 ± 0.02 godina-1 i t0 = - 0.80 ± 0.09 za ženke. Dužinsko-maseni odnos za oba spola vrste Zosterisessor ophiocephalus je Wt = 0,021 TL 2.789. Veličina kod koje 50% ženki i mužjaka sazrijeva bila je 12,65 cm i 13,91 cm ukupne duljine (TL). Dob kod koje 50% ženki i mužjaka sazrijeva je između 2,9 i 3,5 godina starosti

The Consequences of Voluntary Information Disclosure on Firm Value: Case of Tunisian listed firms

The aim of this paper is to examine the impact of voluntary information disclosure on firm value for a sample of Tunisian firms listed on the Tunis Stock Exchange between 2005 and 2007. The results of the study have shown that, in the Tunisian context, (1) Voluntary corporate disclosure has an effect on income smoothing since an increased level of voluntary disclosure allows a detection of income smoothing. (2) Voluntary corporate disclosure has an effect on firm value via income smoothing. Actually, the more the Tunisian companies voluntarily disclose information, the less chance will be for managers to smooth earnings since the information needed to detect any income smoothing is held by investors, which entails an amplified firm value. This finding contributes to the relevant literature, particularly in an emerging market context characterized by a scarcity of studies regarding how the marketplace perceives voluntary disclosure. The paper evaluates comprehensively the value relevance of overall voluntary disclosure to the market participants. Finally, this finding might be accepted as a signal to corporations to disclose more information to the stakeholders. Since an increased level of voluntary disclosure will enhance the firm value. Keywords: voluntary disclosure, income smoothing, firm value, emerging market, income

Existence and non-existence of semi-discrete shocks for a car-following model in traffic flow

29 pagesWe consider a (microscopic) car-following model in traffic flow that can be seen as a semi-discrete scheme (discretization in space only) of a (macroscopic) Hamilton-Jacobi equation. For this discrete model, and for general velocity laws satisfying a strict chord inequality, we construct travelling solutions that are naturally associated to "travelling shocks" for the conservation law derived from the Hamilton-Jacobi equation. These shocks can be interpreted as a phase transition between two states of different car densities. There is no smallness condition on the size of these shocks. This existence and uniqueness of the solution is done at the level of the Hamilton-Jacobi equation. A surprising non-existence result of semi-discrete shocks for this microscopic model is also presented in the case where a shock exists for the associated macroscopic model, but the velocity law V satisfies a non strict chord inequality