Incidences between points and generalized spheres over finite fields and related problems

Let $\mathbb{F}_q$ be a finite field of $q$ elements where $q$ is a large odd prime power and $Q =a_1 x_1^{c_1}+...+a_dx_d^{c_d}\in \mathbb{F}_q[x_1,...,x_d]$, where $2\le c_i\le N$, $\gcd(c_i,q)=1$, and $a_i\in \mathbb{F}_q$ for all $1\le i\le d$. A $Q$-sphere is a set of the form $\lbrace x\in \mathbb{F}_q^d | Q(x-b)=r\rbrace$, where $b\in \mathbb{F}_q^d, r\in \mathbb{F}_q$. We prove bounds on the number of incidences between a point set $\mathcal{P}$ and a $Q$-sphere set $\mathcal{S}$, denoted by $I(\mathcal{P},\mathcal{S})$, as the following. $$| I(\mathcal{P},\mathcal{S})-\frac{|\mathcal{P}||\mathcal{S}|}{q}|\le q^{d/2}\sqrt{|\mathcal{P}||\mathcal{S}|}.$$ We prove this estimate by studying the spectra of directed graphs. We also give a version of this estimate over finite rings $\mathbb{Z}_q$ where $q$ is an odd integer. As a consequence of the above bounds, we give an estimate for the pinned distance problem. In Sections $4$ and $5$, we prove a bound on the number of incidences between a random point set and a random $Q$-sphere set in $\mathbb{F}_q^d$. We also study the finite field analogues of some combinatorial geometry problems, namely, the number of generalized isosceles triangles, and the existence of a large subset without repeated generalized distances.Comment: to appear in Forum Mat

Mass-imbalance induced metal-insulator transition in a three-component Hubbard model

The effects of mass imbalance in a three-component Hubbard model are studied by the dynamical mean-field theory combined with exact diagonalization. The model describes a fermion-fermion mixture of two different particle species with a mass imbalance. One species is two-component fermion particles, and the other is single-component ones. The local interaction between particle species is considered isotropically. It is found that the mass imbalance can drive the mixture from insulator to metal. The insulator-metal transition is a species-selective-like transition of lighter mass particles and occurs only at commensurate particle densities and moderate local interactions. For weak and strong local interactions the mass imbalance does not change the ground state of the mixture

A Comprehensive View of Circumstellar Disks in Chamaeleon I: Infrared Excess, Accretion Signatures and Binarity

We present a comprehensive study of disks around 81 young low-mass stars and brown dwarfs in the nearby ~2-Myr-old Chamaeleon I star-forming region. We use mid-infrared photometry from the Spitzer Space Telescope, supplemented by findings from ground-based high-resolution optical spectroscopy and adaptive optics imaging. We derive disk fractions of 52 (+/-6) % and 58 (+6/-7) % based on 8-micron and 24-micron colour excesses, respectively, consistent with those reported for other clusters of similar age. Within the uncertainties, the disk frequency in our sample of K3-M8 objects in Cha I does not depend on stellar mass. Diskless and disk-bearing objects have similar spatial distributions. There are no obvious transition disks in our sample, implying a rapid timescale for the inner disk clearing process; however, we find two objects with weak excess at 3-8 microns and substantial excess at 24 microns, which may indicate grain growth and dust settling in the inner disk. For a sub-sample of 35 objects with high-resolution spectra, we investigate the connection between accretion signatures and dusty disks: in the vast majority of cases (29/35) the two are well correlated, suggesting that, on average, the timescale for gas dissipation is similar to that for clearing the inner dust disk. The exceptions are six objects for which dust disks appear to persist even though accretion has ceased or dropped below measurable levels. Adaptive optics images of 65 of our targets reveal that 17 have companions at (projected) separations of 10-80 AU. Of the five <20 AU binaries, four lack infrared excess, possibly indicating that a close companion leads to faster disk dispersal. The closest binary with excess is separated by ~20 AU, which sets an upper limit of ~8 AU for the outer disk radius. (abridged)Comment: accepted for publication in the Astrophysical Journa

MORE ENVIRONMENTAL FRIENDLY METHOD OF LEAD RECYCLING FROM WASTE BATTERY PASTE-AN ELECTROCHEMICAL INVESTIGATION

Joint Research on Environmental Science and Technology for the Eart

International typology of agricultural holdings : The case of Vietnam

The typology of agricultural holdings (AHs) aims to characterise different types of production structures and assess their relative importance. The dynamics of these different types allow the transformation of agriculture to be monitored over time to design pertinent support policies for agricultural production units. This paper presents the results of a typology of agricultural holdings in Vietnam that was carried out with a methodology discussed in the WAW initiative. The typology of agricultural households and commercial farms is based on rural household data from the 2010 Vietnamese Household Living Standard Survey (VHLSS) and on commercial farm data from the 2011 Agricultural and Rural Census (ARC). Three variables, capturing (i) the professional qualifications of holding heads (qualifications), (i) the use of family labor in agricultural production (labor), and (iii) the commercialization level of agricultural products (sales), were used for the typology. The statistical method used for the classification was the Partitioning K-mean method. The results suggest that agricultural households and commercial farms in Vietnam can be divided into 5 groups which we propose to name as follows: semi-subsistence household farms (Group 1); market-oriented household farms (Group 3), medium commercial farms (Group 5), large commercial farms (Group 2) and very large commercial farms (Group 4). The groups have clearly different characteristics that confirm the pertinence of the 3 variables used in the typology exercise. Our work demonstrates the importance of large commercial farms in the current transformation of Vietnamese agriculture. However, household farms (Group 1 and Group 3) still constitute around 99% of the 10.4 million rural households in the country (Résumé d'auteur

Power beacon-assisted energy harvesting in a half-duplex communication network under co-channel interference over a Rayleigh fading environment: Energy efficiency and outage probability analysis

In this time, energy efficiency (EE), measured in bits per Watt, has been considered as an important emerging metric in energy-constrained wireless communication networks because of their energy shortage. In this paper, we investigate power beacon assisted (PB) energy harvesting (EH) in half-duplex (HD) communication network under co-channel Interferer over Rayleigh fading environment. In this work, we investigate the model system with the time switching (TS) protocol. Firstly, the exact and asymptotic form expressions of the outage probability (OP) are analyzed and derived. Then the system EE is investigated and the influence of the primary system parameters on the system performance. Finally, we verify the correctness of the analytical expressions using Monte Carlo simulation. Finally, we can state that the simulation and analytical results are the same.Web of Science1213art. no. 257

Characterization of pig farms in Hung Yen, Hai Duong and Bac Ninh provinces

peer reviewedIn order to characterization of pig farms in the Red River Delta, a study was conducted on 90 pig farms in Hung Yen, Hai Duong and Bac Ninh provinces from June to December 2006. Results show that most of the pig farms had been built for five years with a small size (0.5 hectare per farm). The invested capital was about 300-400 millions VND per farm. Four main sow groups used in the farms included crossbred exotic sows (51.1%), crossbred sow between local and exotic breeds (14.4%), purebred Landrace and Yorkshire breeds (15.6 and 18.9%, respectively). The boars were various (Duroc 30%, Yorkshire 21%, Landrace 13%, PiÐtrain × Duroc 36% and others). The pigs farms were faced with several difficulties such as limited land, lack of invested capital, uncontrolled quality of breeding pigs, high costs of feed, poor hygiene condition and diseases