Distinct distances on regular varieties over finite fields

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset $\mathcal{E}$ in a regular variety satisfies $|\mathcal{E}|\gg q^{\frac{d-1}{2}+\frac{1}{k-1}}$, then $\Delta_{k, F}(\mathcal{E})\supseteq \mathbb{F}_q\setminus \{0\}$ for some certain families of polynomials $F(\mathbf{x})\in \mathbb{F}_q[x_1, \ldots, x_d]$

ENVIRONMENTAL ISSUES IN THE DEVELOPMENT OF THE AQUACULTURE FARMING ECONOMY IN VIETNAM

Joint Research on Environmental Science and Technology for the Eart

An optimal schedule model of multi-energy hubs network integrating solar energy

Recently, multi-energy systems based on energy hub are introduced because of significant benefits in reducing energy and emission cost. This paper proposed an optimal schedule model of multi-energy hubs networks consisting of energy hubs, renewable sources, and energy storage which are connected by electrical and natural gas distribution networks. In the proposed mixed-integer nonlinear programming model, the objective is to minimize the operation, energy, and emission costs of energy hubs with both renewable sources and storage and energy distribution networks. The proposed schedule framework allows simultaneously selections of optimal operation structure of EHs together with the optimal operation parameters of energy distribution networks and therefore this model can maximize the profit of the entire large-scale multi-energy hubs network. Besides, the operation parameters and energy loss of both electrical and natural gas distribution networks are considered in conjunction with optimal operation of energy hubs and thus guarantee the operation and optimization of the network in all operational scenarios. The IEEE 5-bus test system is utilized to demonstrate the applicability of the proposed model. The simulation results show the feasibility of the proposed model, and demonstrate that the energy hubs, renewable sources, and energy storage in the proposed structure significantly enhance the efficiency of the multi-energy hubs network by reducing not only energy and operation costs but also emission

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

Analytical study of the velocity of the lubricating fluid in the hydrodynamic journal bearing with the effect of centrifugal force for short bearing type

The paper aims to obtain the expression of the velocity of lubricating fluid in the hydrodynamic journal bearings by analytical method. In the classical short-bearing theory, the fluid flow was studied by ignoring the effect of centrifugal force of the lubricating fluid film. However, the self-oscillation of the shaft of high-power motors does not follow the rules in classical hydrodynamic lubrication theory. To explain this phenomenon, a modified form of Reynolds equation, in which the influence of centrifugal force of the lubricant is not ignored, is established. The study aims to establish the modified Reynolds equation by including the effect of centrifugal forces for the case of the short bearing type. Integration of the Navier-Stokes equations, yield the expressions for the components of velocity of the lubricating fluid in the gap. The oil’s pressure in the hydrodynamic journal bearing is obtained by solving the modified Reynolds equation. The numerical results are considered in the case of the stable equilibrium position of the motion of the shaft, i.e. the symmetry axis of the shaft does not move. The plots of the velocity components in the tangential axial direction are displayed too. The theoretical results of a parabolic velocity distribution similar to that of a Newtonian fluid, derived from a Bingham plastic flow model. The flow in the gap, which are obtained by analytical method, are completely consistent with its boundary conditions and its physical properties. Further, with these results, the paper as a lemma to solve the dynamics problem in floating ring bearing with the influence of the centrifugal force of the lubrican

Development of a system for communication and control of an electrical spindle

Tese de mestrado integrado. Engenharia Mecânica. Universidade do Porto. Faculdade de Engenharia. 201

CeO2 based catalysts for the treatment of propylene in motorcycle's exhaust gases

In this work, the catalytic activities of several single metallic oxides were studied for the treatment of propylene, a component in motorcycles' exhaust gases, under oxygen deficient conditions. Amongst them, CeO2 is one of the materials that exhibit the highest activity for the oxidation of C3H6. Therefore, several mixtures of CeO2 with other oxides (SnO2, ZrO2, Co3O4) were tested to investigate the changes in catalytic activity (both propylene conversion and CO2 selectivity). Ce0.9Zr0.1O2, Ce0.8Zr0.2O2 solid solutions and the mixtures of CeO2 and Co3O4 was shown to exhibit the highest propylene conversion and CO2 selectivity. They also exhibited good activities when tested under oxygen sufficient and excess conditions and with the presence of co-existing gases (CO, H2O)