On the complexity of solving ordinary differential equations in terms of Puiseux series

We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given by Grigoriev [10] for Riccatti differential polynomials associated to ordinary linear differential operators. In this paper, we get the same bound for arbitrary differential polynomials. The algorithm is based on a differential version of the Newton-Puiseux procedure for algebraic equations

Performance enhancement of the photovoltaic cells system by using the pneumatic routers

Solar photovoltaic modules are of immense benefits to ordinary people in terms of independent energy solutions and conventional fuel savings. However, due to the inherent drawback of lower efficiencies per unit area, these technologies adoption rates are very slow and face resistance from domestic consumers for widespread acceptance. Thus, solar photovoltaic thermal hybrid technology was suggested, producing electrical and thermal output from the same unit area. Unfortunately, the lower individual efficiencies of the PV/T collector compared to their individual technologies hinders the potential advantages of this hybrid technology. This is due to the low solar energy absorption and high thermal resistance between the PV cell and the cooling medium. This study aims to develop a novel photovoltaic thermal collector to evaluate PVT performance using three rib configurations with pneumatic guiding devices. This thereby reduced thermal resistance and improved performance using different angles to increase system efficiency and reduce thermal losses resulting from increased temperature. The channel was developed and designed in the new model in three phases to study the improvement of heat transfer. The first phase is to test the simulation of the pneumatic routers numbers in the ribs, while the second phase is to test the simulation of the ribs numbers in the channel. Simulation analysis was conducted using 3D simulation by ANSYS-Fluent software to determine the optimum design of configurations in terms of the airflow channel. The results best from the simulation test indicate that the PVT complex with seven polygons and five vectors was the best design. The simulation results are shown in a combined PVT efficiency of 70.86 % and electrical PVT efficiency of 11.22% with a mass flow rate of 0.17 kg/s and solar irradiance of 1000 W /m². In the third phase, three different angles were chosen for pneumatic routers tested experimentally to determine the best angle. All configurations were set and tested experimentally outdoor under the Iraq climatic conditions to ASHRAE standard at different air mass flow rates. Experimental results of a PV inboard consisting of pneumatic ribs and angle guides with highest daily performance and electrical and thermal efficiency at angle guides of 30 ° compared to 45 ° and 15 ° and an empty PVT collector tube at air mass flow rate of (0.08- 0.17) kg/s. A good agreement was obtained when the 3D simulation and experimental results were compared. It was the average difference in the outlet air temperatures obtained in the numerical and experimental results from 6.18 % to 6.47 % and of the electrical and thermal efficiency from 5.25 % to 6.37 % respectivel

On Permutation Binomials over Finite Fields

Let $\mathbb{F}_{q}$ be the finite field of characteristic $p$ containing $q = p^{r}$ elements and $f(x)=ax^{n} + x^{m}$ a binomial with coefficients in this field. If some conditions on the gcd of $n-m$ an $q-1$ are satisfied then this polynomial does not permute the elements of the field. We prove in particular that if $f(x) = ax^{n} + x^{m}$ permutes $\mathbb{F}_{p}$, where $n>m>0$ and $a \in {\mathbb{F}_{p}}^{*}$, then $p -1 \leq (d -1)d$, where $d = {{gcd}}(n-m,p-1)$, and that this bound of $p$ in term of $d$ only, is sharp. We show as well how to obtain in certain cases a permutation binomial over a subfield of $\mathbb{F}_{q}$ from a permutation binomial over $\mathbb{F}_{q}$

New Method of Measuring TCP Performance of IP Network using Bio-computing

The measurement of performance of Internet Protocol IP network can be done by Transmission Control Protocol TCP because it guarantees send data from one end of the connection actually gets to the other end and in the same order it was send, otherwise an error is reported. There are several methods to measure the performance of TCP among these methods genetic algorithms, neural network, data mining etc, all these methods have weakness and can't reach to correct measure of TCP performance. This paper proposed a new method of measuring TCP performance for real time IP network using Biocomputing, especially molecular calculation because it provides wisdom results and it can exploit all facilities of phylogentic analysis. Applying the new method at real time on Biological Kurdish Messenger BIOKM model designed to measure the TCP performance in two types of protocols File Transfer Protocol FTP and Internet Relay Chat Daemon IRCD. This application gives very close result of TCP performance comparing with TCP performance which obtains from Little's law using same model (BIOKM), i.e. the different percentage of utilization (Busy or traffic industry) and the idle time which are obtained from a new method base on Bio-computing comparing with Little's law was (nearly) 0.13%. KEYWORDS Bio-computing, TCP performance, Phylogenetic tree, Hybridized Model (Normalized), FTP, IRCDComment: 17 Pages,10 Figures,5 Table

Elliptic nets and elliptic curves

An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P_1, ..., P_n are points on E defined over K. To this information we associate an n-dimensional array of values in K satisfying a nonlinear recurrence relation. Arrays satisfying this relation are called elliptic nets. We demonstrate an explicit bijection between the set of elliptic nets and the set of elliptic curves with specified points. We also obtain Laurentness/integrality results for elliptic nets.Comment: 34 pages; several minor errors/typos corrected in v