Multicast Network Coding and Field Sizes

In an acyclic multicast network, it is well known that a linear network coding solution over GF($q$) exists when $q$ is sufficiently large. In particular, for each prime power $q$ no smaller than the number of receivers, a linear solution over GF($q$) can be efficiently constructed. In this work, we reveal that a linear solution over a given finite field does \emph{not} necessarily imply the existence of a linear solution over all larger finite fields. Specifically, we prove by construction that: (i) For every source dimension no smaller than 3, there is a multicast network linearly solvable over GF(7) but not over GF(8), and another multicast network linearly solvable over GF(16) but not over GF(17); (ii) There is a multicast network linearly solvable over GF(5) but not over such GF($q$) that $q > 5$ is a Mersenne prime plus 1, which can be extremely large; (iii) A multicast network linearly solvable over GF($q^{m_1}$) and over GF($q^{m_2}$) is \emph{not} necessarily linearly solvable over GF($q^{m_1+m_2}$); (iv) There exists a class of multicast networks with a set $T$ of receivers such that the minimum field size $q_{min}$ for a linear solution over GF($q_{min}$) is lower bounded by $\Theta(\sqrt{|T|})$, but not every larger field than GF($q_{min}$) suffices to yield a linear solution. The insight brought from this work is that not only the field size, but also the order of subgroups in the multiplicative group of a finite field affects the linear solvability of a multicast network

A Reflection Formula for the Gaussian Hypergeometric Function of Matrix Argument

We obtain a reflection formula for the Gaussian hypergeometric function of real symmetric matrix argument. We also show that this result extends to the Gaussian hypergeometric function defined over the symmetric cones, and even to generalizations of the Gaussian hypergeometric function defined in terms of series of Jack polynomials. We also obtain a quadratic transformation formula for the 2x2 Gaussian hypergeometric function of Hermitian matrix argument.Comment: 11 page

Evaluation System of College Educational Information Management System based on AHP

Aiming at evaluating the college educational information management system, in this paper, taking the YanBian University for example, we construct a three-level evaluation system of college educational information management system. Using AHP, through the hierarchical single rankings and total rankings, the weight of each index is obtained. Meanwhile, we prove that the evaluation system is scientific and reasonable. Finally, we get the conclusion and give some relevant suggestions to make the system more complete

A study of barriers to online learning in distance education in China

China's 'Modern Distance Education' is a government-led initiative prompted by the need to widen access to higher education and by the opportunities offered by the development of a widespread infrastructure of information and communications technologies. Distance education using television, radio and other technologies has a long history in China, but the advent of computer communications opened new possibilities for promoting educational development and the policy goal of modernisation. Distance education in China now involves online learning, to various degrees. However, the effectiveness of online courses depends on learners accessing them and using the resources provided. Does this happen? How well do learners manage their online learning? What barriers do they encounter? This thesis examines these questions through a study of adult distance learners based on analysis of a survey of 2931 learners and in-depth interviews with 21 learners and distance education experts in several locations. I find that: (1) The barriers to online learning faced by the sample learners are of seven types: communication and interaction; teaching and courses; learning resources; learning support services; external support and economic burdens; computer and network operation skills; and conditions for accessing the Internet. (2) Among the seven types of barrier, the 'communication and interaction' barrier is not only acting as the most important one faced by these learners, but also exists as a markedly independent one. (3) Improvements in 'communication and interaction' are the most effective in overcoming the other barriers and also contribute to increasing the learners' learning efficiency. This leads to the perception that working on 'communication and interaction' is very likely to be the best starting point for tackling barriers to online learning. According to these findings, I believe that if the situation of 'communication and interaction' in online learning can be improved for online learners to meet their desire for 'sociability', and once they can thus establish their own 'learning communities' and form relatively stable 'student-to-student' relationships, and 'student-to-teacher' relationships, other learning barriers will be reduced as well. Hence, I argue that we should always pay attention to making 'communication and interaction' occur effectively for online learners in the learning process. We should consider the matter of 'interaction' not only in the delivery process of teaching and tutoring as well as in learning activities, but also in the production of teaching materials and in the provision of learning materials, as well as in the building of learning environments. In a word, it is necessary to put the whole matter of 'interaction' at the core of the instructional system design for online learning

Lime application reduces potassium and nitrate leaching on sandy soils

Kalium (K)-Auslaugung kommt in leicht strukturierten Böden häufig vor und reduziert die im Boden für die Pflanzen verfügbare Menge K. Diese Studie untersuchte die Auswirkung der Kalkanwendung und der K-Raten (null, 20, 60 kg K/ha) auf die K-Auslaugung und andere Sickerwasserparameter von vier sandigen Böden im Westen Australiens. Drei von vier Böden unterschieden sich in der K-Auslaugung nicht zwischen den Raten von Null und 20 kg K/ha, während 60 kg K/ha die K-Auslaugung in allen vier Böden erhöhten. Bei den Merredin-Böden verzögerte die Kalkanwendung die K-Auslaugung bei 60 kg K/ha deutlich und zeigte einen K-Auslaugungspeak bei 4,75 Porenvolumen (PV) im gekalkten Boden (pHCaCl2: 6,20), jedoch bei 3 PV im nicht gekalkten Boden (pHCaCl2: 4,50), und das Kalken reduzierte auch die Gesamt­menge an ausgelaugtem K und NO3. In ähnlicher Weise trat der Peak der K-Auslaugung bei 2–3 PV in den anderen beiden nicht gekalkten Böden auf. Die maximalen NO3-Konzentrationen von Sickerwasser bei 60 kg K/ha betrugen 46 mg/l bei 2 PV mit Kalk gegenüber 110 mg/l bei 1,25 PV ohne Kalk, während die Menge an ausgelaugtem NO3 aus Böden ohne K-Zugabe größer war als aus den mit K behandelten Böden. Die Ergebnisse legen nahe, dass die Kalkung eines sauren Sandes die K- und NO3-Auswaschung verlangsamen und verringern kann und erhebliche Auswirkungen auf das K-Dünger-Management auf solchen Böden hat.Potassium (K) leaching is common in light-textured soils and reduces soil available K to plants. This study examined the effect of lime application and K rates (nil, 20, 60 kg K/ha) on K leaching and other leachate parameters of four sandy soils in Western Australia. Three out of four soils did not differ in K leaching between the rates of nil and 20 kg K/ha, whereas 60 kg K/ha increased K leaching in all four soils. For the Merredin soils, lime applica­tion markedly delayed K leaching at 60 kg K/ha, showing K leaching peak at 4.75 pore volume (PV) in the limed soil (pHCaCl2: 6.20) but at 3 PV in the non-limed soil (pHCaCl2: 4.50), and liming also reduced total amount of leached K and NO3. Similarly, the peak of K leaching occurred at 2–3 PV in the other two non-limed soils. Maximum leachate NO3 concentrations at 60 kg K/ha were 46 mg/L at 2 PV with lime versus 110 mg/L at 1.25 PV without lime, while the amount of leached NO3 from nil K soils was greater than from the K treated soils. The results suggest that liming of an acid sand can slow down and reduce K and NO3 leaching and have significant implication for K-fertilizer management on such soils