On Existence of Primitive Normal Elements of Cubic Form over Finite Fields

For a prime [Formula: see text]and a positive integer[Formula: see text], let [Formula: see text] and [Formula: see text] be the extension field of [Formula: see text]. We derive a sufficient condition for the existence of a primitive element [Formula: see text] in[Formula: see text] such that [Formula: see text] is also a primitive element of [Formula: see text], a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is a primitive element of [Formula: see text], and a sufficient condition for the existence of a primitive normal element [Formula: see text] in [Formula: see text] over [Formula: see text] such that [Formula: see text] is also a primitive normal element of [Formula: see text] over [Formula: see text].

Chordality in Matroids: In Search of the Converse to Hliněný's Theorem

<p>Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chordal graphs of bounded treewidth. Hliněný [25] generalised Courcelle's Theorem for graphs to classes of matroids represented over finite fields and of bounded branchwidth. This thesis has investigated the possibility of obtaining a generalisation of chordality to matroids that would enable us to prove a converse of Hliněný's Theorem [25]. There is a variety of equivalent characterisations for chordality in graphs. We have investigated the relationship between their generalisations to matroids. We prove that they are equivalent for binary matroids but typically inequivalent for more general classes of matroids. Supersolvability is a well studied property of matroids and, indeed, a graphic matroid is supersolvable if and only if its underlying graph is chordal. This is among the stronger ways of generalising chordality to matroids. However, to obtain the structural results that we need we require a stronger property that we call supersolvably saturated. Chordal graphs are well known to induce canonical tree decompositions. We show that supersolvably saturated matroids have the same property. These tree decompositions of supersolvably saturated matroids can be processed by a finite state automaton. However, they can not be completely described in monadic second-order logic. In order to express the matroids and their tree decompositions in monadic second-order logic we need to extend the logic over an extension field for each matroid represented over a finite field. We then use the fact that each maximal round modular flat of the tree decomposition for every matroid represented over a finite field, and in the specified class, spans a point in the vector space over the extension field. This enables us to derive a partial converse to Hliněný's Theorem.</p>

Chordality in Matroids: In Search of the Converse to Hliněný's Theorem

<p>Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chordal graphs of bounded treewidth. Hliněný [25] generalised Courcelle's Theorem for graphs to classes of matroids represented over finite fields and of bounded branchwidth. This thesis has investigated the possibility of obtaining a generalisation of chordality to matroids that would enable us to prove a converse of Hliněný's Theorem [25]. There is a variety of equivalent characterisations for chordality in graphs. We have investigated the relationship between their generalisations to matroids. We prove that they are equivalent for binary matroids but typically inequivalent for more general classes of matroids. Supersolvability is a well studied property of matroids and, indeed, a graphic matroid is supersolvable if and only if its underlying graph is chordal. This is among the stronger ways of generalising chordality to matroids. However, to obtain the structural results that we need we require a stronger property that we call supersolvably saturated. Chordal graphs are well known to induce canonical tree decompositions. We show that supersolvably saturated matroids have the same property. These tree decompositions of supersolvably saturated matroids can be processed by a finite state automaton. However, they can not be completely described in monadic second-order logic. In order to express the matroids and their tree decompositions in monadic second-order logic we need to extend the logic over an extension field for each matroid represented over a finite field. We then use the fact that each maximal round modular flat of the tree decomposition for every matroid represented over a finite field, and in the specified class, spans a point in the vector space over the extension field. This enables us to derive a partial converse to Hliněný's Theorem.</p>

Performance of farming extension field during the COVID-19 pandemic in East Java

The success of farming extension activities cannot be separated from the role of farming extension workers. In this pandemic, farming extension counseling must be continue to make good environment. Social and physical distancing can make limited access for farming extension workers in carry out their roles. The purpose of this study was to analyze the performance of farming extension field and the influenced factors of perfomance farming extension field during the pandemic in East Java. This research is located in East Java province, it was conducted from March 2020 to 2021. The sampling was carried out by cluster random sampling and it got 360 respondents. The data collected by using statistical descriptive analysis which is used a scale and multiple linear regression model. The result of this research during the pandemic was going well. Meanwhile, the was the factors that influence in performance of farming extension (age, work training, topography and availability of infrastructure) but distance, farmer group, and education did not have impact on it.

Brief Motivational Interviewing Training for Outreach in School Health Programming

This study assessed a brief 6-week motivational interviewing (MI) training program for extension field specialists (EFS) involved in supporting a statewide school wellness initiative called SWITCH. A total of 16EFS were instructed in MI principles to support the programming and half (n = 8) volunteered to participate in the hybrid (online and in-person) MI training program. Phone calls between EFS and school staff involved in SWITCH were recorded and coded using the Motivational Interviewing Treatment Integrity (MITI) system to capture data on utilization of MI principles. Differences in MI utilization between the trained (n=8) and untrained (n=8) EFS were evaluated using Cohen’s d effect sizes. Results revealed large differences for technical global scores (d=1.5) and moderate effect sizes for relational global components (d=0.76) between the two groups. This naturalistic, quasi-experimental study indicates a brief MI training protocol is effective for teaching the spirit and relational components of MI to EFS.

Dynamic characteristics of threshold value and extension field selections for vacuum-blowing cleaning system

To provide theoretical guidelines for threshold value selections on performance characteristics of extension field, the flow characteristic in the vacuum-blowing cleaning system was simulated using the average velocity and pressure of the front inlet surface, and the average velocity of the outlet surface, as indices to evaluate the effect of the extension field’s structural parameters. It is found that the extension field parameters have implications for the simulation calculation, and that each parameter has a corresponding threshold. If the structural parameter is greater than the corresponding threshold, the calculation result is not affected, and the threshold values are analyzed by using computational fluid dynamics (CFD). The dimensions of the front, back, left, and right extension fields are recommended as follows: lf=lb=ll=lr=210 mm and θf =θb =θl =θr =55 degree. The flow field distribution characteristic does not have a distinct difference with or without the extension field corner. The extension field with a corner can be used if high accuracy is required. However, to reduce the amount of grid computation and shorten the calculation time, the corner extension field model is not recommended. Finally, the simulation results are verified experimentally and can be used to improve the calculation accuracy and reduce the required computational resources.