In order to further explore the characteristics of slim cigarette processing technology, this study designed different cut width (0.7mm and 0.8mm) of product A, and carried out the experiments of ...making and rolling under the same process conditions, and evaluated the influence of the width of cut tobacco on the quality of slim cigarette. The results showed that: the 0.7mm cut width has the following advantages: Processing characteristics, Short rejection rate, Reducing draw resistance, Weight stability, Uniformity of density is better than 0.8 mm cut width, and 0.7 mm cut width is more suitable for the production of slim cigarette.
This paper revisits the classical edge-disjoint paths (EDP) problem, where one is given an undirected graph
G
and a set of terminal pairs
P
and asks whether
G
contains a set of pairwise edge-disjoint ...paths connecting every terminal pair in
P
. Our aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in
P
in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter tree-cut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded tree-cut width. Our second result shows that EDP parameterized by tree-cut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph.
Abstract The primary objective of this paper is to rigorously analyse the influence of selected parameters on the cut width in the context of Wire Electric Discharge Machining (WEDM). The parameters ...under investigation, each varied at different levels, include pulse width, servo reference mean voltage, time interval between two pulses, discharge frequency, and wire feed speed. As the workpiece material, sintered carbide K10 was used. Data for the response variable, cut width, was meticulously collected using two high-precision instruments: the Zoller Genius 3s and the Alicona InfiniteFocusSL. Among the parameters studied, the mean reference voltage emerged as the most influential variable. It holds a commanding lead with a percentage contribution of as much as 82.4 %, making it nearly 15 times more impactful than the second most influential parameter, which is pulse width. At its lowest setting, or first level, the mean reference voltage results in a record low cut width. Conversely, at its highest setting, or third level, it leads to a record high cut width. This comprehensive analysis not only quantifies the relative importance of each parameter but also provides valuable insights into the optimal settings for achieving desired cut widths. The findings have significant implications for improving the efficiency and precision of WEDM processes.
The tree-cut width of a graph is a graph parameter defined by Wollan (J Combin Theory, Ser B, 110:47–66,
2015
) with the help of tree-cut decompositions. In certain cases, tree-cut width appears to ...be more adequate than treewidth as an invariant that, when bounded, can accelerate the resolution of intractable problems. While designing algorithms for problems with bounded tree-cut width, it is important to have a parametrically tractable way to compute the exact value of this parameter or, at least, some constant approximation of it. In this paper we give a parameterized 2-approximation algorithm for the computation of tree-cut width; for an input
n
-vertex graph
G
and an integer
w
, our algorithm either confirms that the tree-cut width of
G
is more than
w
or returns a tree-cut decomposition of
G
certifying that its tree-cut width is at most 2
w
, in time
2
O
(
w
2
log
w
)
·
n
2
. Prior to this work, no
constructive
parameterized algorithms, even approximated ones, existed for computing the tree-cut width of a graph. As a consequence of the Graph Minors series by Robertson and Seymour, only the
existence
of a decision algorithm was known.
The experimental studies on Al
2
O
3
+ TiO
2
hybrid nanofluid flowing under the turbulent condition in a double-tube heat exchanger with various modified V-cuts twisted tape inserts are performed to ...study the hydrothermal characteristics. The hybrid nanofluid is prepared with a volume concentration of 0.1% by dispersing Al
2
O
3
and TiO
2
nanoparticles by equal volume ratio in distilled water. The effect of using twisted tape turbulator (with and without V-cuts) and hybrid nanofluid on the heat transfer and pressure drop characteristics are evaluated for different twist ratios, V-cut depth ratios, V-cut width ratios and hybrid nanofluid inlet temperatures. Results show that Nusselt number as well as friction factor increases with the decrease in twisting ratio, increase in depth ratio, decrease in width ratio and decrease in nanofluid inlet temperature. Maximum improvements in 132% for Nusselt number and 55% for friction factor are obtained as compared to that for the water in the tube without twisted tape. The values of thermal performance factor and entropy generation ratio are greater than unity for hybrid nanofluid for all modified twisted tape inserts.
Ultra precision machining (UPM) is extensively used to fabricate high accuracy products. However, the problematic material swelling/recovery effect due to the elastic recovery of materials in UPM ...remains unresolved. It causes a ragged surface and extra engineering tolerances which are unadoptable in extremely precise components. In particular to high elastic recovery rate with low thermal conductivity materials like titanium alloys, the swelling effect is intensified during machining processes. In this study, a magnetic field was superimposed on titanium alloys during the single point diamond cutting which aimed to minimize the material swelling effect on the machined surface using the magnetic field influence. In the experiments, titanium alloys were located at the center of two permanent magnets with intensity 0.02T and undergone a diamond groove cutting. The experimental results showed the material swelling/recovery on the machined surface was significantly reduced in presence of magnetic field in comparison to that of diamond cutting without a magnetic assistance; the accuracy of depth of cut, width and radius of cutting groove in a magnetic field reached satisfactorily over 98%. The proposed machining technology solves the problem of material swelling/spingback of low thermal conductivity materials by a cost-efficient way which is needless of complicated equipment.
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•The material swelling of Ti alloys was highly reduced using a magnetic assistance.•Only an extra 0.02T magnetic field was employed for the outstanding results.•The form accuracy of cut groove of MFS reached over 98%.•The method can extensively apply to materials with positive magnetic susceptibility.
A Menger-like property of tree-cut width Giannopoulou, Archontia C.; Kwon, O-joung; Raymond, Jean-Florent ...
Journal of combinatorial theory. Series B,
20/May , Volume:
148
Journal Article
Peer reviewed
Open access
In 1990, Thomas proved that every graph admits a tree decomposition of minimum width that additionally satisfies a certain vertex-connectivity condition called leanness. This result had many uses and ...has been extended to several other decompositions. In this paper, we consider tree-cut decompositions, that have been introduced by Wollan (2015) as a possible edge-version of tree decompositions. We show that every graph admits a tree-cut decomposition of minimum width that additionally satisfies an edge-connectivity condition analogous to Thomas' leanness.
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