Edge-fault diameter of C4-free graphs Alochukwu, Alex; Dankelmann, Peter
Discrete mathematics,
January 2024, 2024-01-00, Letnik:
347, Številka:
1
Journal Article
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Let G be a connected graph and k∈N. The k-edge-fault diameter of G is defined as the largest diameter of the graphs arising from G by deleting k edges. In this paper we show that the k-edge-fault ...diameter of a (k+1)-edge connected graph of order n not containing a 4-cycle cannot exceed 5k2+k+1n+9, and we construct graphs that show that for k+1 a prime power this bound is close to optimal if k is large. For the special case k=2 we improve the above bound and obtain the sharp bound n2 on the 2-edge-fault diameter of 3-edge-connected graphs of order n not containing a 4-cycle.
В статье приведен сравнительный анализ сеянцев, выращенных из семян экземпляров, выделенных побиометрическим показателям. Установлено, что семенное потомство характеризуется ...значительнойизменчивостью, что отражает его наследственную неоднородность и может служить решению селекционныхзадач для оценки направленности естественного отбора в определенных условиях
The article presents a comparative analysis of seedlings grown from seed instances, atzelektronik biometric indicators. Itis established that seed progeny is characterized by significant variability, reflecting its genetic heterogeneity and can serve asthe decision of the selection task to evaluate the direction of natural selection under certain conditions.
•The Deffρe method was proposed to overcome the challenges of using the water equivalent diameter (Dw) method used for SSDE.•The Deffρe method is based on correcting effective diameter (Deff) with ...electron densities of tissues of a scan area.•Results of the Deffρe method showed to be promise for the chest protocols, but was less accurate for other body protocols.•The Deff method was poorer for the chest protocols, but gave good assessments for other body protocols.•Correction of both dimensions, lateral (LAT) and anterior-posterior (AP), did not improve the accuracy of the Deffρe method.
An assessment of the effective diameter of a patient’s body using electron densities of tissues inside the scan area (Deffρe) was proposed to overcome challenges associated with the estimation of water-equivalent diameter (Dw), which is used for size-specific dose estimate (SSDE). The aims of this study were to (1) investigate the Deffρe method in two different forms using a wide range of patient sizes and scanning protocols, and (2) compare between four methods used to estimate the patient size for SSDE.
Under IRB approval, a total of 350 patients of varying sizes have been collected retrospectively from the Hospital. The Dw values were assessed over six different CT body protocols: (1) chest with contrast media, (2) chest High-Resolution Computed Tomography (HRCT) without contrast media, (3) abdomen-pelvis with contrast media, (4) abdomen-pelvis without contrast media, (5) chest-abdomen-pelvis with contrast media, and (6) pelvis without contrast media. A MATLAB-based code was developed in-house to assess the size of each patient using the conventional effective diameter method (Deff), Deffρe by correcting either both the lateral (LAT) and anterior-posterior (AP) dimensions (Deff,LAT+APρe) or LAT only (Deff,LATρe), and Dw at the mid-CT slice of the patient images.
The results of Deff,LAT+APρe and Deff,LATρe provided a better estimation for the chest protocols with the averages of absolute percentage difference (PD) values in the range of 3 – 7 % for all patient sizes as compared to the Dw method, whereas the averages of PD values for the Deff method were 9 – 15 %. However, Deff gave a better estimation for Dw values for the other body protocols, with differences of 2 – 4 %, which were lower than those obtained with the Deff,LAT+APρe and Deff,LATρe methods. For the chest protocols, statistically significant differences were found between Deff and the other methods, but there were no significant differences between all the methods for the other scanning protocols. The results show that the correction of both dimensions, LAT and AP, did not improve the accuracy of the Deffρe method, and, for most protocols, Deff,LAT+APρe gave larger range differences compared to those based on correction of the LAT dimension only.
If the Dw cannot be assessed, the Deff,LATρe method may only be considered for the chest protocols as an alternative approach. The Deff method may also be used for all regions taking into account the application of a correction factor for the chest protocols to avoid a significant under or overestimation of the patient dose.
Given a connected graph G=(V,E) and a vertex subset S⊂V, the Steiner distancedG(S) of S is the size of a minimum spanning tree of S in G. If G has order n and k is an integer such that 2≤k≤n, the ...Steiner k-eccentricity of a vertex v in G is the maximum value of dG(S) over all S⊂V with |S|=k and v∈S. The minimum Steiner k-eccentricity sradk(G) is called the Steinerk-radius ofG and the maximum Steiner k-eccentricity sdiamk(G) is called the Steinerk-diameter ofG. In 1990, Henning, Oellermann, and Swart showed that for any k, there exists a graph Gk such that sdiamk(Gk)=2(k+1)2k−1sradk(Gk) and proved that sdiam3(G)≤85srad3(G) and sdiam4(G)≤107srad4(G) for all connected graphs G. In this note, we show that sdiamk(G)≤k+3k+1sradk(G) for each k≥5 and verify that this bound is tight via a construction.
The Wiener index $ W(G) $ of a graph $ G $ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $ G $. The diameter $ D(G) $ of ...$ G $ is the maximum distance between all pairs of vertices of $ G $, and the conditional diameter $ D(G; s) $ is the maximum distance between all pairs of vertex subsets with cardinality $ s $ of $ G $. When $ s = 1 $, the conditional diameter $ D(G; s) $ is just the diameter $ D(G) $. The authors in <xref ref-type="bibr" rid="b18">18 characterized the graphs with the maximum Wiener index among all graphs with diameter $ D(G) = n-c $, where $ 1\le c\le 4 $. In this paper, we will characterize the graphs with the maximum Wiener index among all graphs with conditional diameter $ D(G; s) = n-2s-c $ ($ -1\leq c\leq 1 $), which extends partial results above.
Premise
Competition is an important driver of tree mortality and thus affects forest structure and dynamics. Tree architectural traits, such as height‐to‐diameter (H‐D) and branch length‐to‐diameter ...(L‐d) relationships are thought to influence species competitiveness by affecting light capture. Unfortunately, little is known about how the H vs. D and L vs. d scaling exponents are related to tree performance (defined in the context of growth vigor) in competition.
Methods
Using data from field surveys of 1547 individuals and destructive sampling of 51 trees with 1086 first‐order branches from a high‐density Pinus massoniana forest, we explored whether the H vs. D and the L vs. d scaling exponents respectively differed numerically across tree performance and branch vertical position in crowns.
Results
The results indicated that (1) the H vs. D scaling exponent decreased as tree performance declined; (2) the L vs. d scaling exponent differed across tree performance classes (i.e., the scaling exponent of “inferior” trees was significantly larger than that of “moderate” and “superior” trees); (3) the L vs. d scaling exponent decreased as branch position approached ground level; and (4) overall, the branch scaling exponent decreased as tree performance improved in each crown layer, but decreased significantly in the intermediate layer.
Conclusions
This study highlights the variation within (and linkage among) length‐to‐diameter scaling relationships across tree performance at the individual and branch levels. This linkage provides new insights into potential mechanisms of tree growth variation (and even further mortality) under competition in subtropical forests.
•Linear relation between bubble departure diameter and contact diameter is obtained.•The accuracy of force balance model is improved by the new bubble growth model.•The force balance model can be ...expressed by a series of dimensionless parameters.•The newly proposed empirical formula performs better than other existed models.
An experiment is carried out using a high-speed camera to closely observe the bubble behaviors on a horizontal aluminum heating surface under high mass flux. Subcooled flow boiling experiments are conducted at Reynolds numbers of 61,850–124,041 for a range of density ratios (0.000647-0.001153), Jacob numbers corresponding to wall superheat (0.012201-0.025096) and for Jacob numbers corresponding to subcooling varying from 0.009549 to 0.02856. The experimental results indicate that both bubble departure diameter (BDD) and bubble contact diameter (BCD) reduce with increasing system pressure, increasing flow velocity, increasing subcooling, and decreasing wall superheat. The experiment confirms that the linear relationship between BCD and BDD is still valid under high mass flux. The BCD is 0.4027 times of the BDD. A force balance model based on the newly modified model of bubble growth rate is used to calculate BDD and its predicted values are in good agreement with the present measured values. The force balance model can be expressed by a series of dimensionless parameters: density ratio, Jacob number corresponding to wall superheat, Jacob number corresponding to subcooling, Prandtl number, Reynolds number, and contact angle. A new empirical formula of BDD in a horizontal channel is developed based on the dimensionless parameters using the Buckingham theorem. The empirical formula considers more comprehensive factors and predicts the BDD obtained in a horizontal channel with an average relative error of 12.08%.
Global importance of large-diameter trees Lutz, James A.; Furniss, Tucker J.; Johnson, Daniel J. ...
Global ecology and biogeography,
July 2018, Letnik:
27, Številka:
7/8
Journal Article
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Aim: To examine the contribution of large-diameter trees to biomass, stand structure, and species richness across forest biomes. Location: Global. Time period: Early 21st century. Major taxa studied: ...Woody plants. Methods: We examined the contribution of large trees to forest density, richness and biomass using a global network of 48 large (from 2 to 60 ha) forest plots representing 5,601,473 stems across 9,298 species and 210 plant families. This contribution was assessed using three metrics: the largest 1% of trees ≥ 1 cm diameter at breast height (DBH), all trees ≥ 60 cm DBH, and those rank-ordered largest trees that cumulatively comprise 50% of forest biomass. Results: Averaged across these 48 forest plots, the largest 1% of trees ≥ 1 cm DBH comprised 50% of aboveground live biomass, with hectare-scale standard deviation of 26%. Trees ≥ 60 cm DBH comprised 41% of aboveground live tree biomass. The size of the largest trees correlated with total forest biomass (r2 = .62, p < .001). Large-diameter trees in high biomass forests represented far fewer species relative to overall forest richness (r2 = .45, p < .001). Forests with more diverse large-diameter tree communities were comprised of smaller trees (r2 = .33, p < .001). Lower large-diameter richness was associated with large-diameter trees being individuals of more common species (r2 = .17, p = .002). The concentration of biomass in the largest 1% of trees declined with increasing absolute latitude (r2 = .46, p < .001), as did forest density (r2 = .31, p < .001). Forest structural complexity increased with increasing absolute latitude (r2 = .26, p < .001). Main conclusions: Because large-diameter trees constitute roughly half of the mature forest biomass worldwide, their dynamics and sensitivities to environmental change represent potentially large controls on global forest carbon cycling. We recommend managing forests for conservation of existing large-diameter trees or those that can soon reach large diameters as a simple way to conserve and potentially enhance ecosystem services.
•Object of analysis: minichannels 5.5, 6.0 and 10 mm deep and 0.5 1.2 mm wide.•Boiling curves for ethanol, FC-72 and Novec-649.•Visualization studies: growing bubble diameter changes and bubble ...departure diameter.•Determining the bubble departure diameter with static and dynamic methods.
Pool boiling heat transfer experiments were conducted with ethanol, Novec-649 and FC-72 at atmospheric pressure on surfaces with deep minichannels. The minichannels 5.5, 6.0 and 10 mm deep and 0.5–1.2 mm wide were uniformly spaced with a pitch of 2.0 mm on the base surfaces. Heat transfer coefficients obtained with ethanol were similar for all surfaces tested. Novec-649 and FC-72 produced the highest coefficients at heat fluxes above 100 kW/m2 in 1 mm wide minichannels. All the working fluids provided a significant increase in the maximum (critical) heat flux. The images were recorded using high speed imaging techniques across the entire surface of the samples. Boiling visualization aimed to study vapor bubble diameter changes during the growth period and measure the bubble departure diameter.
The bubble diameter at departure was also determined analytically according to force balance static and dynamic variants. The dynamic variant provided a high consistency between the theoretical and experimental data for bubble departure diameter with FC-72 and Novec-649.
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