Edge-fault diameter of C4-free graphs Alochukwu, Alex; Dankelmann, Peter
Discrete mathematics,
January 2024, 2024-01-00, Volume:
347, Issue:
1
Journal Article
Peer reviewed
Open access
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.
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%.
•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.
Global importance of large-diameter trees Lutz, James A.; Furniss, Tucker J.; Johnson, Daniel J. ...
Global ecology and biogeography,
July 2018, Volume:
27, Issue:
7/8
Journal Article
Peer reviewed
Open access
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.
Posterior spinal fusion with pedicle screws is commonly used for the treatment of adolescent idiopathic scoliosis (AIS). To reduce radiation exposure, methods other than computed tomography (CT) are ...desirable for preoperative determination of pedicle diameter.
Investigate the differences between magnetic resonance imaging (MRI) and CT measurements of pedicle diameter.
Cross-sectional research.
Twenty-one AIS Lenke type 1 patients (19 female and 2 males, mean age at surgery: 15.4 years) who underwent posterior spinal fusion between April 2009 and October 2019.
Gap between CT and MRI pedicle diameters.
The inner and outer diameters of the right and left pedicles from T1 to L3 were measured separately by two spine surgeons for statistical comparisons.
The respective minimum and maximum CT-MRI values were -3.7 mm and 4.7 mm for inner diameter and -4.6 mm and 5.3 mm for outer diameter. Regarding inter-examiner error, the probability of a 2 mm difference in measurement was less than 5% for both modalities. The probability of a 1 mm difference was also less than 5%, and that of a 3 mm or more difference was 2.1% for the inner diameter and 2.9% for the outer diameter. Whereas low body weight was significantly associated with measurement differences, pedicle laterality was not.
MRI does not have the reliability to measure pedicle size in AIS patients at present. However, with advancements in image processing technology, the accuracy of pedicle size measurement by MRI may soon improve.
The accurate estimation of bark thickness is important for foresters for several reasons. It is crucial for timber volume estimation and can help improve the quality of forestry records, and bark has ...a growing commercial importance as a high-value bioresource. The problem is that models such as the Czech Cubic Tables (CCT) polynomial model are frequently unique. Furthermore, the official method requires rounding down the midspan over-bark diameter (DOB) to the nearest centimetre to estimate the double bark thickness (DBT) and merchantable timber volume. Therefore, we verified the significance of the effects of rounding down the midspan DOB on DBT using a dataset of 438 recently harvested Norway spruce (Picea abies L. Karst.) logs from the Central Bohemian region. The correlation analysis showed that for measured data without rounding down the diameters, the variability of the DBT was able to explain only 8% of the DOB variability. As for the rounded-down data, the coefficient of determination was slightly higher, reaching 9%. The paired-samples T-tests showed a significant difference between the DBT as calculated directly from measured data and that from the rounded-down over-bark diameters (p < 0.05). The polynomial and linear models underestimated the DBT (2.24 and 1.75 mm on average, respectively) on measured data. In contrast, for data from the rounded-down DOB, the models overestimated the DBT (2.70 or 3.18 mm on average, respectively).
Concern about fault tolerance in the design of interconnection networks has raised interest in the study of graphs such that deleting some vertices increases the diameter only moderately. For an ...interconnection network G, the (ω−1)-fault diameterDω(G) is the maximum diameter of a subgraph obtained by deleting fewer than ω vertices of G, and the ω-wide diameterdω(G) is the least ℓ such that any two vertices are joined by ω internally-disjoint paths of length at most ℓ. The enhanced hypercube Qn,k is a variant of the well-known n-dimensional hypercube Qn in which an edge is added from each vertex xn,…,x1 to the vertex obtained by complementing xk,…,x1. Yang, Chang, Pai, and Chan gave an upper bound for dn+1(Qn,k) and Dn+1(Qn,k) and posed the problem of finding the wide diameter and fault diameter of Qn,k. By constructing internally disjoint paths between any two vertices in the enhanced hypercube, for n≥3 and 2≤k≤n we prove that Dω(Qn,k)=dω(Qn,k)=d(Qn,k) for 1≤ω<n−⌊k2⌋; Dω(Qn,k)=dω(Qn,k)=d(Qn,k)+1 for n−⌊k2⌋≤ω≤n+1, where d(Qn,k) is the diameter of Qn,k. These results mean that interconnection networks modeled by enhanced hypercubes are extremely robust.
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