Border Lengths Research Articles

A natural bijection for contiguous pattern avoidance in words

Two words p and q are avoided by the same number of length-n words, for all n, precisely when p and q have the same set of border lengths. Previous proofs of this theorem use generating functions but do not provide an explicit bijection. We give a bijective proof for all pairs p,q that have the same set of proper borders, establishing a natural bijection from the set of words avoiding p to the set of words avoiding q.

Morphological and clinical significance of the suprameatal region: a topographic study

The suprameatal approach, which does not require mastoidectomy, uses the method of tunneling over the facial nerve to enter the middle ear in cochlear implantation. Even if the SMA approach is also used to drain the mastoid antrum, the depth of the triangle and protrusion types may be important for surgical approaches in this region. This descriptive study was conducted with 58 dry skulls found in the laboratories of the University Faculty of Medicine. Important landmarks were used on the left and right sides of the skulls. All the distances were measured with a vernier caliper to the nearest millimeter. No statistical significance was found between the right and left sides (p>0.05). The border lengths of the suprameatal triangle were respectively 14.88±1.67 mm, 18.17±1.09 mm, 14.56±1.59 mm on the right and 15.34±1.65 mm, 19.01±0.56 mm, 15.89±0.52 mm on the left. Consequently, it was determined that the left side was wider than the right, and there was statistical significance between the sides. The mean ST area was found to be 112.7±16.90 mm2. The crest was observed mostly on the right side (n=30 (51.72%)), and the triangular suprameatal protrusion was observed mostly on the right side (n=10 (31.03%)). We think that knowing this area’s borders and morphological features well, nominated before the surgical procedure, will be a guide in preventing possible operative and postoperative complications.

Optimized border irrigation delays winter wheat flag leaf senescence and promotes grain filling.

Border irrigation is still the main irrigation method in the Huang-Huai-Hai Plain of China (HPC), and the suitable irrigation border length for water saving and high yield under traditional irrigation is still unclear. Therefore, a 2-year traditional border irrigation experiment (2017-2019) was conducted on the HPC. Four border lengths were tested: 20m (L20), 30m (L30), 40m (L40), and 50m (L50). These treatments were given supplementary irrigation at jointing and anthesis. An exclusively rainfed condition formed the control treatment. Compared with other treatments, the activities of superoxide dismutase antioxidant and sucrose phosphate synthetase, and the contents of sucrose and soluble proteins after anthesis were higher in the L40 and L50 treatments, while the content of malondialdehyde content was lower. Therefore, the L40 treatment effectively delayed the decrease in the soil plant analysis development (SPAD) value and chlorophyll fluorescence characteristics, promoted grain filling, and achieved the highest thousand-grain weight. Compared with the L40 treatment, the grain yields of the L20 and L30 treatment were significantly reduced, while the water productivity of the L50 treatment was significantly reduced. These findings suggest that 40m was the optimal border length for both high yield and water saving in this experiment. This study provides a simple and low-cost water-saving irrigation method for winter wheat in the HPC under traditional irrigation, which can help alleviate the pressure of agricultural water use.

Optimized border irrigation improved soil water content, increased winter wheat grain yield and water productivity

Border irrigation is still the main irrigation method in the Huang-Huai-Hai Plain of China (HPC), we aimed to find a suitable border length to reduce the quantity of irrigation water through a traditional border irrigation system to alleviate groundwater depletion. A 2-year experiment (2017–2019) was conducted with four border lengths: 20 m (L20), 30 m (L30), 40 m (L40) and 50 m (L50); supplementary irrigation was implemented during jointing and anthesis. The results showed that compared with the L20 and L30 treatments, the L40 treatment did not significantly increase the total water consumption. Compared with the L50 treatment, the L40 treatment significantly reduced the water consumption of ineffective tillers from jointing to anthesis. There was no significant difference in flag leaf net photosynthetic rate (Pn) between L40 treatment and L50 treatment at 14–28 days after anthesis, which was 12.36% and 21.31% higher than L30 and L20 treatments respectively, and significantly increased dry matter accumulation after anthesis. Grain yield were the higher in the L40 and L50 treatments, while the water productivity (WP) was highest in the L40 treatment, which was 3.98%, 4.54% and 7.94% higher than L50, L30, and L20 treatments, respectively. Hence, the irrigation field treatments with a border length of 40 m were considered the most efficient, which provides a theoretical basis for optimizing the traditional irrigation border length in HPC.

Optimized Border Irrigation Improved Nitrogen Accumulation, Translocation of Winter Wheat and Reduce Soil Nitrate Nitrogen Residue

We aimed to optimize field border length in the Huang-Huai-Hai Plain of China (HPC) to reduce soil inorganic nitrogen residues and increase nitrogen absorption and utilization by wheat plants using a traditional border irrigation system. In a two-year experiment (2017–2019) conducted in the HPC, four border lengths were tested: 20 m (L20), 30 m (L30), 40 m (L40), and 50 m (L50). Supplementary irrigation was implemented during jointing and anthesis stages, and control fields received treatment without irrigation. The results showed that, compared with irrigation of other border lengths, L40 irrigation significantly increased nitrogen transport in stems and leaves. In addition, L40 irrigation had the highest rate of grain nitrogen accumulation after anthesis. The risk of nitrate leaching to deep layers increased with increasing border length; however, L40 irrigation improved the plants’ capacity to absorb soil nitrogen, and the soil inorganic nitrogen residue was significantly lower than that with irrigation of other border lengths. Therefore, the grain yield and nitrogen fertilizer utilization under L40 irrigation were significantly higher than those under irrigation of other border lengths, and L40 was considered as the best border irrigation length.

Anatomic Considerations of the Distal Fibula: A Computed Tomography Guided Analysis

Category:Ankle; Basic Sciences/Biologics; Trauma; OtherIntroduction/Purpose:Ankle fractures are a common injury in the general population with nearly sixty thousand operations performed in California for fractures involving the tibiotalar joint over a 10-year span. Reestablishing anatomic fibular alignment after fracture reduction leads to improved patient outcomes by restoring ankle mortise congruence. An in-depth understanding of fibular morphology may aid in fracture reduction, preoperative planning, plate positioning and intra-operative contouring. The goal of this study is to perform quantitative morphologic analysis of distal fibular anatomy using computed tomography (CT).Methods:Using Nuance mPower Clinical Analytics software, a database of CT tibia-fibula reports for patients ages 18 through 35 performed at our institution were searched for the term 'normal.' Inclusion criteria was absence of any reported osseous pathology. Examinations were excluded if the fibula was incompletely imaged. Twenty CTs were collected and analyzed.Measurements were performed at 5 mm increments from the tip of the fibula extending proximally to 10 cm. At each level the following measurements were obtained: lateral and posterior border lengths, lateral to medial (LM) bicortical distances at ¼, ½, and ¾ the length of the lateral border, posteroanterior (PA) bicortical distance at the center of the posterior border, and the angles of the lateral and posterior borders relative to the PA axis of the tibia (figure 1). The location of the maximal bicortical distance in the LM direction was recorded at each level.Results:The posterior border of the fibula broadens from an apex distally to 8.4+-1.6 mm at 10 cm proximal while rotating an average of 97.5 degrees. The lateral border of the fibula rotates 6.3 degrees from distal to proximal and begins with a width of 12.8+-3.1 mm and comes to an apex at 9 cm. In the distal fibula, the ratio of the maximal LM to PA bicortical length is 0.56. By 3 cm proximal, the ratio approaches 1 and is 1.6 at 10 cm. The distal 1 cm of the fibula has the largest LM diameter anteriorly and medially but from 1.5 cm to 10 cm proximal the posterior ¼ has the largest LM diameter.Conclusion:The fibula has a complex distal geometry which changes with progression from the distal tip to 10 cm proximal. The posterior border of the fibula broadens and rotates over 90 degrees to become the lateral border proximally. The lateral border distally is broad but comes to an apex proximally with minimal rotation. The ratio of bicortical distances changes from distal to proximal as the distal posterior border rotates to face in a LM direction proximally. This information may aid in surgeons' understanding of the complex distal fibular morphology and assist with intra-operative decision making regarding hardware size, placement and manipulation.

Left ventricular global longitudinal strain calculated from manually traced endocardial border lengths utilizing the images for routine ejection fraction measurement by biplane method of disks.

The purpose of this study was to test whether the fractional change in the endocardial border length between end-diastole and end-systole as manually traced in left ventricular ejection fraction (LVEF) measurement using the biplane method of disks (MOD) was consistent with the global longitudinal strain derived from speckle-tracking echocardiography. For 105 patients who underwent echocardiography, two- and four-chamber images with manually traced endocardial lines for LVEF measurement by MOD were stored. LV endocardial lengths at end-diastole and at end-systole were measured on both images to calculate the fractional length changes, which were averaged (GLSMOD). Speckle-tracking analysis was performed to measure global longitudinal strains in the apical two- and four-chamber and long-axis images, and the three values were averaged (GLSSTE) according to the ASE and EACVI guidelines. There was no significant difference between GLSMOD and GLSSTE. GLSMOD correlated well with GLSSTE (r = 0.81, p < 0.001), and there was no fixed bias in the Bland-Altman analysis. The intraclass correlations for the intra- and inter-observer comparisons for GLSSTE were excellent, and those for GLSMOD were adequate. The fractional LV endocardial border length change, GLSMOD, showed sufficient agreement with GLSSTE to justify its use as a substitute for the STE-derived global longitudinal strain.

Effect of Initial Soil Water Content on Output Parameters of Sirmod Software Under Types of Different Irrigation Management

AbstractThe main objective of this study was to investigate the sensitivity of the output parameters of SIRMOD software relative to initial soil water content. The treatments consisted of three irrigation water qualities, two types of soil water content management (FC and 30% FC; FC is field capacity) and three irrigation events. The HYDRUS‐1D software was calibrated to simulate infiltration under different initial soil water contents. Subsequently, the infiltration coefficients obtained from the HYDRUS model were used to simulate the border irrigation system under the different border lengths and inflow rates using the SIRMOD software. The results showed that soil was more permeable under FC management than under 30% FC. The sensitivity of the output parameters of the SIRMOD software under FC was more sensitive compared to 30% FC. The high‐ and low‐sensitive treatments were in the FC and 30% FC management with high saline‐sodic water, respectively. Due to the high permeability under FC, in order to increase the irrigation application efficiency and reduce its sensitivity, the inflow rate should be greater while border length has to be less, compared to 30% FC. Sensitivity analysis of the output parameters showed that the advance time and tailwater fraction were identified as the most and least sensitive parameters, respectively. © 2019 John Wiley &amp; Sons, Ltd.

Evaluation and optimization of border irrigation in different irrigation seasons based on temporal variation of infiltration and roughness

Soil infiltration and Manning’s roughness values are key parameters to determine the performance of surface irrigation. However, temporal variability in these parameters due to tillage practices, irrigation, and crop growth greatly hinders efforts to improve irrigation quality. The objective of this experiment was to evaluate effects of infiltration and surface roughness variation on irrigation water movement and irrigation performance indicators for border irrigation with three border lengths. Field experiments were conducted from 2013 to 2015 in a wheat (Triticum aestivum)-maize (Zea mays L.) rotation planting system at the Jinghui Canal Irrigation Area in Guanzhong Plain of northwest China. In this work, Manning’s equation and a surface irrigation simulation model (WinSRFR) were used to estimate Manning’s roughness values and Kostiakov soil infiltration parameters. We determined that both parameters reached moderate levels of variation for both deep and shallow tillage treatments. The impacts of temporal variation in soil infiltration and surface roughness on irrigation water movement and irrigation quality were then evaluated. Results showed that water advance times varied significantly while recession times varied much more, affecting irrigation water amounts at various distances along the length of the border. Irrigation performance indicators were significantly different over various irrigation seasons, especially for borders that were 235 m in length. Finally, considering these temporal variations during the two rotation cycles, combinations of inflow rate and cut-off ratio during different irrigation seasons were optimized, and high irrigation quality could be achieved for 80 m and 120 m borders, but not for 235 m borders. Water percolation amounts during the 2013–2014 and 2014–2015 growing periods were reduced by 55 mm and 107 mm for 235 m borders, 26 mm and 23 mm for 120 m borders, and 36 mm and 39 mm for 80 m borders, respectively. Therefore, utilizing optimal combinations of inflow rate and cut-off ratio and considering temporal variation in soil infiltration and Manning’s roughness could maintain high water application efficiency and sustainable utilization of limited water resources.

Local and landscape-scale heterogeneity shape spotted wing drosophila (Drosophila suzukii) activity and natural enemy abundance: Implications for trophic interactions

Like natural enemies, invasive polyphagous pests may respond positively to local and landscape-scale diversity, making them more serious challenges to sustainable management than specialists. Yet the current view of landscape effects on pests rarely considers perennial systems or polyphagous pests. We investigated Drosophila suzukii (SWD) and natural enemy distributions and trophic interactions in blueberry systems of the southeast US in relation to local management and landscape structure. Fields were nested in 1-km landscapes along gradients of crop and forest heterogeneity (landscape compositional diversity) and field border and crop border lengths (landscape configurational diversity). Yeast-sugar bait traps were used to collect SWD and canopy suction sampling for natural enemies. Management practices at the local scale did not influence SWD abundance, but natural enemy abundance was higher in organic systems and fields with vegetation present between rows. Landscape configurational diversity and greater proportion of non-cropping habitat promoted higher SWD populations. Natural enemy communities were composed of highly generalized species, and contrary to our predictions, we observed lower abundances in landscapes with higher proportion of non-cropping area. Few predators were detected to have fed on SWD, and communities were dominated by predators with low specialization on prey in blueberry. Our results indicate that local and landscape features in blueberry landscapes have differential effects on a polyphagous pest and generalist natural enemies. Our initial analysis of predator diets, using a metabarcoding approach, suggests spatial structure in specialization on prey with high diversity of prey in predators collected in forested margins.

The Assessment Of Geographical Borders In Economic Research

The length of common border between two geographical units is frequently used as a basic weight in spatial analysis. The newest methodological propositions such as tests for hierarchical relations (Markowska et. al. 2014; Sokołowski et. al. 2013), regional spatial moving average and new spatial correlation coefficient (Markowska et. al. 2015) are using border lengths. In cited references new methods have been illustrated by analyses for EU NUTS2 regions. It is obvious that borders between regions belonging to different countries have different socio-economic impact than borders between regions lying in the same country. A new simple method for assesment the importance of borders is proposed in the paper. It is based on a chosen macroeconomic variable available at NUTS 2 level (e.g. GDP, infant mortality, Human Development Index). For neighboring regions bigger value is divided by smaller value giving the local importance of the given border. These measures of local border importance can be than average for borders within the same country and for borders for each pair of neighboring countries.

Combinatorics on partial word borders

We develop a powerful graph theoretical approach that can compute the number of partial words, sequences with wildcard or hole characters, having a set of strong and weak periods, the number of partial words having a set of border lengths, the number of partial words having a maximum border length, the population size of a border array, the number of partial words having any set of required compatibilities and incompatibility sets, any of the above restricting to a fixed number of holes, any of the above restricting to a set of hole positions, to name a few. In the process, we establish some elegant relationships between these numbers, the Bell numbers, and the Stirling numbers of the second kind.

English

The morphometrical data related to the menisci of the adults have been reported by few authors but data specific to the population of East Goadavari region have not been reported. The aims of the present study were to analyse the external circumference thickness, the width, peripheral and inner border lengths, and the distance between anterior and posterior horns of the menisci and to compare them with those which are available in the literature. The menisci from 100 knee joints of the formalin fixed cadavers which were obtained from the Anatomy department of Rangaraya Medical College, Kakinada and Konaseema Institute of Medical Sciences and Research Foundation, Amalapuram were analysed. The cadavers which had musculoskeletal anomalies were excluded from the study. A vernier calliper of 0.02 mm accuracy and a non-elastic cotton thread were used for the morphometry. After comparing the meniscal dimensions of the present study with the other available literature, we established that there are some morphological differences of meniscus in this set of population.

WATER MOVEMENT IN CALCAREOUS SOIL UNDER TILLAGE, LEVELING AND BORDER IRRIGATION

A field experiment was conducted at the Agricultural Experimental Station of the Desert Research Center, at Maryut,Alexandria Governorate. The main objective of the present work is optimizing of water movement and some soil physical properties in calcareous soil in respect to the effect of leveling methods (laser, traditional and no-leveling), tillage depths (15, 20 and 25 cm), border irrigation length (25, 50 and 75 m) and irrigation cut off after 80 and 90% of border length. The obtained results can be summarized as follows: The highest bulk density and penetration resistance increasing were 13.04 and 26.83 % at 0-10 cm soil layer by using laser leveling and 15 cm tillage depth. Meanwhile, the lowest values were 1.42 and 5.35% at 20-30 cm soil layer by using traditional leveling and 15 cm tillage depth. The highest infiltration rate decreasing was 22.95% after using laser leveling and 15 cm tillage depth. Data presented indicate that increasing the tillage depth from 15 to 20 and to 25 cm, the advance time at 25 m border length when irrigation cut off after 90% of border length, increased from 8.8 to 10.7 and to 13.4 min; 9.4 to 10.8 and to 14.1min and 9.2 to 11.2 and to 15.7 min under laser, traditional and no-land leveling respectively. Data presented indicated that with laser land leveling and 20 cm tillage depth, the recession time when irrigation cut off after 90% of border length decreased by 14.29 and 38.84%; 17.46 and 41.75% and 20.16 and 37.39% under 25, 50 and 75 m border lengths compared to traditional and no-land leveling respectively. Data presented indicated that increasing the border length from 25 to 50 and to 75 m, the opportunity time at 20 cm tillage depth when irrigation cut off after 90% of border length, increased from 31.5 to 39.4 and to 47.8 min; 49.1 to 61.1 and to 71.7 min and 65.2 to 77.8 and to 82.9 min under laser, traditional and no-land leveling respectively.

Controlled electric field in multiply connected circular structure

This paper presents the analysis and calculation of homogeneity zone of controlled (rotating) electric field in the internal area with circular multiply connected border and equal lengths of boundary arcs depending on the order of border connectivity, potential distribution across the boundary arcs, and the ratio between the lengths of boundary arcs and gaps between the arcs. Mathematical expressions are presented both in the form of complex variable functions and as sums of spatial harmonics.

Electric field density in the region with circular multiply connected border and equal lengths of bounding arcs

In the present paper the problem of determining electric field density in outer and inner parts of the region, bounded by the circular multiply connected structure with equal arcs’ lengths and equal spacing between them, is investigated. Expressions for electric field density in case of arbitrary order of connectivity n are obtained. The structures of fields are calculated for the given values of n.

Fatigue life enhancement by laser surface treatment

A laser surface treatment (LST) which can enhance fatigue resistance of metallic parts has been developed. The LST is useful both for improving the surface microstructure of undamaged specimens, thereby increasing the original fatigue life, and for healing in service metallic parts subjected to cyclic loading. The LST method was applied to three point bend specimens of Ti–6Al–4V alloy at different stages of fatigue life. Results show a significant improvement in fatigue resistance, with a distinct treatment optimum point at about two-thirds of the original lifetime. In addition, changes in the near surface microstructure, including grain size and shape distribution, phase ratios, etc., have been studied. The relative α phase surface area, as well its grain size, decreased considerably, showing large perimeter curvatures and larger total grain border lengths.

Changes in alveolar septal border lengths with postnatal lung growth.

Evaluation of alveolar development beyond the postnatal period of rapid septation has generally involved alveolar counting. We used an alternate approach to assess postseptation parenchymal development: measurement of the lengths of various types of alveolar septal borders. This technique directly addresses changes in the elastin fiber network that determines parenchymal complexity. Lungs from weanling and adult ferrets, inflated to 15 cmH2O, were perfusion fixed and dehydrated, and 2-micrometer sections were stained with Miller's elastin stain for light microscopy. We used standard morphometric methods to measure the lengths of the various types of alveolar septal borders. Three types comprised >90% of all septal borders: 1) free septal ends ("ends") containing an elastin cable; 2) angled meetings of two alveolar septa ("bends"), also with a cable; and 3) the near-symmetrical intersections of three septa ("junctions") devoid of elastin. When scaled for lung volume, ends and bends were 23 and 37% greater in adults (P < 0.001), reflecting the increase in parenchymal complexity with growth. The 17% difference in scaled junction lengths was not significant (P = 0.10). Bends increased out of proportion to the increase in ends, and both bends and ends increased to a greater degree than any possible increase in junctions (P < 0.001 for all comparisons). Although the interpretation of changes in the distribution of alveolar border lengths is not straightforward, an increase in bends resulting in an increase in the complexity of individual alveoli may contribute to the increase in alveolar gas-exchanging surface area with growth. Septation, the process responsible for the rapid early postnatal increase in parenchymal complexity in many species, should tend to increase the lengths of ends and junctions and decrease the lengths of bends. Therefore, these data suggest that septation is not the predominant mechanism of later postnatal parenchymal development in the ferret.

Scapula form and biomechanics in gorillas.

Gorillas are generating renewed interest as mounting evidence from field and molecular studies strongly suggests the western lowland (Gorilla gorilla gorilla) and eastern mountain (Gorilla gorilla beringei) gorillas are considerably more distinct than has previously been accepted. Schultz (1927, 1930, 1934) was one of the earliest investigators to document morphological differences between the two groups, noting differences in pedal, limb and scapular morphology. These differences led Schultz to conclude that while lowland gorillas retained some features suited to an arboreal habitat, the mountain gorilla had evolved into a specialized terrestrial quadruped. In particular, he noted that mountain gorillas exhibited lower values for the scapular index, higher values for ratios of infraspinous fossa vs. scapula length and spine length vs. scapula length and variability in the extent of curvature of the vertebral border. However, Schultz' observations were based upon small sample sizes of mostly adult specimens. This study extends Schultz' preliminary work by assessing, with appreciably larger sample sizes, patterns of relative growth of the scapula in these two subspecies of Gorilla. Scapula measurements were obtained for ontogenetic series of G.g. gorilla (n = 366) and G. g. beringei (n = 43). Statistical analyses reveal mountain gorillas exhibit significantly (P < 0.05) greater spine lengths and scapula breadths and smaller scapula lengths than lowland gorillas of comparable superior border lengths. However, at comparable body weights, mountain gorillas exhibit significantly shorter spines and superior borders than lowland gorillas. These differences in scapula proportions are evaluated in the context of biomechanical predictions regarding scapula form and locomotion.

Wheat Yield Variability in Irrigated Level Basins

ABSTRACT SPATIAL variability in irrigated crops is a major problem in transferring plot-size yield and water use information to field-size, surface irrigation conditions. A 1985 study evaluated wheat yield variability for three irrigation schedules and two border lengths using a level-basin irrigation system. Mean grain yields increased significantly from the dry to wet irrigation treatments; however, yield and irrigation water application amounts were not positively correlated from location to location in the wet treatment. Variations in seasonal water applications, water use, and seasonal average soil water contents accounted for less than 35% of the variability in grain yield. Yields were not affected by differences in border lengths, but yield variability was significantly influenced by field position. Yield variability, as measured by the statistical coefficient of variation, was less extensive in a wet (12.5%) irrigation treatment than a medium (19.4%) or dry (32.4%) treatment. The maximum distance of spatially interdependent yields varied from 45 m (150 ft) in the medium to 19 m (60 ft) and 8 m (25 ft) in the wet and dry treatments, respectively. The optimum level of seasonal gross water applied for maximum wheat yields was 7% higher than that required for maximum water use efficiency; however, the uncertainty in both estimates was ± 18%. A recommendation to the irrigation farmer with a heterogeneous soil and an efficient level-basin irrigation system would be to schedule irrigations near full evapotranspiration requirements in order to minimize yield differences due to field variability, attain high wheat yields, and approach maximum water use efficiency..