Rounded Rim Research Articles

Subsurface pulse, crater and ejecta asymmetry from oblique impacts into granular media

We carry out experiments of 104 m/s velocity oblique impacts into a granular medium (sand). Impact craters have nearly round rims even at a grazing angle of about 10°, however, the strength of seismic pulses excited by the impact is dependent upon impact angle, and the ratio between uprange and downrange velocity peaks can be as large as 5, particularly at shallow depths. Crater slope, an offset between crater center and impact site, crater volume, azimuthal variation in ejection angle, seismic pulse shapes and subsurface flow direction are also sensitive to impact angle, but to a much lower degree than subsurface pulse strength. Uprange and downrange pulse peak amplitudes can be estimated from the horizontal and vertical components of the momentum imparted to the medium from the projectile.

Сероглиняные рыбные блюда из меотских могильников правобережья Кубани

In the 4th cent. BC, under the influence of ancient cultural and pottery traditions, new forms and types of vessels appeared among the Maeotians, including fish plates. In this work, 26 fish plates from three Maeotian sites are collected — burial grounds of the Elizavetinskaya settlement, Prikubansky and Lebedi 3. The plates are divided into three groups according to the main method of design of their rim: I — with an overhanging rim; II — with a finely trimmed rim; III — with a rounded rim. Within these groups, variants of rims of various modifications are distinguished. The narrow dates of most plates are determined by the context of the finds: Greek amphorae, local gray clay and imported red clay vessels. The general chronology of the existence of fish plates among the Maeotians from the right bank of the Kuban covers the period from the 4th — the beginning of the 1st cent. BC. Moreover, the early samples of the 4th — beginning of the 3rd centuries are accurately copied Greek imported vessels, and the later ones, basically, are presented by the variants, remade by the Maeotian potters, adapted to the local needs.

Species-specific differences in the egg exochorium of the sympatric taxa Triatoma costalimai and Triatoma jatai (Hemiptera: Reduviidae: Triatominae).

Triatoma costalimai and Triatoma jatai are related species, which occur in sympatry in Paranã, Tocantins, Brazil, in rocky outcrops and in peridomicile and intradomicile environments. This study compared morphologic and morphometric aspects of the eggs of these species using optical microscopy (OM) and scanning electron microscopy (SEM). Operculum cells (OP) and egg body (EB) were drawn and photographed, their surfaces were measured, and spots were quantified. Statistical analyses were performed using ANOVA and t-tests. OM showed an egg exochorium with spots in T. costalimai and a predominance of short lines in T. jatai. We found significant differences in egg length and width, which were larger in T. costalimai. SEM analysis showed that the operculum of both species had cells with straight and/or rounded rims, with a smooth aspect, random spots, and predominantly pentagonal shape. In the EB, hexagonal cells were predominant, with indices exceeding 60% in both species. Triatoma costalimai cells were flat, with a discrete definition of the rims, whereas T. jatai cells were smooth with well-defined rims. Statistical tests showed significant differences for EB, where T. costalimai cells were larger and have more spots than T. jatai. The eggs can thus be differentiated, thereby contributing to integrative taxonomy.

The effect of atmospheric density on splash of spheres during water entry

The dynamics of splash curtain by vertical water entry of a sphere under various atmospheric densities is investigated in the present study. To understand the mechanism of air density on the splash evolution, a simplified model is proposed to analyze the experimental results, revealing both the size of splash and surface seal time increase as the atmospheric density decreases. Considering the pressure drop caused by air flowing into the cavity and surface tension, the present model focuses on the rounded rim at the tip of splash, reducing the complex splash evolution to a ballistics problem. The results show that when pressure drop force is the dominant factor, the trajectory of the rounded rim is approximately a circular arc. As the atmospheric density decreases, the effect of pressure drop force is weakening and the surface tension gradually plays a role. This results in the increasing size of the splash curtain and longer surface seal time, transforming the trajectory into a spiral. Under the extreme conditions, the evolution of splash is such extended by surface tension that the surface seal may even disappear.

Role of Biofilms in Post-Tympanostomy Tube Otorrhea.

Nearly half of children who undergo tympanostomy tube (TT) insertion may experience otorrhea following surgery. We sought to review the evidence for the role of bacterial biofilms in post-tympanostomy tube otorrhea (PTTO) and the accumulated experience regarding the preventive measures for biofilm formation/adhesion on TTs. English literature search for relevant MeSH keywords was conducted in the following databases: MEDLINE (via PubMed), Ovid Medline, Google Scholar, and Clinical Evidence (BMJ Publishing) between January 1, 1995, and December 31, 2019. Subsequently, articles were reviewed and included if biofilm was evident in PTTO. There is an increased evidence supporting the role of biofilms in PTTO. Studies on TT design and material suggest that nitinol and/or silicone TTs had a lower risk for PTTO and that biofilms appeared in specific areas, such as the perpendicular junction of the T-tubes and the round rims of the Paparella-type tubes. Biofilm-component DNAB-II protein family was present in half of children with PTTO, and targeting this protein may lead to biofilm collapse and serve as a potential strategy for PTTO treatment. Novel approaches for the prevention of biofilm-associated PTTO include changing the inherent tube composition; tube coating with antibiotics, polymers, plant extracts, or other biofilm-resistant materials; impregnation with antimicrobial compounds; and surface alterations by ion-bombardment or surface ionization, which are still under laboratory investigation. Currently, there is no type of TT on which bacteria will not adhere. The challenges of treating PTTO indicate the need for further research in optimization of TT design, composition, and coating.

CAMULODUNUM 184 AMPHORAE FROM TYRAS

The Camulodunum 184 amphorae are one of the most well-known varieties of early Roman containers in the Mediterranean region. At the same time, such vessels are not believed to enter the Black Sea region, with the area of their distribution being limited only to the territory of the Roman Empire. The aim of this article is introduction and comprehensive study of the Camulodunum 184 amphorae findings from Tyras. This will allow shedding light on the issues related to Tyras’ trade contacts, as well as expanding our notion about the economic relations between the Pontic and Mediterranean regions in the Roman era. The findings of Camulodunum 184 amphorae in Tyras are few in number and represented only by fragments. Such vessels are characterized by high, straight and wide neck with rounded rim, elongated ovoid body, conical stem and «horn-shaped» handles. Their volume is mainly 13,6 liters, although a specimen is known, containing only 8,5 liters. The main product transported in such amphorae was passum – a raisin wine made from dried grapes. This expensive kind of wine was very popular in the capital of the Roman Empire and among the prosperous population of its provinces. The Camulodunum 184 amphorae were produced from the late 1st century BC till the late 2nd century AD, and their production reached a peak in the turn of the eras – mid-2nd century AD. Such vessels were produced in Rhodes, Rhodian Peraea, Kos, in some centers of Asia Minor north-west coast. The Camulodunum 184 amphorae came to Tyras from several workshops. Based on visual differences in composition of fabric and its color, the fragments found in Tyras can be divided into five groups, three of which appear to originate from Rhodes and Rhodian Peraea. The vessels attributed to the other two groups could also have been produced in the Eastern Mediterranean, possibly not far from Rhodes. The fragments of such amphorae from Tyras were found in the redeposited layers, making it difficult to establish the time of their entry to the city. Probably, the Camulodunum 184 amphorae were exported to the Black Sea region during their highest production intensity. Thus, fragments of similar vessels from Panticapaeum date to the 1st – second quarter of the 2nd centuries AD. Thus, in the 1st – second quarter of the 2nd centuries AD Tyras imports passum contained in the Camulodunum 184 amphorae. It was brought in from Rhodes, Rhodian Peraea and unidentified Eastern Mediterranean centers. These supplies were intended for the city’s prosperous population and were few in number. The entry of such amphorae to Tyras was most likely a consequence of the restoration of trade relations with Rhodes and Rhodian Peraea, incorporated to the Roman Empire by this time. However, these contacts were no longer as intense as during the Hellenistic period and were sporadic. The findings in Tyras allow expanding the distribution area of the Camulodunum 184 amphorae to the North-West Black Sea region.

Evaluation of two wheelchair hand rim models: contact pressure distribution in straight line and curve trajectories

Manual wheelchairs are essential for people with disabilities or limited mobility. However, manual propulsion causes biomechanical loads, including contact pressures on the palms of the hands. The hand rim design has received little attention over time, remaining almost unchanged since its creation. This study investigated how two different designs of such devices – one standard and another with a contoured design – influence the contact pressure on the surface of the hands. The procedures included a figure-of-eight shape propulsion task on a regular floor, using both models on a wheelchair. A pressure-mapping system coupled with a pair of fabric gloves recorded the data. The results show that the contoured hand rim provides lower pressure in most of the analysed regions. Considering that manual propulsion is performed during a considerable part of the day as a routine activity, improving the hand rim interface may benefit the user’s comfort and safety during wheelchair use. Practitioner summary: The design of the hand rim used in wheelchair propulsion influences the contact pressure on the hands. Conventional round tube rims tend to concentrate high levels of pressure on the distal phalanges and metacarpal regions. A contoured design generally provides better stability and promotes the distribution of pressure. Abbreviations: AT: assistive technology; kPa: kilopascal

Impaired Nucleoporins Are Present in Sporadic Amyotrophic Lateral Sclerosis Motor Neurons that Exhibit Mislocalization of the 43-kDa TAR DNA-Binding Protein.

Background and PurposeDisruption of nucleoporins has been reported in the motor neurons of patients with sporadic amyotrophic lateral sclerosis (sALS). However, the precise changes in the morphology of nucleoporins associated with the pathology of the 43-kDa TAR DNA-binding protein (TDP-43) in the disease process remain unknown. We investigated the expression of nucleoporins that constitute the nuclear pore complex (NPC) in spinal motor neurons that exhibit sALS in relation to TDP-43 pathology, which is a reliable neuropathological hallmark of sALS.MethodsParaffin-embedded sections of the lumbar spinal cord were obtained for immunofluorescence analysis from seven control subjects and six sALS patients. Anti-TDP-43 antibody, anti-nucleoporin p62 (NUP62) antibody, and anti-karyopherin beta 1 (KPNB1) antibody were applied as primary antibodies, and then visualized using appropriate secondary antibodies. The sections were then examined under a fluorescence microscope.ResultsNUP62 and KPNB1 immunoreactivity appeared as a smooth round rim bordering the nuclear margin in normal spinal motor neurons that exhibited nuclear TDP-43 immunoreactivity. sALS spinal motor neurons with apparent TDP-43 mislocalization demonstrated irregular, disrupted nuclear staining for NUP62 or KPNB1. Some atrophic sALS spinal motor neurons with TDP-43 mislocalization presented no NUP62 immunoreactivity.ConclusionsOur findings suggest a close relationship between NPC alterations and TDP-43 pathology in the degenerative process of the motor neurons of sALS patients.

PRODUCTS OF POLTAVA POTTERS OF THE 18th CENTURY: THE POTS

The article considers the products of the Poltava potters of the 18th c. In particular, the pots: their form, decoration and chronological types. The author pays spesial attention to local morphological features and ornamental schemes. Among distinctive once are the next: a terracotta shard, straight rounded rims, low body, decorated with colorful ornamental patterns in upper part, which include lines, curvelets, and other elements.

Tympanostomy tube otorrhea in children: prevention and treatment.

One in two children treated with tympanostomy tubes, experience episodes of otorrhea whilst their tubes are in place. In this review, we present the results of the most recent publications on prevention and treatment of tympanostomy tube otorrhea (TTO). Recent systematic reviews on water precautions for children with tympanostomy tubes support the American Academy of Otolaryngology - Head and Neck Surgery guideline recommendation against such preventive measures as there is no evidence that it protects against TTO. Studies on tympanostomy tube design and material suggest that silicone tubes have a lower TTO risk and that biofilms appear to be mainly located in the perpendicular junction of the T-tubes and the round rims of the Paparella-type tubes. Another study shows that the biofilm-component DNAB-II protein is present in otorrhea of half of children with TTO. Targeting this protein could lead to a collapse of the biofilm structure and as such a potential new treatment for chronic TTO. New systematic reviews show that antibiotic eardrops are the most effective first-line treatment of acute TTO and suggest that an antibiotic-corticosteroid combination is more effective than antibiotic only. Although in many countries, quinolone eardrops are the preferred choice because of being non-ototoxic, one study found a higher risk of persistent perforation after tube extrusion in children treated with quinolone eardrops as compared with children treated with aminoglycoside eardrops. Recent evidence confirms that water precautions for children with tympanostomy tubes are not effective in preventing TTO. Antibiotic-corticosteroid eardrops are the most effective treatment of acute TTO.

Morphological and molecular study of Neorhadinorhynchus nudus (Harada, 1938) (Acanthocephala: Cavisomidae) from Auxis thazard Lacepede (Perciformes: Scombridae) in the South China Sea.

In the present study, Neorhadinorhynchus nudus (Harada, 1938) is reported from the frigate tuna Auxis thazard (Lacepéde) (Perciformes: Scombridae), in the South China Sea for the first time. The detailed morphology of N. nudus was studied using light and scanning electron microscopy based on the newly collected material. The results showed some morphometric variability between our specimens and previous studies, including the number of hooks per longitudinal row and the size of copulatory bursa and eggs. Our SEM observations also revealed all proboscis hooks emerged from elevated round rims on proboscis surface. In addition, N. nudus was firstly characterised using molecular methods by sequencing and analysing the ribosomal ITS and mitochondrial cox1 regions. There is no nucleotide divergence found in the ITS sequences, but a low level of nucleotide variability detected in the cox1 regions (the level of intraspecific nucleotide variability being 0.75% to 2.54%). The DNA sequence data obtained herein will indeed be a useful reference for rapid and accurate species identification of Neorhadinorhynchus.

Comment on “First records of syn-diagenetic non-tectonic folding in Quaternary thermogene travertines caused by hydrothermal incremental veining” by Billi et al. Tectonophysics 700–701 (2017) 60–79

Billi et al. (2017) proposed a new interpretation for the origin and internal structure of thermogene travertine deposits. On the basis of evidence from two quarries located in southern Tuscany (Italy), they interpreted some travertine beds as calcite veins and argued that undulating travertine beds formed by syn-diagenetic (i.e. non-tectonic) folding that was caused by laterally-confined volume expansion caused by incremental veining. They assumed that such a process causes changes to the rock properties, including porosity reduction, rock strengthening, and age rejuvenation. The interpretations by Billi et al. (2017) challenge and question the current understanding and interpretation of thermogene travertine deposits. This understanding, based on numerous studies since the 1980s, is that these deposits form from thermal water flowing downslope, and precipitating calcium carbonate. Here, we explain how the comparison with active depositional systems is essential for the understanding the origin of structures in older, inactive travertine deposits, such as those studied by Billi et al. (2017). We further argue that the three-dimensional setting of travertine deposits should be taken into account in order to discuss the possible development of secondary structures. Indeed travertine deposition on slopes typically leads to the formation of terraced morphologies with pools bordered by rounded rims and separated from each other by steep walls. The resulting three-dimensional structures can be misinterpreted as asymmetric folds in two-dimensional views (i.e., in saw-cut walls of quarry). In this paper we debate the interpretations offered by Billi et al. (2017) and their criteria to recognise syn-diagenetic, non-tectonic folds in travertine deposits, and explain why many of their ideas are questionable.

Facies character and depositional architecture of hydrothermal travertine slope aprons (Pleistocene, Acquasanta Terme, Central Italy)

Hydrothermal travertines develop various depositional geometries, from tabular to high-relief mounds or aprons with steep slopes, under the control of local topography, location and geometry of the vents, fault activity, hydrology, water physico-chemical properties, rates of thermal water flow and carbonate precipitation rates. This study focuses on two Pleistocene, tens of metres thick, travertine slope aprons accumulated on fluvial terraces in the Tronto River Valley (Acquasanta Terme, Central Italy) to investigate their facies character, geochemical signature, porosity and evolution of the depositional geometry through time.The two travertine aprons consist of four aggradational-progradational units, vertically and laterally stacked with onlap and downlap stratal terminations, separated by erosional unconformities produced by events of non-deposition and erosion, due to temporary interruptions of vent activity, shifts of the vent location and/or deviation of the flow directions. The travertine units include various depositional environments: 1) smooth slope, 2) terraced slope with metre-scale sub-horizontal pools separated by rounded rims and vertical walls, and 3) sub-horizontal, tens of metres wide ponds. Smooth slope clinoforms are made of centimetre to decimetre thick layers of crystalline dendrite cementstone, laminated boundstone and radial coated grain grainstone, precipitated by fast-flowing water on inclined substrates. Rims and walls of terraced slopes are built by crystalline dendrites and laminated boundstone. Sub-horizontal layers of terrace pools and ponds consist of facies precipitated by slow-flowing to standing water (clotted peloidal micrite dendrite, coated bubble boundstone, raft rudstone) associated with radial coated grains and laminated boundstone. Carbonate coated reeds occur in distal ponds adjacent to toe of slopes or overlie packstone/rudstone with travertine intraclasts and substrate extraclasts, marking events of subaerial exposure and erosion. Travertine facies porosity and permeability range from 4 to 21% and 0.03 to 669 mD, respectively, showing no direct correlation. Stable isotope values (δ13C: 5.7–9.3‰; δ18O −9.6‰ to −12.2‰) are similar to other travertines precipitated by thermal water in Central Italy.This study identifies the centimetre-scale travertine facies variability linking it to the environment of deposition and to the depositional geometry of travertine units affected by the substrate topography and lateral shifts of the active springs. Despite the different scale and facies composition, the geometry of aggradational-progradational units of travertine aprons might resemble marine flat-topped high-relief carbonate platforms. Travertine units in the subsurface, if present with sizes that can be seismically resolved, might be wrongly interpreted as carbonate platforms with steep slopes without a detailed facies analysis.

Pseudomonal Biofilm Topographic Distribution on Tympanostomy Tubes: An In Vitro Model.

In vitro growth of Pseudomonas aeruginosa biofilm on tympanostomy tubes showed that in Armstrong T-tubes, biofilm colonies were mainly located in the perpendicular junction between the body and the flanges, but in Paparella-type tube, they concentrated on the round rims. These "weakness" zones can be the future target areas for geometry changes, and can be specifically coated with antibiofilm materials.

Viscous drop in compressional Stokes flow

AbstractThe dynamics of the deformation of a drop in axisymmetric compressional viscous flow is addressed through analytical and numerical analyses for a variety of capillary numbers, $\mathit{Ca}$, and viscosity ratios, $\lambda $. For low $Ca$, the drop is approximated by an oblate spheroid, and an analytical solution is obtained in terms of spheroidal harmonics; whereas, for the case of equal viscosities ($\lambda = 1$), the velocity field within and outside a drop of a given shape admits an integral representation, and steady shapes are found in the form of Chebyshev series. For arbitrary $Ca$ and $\lambda $, exact steady shapes are evaluated numerically via an integral equation. The critical $\mathit{Ca}$, below which a steady drop shape exists, is established for various $\lambda $. Remarkably, in contrast to the extensional flow case, critical steady shapes, being flat discs with rounded rims, have similar degrees of deformation ($D\sim 0. 75$) for all $\lambda $ studied. It is also shown that for almost the entire range of $\mathit{Ca}$ and $\lambda $, the steady shapes have accurate two-parameter approximations. The validity and implications of spheroidal and two-parameter shape approximations are examined in comparison to the exact steady shapes.

Needleless electrospinning: influences of fibre generator geometry

The fibre generator shape and dimension are key factors affecting the needleless electrospinning process and fibre fineness. In this work, cylinder with rounded rim, disc and ball were used as spinnerets to electrospin polyvinyl alcohol and polyacrylonitrile solutions. A finite element method was used to analyse how the spinneret geometry affected the electric field generated during electrospinning and the associated changes in fibre diameter and productivity. For cylinder spinnerets, increasing the rim radius reduced the discrepancy of electric field intensity between the cylinder end and middle area, which affected the fibre productivity. The electrospinning failed to operate when the rim radius was over 20 mm. With decreasing cylinder diameter, the electric field intensity in the middle area increased, improving the fibre productivity. Thinner disc spinnerets increased the electric field intensity, resulting in finer nanofibres and higher productivities. Ball spinnerets produced evenly distributed electric field, but failed to electrospin fibres when the diameters were below 60 mm. It has been found that strong and narrowly distributed electric field in the fibre-generating area can significantly facilitate the mass production of quality nanofibres.

Crossover between Dewetting and Stabilization of Ultrathin Liquid Crystalline Polymer Films

Thin spin-coated films of a smectic liquid crystalline main chain polymer with an azoxybenzene as mesogen were investigated as a function of temperature and thickness. Both lateral and vertical order of the polymer film in the various mesophases were determined by scanning force microscopy in tapping mode and by specular and off-specular X-ray scattering. For films thicker than 10 nm, we observed a stabilizing effect of the smectic organization within the film. No dewetting was detected. The bulk structure of the film consists of smectic layers with a thickness of 3.5 nm, oriented parallel to the substrate. The excess material formed smectic islands on top of the film, corresponding to a noncomplete smectic layer. For films thinner than 10 nm, corresponding to one or two smectic layers only, we observed dewetting with the formation of holes. The holes were dry without any remaining monolayer on the substrate. However, the withdrawing polymer did not accumulate in rounded rims such as for amorphous polymers but in smectic towers, due to the packing of the polymer chain.

Composition and U–Th–total Pb model ages of polygenetic zircons from the Vånga granite, south Sweden: An electron microprobe study

U–Th–total Pb dating of zircons from the Vånga granite, south Sweden, by electron microprobe (EMP) revealed three different zircon generations. U–Th–Pb analyses of finely zoned zircons, existing both as rounded cores and overgrowth rims, yielded a well defined U–Th–total Pb model age of 1448±25 Ma (1[sgrave]). This age is interpreted to date the intrusion of the Vånga granite, which is notably older than previously suggested. Hf- and F-rich overgrowths yielded a U–Th–total Pb model age of 1128±51 Ma (1[sgrave]). Based on the Hf- and F-enrichment and morphological features, it is suggested that the overgrowths formed by a dissolution–precipitation process in a hydrothermal environment. In few cases magmatic zircon overgrows clear, unzoned cores, which could hardly be dated by EMP due to low U, Th, and Pb contents. A single analysis of one of these cores, however, yielded a U–Th–total Pb model age of c. 1700 Ma, which fits with a previously determined age of refractory zircons in a c. 1445–1465 Ma old Karlshamn-type granite. This agreement supports the previous interpretation that the Vånga granite crystallized from a residual liquid separated from the Karlshamn granite magma. The new intrusion age of c. 1450 Ma indicates that the Vånga granite intruded contemporaneously with an extensive thermomagmatic activity further west in the Eastern Segment of the Sveconorwegian orogen. The c. 1130 Ma age of zircon overgrowths has tectonic implications on the N–S trending Protogine Zone; a major shear zone that marks the eastern boundary of Sveconorwegian reworking. Since equally old syenites and dolerites occur within the Protogine Zone, the age of these hydrothermal overgrowths indicates that the crust affected by Protogine Zone deformation is not exotic relative to the crust of Blekinge, nor is it conceivable to relate the metamorphic contrast across the Protogine Zone to deformation east thereof.

Prediction of reduction in developmental dysplasia of the hip by magnetic resonance imaging.

The acetabular rim of 33 hips in 29 patients with developmental dysplasia of the hip was evaluated using magnetic resonance imaging (MRI). The hips were classified into the following three groups according to the shape of the acetabular rim: 12 hips with sharp acetabular rim (group 1), 13 hips with dysplastic and round acetabular rim (group 2), and eight hips with inverted acetabular rim (group 3). The position of the femoral head with the hip flexed and abducted was also recorded, according to the criteria proposed by Suzuki. They were all treated initially with the Pavlik harness. All group 1 hips were successfully reduced with the Pavlik harness, whereas in group 2 hips, all but three hips were reduced. In all group 3 hips, reduction was not successful. MRI provided useful information regarding the probability of reduction with the Pavlik harness.

REGENERATION OF THE SUNFLOWER CAPITULUM AFTER CYLINDRICAL WOUNDING OF THE RECEPTACLE

Using the young capitulum of Helianthus annuus L., a cylindrical plug of undifferentiated receptacle tissue, 1 mm in diameter, was isolated from lateral communication with the rest of the receptacle surface by a vertical circular wound cut, while retaining continuity with the subapical meristem. Within 24 hr, active cell division was induced at the inner and outer surfaces of the wound and in the receptacle epidermis bordering the wound edges, creating a rounded rim at the top of the wound. Within 3–6 days, floral initials, spaced 133–166 μm apart appeared on the flanks of both rims and later on the top of the plug and surrounding receptacle surface. The first formed initials developed into involucral bracts or ray florets and the later ones into disc florets which were organized into contact parastichies, the number of which did not conform with the Fibonacci series. The base of the plug developed into a stem‐like structure completing the regeneration of a fully formed functional capitulum. This operation was demonstrated for two sunflower cultivars and occurred in both long and short daylengths.