Triangular Space Research Articles

[formula omitted]-conforming triangular spectral element method for quad-curl problems

In this paper, we consider the H(curl2)-conforming triangular spectral element method to solve the quad-curl problems. We first explicitly construct the H(curl2)-conforming elements on triangles through the contravariant transform and the affine mapping from the reference element to physical elements. These constructed elements possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. We then establish H(curl2)-conforming triangular spectral element spaces and the corresponding mixed formulated spectral element approximation scheme for the quad-curl problems and related eigenvalue problems. Subsequently, we present the best spectral element approximation theory in H(curl2;Ω)-seminorms. Notably, the degrees of polynomials in the kernel space solely impact the convergence rate of the (L2(Ω))2-norm of uh, without affecting the semi-norm of H(curl;Ω) and H(curl2;Ω). This observation enables us to derive eigenvalue approximations from either the upper or lower side by selecting different degrees of polynomials for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.

Constructing coherent/semi-coherent phase boundaries to enhance toughness of superhard cBN-B composite

Harsh synthesized pressure is required in constructing of excellent grain boundary (GB) connection for nano-polycrystalline cubic boron nitride (nPcBN) to yield high hardness and toughness. Therefore, it is urgent to fabricate robust nPcBN composite under relatively mild pressure by developing the hard nonmetal binders to form coherent/semi-coherent phase boundary (cPB, scPB) with cBN. Here, the slight content of nano‑boron was composited with nPcBN to achieve superhard property of 45.2 GPa and high fracture toughness 8.4 MPa‧m0.5 under a relatively mild condition of 5 GPa and 1800 °C. The hardness is comparable with single crystal cBN and the toughness is about three times higher than single crystal cBN. The nano boron connects the nano cBN grains by cPB and scPB, and nano boron filled the triangular space of cBN crystals, which eliminates the defects to prohibit the crack trigger sources and enhances the strength. This work provides a reference and a new strategy on composite engineering in superhard materials with high toughness by relatively mild synthesized pressure.

The influence of turbulators on the flow and heat transfer characteristic of helium-xenon mixture inside the tight lattice rod bundles

The gas-cooled nuclear reactor combined with the closed Brayton cycle is the ideal choice for future high-power space missions. The helium-xenon mixture is a suitable working medium for the reactor due to its good compressibility and heat transfer capacity. For the further development and application of a more lightweight compact reactor, the influence mechanism of turbulator structures with different angles and layouts on the heat transfer enhancement of a helium-xenon mixture in the sub-channel of a gas-cooled nuclear reactor is numerically studied. The results show that the heat transfer is effectively enhanced due to the vortex and secondary flow induced by the turbulator, leading to periodic fluctuations in the Nusselt number. When comparing the results at different angles, it is observed that the heat transfer enhancement from the turbulator at a 90° angle is relatively small, while the pressure drop is significant. Due to the secondary flow in a narrow triangular space induced by a turbulator with a 45° angle, the mixing between high and low-temperature fluids is effectively enhanced, leading to a more significant improvement in heat transfer. The heat transfer performance and thermal efficiency index of different turbulator layouts are summarized and compared, providing a reference for the heat transfer design of gas-cooled nuclear reactors.

Effect of shade on simultaneous estimation of non-photosynthetic and photosynthetic vegetation cover using the NDVI-NSSI normalized difference triangular space

ABSTRACT The non-photosynthetic vegetation – soil separation index (NSSI) and normalized difference vegetation index (NDVI) can be used to simultaneously estimate the fractional cover of non-photosynthetic vegetation (fNPV), photosynthetic vegetation (fPV), and bare soil (fBS) in vegetation ecosystems. However, these estimates suffer from problems due to shading by dense vegetation or topography. Based on field-measured data and on hyperspectral data acquired by unmanned aerial vehicles, we analyse how shading affects the morphology of NDVI-NSSI and enhanced vegetation index – NSSI (EVI-NSSI). We also investigate the simultaneous estimation of fNPV, fPV, and fBS. The results show that the NDVI-NSSI normalized difference feature space mitigates the impact of shade. Shade causes the NDVI-NSSI and EVI-NSSI to shift rightward parallel to the BS axis and leftward parallel to the PV axis, respectively. Although such shifts may hinder the determination of NPV, PV, and BS endmembers, they do not affect the spectral separation of NPV. Overall, with the NDVI-NSSI and EVI-NSSI methods, the estimation error for fNPV under shaded conditions is approximately 5% greater than that under illuminated conditions. Shaded green vegetation more strongly affects the estimation error of fPV and fBS in EVI-NSSI than in NDVI-NSSI, whereas fBS and fPV depend more strongly on shade than fNPV.

Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations.

Vowel articulation and intelligibility of speech in Spanish speakers with Parkinson's disease treated with deep brain stimulation of the subthalamic nucleus

Parkinson's disease (PD) can affect the intelligibility of speech. Although studies of vowel production are useful for measuring this impairment, they do not exist in Spanish speakers with the disease who have been treated with subthalamic nucleus deep brain stimulation (STN-DBS). STN-DBS is an effective treatment for the classic signs of PD, but with varied effects on speech. Data from two individuals with PD treated with STN-DBS were studied: one (P1) had impairment and the other (P2) had stable speech intelligibility after STN-DBS implantation. The triangular vowel space area (tVSA) and the vowel articulation index (VAI) were measured and compared before the implantation surgery, and at three, six and nine months after surgery. These measurements were compared with measurements of speech intelligibility (percentage of words correctly identified and degree of intelligibility). Both participants presented variations in measurements of vowel articulation after surgery. In P1, the reduction in the tVSA, but not the post-surgical change in the VAI, was consistent with reduced speech intelligibility. However, in P2, both measurements (tVSA and VAI) reflected stable speech intelligibility after surgery. Reduced speech intelligibility in Spanish speakers with PD after STN-DBS implantation may be reflected in a reduced tVSA.

Costoclavicular block – single to double injection – time to see the premiere of triple injection

Sir,Securing the phrenic nerve when achieving effective anesthesia block for the upper limb has been a topic intriguing regional anesthesia enthusiasts ever since. Interscalene brachial plexus block is known to involve the phrenic nerve in 100% of the cases and costoclavicular block which has gained momentum since 2015 is declared to involve the phrenic nerve in 0% of the cases. Besides this the compact, reliable topography of the cords in the triangular costoclavicular space along with an expedited sensorimotor block with local anesthesia deposited in the center of the three cords makes costoclavicular block an attractive option for elbow and below elbow surgeries. According to the studies, the success rate of the blockade is 92.5% with single injection in the center of the cords. Another study by Sebastian, where apart from classical single injection, another injection was given after redirecting the needle, between the medial cord and subclavian artery (labeling it a corner pocket technique) for costoclavicular block. They concluded that the block’s onset time and total anesthesia-related time were significantly shortened with the double injection technique compared with single injection. The basis of this was explanation laid by Dr. Monzo and Hadzic where they proposed in a series of 40 patients a linear septum arising from the lateral part of axillary artery separating the lateral code from the posterior and the medial code, thus compartmentalizing the costoclavicular space. They reported a success rate of 97.5% in their study on 40 patients.4 Hence,double injection is used to overcome the septum “issue.” Pornpatra is defined a high definition ultrasonographic presence of paraneural sheath and facial compartments surrounding the brachial plexus cords at the lateral infraclavicular fossa and the costoclavicular space. We propose that a triple injection with 3rd injection in the vicinity of the lateral cord just before withdrawing the needle apart from the other two injections significantly shortens the onset time of sensory block from 16 min to 9 min. The various sites for injection are shown in the figure below, but the exact point of injection of the second and third is more prominent after giving the first injection. The chances of the median nerve sparing as has been reported in some cases in previous studies are almost nil by this technique - the corner pocket injection that involves the medial root of the median nerve and the lateral cord that is specifically blocked separately covering the lateral root of the median nerve. CONCLUSIONWe did a case series in 15 cases and although the sample size is small and this is definitely not a randomized control trial, to make such a bold statement, we would like to decipher a positive future of the costoclavicular block with triple injection technique with an RCT already underway.

Acoustic Voice Analysis as a Useful Tool to Discriminate Different ALS Phenotypes.

Approximately 80-96% of people with amyotrophic lateral sclerosis (ALS) become unable to speak during the disease progression. Assessing upper and lower motor neuron impairment in bulbar regions of ALS patients remains challenging, particularly in distinguishing spastic and flaccid dysarthria. This study aimed to evaluate acoustic voice parameters as useful biomarkers to discriminate ALS clinical phenotypes. Triangular vowel space area (tVSA), alternating motion rates (AMRs), and sequential motion rates (SMRs) were analyzed in 36 ALS patients and 20 sex/age-matched healthy controls (HCs). tVSA, AMR, and SMR values significantly differed between ALS and HCs, and between ALS with prevalent upper (pUMN) and lower motor neuron (pLMN) impairment. tVSA showed higher accuracy in discriminating pUMN from pLMN patients. AMR and SMR were significantly lower in patients with bulbar onset than those with spinal onset, both with and without bulbar symptoms. Furthermore, these values were also lower in patients with spinal onset associated with bulbar symptoms than in those with spinal onset alone. Additionally, AMR and SMR values correlated with the degree of dysphagia. Acoustic voice analysis may be considered a useful prognostic tool to differentiate spastic and flaccid dysarthria and to assess the degree of bulbar involvement in ALS.

Saphenophemoral Junction and its Related Anatomical Variation in Black Bengal Goat

Blood circulation especially venous distribution is an important subject in any kind of surgical procedure. In the case of the hind leg from the ankle to the groin blood is supplied by the saphenous vein. For venous drainage in hind limbs saphenous vein has a significant role that extends from the ankle to the groin. Basically median and lateral saphenous veins join together as great saphenous veins and enter into gastrocnemius muscle. The ventral to the muscle layer of the tensor fascia lata saphenous vein joins with the femoral vein and forms a junction, which is known as the saphenofemoral junction. It’s also known as the great saphenous vein. Between the deep and aponeurotic fascia of the tensor fascia lata saphenous vein has been found. Many tributaries such as the circumflex iliac vein, external pudendal, and deep pudendal vein were examined in this case. Four cadaveric lower limbs were dissected to examine anatomical variations of these veins and describe their relation to the deep fascia of the thigh. A saphenous compartment is actually a triangular structure. This triangular space is formed by the adductor muscle, fascia lata, and Sartorius muscle. The range of saphenous veins in the saphenous compartment ranged from 5.7-8.1 (7±1.3) cm.

Limitation of fenestrated clips during clipping of middle cerebral artery aneurysm: Technical note.

The middle cerebral artery (MCA) is a common site of cerebral aneurysms and 82.6% occur at the bifurcation. When surgery is selected as a therapeutic option, it intends to clip the neck completely because if some remnant occurs, there exists the possibility of regrowth and bleeding in the short- or long-term. We analyzed one drawback of the fenestrated clips of Yasargil and Sugita types to occlude the neck totally at a specific point formed by the union of the fenestra with the blades, creating a triangular space where the aneurysm can protrude, giving place to a remnant that can lead to a future recurrence and rebleeding. We show two cases of ruptured MCA aneurysms in which a cross-clipping technique occluded a broad base and dysmorphic aneurysm using straight fenestrated clips. In both cases (one using a Yasargil clip and the other with a Sugita clip), a small remnant was visualized when fluorescein videoangiography (FL-VAG) was used. In both cases, the small remnant was clipped with a 3 mm straight miniclip. We should be aware of this drawback when clipping aneurysms using fenestrated clips to ensure a complete obliteration of the aneurysm's neck.

Estimation of Forest Fire Burned Area by Distinguishing Non-Photosynthetic and Photosynthetic Vegetation Using Triangular Space Method

The forest fire burned area is one of the most basic factors used to describe forest fires and plays a vital role in damage assessment. The development of the NSSI-NDVI vegetation index triangular space method enables simultaneous calculation of the flammable non-photosynthetic vegetation (NPV), combustible photosynthetic vegetation (PV), and incombustible bare soil (BS) fractional cover in forest areas. This can be used to compensate for the calculation method that was based on NDVI vegetation index only by comparing vegetation cover before and after forest fires, with the omission of the NPV burned area. To this end, the NSSI-NDVI triangular space shape consistency before and after forest fires was elucidated through combustion and ash wetting experiments. In addition, the feasibility of the NSSI-NDVI triangular space method for the accurate calculation of the post-fire vegetation damage area was verified. Finally, the applicability and accuracy of this research method were verified based on 10 m spatial resolution satellite hyperspectral images from before and after the forest fire in Lushan, Sichuan Province, China. The NSSI-NDVI triangular space method was used to calculate the PV, NPV, and BS coverage simultaneously, and component transformation was used to calculate the burned area and burned site separately.

A consistent projection integration for Galerkin meshfree methods

An efficient and inherently consistent integration method, named projection integration(PI), is proposed for Galerkin meshfree methods with arbitrary order. In contrast to traditional numerical integration methods, PI defines a projection operator based on a weighted norm to systematically approximate meshfree shape functions in an appropriate and consistent function space. Then a substitute function space is established by utilizing projected shape functions as a basis, and Galerkin weak form is approximately calculated by substituting the projected shape functions for the original meshfree shape functions. Owing to the projection consistency of the projection operator, the projected shape functions can still meet consistent conditions. For convenient implementations, the triangular finite element space is selected to approximate meshfree shape functions and the weight function in the weighted norm is carefully chosen to simplify the projection operator in this paper. Arbitrary order integration constraint conditions can be easily met by utilizing the corresponding order triangular finite element shape functions with low order Gauss quadrature rules, which means the optimal convergence rate can be obtained. A series of numerical examples are presented to demonstrate the proposed method’s efficiency and superior convergence performance.

CLINICAL PATHOLOGIC CONFERENCE CASE 1: A MULTILOCULAR RADIOLUCENCY OF THE RIGHT MANDIBLE

CLINICAL PATHOLOGIC CONFERENCE CASE 1: A MULTILOCULAR RADIOLUCENCY OF THE RIGHT MANDIBLE

Analysis of Projectile Impact Resisting Characteristics of Hollow Triangular Matrix Structure

The numerical simulation of engineering structural elements and spatial combination form of the polarizing body using common engineering materials is carried out, and the triangular hole matrix space combination structure is proposed. The penetration depth and deflection angle of the projectile under different projectile velocities and incident positions are obtained by numerical simulation of the projectile impacting the composite structure under various working conditions. At the same time, through the comparative study of ordinary solid shell shielding structures, it is found that the higher the projectile velocity, the higher the shell shielding effectiveness of triangular hole matrix space composite structure.

The conjoined latissimus dorsi and parascapular free flap for reconstruction of extensive soft tissue defects

Durable and resilient soft tissue reconstruction of vast defects of the extremities or the torso. Reconstruction of disproportionately large defects, particularly in cases of simultaneous bone and joint reconstruction. History of surgery or irradiation of upper back and axilla, impossibility of surgery under lateral positioning; relative contraindications in wheelchair users, hemiplegics, or amputees. General anesthesia and lateral positioning. First, the parascapular flap is harvested, with the initial skin incision made medially in order to identify the medial triangular space and the circumflex scapular artery. Flap raising then proceeds from caudal to cranial. Second, the latissimus dorsi is harvested, with the lateral border being dissected free first, before the thoracodorsal vessels are visualized on its undersurface. Flap raising then proceeds from caudal to cranial. Third, the parascapular flap is advanced through the medial triangular space. If the circumflex scapular and thoracodorsal vessels originate separately from the subscapular axis, an in-flap anastomosis is warranted. Subsequent microvascular anastomoses should be performed outside the zone of injury, typically in an end-to-end fashion of the vein and end-to-side fashion of the artery. Postoperative anticoagulation with low-molecular-weight heparin under anti-Xa monitoring (semitherapeutic in normal-risk and therapeutic in high-risk cases). Hourly clinical assessment of flap perfusion for 5consecutive days, followed by stepwise relaxation of immobilization and commencement of dangling procedures in cases of lower extremity reconstruction. Between 2013 and 2018, 74conjoined latissimus dorsi and parascapular flaps were transplanted to cover vast defects of the lower (n = 66) and upper extremity (n = 8). The mean defect size was 723 ± 482 cm2 and the mean flap size was 635 ± 203 cm2. Eight flaps required in-flap anastomoses for separate vascular origins. There was no case of total flap loss.

A Modified Temperature Vegetation Dryness Index (mTVDI) for Agricultural Drought Assessment Based on MODIS Data: A Case Study in Northeast China

Satellite-based drought indices have been shown to be effective and convenient in detecting drought conditions. The temperature vegetation dryness index (TVDI) is one of the most frequently used drought indices; however, it is not suitable for areas with high fractional vegetation cover (FVC). In this study, a modified temperature vegetation dryness index (mTVDI) was constructed by using the multispectral vegetation dryness index (MVDI) proposed by a PROSAIL simulation and water stress experiments which was based on the theory of the TVDI and utilized MODIS data. Compared with the TVDI, the mTVDI presents a more triangular feature space, as well as obviously increased R2 values for dry and wet edges (from 0.37–0.90 to 0.53–0.91 for dry edges and from 0.00–0.77 to 0.24–0.80 for wet edges). The mTVDI was evaluated using standardized precipitation evapotranspiration indices (SPEIs), precipitation, potential evapotranspiration (PET), and the crop water deficit index (CWDI), and the results confirmed that the mTVDI can better reflect the actual spatial changes, compared to the TVDI, under high FVC, as well as presenting an increased Pearson correlation coefficient (by 0.06–0.10) when compared with SPEIs. Moreover, the good performance of the mTVDI in major drought events indicates its reliability and accuracy for drought monitoring. Overall, the mTVDI is a reliable and accurate satellite-based dryness index suitable for high FVC conditions.

Using NDVI-NSSI feature space for simultaneous estimation of fractional cover of non-photosynthetic vegetation and photosynthetic vegetation

The NDVI-NSSI feature space, which is constructed by the NPV soil separation index (NSSI) calculated from the two near-infrared bands and the normalized difference vegetation index (NDVI), is often represented as a triangle. It can be combined with the pixel decomposition method to achieve simultaneous estimation of the fractional cover of non-photosynthetic vegetation, photosynthetic vegetation, and bare soil (fNPV, fPV, and fBS, respectively). However, NDVI saturation in dense vegetation and the deleterious effects of shading due to topography are inevitable. To overcome this difficulty, we compare and analyze the NDVI-NSSI and enhanced vegetation index-NSSI (EVI-NSSI) triangular spaces and their differences when applying on the Sentinel-2A/B images. The results show that EVI-NSSI index combination still forms a triangle-like feature, with the triangle transformed from obtuse to acute, and it can be better used for pixel three-decomposition when PV cover is high. NDVI-NSSI underestimates (overestimates) fPV when PV cover is low (high). The NDVI-NSSI and EVI-NSSI produce significantly different estimates of fPV and fBS but similar estimates of fNPV and can be combined for estimation of a wider range of NPV cover in different seasons, including sparse or dense green vegetation scenarios.

Simultaneous estimation of fractional cover of photosynthetic and non-photosynthetic vegetation using visible-near infrared satellite imagery

In vegetation-abundant ecosystems, accurate fractional cover estimation of multiple targets, including non-photosynthetic vegetation (NPV), photosynthetic vegetation (PV) and bare soil (BS) is an important indicator of carbon storage and climate change, and a contributing factor to soil and water conservation, wildfire, and drought. Satellite remote sensing began with sensors limited to the visible and near infrared (VNIR, 380 nm to 1000 nm), and advancing to sensors spanning the whole solar domain (350 nm to 2500 nm) over the last five decades. However, NPV is still difficult to distinguish from BS in satellite images covering large spatial areas, since their spectral reflectances are always mixed and have subtly different spectral features. Many spectral indices have been proposed to identify NPV, however, most include a short-wave infrared band which is lacking on many current and historical spaceborne sensors. To fully utilize current and historical airborne/satellite images with only VNIR bands, a novel spectral index – the VNIR spectral shape index (SSI) – is proposed in this paper. Using spectra of PV, NPV, and BS acquired from world-recognized spectral libraries, the SSI was devised using only blue, green, red, and NIR bands. When applied to Sentinel-2 MSI images, the SSI was effective in estimating/mapping the fractional cover of PV, NPV, and BS using the triangular space method. The resulting fractional cover was evaluated in three 3 km × 2 km study areas including one grassland, one woodland, and one cropland. The spectral reflectance collected by spectroradiometer in field work and digital image collect by digital camera mounted on unmanned aerial vehicle (UAV) support that the triangular space method is able to estimate the fractional cover of photosynthetic and non-photosynthetic vegetation simultaneously, and that endmember selection relying solely on satellite images is reasonable. Comparing the abundance of each target in UAV images to corresponding MSI pixels, the SSI index and triangular space method proved effective for fractional cover estimation in varied vegetated ecosystems. For fractional cover evaluation in grassland, woodland, and cropland, the R2 reaching to 0.59, 0.62, and 0.70, respectively. These results demonstrate that the SSI is feasible for multiple sensors, enabling potential large temporal and/or spatial scale applications.

Grieks zonder grenzen

It has often been claimed that Greek literature of the Roman world is obsessed with the (classical) Greek past and detached from the real world in which it was written. This article, however, argues that Greek texts of the imperial period offer a fascinating glimpse of the polyphonic and multicultural world of the Roman Empire. The Roman Empire was characterized by globalization, migration, and mobility. While Greek was the lingua franca of a large part of the Mediterranean world, especially in the East, writers of Greek literature came from many different places and regions, flexibly moving in a triangular space between local, Greek, and Roman identities. Three different examples are discussed: an epigram by Crinagoras of Mytilene, a passage from Pseudo-Longinus’ On the Sublime, and Lucian’s interview with Homer in True History. In different ways, these texts construct intercultural dialogues, which invite the reader to perceive the world and its literature as more diverse than just Greek and Roman.

Anatomical and surgical considerations and outcomes in infantile Terson syndrome.

To study the presentation and outcomes of infantile Terson syndrome (TS). This was a retrospective analysis of 18 eyes of nine infants diagnosed to have TS-related intraocular hemorrhage (IOH). Nine infants (seven males) were diagnosed to have IOH secondary to TS, of which eight infants had imaging features suggestive of intracranial bleed meeting our definite criteria. Median age at presentation was 5 months. In 11 eyes of six infants with suspected birth trauma, the median age of presentation was 4.5 months (range 1-5 months) of which one baby had a history of suction cup-aided delivery and four babies had a history of seizures. Vitreous hemorrhage (VH) was noted in 15 eyes (extensive in 11 eyes). Ten of these eyes showed membranous vitreous echoes, or triangular hyperechoic space with apex at the optic nerve head (ONH) posteriorly and base at the posterior lens capsule anteriorly, with or without dot echoes in the rest of the vitreous cavity, with a configuration of "tornado-like hemorrhage" suggestive of Cloquet's canal hemorrhage (CCH). Eight eyes underwent lens-sparing vitrectomy (LSV) and one eye underwent lensectomy with vitrectomy (LV). On follow-up, disc pallor and retinal atrophy were noted in 11 and 10 eyes, respectively. The mean follow-up was 62 months (1.5 month-16 years). Visual acuity/behavior improved in all cases at the final follow-up. Developmental delay was noted in four children. Unexplained and altered vitreous hemorrhage with typical ultrasonography (USG) features should raise the suspicion of CCH in TS. Despite early intervention to clear visual axis, anatomical and visual behavior may remain subnormal.