Oblique Resonance Research Articles

An Examination of Temporomandibular Joint Disc Displacement through Magnetic Resonance Imaging by Integrating Artificial Intelligence: Preliminary Findings.

Background and Objectives: This research was aimed at constructing a complete automated temporomandibular joint disc position identification system that could assist with magnetic resonance imaging disc displacement diagnosis on oblique sagittal and oblique coronal images. Materials and Methods: The study included fifty subjects with magnetic resonance imaging scans of the temporomandibular joint. Oblique sagittal and coronal sections of the magnetic resonance imaging scans were analyzed. Investigations were performed on the right and left coronal images with a closed mouth, as well as right and left sagittal images with closed and open mouths. Three hundred sagittal and coronal images were employed to train the artificial intelligence algorithm. Results: The accuracy ratio of the completely computerized articular disc identification method was 81%. Conclusions: An automated and accurate evaluation of temporomandibular joint disc position was developed by using both oblique sagittal and oblique coronal magnetic resonance imaging images.

Asymptotic boundary condition for numerical modeling of wave packets in a supersonic boundary layer

Within the framework of linear stability theory, a simple non-stationary boundary condition is developed to simulate the far-field asymptotic behavior of linear wave packets propagating in a compressible boundary layer. This condition allows us to skip the linear stage of instability evolution in direct numerical simulations (DNS) of laminar-turbulent transition. It is also suggested to perform numerical simulations of the linear stage without recalculating the Jacobi matrix in the Newton iteration procedure. Robustness and efficiency of the both approaches are evaluated by computations of the first-mode wave packet propagating in the boundary layer on a flat plate at freestream Mach number 2. DNS of the nonlinear stage show that the wave packet quickly breaks down into a turbulent spot, if its hump amplitude is umax′≥0.1U∞. This confirms an amplitude nature of the transition onset criterion. The spectral analysis indicates that the breakdown mechanism differs from the oblique, fundamental or subharmonic resonance and requires additional studies.

Linear and Nonlinear Disturbance Evolution on the Frustum of Hypersonic Ogive Cylinders

Aspects of transition mechanisms on a 14° sharp-nosed ogive cylinder at Mach 6 are elucidated by considering linear and nonlinear disturbance evolution of freestream stochastic and wave packet forcing at different locations downstream of the ogive-cylinder junction. The spectral response of the stochastic forcing displays favorable agreement with experimental observations from Air Force Research Laboratory on which the configuration is based. Intermittent wave packets are generated from small-amplitude continuous freestream pressure forcing. Linear wave packet evolution reveals that Mack modes are the dominant primary instabilities, followed by relatively weaker first-mode waves. The nonlinear wavepacket displays a three-legged wall pressure perturbation signature, which is traced to spanwise curvature effects, and fundamental resonance is the dominant secondary instability mechanism. At higher amplitudes of excitation, weak signatures of subharmonic and oblique resonance phenomena are identified. Downstream placement of the small-amplitude disturbance diminishes amplification of first-mode waves; however, with high-amplitude forcing, the location of actuation does not significantly vary the disturbance evolution signature or the secondary instability mechanisms.

The remaining teres minor and subscapularis may contribute to preventing superior migration of the humeral head and progression of osteoarthritic change in rotator cuff tears

Superior migration of the humeral head is common in large and massive rotator cuff tears (RCTs). Humeral heads migrate superiorly according to an increase in the RCT size; however, the relevance of the remaining cuff has not been elucidated. This study investigated the relation between superior migration of the humeral head and the remaining rotator cuff, especially the teres minor (TM) and subscapularis (SSC), in RCTs involving tears and atrophy of the infraspinatus (ISP). Plain anteroposterior radiographic and magnetic resonance imaging examinations were performed on 1345 patients between January 2013 and March 2018. A total of 188 shoulders with tears of the supraspinatus and ISP with atrophic ISP were evaluated. Gradings of superior migration of the humeral head and osteoarthritic change were evaluated using the acromiohumeral interval, Oizumi classification, and Hamada classification on plain anteroposterior radiographs. The cross-sectional area of the remaining rotator cuff muscles was evaluated using oblique sagittal magnetic resonance imaging. The TM was classified as hypertrophic (H) and normal and atrophic (NA). The SSC was classified as nonatrophic (N) and atrophic (A). All shoulders were classified as groups A (H-N), B (NA-N), C (H-A), and D (NA-A). Age- and sex-matched patients with no cuff tears were also enrolled (control). The acromiohumeral intervals of the control group and groups A-D were 11.4±2.4, 9.5±3.8, 7.8±4.1, 7.2±4.0, and 5.4±3.5 mm (84, 74, 64, 21, and 29 shoulders, respectively), with significant differences between groups A and D (P<.001) and groups B and D (P=.016). Grade 3 of the Oizumi classification and grades 3, 4, and 5 of the Hamada classification were significantly higher in group D than in others (P<.001). The group showing hypertrophic TM and nonatrophic SSC prevented significantly migration of the humeral head and cuff tear osteoarthritis compared to the group showing atrophic TM and SSC in posterosuperior RCTs. The findings indicate that the remaining TM and SSC may prevent superior migration of the humeral head and progression of osteoarthritic change in RCTs. In treating patients with large and massive posterosuperior RCTs, the status of the remaining TM and SSC muscles should be assessed.

Numerical Investigations of Laminar Separation Bubbles Under the Influence of Periodic Gusts

Direct numerical simulations were performed to investigate the behavior of laminar separation bubbles subject to vertical gusts in an airfoil flow. Oscillating boundary-layer flows containing gusts—including unsteady pressure gradients—were prescribed via boundary conditions as well as forcing terms on a domain located in the upper rear section of a natural laminar flow airfoil. For this hybrid approach, unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of the entire flowfield were carried out in conjunction with the so-called disturbance velocity approach, providing transient boundary conditions for the direct numerical simulation. A steady-state reference case with a Reynolds number of is compared and validated with results from wind tunnel experiments. Results of simulations at four different gust frequencies at the same amplitude , each with and without additional disturbances to the boundary layer introducing oblique resonance, are presented and discussed in this paper. The time-dependent behavior of convective instability modes is evaluated by using the continuous wavelet transform and linear stability theory with an unsteady extension. Furthermore, the contribution of the absolute instability—which appears to be larger in the case of oscillating flow compared to the steady-state case—is discussed. Lock-in effects are identified at high gust frequencies.

Total conversion between the longitudinal and transverse waves by an ultrathin elastic metamaterial plate with U-shaped slits

In this work, we propose an elastic metamaterial plate made by an aluminum block tailored with a row of periodic pair of U-shaped slits. Total conversion between longitudinal and transverse modes can be achieved by the metamaterial plate. The conversion is induced by an oblique dipolar resonance, not relying on the Fabry–Pérot resonance or the design of effective parameters. The plate’s thickness can be orders smaller than the working wavelength, showing good potential in practical applications.

An experimental study on the influence of incident characteristics on sound insulation between rooms: Study on the incident sound field in the insulation performance measurement for partition walls. Part 2

AbstractThe sound field characteristics due to room modes are considered to have strong influences on the low‐frequency sound insulation between rooms in field. In this paper, the sound field analysis using the propagation mode expansion method proposed by the authors was applied to the test rooms where the dwelling rooms and the separating wall of an RC apartment building were reproduced. First, the proposed method was validated through the reconstruction of the expanded sound fields and the measurement of the incident directivity. Next, the comparison of the multiple geometries of the source room with two finishing conditions of the RC separating wall demonstrated the influence of the incident sound field on the sound insulation. The mechanism of the sound insulation between rooms was investigated using the proposed method. For the RC single wall, the sound field analysis showed an influence of mode matching between rooms on the low‐frequency transmitted sound. For the composite wall which was composed of the RC separating wall and the additional linings, it was demonstrated that the low‐frequency resonance transmission phenomenon is affected by the matching of the oblique incidence resonance frequency of the wall and the incident characteristics.

The prevalence of posterior inferior tibiofibular ligament and inferior tibiofibular transverse ligament injuries in syndesmosis-injured ankles evaluated by oblique axial magnetic resonance imaging: a retrospective study

BackgroundTransverse ligament and posterior inferior tibiofibular ligament injuries have not been investigated till date because these are difficult to evaluate using standard magnetic resonance imaging. This study aimed to investigate the prevalence of transverse ligament and posterior inferior tibiofibular ligament injuries in syndesmosis-injured ankles using oblique axial magnetic resonance imaging.MethodsThe patients who were diagnosed with syndesmosis injury using magnetic resonance imaging (MRI) within 7 days of the trauma were included. Patients with concomitant fractures were excluded. A total of 34 patients (1 woman and 33 men) with an average age of 22 years (range, 14–64 years) were included. The anterior inferior tibiofibular, interosseous, transverse, and posterior inferior tibiofibular ligaments were classified as intact, partial tear, or complete tear using usual axial and oblique axial MRIs.ResultsThere were 8 (23.5%) ankles with an intact, 21 (61.8%) ankles with a partially torn, and 5 (14.7%) ankles with a complete tear of transverse ligament. There were 20 (58.8%) ankles with an intact, 12 (35.3%) ankles with a partially torn, and 2 (5.9%) ankles with a complete tear of posterior inferior tibiofibular ligament. Overall, 50% of the transverse ligament injuries occurred without posterior inferior tibiofibular ligament involvement.ConclusionsThe oblique axial magnetic resonance imaging scan revealed that the prevalence of transverse ligament and posterior inferior tibiofibular ligament injuries in syndesmosis-injured ankles were 76.5 and 41.2%, respectively.

Assessment of Femoral Torsion on Magnetic Resonance Imaging is More Reliable Using Axial-Oblique Sequences Compared With Standard Axial Slices in Patients With Femoroacetabular Impingement Syndrome

To determine the agreeability of femoral torsion measurements on axial and oblique axial magnetic resonance imaging (MRI) sequences in patients with femoroacetabular impingement syndrome (FAIS). Patients who underwent primary hip arthroscopy for FAIS between January 2012 to January 2019 were identified. Inclusion criteria were all patients with an MRI scan containing the pelvis and knee imaging. MRI-based measurements of femoral torsion were performed on axial and oblique-axial slices by 2 raters, and inter-rater and intrarater reliability was assessed. Bland Altman plots were constructed to evaluate the agreeability between femoral torsion measurements performed using axial and oblique-axial slices. Bivariate correlation analyses were performed to assess the relationship between measurement methods on each respective scan. A linear regression was performed between measurements performed using axial and oblique-axial sequences. A total of 164 patients were included. The mean true-axial and oblique axial femoral torsion were 12.2° ± 9.9° and 11.1° ± 9.2°, respectively. The intrarater reliability for axial and oblique-axial measurements were 0.993 and 0.997, respectively. The inter-rater reliability for axial and oblique-axial measurements were 0.925 and 0.965, respectively. The number of differences within the limits of agreement for axial and oblique-axial femoral torsion measurements was 58.54%. On Pearson correlation analysis, strong positive correlations were found between oblique-axial measurements at multiple time points (r= 0.994, P<.001), as well as axial measurements at multiple time points (r= 0.986, P < .001). A strong positive correlation was found between axial and oblique-axial measurements (r= 0.894, P < .001). A significant regression equation indicated that for each additional increase in axial femoral torsion, the oblique-axial femoral torsion increased 0.837 (95% confidence interval 0.772-0.901). Femoral torsion values measured on oblique-axial sequences are smaller than on true-axial sequences. Femoral torsion measurements on axial and oblique-axial MRI sequences exhibit poor agreement. Oblique-axial sequences demonstrated greater measurement consistency at multiple timepoints. When evaluating torsional measurements, it is important to delineate which axial sequence was used, especially inpatients with suspected severe femoral antetorsion. Standardization of MRI femoral version protocols within one'spractice can ensure more consistent decision-making, especially in patients with suspected femoral antetorsion. Retrospective cohort, level III.

Distance between the supraspinatus and long head of the biceps tendon on sagittal MRI: a new tool to identify anterior supraspinatus insertion injury

PurposeAnterior insertion of the supraspinatus muscle plays an essential role in rotator cuff tissue. We aimed to determine whether the distance between the midpoints of the supraspinatus central tendon and long head of the biceps tendon on a sagittal shoulder magnetic resonance imaging scan can help to preoperatively diagnose an injury of the anterior insertion of the supraspinatus.MethodThis retrospective study reviewed 103 patients with a full-thickness supraspinatus tendon tear: 50 patients with (injured group) and 53 patients without (intact group) anterior supraspinatus insertion tear. The inter-tendon distance was measured based on an oblique sagittal magnetic resonance imaging scan. SPSS was used for statistical analyses. Two independent samples t-test and receiver operating curve analysis were also performed.ResultsThe measurements of inter-tendon distance revealed good intra- and inter-observer reliabilities with intra-class correlation coefficients of 0.92 and 0.97, respectively. The inter-tendon distance of the injured group was significantly greater than that of the intact group (10.1 ± 2.7 vs 8.0 ± 2.3 mm, P < 0.001). The diagnostic ability of the inter-tendon distance was fair (area under the curve = 0.745), and a threshold of 9 mm had a specificity of 73% and sensitivity of 74%.ConclusionThe distance between the supraspinatus central tendon and long head of the biceps tendon on magnetic resonance imaging was greater in patients with anterior supraspinatus insertion injury than those without the injury. A distance of 9 mm may be the cut-off value and a good diagnosis marker for anterior supraspinatus insertion injury.Level of evidenceLevel III, diagnostic case–control study.

Numerical simulations of MHD flows around a 180-degree sharp bend under a strong transverse magnetic field

The quasi-two-dimensional flow of a liquid metal subjected to a strong transverse magnetic field around a 180-degree sharp bend is investigated by means of parametric numerical simulations where the Reynolds number Re, Hartmann number Ha and the gap ratio β (defined as the ratio of the gap thickness to the inlet width) vary in the respective ranges [100–50 000], [100–2000] and [0.04–1]. Both steady-state flow solutions and the evolution of unsteady flow regimes can be captured within this parameter space. The critical Reynolds number for transition from steady to unsteady flow increases as Ha increases for all β. It is shown, for 0.04 ⩽ β ⩽ 0.25, the critical Reynolds number remains almost linear relationship with the parameter Re/Ha0.9, whereas for β = 1, the key parameter is dominated by Re/Ha0.6. The present simulations aim to investigate the physical mechanism of this phenomenon and characterizing the position where the vortices are shed from the free shear layer. We discover that the vortices shedding is originated in the outlet region for 0.04 ⩽ β ⩽ 0.25 other than the turning part in bend region for β = 1. Additionally, the free shear layer separates the recirculation bubble from mainstream and its instability is proposed to interpret the transition, commonly known as Kelvin–Helmholtz instability. The effect of a strong transverse magnetic field on flow characteristics is considered such as the length of recirculation bubbles and the pressure drop between inlet and outlet. A further frequency analysis reveals that at the end of vortices shedding, the oblique waves resonance exists, or a new vortex street consisting of the vortices detached from the boundary layer and upstream fluctuations appears. Finally, according to the influence of β on the transition, we present a modified map of fluid regimes for prediction, which provides useful information for improved mixing and heat transport.

Accuracy of omni-planar and surface casting of epileptiform activity for intracranial seizure localization.

Intracranial electroencephalography (ICEEG) recordings are performed for seizure localization in medically refractory epilepsy. Signal quantifications such as frequency power can be projected as heatmaps on personalized three-dimensional (3D) reconstructed cortical surfaces to distill these complex recordings into intuitive cinematic visualizations. However, simultaneously reconciling deep recording locations and reliably tracking evolving ictal patterns remain significant challenges. We fused oblique magnetic resonance imaging (MRI) slices along depth probe trajectories with cortical surface reconstructions and projected dynamic heatmaps using a simple mathematical metric of epileptiform activity (line-length). This omni-planar and surface casting of epileptiform activity approach (OPSCEA) thus illustrated seizure onset and spread among both deep and superficial locations simultaneously with minimal need for signal processing supervision. We utilized the approach on 41 patients at our center implanted with grid, strip, and/or depth electrodes for localizing medically refractory seizures. Peri-ictal data were converted into OPSCEA videos with multiple 3D brain views illustrating all electrode locations. Five people of varying expertise in epilepsy (medical student through epilepsy attending level) attempted to localize the seizure-onset zones. We retrospectively compared this approach with the original ICEEG study reports for validation. Accuracy ranged from 73.2% to 97.6% for complete or overlapping onset lobe(s), respectively, and ~56.1% to 95.1% for the specific focus (or foci). Higher answer certainty for a given case predicted better accuracy, and scorers had similar accuracy across different training levels. In an era of increasing stereo-EEG use, cinematic visualizations fusing omni-planar and surface functional projections appear to provide a useful adjunct for interpreting complex intracranial recordings and subsequent surgery planning.

Femoral Trochlear Geometry in Patients with Trochlear Dysplasia Using MRI Oblique Trochlear View.

The objective of this study was to evaluate trochlear morphology in patients with trochlear dysplasia using a new oblique trochlear magnetic resonance imaging (MRI) view (OTV) in comparison with standard axial MRI sequences. MRI exam of 73 patients with patellofemoral instability (PFI) and the same number of controls were retrospectively reviewed. The oblique trochlear sequence was acquired by inclining the axial plane parallel to the intercondylar roof of the sagittal image, showing the anterior cruciate ligament (ACL) in its entire length. Trochlear morphology was assessed on axial and oblique trochlear sequences at three levels: level 1 at 25%, level 2 at 50%, and level 3 at 75% of the length of the trochlear groove. Trochlear sulcus angle and sulcus depth were measured at these three levels and compared between the new trochlear and standard axial sequences. Trochlear sulcus angle and sulcus depth were statistically different between axial and oblique trochlear views at all three levels (p < 0,05). Additionally, OTV displayed more uniform sulcus angle and depth along the trochlea. The oblique trochlear view on the MRI can more accurately evaluate trochlear morphology and also better characterize trochlear dysplasia in patients with PFI. This is Level III, retrospective comparative study.

The power of online connectivity: is the future of Australia's midwifery education a flexible online learning experience?

Spontaneous nasalization is the emergence of distinctive nasalization in contexts lacking an historical etymological nasal. In Thai, low and mid-low vowels nasalize after /h/ and to a lesser degree after /ʔ/. It has been reasoned that nasalization after /h/ may occur because breathiness and nasalization are acoustically similar; both introduce higher energy at low frequencies and increase spectral tilt. Glottal consonants may generally facilitate nasalization because aerodynamically they do not require velopharyngeal closure. We investigated velopharyngeal opening (VPO) during vowels after /h/ and/ ʔ/ and measured spectral tilt (H1–H2). We measured VPO by processing oblique ultra-fast magnetic resonance images of the velopharyngeal port. Four Thai speakers exhibited a complex system of VPO that varied based on vowel height and preceding consonant. Low vowels after /h/ manifested more physiological nasalization than low vowels after /ʔ/, while the former were often produced with higher spectral tilt, which may be indicative of either increased breathiness or nasalization. While VPO is likely responsible for impressions of greater nasalization after /h/, our findings suggest that breathiness and VPO may interact in the spontaneously nasalized vowels of Thai.

Oblique resonance wave phenomena for nonlinear coupled evolution equations with fractional temporal evolution

This work investigates the obliquely propagating resonance wave phenomena described by coupled model equations with fractional temporal evolution arising in many branches of physics. The (2 + 1) -dimensional coupled nonlinear Schrodinger equation (NLSE), long wave-short wave resonance interaction (LSRI) equation and Maccari system (MS) having fractional time evolution are considered to study such physical phenomena. The modified Kudryashov method (mKM) with the properties of Khalil's conformable fractional derivatives is implemented to divulge scattered oblique wave solutions of considered equations. The effects of obliqueness and fractional parameter on obtained results are demonstrated graphically along with the physical descriptions. It is found that the resonance wave phenomena are changed with the increase of obliqueness as well as fractional parameter.

Whistler Waves in the Plasmasphere Boundary Layer: Nonlinear Parametric Excitation

AbstractWe present the initial results of numerical simulations of nonlinear coupling between quasi‐electrostatic lower hybrid oblique resonance and fast magnetosonic waves, which was suggested to explain the observations of Very Low Frequency (VLF) electromagnetic emissions at frequencies well above the lower hybrid resonance frequency in the turbulent plasmasphere boundary layer. These emissions represent a distinctive subset of the substorm/storm‐related VLF whistler activity contributing to the alteration of the outer radiation belt boundary. As the turbulent plasmasphere boundary layer is interior to the plasma sheet inner boundary and thus devoid of substorm‐injected kiloelectron volt electrons, the “standard” whistler generation mechanism must be excluded. The simulations show that the parametric coupling of lower hybrid oblique resonance and magnetosonic waves creates VLF electromagnetic emissions with the spectral characteristics consistent with the observations.

Ducting of upper-hybrid waves by density depletions in a magnetoplasma with weak spatial dispersion

The effects of wave trapping and ducting inside a plasma density depletion are studied in a large laboratory magnetoplasma in the upper-hybrid (UH) range of frequencies. A field-aligned density depletion is generated via localized rf plasma heating and subsequent plasma thermal diffusion. Test UH waves are emitted and detected by small-size electric monopole antennas. For a given set of experimental parameters, propagation of UH waves can be considered as collisionless. At the same time, wave surface topology in the UH range is determined by weak spatial dispersion, which is conditioned by the thermal motion of electrons and the ambient magnetic field. For various density depletion depths and diameters, ducting of UH waves belonging to different characteristic parts of the “dumbbell-shaped” wave surface can be observed. Particularly, quasiparallel Langmuir (L-mode) waves and oblique resonance cone (X-mode) waves can be ducted in different regimes. A qualitative explanation of ducting regimes is given based on ray tracing analysis.

The Effect of Oblique Magnetic Resonance Imaging on Surgical Decision Making for Patients Undergoing an Anterior Cervical Discectomy and Fusion for Cervical Radiculopathy.

The purpose of this study was to determine if oblique magnetic resonance imaging (MRI) sequences affect the surgical treatment recommendations for patients with cervical radiculopathy. In this cohort study consecutive clinical cases of persistent cervical radiculopathy requiring surgical intervention were randomized, blinded, and reviewed by 6 surgeons. Initially each surgeon recommended treatment based on the history, physical examination, and axial, coronal and sagittal preoperative magnetic resonance (MR) images; when reviewing the cases the second time, the surgeons were provided oblique MR images. This entire process was then repeated after 2 months. Change in surgical recommendation, interobserver and intraobserver reliability and the average number of levels fused was determined. The addition of the oblique images resulted in the surgical recommendation being altered in 49.2% (59/120) of cases; however, the addition of oblique images did not substantially improve the interobserver reliability of the treatment recommendation (κ = .57 versus.57). Similarly, the overall intraobserver reliability using only traditional MRI sequences (κ = .64) was only slightly improved by the addition of oblique images (κ = .66). Lastly, the addition of oblique images did not change the average number of levels fused (traditional MRI = 1.38, oblique MRI = 1.41, P = .53), or the total number of 3-level fusions recommended (6 versus 6, P = 1.00). The additional oblique images resulted in a change to the surgical plan in almost 50% of cases; however, it had no substantial effect on the reliability of surgical decision making. Further studies are needed to see if this alteration in treatment affects clinical outcomes. 3.

Spontaneous nasalization after glottal consonants in Thai

Spontaneous nasalization is the emergence of distinctive nasalization in contexts lacking an historical etymological nasal. In Thai, low and mid-low vowels nasalize after /h/ and to a lesser degree after /ʔ/. It has been reasoned that nasalization after /h/ may occur because breathiness and nasalization are acoustically similar; both introduce higher energy at low frequencies and increase spectral tilt. Glottal consonants may generally facilitate nasalization because aerodynamically they do not require velopharyngeal closure. We investigated velopharyngeal opening (VPO) during vowels after /h/ and/ ʔ/ and measured spectral tilt (H1–H2). We measured VPO by processing oblique ultra-fast magnetic resonance images of the velopharyngeal port. Four Thai speakers exhibited a complex system of VPO that varied based on vowel height and preceding consonant. Low vowels after /h/ manifested more physiological nasalization than low vowels after /ʔ/, while the former were often produced with higher spectral tilt, which may be indicative of either increased breathiness or nasalization. While VPO is likely responsible for impressions of greater nasalization after /h/, our findings suggest that breathiness and VPO may interact in the spontaneously nasalized vowels of Thai.

Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

In this article, the oblique resonance wave phenomena are investigated by considering nonlinear coupled evolution equations with fractional time evolution. In order to investigate such physical phenomena arising in many branches of physics, the time fractional coupled (2 + 1)-dimensional nonlinear Schrodinger and long-short wave resonance interaction evolution equations are considered. The analytical solutions of considered equations are achieved by implementing the proposed auxiliary ordinary differential equation method along with the properties of Khali’s fractional derivatives. The obtained outcomes may be useful for better understanding the basic properties of internal oblique propagating wave dynamics in many branches of science and engineering.