In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.
Since December 2019, the whole world has been facing the big challenge of Covid-19 or 2019-nCoV. Some nations have controlled or are controlling the spread of this virus strongly, but some countries are in big trouble because of their poor control strategies. Nowadays, mathematical models are very effective tools to simulate outbreaks of this virus. In this research, we analyze a fractional-order model of Covid-19 in terms of the Caputo fractional derivative. First, we generalize an integer-order model to a fractional sense, and then, we check the stability of equilibrium points. To check the dynamics of Covid-19, we plot several graphs on the time scale of daily and monthly cases. The main goal of this content is to show the effectiveness of fractional-order models as compared to integer-order dynamics.
The renal artery is known to exhibit variations in its number and position. The present study was performed on 50 cadaveric kidneys to observe the topographical anatomy of the accessory renal arteries (ARA) entering the upper or lower poles of the kidney. Out of 50 kidney cadaveric specimens (irrespective of sex) studied, 2 kidneys (4%) showed the presence of ARA. The presence of ARA was observed on the left and right kidneys, respectively. In one left kidney, we observed in addition to the usual renal artery, an ARA near the lower pole of the kidney which divided into anterior and posterior branches. Another right kidney specimen exhibited the presence of single and double ARA at the upper and the lower poles, respectively. The presence of ARA, both at the upper and lower poles is a rare entity. No medical history of the cadavers was available to corroborate the clinical findings. Additional renal vessels may signify a developmental defect. Anatomical knowledge of the variations in the renal vascular supply may be important for abdominal imaging studies and surgical operations involving renal transplantations. The present study discusses in detail the anatomical features and clinical implications of ARA located at both the upper and lower poles of the kidney (Fig. 2, Ref. 15). Full Text (Free, PDF) www.bmj.sk.
Atlanto-occipital fusion may be symptomatic or asymptomatic in nature. The anomaly may be incidentally detected at autopsies or during routine cadaveric dissections. The fusion of the atlas with occipital bone may result in the compression of vertebral artery and first cervical nerve.
The sphenoid bone is known to have several foramina and the foramen ovale is one amongst them. The foramen ovale transmits the mandibular nerve, accessory meningeal artery, lesser petrosal nerve and the emissary veins. There have been past reports on the variations of the different foramina present in the skull but there are no reports on the variations of the skull foramina from any of the South-East Asian countries. The present study aims to highlight the presence of an accessory foramen ovale in the skull in Malaysian population. Both sides of fifteen adult skulls (n = 30) were taken for observation of any variations in the foramen ovale. We observed the presence of accessory foramen ovale on the left side of a single skull (3.33%). The minute accessory foramen ovale was located 0.1 cm medial to the normal foramen ovale. The anomalous accessory foramen ovale was circular in shape and measured 0.1 cm in diameter. Anatomical knowledge of the foramen ovale is important for all neurosurgical procedures involving the trigeminal nerve and administration of anaesthesia in the mandibular nerve. Interestingly, the percutaneous biopsy of the cavernous sinus is also performed through the foramen ovale. Prior knowledge of the presence of an accessory foramen ovale may be important for academic, anthropological, forensic and clinical purpose and the present study aims to highlight such.
The extensor digitorum (ED) muscle of the hand originates from the lateral condyle of the humerus and splits into four tendons; each for one phalanx except the thumb. Literature reports have described multiple tendons (usually two) to each digit but in the presented study we observed four tendons to the ring finger, what is rare. During a routine dissection of the cadavers, we observed an anomalous arrangement of the ED tendon on the left hand of a 42-year-old male. The anomalous tendons to the ring finger were studied in detail, the surrounding structures were carefully delineated and the specimen was photographed. The ED muscle originated as usual from the lateral condyle of the humerus, continued downwards, passing inferiorly to the extensor retinaculum to split into individual tendons for each of the digits. There was a single tendon to the index, middle and ring finger as usual but the ring finger displayed four tendons. All the tendons attached to the phalanges were as described in anatomy textbooks. The arrangement of the anomalous tendons of ED to each of the digits is not uncommon, but existence of four tendons to the ring finger is extremely rare. The increased number of tendons to the ring finger may increase the extension component of the ring finger. Anatomical knowledge of the tendons of the extensor muscles of the hand may be also beneficial for hand surgeons performing graft operations (Fig. 2, Ref. 11). Full Text (Free, PDF) www.bmj.sk.
In this numerical investigation, completely developed laminar convective heat transfer characteristics of a Williamson hybrid ferronanofluid over a cylindrical surface are reported. This new model in 2D is engaged to examine the effects of the magnetic field, thermal radiation factor, volume fraction of ultrafine particles, and Weissenberg number with the help of the Keller box method. The numerical calculations are implemented at a magnetic parameter range of 0.4 to 0.8, volume fraction range of 0.0 to 0.1, and a Weissenberg number range of 0.1 to 0.8. The numerical outcomes concluded that the velocity increases when the thermal radiation parameter and the volume fraction of a nanoparticle are increased, but inverse impacts are obtained for the magnetic parameter and the Weissenberg number. The rate of energy transport increases with increasing thermal radiation and volume fraction, while it declines with increasing the magnetic parameter and Weissenberg number. The drag force shows a positive relationship with the thermal radiation parameter and has an opposite relationship with the Weissenberg number and the magnetic parameter. Furthermore, even when the magnetic field, thermal radiation, volume fraction, and Weissenberg number are all present, the heat transfer rate of Williamson hybrid ferronanofluid is greater than that of mono Williamson ferronanofluid.
In this paper, we introduce a category of Novel Jerk Chaotic (NJC) oscillators featuring symmetrical attractors. The proposed jerk chaotic system has three equilibrium points. We show that these equilibrium points are saddle-foci points and unstable. We have used traditional methods such as bifurcation diagrams, phase portraits, and Lyapunov exponents to analyze the dynamic properties of the proposed novel jerk chaotic system. Moreover, simulation results using Multisim, based on an appropriate electronic implementation, align with the theoretical investigations. Additionally, the NJC system is solved numerically using the Dormand Prince algorithm. Subsequently, the Jerk Chaotic System is modeled using a multilayer Feed-Forward Neural Network (FFNN), leveraging its nonlinear mapping capability. This involved utilizing 20,000 values of x1, x2, and x3 for training (70%), validation (15%), and testing (15%) processes, with the target values being their iterative values. Various network structures were experimented with, and the most suitable structure was identified. Lastly, a chaos-based image encryption algorithm is introduced, incorporating scrambling technique derived from a dynamic DNA coding and an improved Hilbert curve. Experimental simulations confirm the algorithm's efficacy in enduring numerous attacks, guaranteeing strong resiliency and robustness.