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The calculation of charged particles density in Extensive Air Showers (EAS) that reach the earth’s surface is described through estimating the lateral distribution function (LDF) at very high energies of different primary particles. The simulation of LDF is performed through the simulator of air shower which is called AIR-shower Extended Simulations (AIRES) system (2.8.4a version). The LDF simulation is performed for different charged particles like the muons, electron-positron pair production and all charged particles as well as gamma rays at very high energies (10 16 , 10 18 and 10 19 ) eV. The influence of the primary energies, primary particles (such as the proton and the iron nuclei) and the zenith angle (θ) on the charged particles LDF that generated in the EAS has been taken into the account. The calculation of charged particles LDF is fulfilled using “Nishimura-Kamata-Greisen” (NKG) function. The LDF using NKG function is compared with that simulated using AIRES system and gave a good agreement at high energies for (electron and positron) secondary particles, which were initiated by the primary proton.

In this research, the simulation of lateral distribution function (LDF) of Cherenkov radiation was performed using CORSIKA software for two hadronic models QGSJET and GHEISHA. This simulation was performed for several elementary particles such as protons, iron nuclei, electrons and gamma quanta, in the range of energies 1-20 PeV for three zenith angles 0°, 20° and 30°. A parameterization of Cherenkov light LDF was performed for that simulated curves using Lorentzian function. The comparison between the obtained results for LDF of Cherenkov light with that measured with Yakutsk EAS array gave a good agreement within the distances of 100-1000 m from the shower axis.

The Cherenkov light Lateral Distribution Function (LDF) from particles initiated Extensive Air Showers (EAS) with ultrahigh energies ( E > 10 16 eV) was simulated using CORSIKA program for configuration of Tunka and Yakutsk EAS arrays for different primary particles (p, Fe and O 2 ) and different zenith angles. By depending on the Breit–Wigner function, a parametrization of the Cherenkov light LDF was reconstructed on the basis of this simulation as a function of the primary energy. The comparison of the approximated Cherenkov light LDF with that measured on Tunka and Yakutsk EAS arrays gives the possibility of identification of energy spectrum and mass composition of particles initiating EAS about the knee region of the cosmic ray spectrum. The extrapolation of approximated Cherenkov light LDF for energies 20, 30 and 50 PeV was obtained for different primary particles and different zenith angles.

This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

Purpose Lateral ankle sprains are common and can manifest into chronic ankle instability (CAI) resulting in altered gait mechanics that may lead to subsequent ankle sprains. Our purpose was to simultaneously analyse muscle activation patterns and plantar pressure distribution during walking in young adults with and without CAI. Methods Seventeen CAI and 17 healthy subjects walked on a treadmill at 4.8 km/h. Plantar pressure measures (pressure–time integral, peak pressure, time to peak pressure, contact area, contact time) of the entire foot and nine specific foot regions and medial–lateral location of centre of pressure (COP) were measured. Surface electromyography (EMG) root mean square (RMS) amplitudes throughout the entire stride cycle and area under RMS curve for 100 ms pre-initial contact (IC) and 200 ms post-IC for anterior tibialis, peroneus longus, medial gastrocnemius, and gluteus medius were collected. Results The CAI group demonstrated a more lateral COP throughout the stance phase ( P  < 0.001 and Cohen’s d  > 0.9 for all 10 comparisons) and significantly increased peak pressure ( P  = 0.025) and pressure–time integral ( P  = 0.049) under the lateral forefoot. The CAI group had lower anterior tibialis RMS areas ( P  < 0.001) and significantly higher peroneus longus, medial gastrocnemius, and gluteus medius RMS areas during 100 ms pre-IC ( P  < 0.003). The CAI group had higher gluteus medius sEMG amplitudes during the final 50 % of stance and first 25 % of swing ( P  < 0.05). Conclusions The CAI group had large lateral deviations of their COP location throughout the entire stance phase and increased gluteus medius muscle activation amplitude during late stance through early swing phase. Level of evidence III.

Sustainability is key factor for transforming traditional supply chain networks into modern ones. This study, for the first time, considers the impacts of the backup suppliers and lateral transshipment/resupply simultaneously on designing a Sustainable Closed-Loop Supply Chain Network (SCLSCN) to decrease the shortage that may occur during the transmission of produced goods in the network. In this manner, the fuzzy multi-objective mixed-integer linear programming model is proposed to design an efficient SCLSCN resiliently. Moreover, the concept of circular economy has been studied in this paper to reduce environmental effects. This study aims to optimize total and environmental costs, including energy consumption and pollution emissions, while increasing job opportunities. A demand uncertainty component is considered to represent reality more closely. Due to the importance of demand, this parameter is estimated using the Fuzzy Inference System (FIS) as an input into the proposed mathematical model. Then, the fuzzy robust optimization approach is applied in a fuzzy set's environment. The model is tackled by a Multi-Choice Goal Programming Approach with Utility Function (MCGP-UF) to be solved in a timely manner, and the equivalent auxiliary crisp model is employed to convert the multi-objective function to a single objective. The proposed model is tested on the case study of the tire industry in terms of costs, environmental impacts, and social effects. The result confirmed that considering the concept of lateral resupply and backup supplier could considerably decrease the total costs and reduce shortages on the designed SCLSCN. Finally, sensitivity analysis on some crucial parameters is conducted, and future research directions are discussed.

Purpose To compare the effect of the lateral meniscus (LM) complete radial tear at different tear sites on the load distribution and transmission functions. Methods A compressive load of 300 N was applied to the intact porcine knees ( n  = 30) at 15°, 30°, 60°, 90°, and 120° of flexion. The LM complete radial tears were created at the middle portion (group M), the posterior portion (group P), or the posterior root (group R) ( n  = 10, each group), and the same loading procedure was followed. Finally, the recorded three-dimensional paths were reproduced on the LM-removed knees. The peak contact pressure (contact area) in the lateral compartment and the calculated in situ force of the LM under the principle of superposition were compared among the four groups (intact, group M, group P, and group R). Results At all the flexion angles, the peak contact pressure (contact area) was significantly higher (lower) after creating the LM complete radial tear as compared to that in the intact state ( p  < 0.01). At 120° of flexion, group R represented the highest peak contact pressure (lowest contact area), followed by group P and group M ( p  < 0.05). The results of the in situ force carried by the LM were similar to those of the tibiofemoral contact mechanics. Conclusion The detrimental effect of the LM complete radial tear on the load distribution and transmission functions was greatest in the posterior root tear, followed by the posterior portion tear and the middle portion tear in the deep-flexed position. Complete radial tars of the meniscus, especially at the posterior root, should be repaired to restore the biomechanical function.

This study presents a procedure applied to design problems for lateral loaded piles. Calculations for a rigid concrete pile in non-cohesive soil are conducted with the aim of estimating the allowable horizontal force using the methods of Broms and Petrasovit. Random sets are applied to represent the uncertainties of soil parameters, including the internal friction angle and unit weight. Random variables are described using log-normal and beta distributions. Random set theory is utilised to represent variability in the form of probability boxes, possibility distributions, cumulative distribution functions, or intervals. Based on the assumed distributions of the subsoil, the lower and upper bounds for the precise probability of fulfilment of the limit state function of a laterally loaded pile are estimated. The reliability calculation procedure is implemented using the R package (R Studio v2024.12.1+563), and the limit forces and reliability indicators calculated using the two considered methods are compared. The presented procedure serves as an example of the use of a probabilistic approach for the assessment of the capacity of a laterally loaded pile, using a setup for the task involving set-based data and discrete probability distributions.

BackgroundResearch on laparoscopic schwannoma resection (LSR) in the lateral pelvic space (LPS) remains limited. This study aimed to compare the short-term and oncological outcomes of LSR and conventional open schwannoma resection (OSR).MethodsClinical data of 38 patients with lateral pelvic schwannomas were retrospectively collected. LSR in the LPS was based on fascial-oriented techniques. Operation-related results, neurological function, and oncological outcomes were compared.ResultsA total of 38 patients were enrolled, including 18 and 20 patients who underwent LSR and OSR, respectively. The baseline characteristics showed no significant differences between the groups. The median blood loss and incision length in the LSR group were significantly lower (40.0 vs. 300 mL, 4.5 vs. 15 cm, P < 0.001). The LSR group showed less time to the first flatus (2.0 vs. 3.0 days, P = 0.029), time to pull drainage (5.0 vs. 6.0 days, P = 0.042), time to pull catheter (3.0 vs. 4.0 days, P = 0.027), and postoperative hospital stay (6.0 vs. 8.0 days, P = 0.048). The LSR group also showed fewer postoperative complications than the OSR group, although the difference was not significant (40.0% vs. 16.7%, P = 0.113). At a median follow-up of 36 months, no local recurrence was observed.ConclusionsFascial-oriented laparoscopic resection of schwannomas in the LPS is feasible without compromising oncological safety. LSR shows clear advantages, most notably small incisions, less blood loss, and quick recovery, as well as potential benefits of neurological function.

AimIn contrast with findings in amyotrophic lateral sclerosis (ALS), cognitive impairments have as yet not been shown in the lower motor neuron variant of motor neuron disease, progressive spinal muscular atrophy (PMA). The objective of this study was to investigate cognitive function in PMA and to compare the cognitive profile with that of ALS. In addition, visuospatial functions were assessed comprehensively; these tests are underrepresented in earlier neuropsychological investigations in ALS.Methods23 PMA and 30 ALS patients (vital capacity >70% of predicted value) underwent a neuropsychological assessment adapted to motor impairments: global cognitive and executive functioning, psychomotor speed, memory, language, attention and visuospatial skills. The results were compared with age, education and sex matched controls and with normative data.ResultsCompared with controls, PMA patients performed worse on attention/working memory (digit span backward), category fluency and the Mini-Mental State Examination. Compared with normative data, PMA patients most frequently showed impairment on three measures: letter–number sequencing, and immediate and delayed story recall. 17% of PMA patients showed cognitive impairment, defined as performance below 2 SDs from the mean of normative data on at least three neuropsychological tests. In ALS, similar but more extensive cognitive deficits were found. Visuospatial dysfunction was not found in PMA and ALS.Conclusions17% of PMA patients have executive and memory impairments. PMA with cognitive impairment adds a formerly unknown phenotype to the existing classification of motor neuron diseases.