A non-local regularization-based fractional-order total variational compressive sensing algorithm for effective recovery of Geiger-mode avalanche photodiode LiDAR images by Yuchao Wang, Xuyang Wei, Chunyang Wang, Xuelian Liu, Da Xie, Kai Yuan, Rong Li

“…Subsequently, a non-local regularization-based fractional-order total variational CS model for GM-APD LiDAR image recovery is proposed, leveraging the sparse and constrained isometric properties of CS as well as the memorability of fractional-order calculus. This model aims to compress and sample high-dimensional range images while performing a sparse representation. …”
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Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative by Ndolane Sene, Babacar Sène, Seydou Nourou Ndiaye, Awa Traoré

“…Recent studies in fractional calculus have included new fractional derivatives with exponential kernels and Mittag-Leffler kernels. …”
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Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense by Md. Nur Alam

“…The research employs both Itô and Stratonovich stochastic calculus (SSC) to assess the dynamic behavior of these random solutions, providing graphical representations to effectively demonstrate these behaviors. …”
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Fractional Stress Relaxation Model of Rock Freeze-Thaw Damage by Q. Liu, W. Chen, J. K. Guo, R. F. Li, D. Ke, Y. Wu, W. Tian, X. Z. Li

“…To accurately describe the mechanical behaviour of stress relaxation of rocks under freeze-thaw, the software element is constructed based on the theory of fractional calculus to replace the ideal viscous element in the traditional element model. …”
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Mathematical model and its solution for water-altering-gas (WAG) injection process incorporating the effect of miscibility, gravity, viscous fingering and permeability heterogeneit... by Mohammad Yunus Khan

“…The model was generated in the form of a quasi-linear first-order partial differential equation, which was solved analytically in two dimensions (2-D) utilizing vector calculus. Next, this model was solved analytically by applying wave theory to practical constant pressure boundary conditions, which generate distinct waves at different times to provide pressure and saturation at the displacement front location. …”
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Two Versus Three Narrow-Diameter Implants with Locator Attachments Supporting Mandibular Overdentures: A Two-Year Prospective Study by Ali M. El-Sheikh, Omar F. Shihabuddin, Sahar M. F. Ghoraba

“…Standardized clinical and radiographic parameters (survival rate, plaque index, calculus index, gingival index, bleeding index, probing depth and marginal bone loss) were evaluated at the time of the completion of the prosthetic treatment (baseline) and after 6, 12 and 24 months of functional loading. …”
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Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making by Omid Nikan, Jalil Rashidinia, Hossein Jafari

“…Reliable and efficient numerical techniques are essential for solving fractional differential models due to the global characteristics of fractional calculus. This paper focuses on the numerical solution for the TFBSE for American and European option pricing models by means of the local meshless radial basis function (RBF) interpolation. …”
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Relationship of Secondary School Mathematics Achievement with Engineering Mathematics 2 in Polytechnics by Husnira Binti Hussin, Marina Binti Majid, Rohayu Binti Ab Wahab

“…This is because the subject of Engineering Mathematics 2 is mostly related to calculus and only students who have taken Additional Mathematics subject during secondary school had a basic in the Engineering Mathematics 2. …”
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Exact boundaries of the scope of the approximate solution for a certain class of nonlinear differential equations in the complex domain by V. N. Orlov, M. V. Gasanov

“…Applying elements of differential calculus to estimate the error of the solution, in this work, it is possible to expand the scope of the approximate solution and bring it closer to the initially obtained area.Results. …”
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The Effect of Home Bleaching on Color Match with Anterior Single Shade Composite Restoration by Buse Kesgin, Özhan Yağcı, Pınar Güvenç, Gamze Paken, Merve Ünal

“…Methods: In this study, 20 human incisors that were free of caries or enamel abnormalities and freshly extracted for periodontal or orthodontic reasons were cleaned of blood, debris, and calculus. Mesial and distal surfaces were restored with single-shade composite (Omnichroma, Tokuyama, Japan). …”
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The correlation of region-specific lifestyle and subjective perception of oral health with oral health-related quality of life among Tibetan early adolescents in Ganzi: a cross-sec... by Shaoying Duan, Renjie Tang, Chenchen Zhang, Qianqian Su, Huiyu Yang, He Cai, Tao Hu

“…Binary logistic regression was used to explore the association between region-specific lifestyle, subjective perception of oral health, clinician oral health conditions (gingival bleeding on probing (BOP), dental calculus (DC), and decayed, missing, and filled teeth (DMFT)), and OHRQoL. …”
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Defense strategy of industrial control worm based on SEIPQR model by Jie PAN, Lan YE, He ZHAO, Xinlei ZHANG

“…Computer viruses keep evolving with the development of society and progress of technologies, and they become more complex and hidden.The worm virus is the earliest computer virus, which has evolved to an industrial control worm virus and caused a great impact on the safety of the industrial system.Neither the single network isolation nor the patching immunity is unable to keep up with the spreading of the worm virus.The propagation mode and characteristics of the worm virus in the industrial control system were analyzed.Based on the related works of network isolation and patching, a defense strategy against the worm virus was proposed.This strategy was originated from the fundamental infectious disease model, and then a mathematics model (SEIPQR) was proposed to simulate the trend of worm virus propagation.The model included six situations: Susceptible, Exposed, Infected, Quarantine and Recovered.The state transition diagrams of the model was created, and the calculus equations were obtained from the state transition diagrams.Under the condition that the number of system equipment is fixed, the equations were transformed.The equations were solved by solving the basic regeneration number R0, and six equation expressions of the model ware analyzed when the number of exposed hosts and infected hosts is zero.According to the principle of the Routh-Hurwitz, the system is asymptotically stable when R₀＜1, and unstable if R₀＞1.Then the dynamic characteristics of the SEIPQR model under different patching probability, different isolation rate and different infection rate were compared by numerical simulation.Furthermore, the disease-free equilibrium point and endemic equilibrium point of the model were obtained.The simulation results showed that, when the whole system is infected with worm virus, timely patching the susceptible devices and isolating the network can effectively inhibit the spread of industrial control worm virus.…”
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On the Possibility of the Jerk Derivative in Electrical Circuits by J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, M. G. López-López, V. M. Alvarado-Martínez, V. H. Olivares-Peregrino

“…In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ. We consider fractional LC and RL electrical circuits with 1⩽γ<2 for different source terms. …”
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The g-generalized Mittag-Leffler (p,s,k)-function by Umbreen Ayub, Madiha Shafiq, Amir Abbas, Umair Khan, Anuar Ishak, Y.S. Hamed, Homan Emadifar

“…This paper introduces the generalization of ML function, hereafter referred to as the g-generalized ML (p,s,k)-function, which extends the applicability of fractional calculus and complex analysis to a broader range of problems. …”
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Stratifications and foliations in phase portraits of gene network models by V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina

“…Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section “Investigation of functions and plot of their graphs” of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. …”
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College algebra students’ perceptions of exam errors and the problem-solving process by Mary E. Pilgrim, Linda C. Burks, Megan Ryals, Sloan Hill-Lindsay

“…This becomes considerably difficult when students lack the background knowledge needed to begin in Calculus and instead take College Algebra or Precalculus as a first mathematics course. …”
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A Peculiar Cause of Shock: Analysing Two Clinical Cases by João Oliveira, Alberto Costa-Silva, Luís Vale, Daniel Costa, Rui Almeida-Pinto, Carlos Martins-Silva, Tiago Antunes-Lopes, João Silva

“…CT demonstrated a staghorn calculus, hydronephrosis, and signs compatible with xanthogranulomatous pyelonephritis in the right kidney. …”
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Real Time Fractional Robust Adaptive Scheme for Frequency Regulation in Double Area Hybrid Power System With Renewables by Ahmed Ragab, Dalia Allam, Ahmed F. Zobaa, Hazem Ali Attia

“…The first one is a novel fractional order model reference adaptive controller where fractional calculus merits and e-modification robust algorithm have been merged with the adaptive skills creating the fractional order model reference robust-adaptive controller. …”
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Management of forgotten double J stents: insight from a systematic review of case reports by Antonius Galih Pranesdha Putra, Yufi Aulia Azmi, Soetojo Wirjopranoto, Nadya Rahmatika, Agustin Junior Nanda De Niro, Alviano Satria Wibawa, Kevin Muliawan Soetanto

“…The complications experienced were encrustation, multiple stones formation, emphysematous pyelonephritis, emphysematous perinephric abscess, fragmentation, and vesical calculus. In management, it was found that procedures were selected according to patient's situation at that time and the condition of the stent. …”
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Severe Renal Hemorrhage in a Pregnant Woman Complicated with Antiphospholipid Syndrome: A Case Report by Shohei Kawaguchi, Kouji Izumi, Takahiro Nohara, Tohru Miyagi, Hiroyuki Konaka, Atsushi Mizokami, Eitetsu Koh, Mikio Namiki

“…An initial diagnosis of left ureteral calculus was made. Subsequently abdominal-pelvic computed tomography was required for diagnosis because of the appearance of severe contralateral pain. …”
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