Search Results (550)

The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the $(G^{\prime }/G)$ expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article

Whether pattern or amount of daily activity determines neuromuscular properties is the focus of this review. The fast-to-slow conversion of many properties of fast-twitch muscles, by stimulating their nerves electrically with the continuous low-frequency pattern typical of slow motoneurons, argued that muscle properties are determined by their pattern of activity. However, the composition of the motor units (MUs) in almost all muscles is heterogeneous, with the MUs grouped into slow, fast-fatigue-resistant and fast-fatigable types that match corresponding histochemical fiber types. Nonetheless, their contractile forces lie on a continuum, with MUs recruited into activity in order of their size. This ‘size principle’ of MU organization and function applies in normally innervated and reinnervated muscles and, importantly, begs the question of whether it is the amount rather than the pattern of the MU activation that determines their properties. Experimental evidence that uniform daily amounts of ~<0.5, 5%, and 50% ES, converted motoneuron, nerve, and muscle properties to one physiological and histochemical type, argued in favor of the amount of activity determining MU properties. Yet, that the properties were not confined to the expected narrow range argued that factors other than the pattern and/or amount of neuromuscular activity must be considered. These include the progressive increase in the synaptic inputs onto motoneurons. The range of the effects of endurance and intermittent exercise programs on healthy subjects and those suffering nerve injuries and disease is also consistent with the argument that factors other than pattern or amount of neuromuscular activity should be investigated. Full article

In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding symmetry groups. Then, we attempt to solve IOPM by means of two methods. We provide some wave solutions and give further details of the solution using 2D and 3D graphs. These results are interpreted as important clarifications in financial mathematics and deepen our understanding of the dynamics involved during the pricing of options. Secondly, the quasi-periodic behavior of the two-dimensional dynamical system and its perturbed system are plotted using Python software (Python 3.13.5 version). Various frequencies and amplitudes are considered to confirm the quasi-periodic behavior via the Lyapunov exponent, bifurcation diagram, and multistability analysis. These findings are particularly in consonance with current research that investigates IOPM as a nonlinear wave alternate for normal models and the importance of graphical representations in the understanding of financial derivative dynamics. We, therefore, hope to fill in the gaps in the literature that currently exist about the use of multi-solution methods and their effects on financial modeling through the employment of sophisticated graphical techniques. This will be helpful in discussing matters in the field of financial mathematics and open up new directions of investigation. Full article

Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in ${\mathbb{R}}^d$. The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system. Full article

Background: Diabetic foot disease is a public health problem. The challenges of its management lie in the complexity of wound healing and, in particular, the high rate of lesion recurrence. Objectives: The primary objective of the study was to evaluate whether optimized post-healing follow-up by a multidisciplinary team can reduce the recurrence rate of foot ulcers in people living with diabetes. The secondary objectives were to assess patient needs in terms of hospitalization for recurrence, the number of amputations, pedicure care, and the use of adapted footwear. Participants: The study included 129 patients with diabetes presenting a healed foot ulcer. A total of 38 patients underwent an annual post-healing follow-up visit with a multidisciplinary team (optimized follow-up), while 91 had a visit every 2 years (minimum follow-up). Results: Of the 38 patients with optimal follow-up, 8 presented a wound recurrence (21.1%) compared with 38 out of 91 patients (41.8%) receiving minimum follow-up. The recurrence rate decreased significantly between the two groups (p < 0.05). The use of adapted shoes was also significantly better in the group with optimized follow-up (p = 0.02). Conclusions: Regular post-healing follow-up with a multidisciplinary team seems to be a contributing factor to reducing the recurrence of diabetic foot ulcers among people living with diabetes. Full article

Background/Objectives: Childhood obesity is a global epidemic. Addressing the modifiable risk factors with effective policies is crucial for both prevention and intervention. This scoping review aims to provide a situational analysis of childhood obesity in Greece by mapping the available evidence on the prevalence of obesity among Greek children and adolescents and exploring the existing policies implemented to address this issue. Methods: A systematic literature search was conducted on 15 September 2023, using the PubMed, Scopus, and IATROTEK-online databases to identify studies related to childhood obesity and policies in Greece. Keyword groups were developed for “childhood obesity,” “Greece,” and either “prevalence” or “policies”. Additional sources, including Google and Google Scholar, were screened to ensure comprehensiveness. Results: A total of 66 studies were included: 61 on obesity prevalence (≤18 years of age) and 5 on existing policies tackling childhood obesity, all in Greece. The collective prevalence was observed to lie within the subsequent range of values: 2.8–21.2%. Regarding both genders, the observed prevalence ranged from 2.8% to 26.7% in males, and between 1.3% and 33.7% in females. The policies adopted in Greece cover various domains (healthy nutrition, public preferences, physical activity, school policies, and programs related to childhood obesity). Conclusions: Childhood obesity in Greece is a major challenge. Greece currently uses some policies and strategies to combat childhood obesity. There is still work to be done: policies play a pivotal role as a key tool to influence lifestyle habits on a broad scale and exert a considerable impact on the reduction in this prevalent health concern. Full article

Consensus protocols for a multi-agent networked system consist of strategies that align the states of all agents that share information according to a given network topology, despite challenges such as communication limitations, time-varying networks, and communication delays. The special orthogonal group $SO\left(n\right)$ plays a key role in applications from rigid body attitude synchronization to machine learning on Lie groups, particularly in fields like physics-informed learning and geometric deep learning. In this paper, N-agent consensus protocols are proposed on the Lie group $SO\left(4\right)$ and the corresponding tangent bundle $TSO\left(4\right)$, in which the state spaces are $SO{\left(4\right)}^N$ and $TSO{\left(4\right)}^N$, respectively. In particular, when using communication topologies such as a ring graph for which the local stability of non-consensus equilibria is retained in the closed loop, a consensus protocol that leverages a reshaping strategy is proposed to destabilize non-consensus equilibria and produce consensus with almost global stability on $SO{\left(4\right)}^N$ or $TSO{\left(4\right)}^N$. Lyapunov-based stability guarantees are obtained, and simulations are conducted to illustrate the advantages of these proposed consensus protocols. Full article

Background and Objectives: Blood-borne inflammatory ratios have been proposed as inexpensive prognostic tools across a range of diseases, but their role in pulmonary tuberculosis (TB) remains uncertain. In this retrospective case–control analysis, we explored whether composite indices derived from routine haematology—namely the neutrophil-to-lymphocyte ratio (NLR), the platelet-to-lymphocyte ratio (PLR), the systemic immune–inflammation index (SII) and a novel CRP–Fibrinogen Index (CFI)—could enhance risk stratification beyond established cytokine measurements among Romanian adults with culture-confirmed pulmonary T. Materials and Methods: Data were drawn from 80 consecutive TB in-patients and 50 community controls. Full blood counts, C-reactive protein, fibrinogen, and four multiplex cytokines were extracted from electronic records, and composite indices were calculated according to standard formulas. The primary outcomes were in-hospital mortality within 90 days and length of stay (LOS). Results: Among TB patients, the median NLR was 3.70 (IQR 2.54–6.14), PLR was 200 (140–277) and SII was 1.36 × 10⁶ µL⁻¹ (0.74–2.34 × 10⁶), compared with 1.8 (1.4–2.3), 117 (95–140) and 0.46 × 10⁶ µL⁻¹ (0.30–0.60 × 10⁶) in controls. Those with SII above the cohort median exhibited more pronounced acute-phase responses (median CRP 96 vs. 12 mg L⁻¹; fibrinogen 578 vs. 458 mg dL⁻¹), yet median LOS remained virtually identical (29 vs. 28 days) and early mortality was low in both groups (8% vs. 2%). The CFI showed no clear gradient in hospital stay across its quartiles, and composite ratios—while tightly inter-correlated—demonstrated only minimal association with cytokine levels and LOS. Conclusions: Composite cell-count indices were markedly elevated but did not predict early death or prolonged admission. In low-event European cohorts, their chief value may lie in serving as cost-free gatekeepers, flagging those who should proceed to more advanced cytokine or genomic testing. Although routine reporting of NLR and SII may support low-cost surveillance, validation in larger, multicentre cohorts with serial sampling is needed before these indices can be integrated into clinical decision-making. Full article

Classical algebraic structures—such as magmas, groups, and Lie groups—are characterized by increasingly strong requirements in binary operation, ranging from no additional constraints to associativity, identity, inverses, and smooth-manifold structures. The hyperstructure paradigm extends these notions by allowing the operation to return subsets of elements, giving rise to hypermagmas, hypergroups, and Lie hypergroups, along with their variants such as quotient, reduced, and fuzzy hypergroups. In this work, we introduce the concept of superhyperstructures, obtained by iterating the powerset construction, and develop the theory of superhypermagmas and Lie superhypergroups. We further define and analyze quotient superhypergroups, reduced superhypergroups, and fuzzy superhypergroups, exploring their algebraic properties and interrelationships. Full article

This study investigates the potential Kadomtsev–Petviashvili equation incorporating a power-type nonlinearity (PKPp), a model that features prominently in various nonlinear phenomena encountered in physics and applied mathematics. A complete Noether symmetry classification of the PKPp equation is conducted, revealing four distinct scenarios based on different values of the exponent $p$, namely, the general case where $p\ne 1,-1,-2,$ and three special cases where $p=1,$$p=-1,$ and $p=-2.$ Corresponding to each case, conservation laws are derived through a second-order Lagrangian framework. Furthermore, Lie group analysis is employed to reduce the nonlinear partial differential Equation (NLPDE) to ordinary differential Equations (ODEs), thereby enabling the effective application of the Kudryashov method and direct integration techniques to construct exact solutions. In particular, exact solutions of of the considered nonlinear partial differential equation are obtained for the cases $p=1$ and $p=2,$ illustrating the practical implementation of the proposed approach. The solutions obtained include solitary wave, periodic, and rational-type solutions. These results enhance the analytical understanding of the PKPp equation and contribute to the broader theory of nonlinear dispersive equations. Full article

The subject of this study is almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds. The considerations are restricted to a special class of these manifolds, namely those of the Sasaki-like type, because of their geometric construction and the explicit expression of their classification tensor by the pair of B-metrics. Here, each of the two B-metrics is considered as an $\eta$-Ricci–Bourguignon almost soliton, where $\eta$ is the contact form. The soliton potential is chosen to be a conformal Killing vector field (in particular, concircular or concurrent) and then a generalization of the notion of conformality using contact conformal transformations of B-metrics. The resulting manifolds, equipped with the introduced almost solitons, are geometrically characterized. In the five-dimensional case, an explicit example on a Lie group depending on two real parameters is constructed, and the properties obtained in the theoretical part are confirmed. Full article

While digital transformation in e-commerce receives the most publicity, applications in energy and water utilities have been ongoing for decades. Using a methodology based on a systematic review, the paper offers a model of how it occurs in water utilities, reviews experiences from the field, and derives lessons learned to create a road map for future research and implementation. Innovation in water utilities occurs more in the field than through organized research, and utilities share their experiences globally through networks such as water associations, focus groups, and media outlets. Their digital transformation journeys are evident in business practices, operations, and asset management, including methods like decision support systems, SCADA systems, digital twins, and process optimization. Meanwhile, they operate traditional regulated services while being challenged by issues like aging infrastructure and workforce capacity. They operate complex and expensive distribution systems that require grafting of new controls onto older systems with vulnerable components. Digital transformation in utilities is driven by return on investment and regulatory and workforce constraints and leads to cautious adoption of innovative methods unless required by external pressures. Utility adoption occurs gradually as digital tools help utilities to leverage system data for maintenance management, system renewal, and water loss control. Digital twins offer the advantages of enterprise data, decision support, and simulation models and can support distribution system optimization by integrating advanced metering infrastructure devices and water loss control through more granular pressure control. Models to anticipate water main breaks can also be included. With such advances, concerns about cyber security will grow. The lessons learned from the review indicate that research and development for new digital tools will continue, but utility adoption will continue to evolve slowly, even as many utilities globally are too stressed with difficult issues to adopt them. Rather than rely on government and academics for research support, utilities will need help from their support community of regulators, consultants, vendors, and all researchers to navigate the pathways that lie ahead. Full article

This paper investigates the role of solvable and nilpotent Lie algebras in the domains of cryptography and steganography, emphasizing their potential in enhancing security protocols and covert communication methods. In the context of cryptography, we explore their application in public-key infrastructure, secure data verification, and the resolution of commutator-based problems that underpin data protection strategies. In steganography, we examine how the algebraic properties of solvable Lie algebras can be leveraged to embed confidential messages within multimedia content, such as images and video, thereby reinforcing secure communication in dynamic environments. We introduce a key exchange protocol founded on the structural properties of solvable Lie algebras, offering an alternative to traditional number-theoretic approaches. The proposed Lie Exponential Diffie–Hellman Problem (LEDHP) introduces a novel cryptographic challenge based on Lie group structures, offering enhanced security through the complexity of non-commutative algebraic operations. The protocol utilizes the non-commutative nature of Lie brackets and the computational difficulty of certain algebraic problems to ensure secure key agreement between parties. A detailed security analysis is provided, including resistance to classical attacks and discussion of post-quantum considerations. The algebraic complexity inherent to solvable Lie algebras presents promising potential for developing cryptographic protocols resilient to quantum adversaries, positioning these mathematical structures as candidates for future-proof security systems. Additionally, we propose a method for secure message embedding using the Lie algebra in combination with frame deformation techniques in animated objects, offering a novel approach to steganography in motion-based media. Full article

This article presents a comprehensive study of the (2+1)-dimensional Zakharov–Kuznetsov (ZK) $(q,p,r)$ equation with time fractional derivativeUtilizing the fractional Lie group method, we derive several results, including the symmetries, similarity reductions and conservation laws for this equation. Our findings not only correct previous errors in the literature but also introduce new results, such as the Lie transformation group and optimal system for this model. The study provides a rigorous mathematical framework for analyzing this fundamental model, which describes nonlinear ion-acoustic wave evolution in magnetized plasmas. Full article

In this paper, we scrutinize a generalized (2+1)-dimensional nonlinear wave equation (NWE) which describes the waves propagation in plasma physics by utilizing Lie group analysis, Lie point symmetry are obtained and thereafter symmetry reductions are performed which lead to nonlinear ordinary differential equations (NODEs). These NODEs are then solved using various methods that includes the direct integration method. This then leads us to explicit exact solutions of NWE. Graphical representation of the achieved results is given to have a good understanding of the nature of solutions obtained. In conclusion, we construct conserved vectors of the NWE by invoking Ibragimov’s theorem. Full article