By introducing a 3×3 matrix Lie algebra and employing the generalized Tu scheme, a AKNS isospectral–nonisospectral integrable hierarchy is generated by using a third-order matrix Lie algebra. Through a matrix transformation, we turn the 3×3 matrix Li...
In the paper, we introduce an efficient method for generating non-isospectral integrable hierarchies, which can be used to derive a great many non-isospectral integrable hierarchies. Based on the scheme, we derive a non-isospectral integrable hierarc...
Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to...
In this article, we adopt two kinds of loop algebras corresponding to the Lie algebra B(0,1) to introduce two line spectral problems with different numbers of even and odd superfunctions. Through generalizing the time evolution λt to a polynomial of...
This paper applies a pair of identical group reductions or similarity transformations to formulate integrable models. An application to the Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problems leads to reduced matrix modified...
In this paper, we first generalize the Dirac spectral problem to isospectral and non-isospectral problems and use the Tu scheme to derive the hierarchy of some new soliton evolution equations. Then, integrable coupling is obtained by solving the isos...
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formu...
Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is...
Determining mineral prospecting targets is crucial for mineral prediction and evaluation. In this study, an evaluation index system for solid mineral exploration and metallogenic target assessment was established using the Analytic Hierarchy Process...
In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Ha...
A new three-dimensional Lie algebra and its loop algebra are proposed by us, whose commutator is a vector product. Based on this, a positive flow and a negative flow are obtained by introducing a new kind of spectral problem expressed by the vector p...
The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. The...
We present three reduced integrable hierarchies of nonlocal integrable nonlinear Schrödinger-type equations, starting from a given vector integrable hierarchy generated from a matrix Lie algebra of B type. The basic tool is the zero curvature fo...
A formalism for the systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra...
Pope Francis’s Laudato Si’ advocates for an “ecological conversion” to the ideal of “integral ecology”. In so doing, it offers insights into different scales of moral attention, resonating with sophisticated thinki...
A new vector-product Lie algebra is constructed for a reductive homogeneous space, which can lead to the presentation of two corresponding loop algebras. As a result, two integrable hierarchies of evolution equations are derived from a new form of ze...
The impact of exposure to multiple chemicals raises concerns for human and environmental health. The adverse outcome pathway method offers a framework to support mechanism-based assessment in environmental health starting by describing which mechanis...
As a new perspective of understanding and explaining the world, system theory provides a new approach for studying Chinese ancient philosophy. Starting with a systematic perspective, this paper takes Wang Fuzhi, a philosopher in ancient China, as a c...
We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assumi...
We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based...
For business-to-business (B2B) companies, selecting new product concepts is vital to new product development (NPD), since it significantly contributes to the ultimate success and reputation of the product in terms of quality and function. The researc...
This study introduces a 4×4 matrix eigenvalue problem and develops an integrable hierarchy with a bi-Hamiltonian structure. Integrability is ensured by the zero-curvature condition, while the Hamiltonian structure is supported by the trace iden...
With the increase in environmental pressure and rapid development of renewable energy technologies, an integrated energy system has been recognized as an effective approach to accommodate large-scale renewables and achieve environmental sustainabilit...
In the process of shield tunneling, the cutter will inevitably be worn and damaged and will need to be replaced frequently. The low efficiency and high safety risk of traditional manual cutter change have prompted robotic cutter change to become the...
A persistent conflict exists between heritage site conservation and local residents’ livelihood development, often described as “site conservation restricting regional development, and regional development damaging site conservation&rdquo...
Optimizing the siting and servicing of urban facilities is a core operations research problem that must reconcile heterogeneous demand, spatial constraints, and network-realistic travel. We present GD-ARISE, a GIS-integrated and data analytics pipeli...
Empty fruit bunch (EFB) utilization to produce valuable bio-chemicals is seen as an economical and sustainable alternative to waste management in palm oil industries. This work proposed an integrated biorefinery configuration of EFB valorization cons...
Subways play an irreplaceable role in alleviating urban traffic congestion and showcasing a city’s historical and cultural heritage. Their speed and environmental benefits make them a vital component of sustainable urban development. Historical...
Forest fires pose significant environmental and economic risks, particularly in fire-prone regions like the Mediterranean coast of Türkiye. This study presents a comprehensive Forest Fire Danger Assessment System (FoFiDAS), by integrating Geogra...
Coastal areas are highly dynamic environments, vulnerable to natural processes and human interventions. This study presents the first application of the Integrated Coastal Vulnerability Index (ICVI) in Cyprus, focusing on two major tourism-dependent...
The historical monuments of the National Preserve “Kyiv-Pechersk Lavra” play an important role in the context of preserving the UNESCO World Heritage. The scientific understanding of the buildings and structures safety management the prio...
Power-to-gas is an energy storage and vector technology which can utilize off-peak power, assist in the integration of renewable power and provide needed fuel for industry and transportation. Further, power-to-gas is a useful technology for balancing...
As a part of the service industry, product design practitioners should possess an understanding of the multifaceted factors and solutions that contribute to delivering exceptional service quality. However, related research on the service quality fact...
This paper introduces a specific matrix spectral problem involving four potentials and derives an associated soliton hierarchy using the zero-curvature formulation. The bi-Hamiltonian formulation is derived via the trace identity, thereby establishin...
In the operation period of long-distance water delivery tunnels, safety may be impacted by the risks that arise from different aspects including the complex geological conditions with fault fracture zones and karst caves, the diverse environment affe...
This article delineates the outcomes of a comprehensive analysis of occupational conditions in coal mining, focusing on dust exposure. A multifaceted model is proposed for the holistic evaluation of occupational environments, integrating risk assessm...
Our study deals with the control of Hungarian state-owned business associations in order to find out whether there is any correlation between corporate sustainability and compliance. According to our hypothesis, the state has a greater responsibility...
The authors frame greenhouse operation as a Controlled Environment Agriculture (CEA) challenge involving multiple interdependent targets: air temperature and humidity, CO2 enrichment, photoperiod-constrained lighting, and irrigation under dynamic and...
In the recent past, Integrated Water Resource Management (IWRM) has emerged as the method of choice for resolving a wide range of water-related conflicts that arise between governments and stakeholders all over the globe. Despite a variety of regulat...
Nepal is highly susceptible to natural hazards, including earthquakes, flooding, and landslides, all of which may occur independently or in combination. Climate change is projected to increase the frequency and intensity of these natural hazards, pos...
Scientific research on the mitigation hierarchy has steadily increased over the past few years at the international level. While some seek to improve the application of this public action instrument, others point out its shortcomings and risks. This...
Gas-fired power plants are environmentally friendly because of their high efficiency rates and low CO2 emissions. On the other hand, the output power of renewable generators is stochastic, meaning that additional capacity must be held in reserve thro...
This paper proposes an innovative method that exploits a complex deep learning network architecture, called Hierarchical Deep Neural Network (HDNN), specifically developed for the eXtreme Multilabel Text Classification (XMTC) task, when the label set...
This research aims to help develop aviation safety policies for the general aviation industry, especially for flight training schools. The analytical hierarchy process (AHP), fuzzy AHP, and fuzzy integral methods were used to find variables that impa...
Industries have to integrate environmental, social, and economic aspects into their supply chain management to achieve sustainability. Hence, the industry needs to take appropriate actions in choosing the right suppliers. The aim of this study is to...
The intelligent vehicle infrastructure system (IVIS) requires systematic testing before being put into large-scale applications. IVIS testing under closed conditions includes stress tests for typical scenarios and extreme scenario strength testing. T...
The globalization of tourism poses complex challenges for destination planning and management, requiring the involvement of various stakeholders and strategic decision-making at various scales. Gastronomic tourism, a key factor in tourist satisfactio...
This paper introduces a pioneering model that merges coupled Markov chains (CMC) with the fuzzy analytic hierarchy process (FAHP) to enhance multi-criteria decision making (MCDM) amidst the dynamic interplay of criteria. Traditional MCDM frameworks o...
In current Chip Multi-Processor (CMP) systems, data sharing existing in cache hierarchy acts as a critical issue which costs plenty of clock cycles for maintaining data coherence. Along with the integrated core number increasing, the only shared cach...
The analytic hierarchy process (AHP) has been a widely used method for handling multi-criteria decision-making (MCDM) problems since the 1980s. However, it postulates that criteria are independent and static, which may not always hold true in realist...
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