Search Results (34)

In this paper, we investigate the existence of multiple solutions for a Kirchhoff-type equation with Dirichlet boundary conditions defined on locally finite graphs. Our study extends some previous results on nonlinear Laplacian equations to the more complex Kirchhoff equation which incorporates a nonlocal term. By employing an abstract three critical points theorem that is based on Morse theory, we provide sufficient conditions that guarantee the existence of at least three distinct solutions, including two strictly positive solutions. We also present an example to verify our results. Full article

Location-based services and applications can provide large-scale vehicle trajectory data. However, these data are often sparse due to human factors and faulty positioning devices, making it challenging to use them in research tasks that require precision. This affects the efficiency and optimization of sustainable transportation systems. Therefore, this paper proposed a trajectory recovery model based on road network constraints and graph contrastive learning (RNCGCL). Vehicles must drive on the road and their driving processes are affected by the surrounding road network structure. Based on the motivations, bidirectional long short-term memory neural networks and an attention mechanism were used to obtain the spatiotemporal features of trajectory. Graph contrastive learning was applied to extract the local feature representation of road networks. A multi-task module was introduced to guarantee the recovered points strictly projected onto the road. Experiments showed that RNCGCL outperformed other benchmarks. It improved the F1-score by 2.81% and decreased the error by 8.62%, indicating higher accuracy and lower regression errors. Furthermore, this paper validated the effectiveness of the proposed method by case studies and downstream task performance. This study provides a robust solution for trajectory data recovery, contributing to the overall efficiency and sustainability of transportation. Full article

In this study, we research a nonautonomous, three-species, delayed reaction–diffusion predator–prey model (RDPPM). Firstly, we derive sufficient conditions to guarantee the existence of a strictly positive, spatially homogeneous periodic solution (SHPS) for the delayed, nonautonomous RDPPM. These conditions are obtained using the comparison theorem for delayed differential equations and the fixed point theorem. Secondly, we present sufficient conditions to ensure the global asymptotic stability of the SHPS for the delayed, nonautonomous RDPPM. These conditions are established through the application of the upper and lower solution method (UALSM) for delayed parabolic partial differential equations (PDEs), along with Lyapunov stability theory. Finally, to demonstrate the practical application of our results, we numerically validate the proposed conditions using a 2-periodic, delayed, nonautonomous RDPPM. Full article

Therapeutic communities face high drop-out rates and general distrust of their effectiveness among substance users. Actively involving users early in treatment promotes greater compliance with the treatment and is predictive of better outcomes. However, users often occupy a passive and subordinate role, exacerbated by the lack of research that explores their perspectives, beliefs, and experiences. This study examined the discourses of 57 consumers who were part of a community for less than 15 days, investigating the meanings attributed to service entry and treatment. A protocol of four written open-ended questions was employed and analysed through discourse analysis and positioning theory. The results indicate that participants configure the community as a place symbolically and spatially distinct from the rest of the world, where they isolate themselves to seek support during times of extreme difficulty. However, what they are seeking is a solution to acute distress caused by substance use, intertwined with social, economic, and relational issues. The concept of treatment is built on the image of the substance user as an individual making a weak request for help, attributing the problem solely to drugs and exhibiting reduced agency in addressing their issues. The collected texts provide a better understanding of the experiences of new users, highlighting the importance of co-constructing personalised projects that empower consumers to feel actively involved in their own change, exploring their theories and definitions of self to structure pathways based strictly on their needs. Full article

A minimum principle for a Sturm–Liouville (S-L) inequality is obtained, which shows that the minimum value of a nonconstant solution of a S-L inequality never occurs in the interior of the domain (a closed interval) of the solution. The minimum principle is then applied to prove that any nonconstant solutions of S-L inequalities subject to separated inequality boundary conditions (IBCs) must be strictly positive in the interiors of their domains and are increasing or decreasing for some of these IBCs. These positivity results are used to prove the uniqueness of the solutions of linear S-L equations with separated BCs. All of these results hold for the corresponding second-order differential inequalities (or equations), which are special cases of S-L inequalities (or equations). These results are applied to two models arising from the source distribution of the human head and chemical reactor theory. The first model is governed by a nonlinear S-L equation, while the second one is governed by a nonlinear second-order differential equation. For the first model, the explicit solutions are not available, and there are no results on the existence of solutions of the first model. Our results show that all the nonconstant solutions are increasing and are strictly positive solutions. For the second model, many results on the uniqueness of the solutions and the existence of multiple solutions have been obtained before. Our results are applied to prove that all the nonconstant solutions are decreasing and strictly positive. Full article

A double optimal solution (DOS) of a least-squares problem $\mathbf{A}\mathbf{x}=\mathbf{b},\mathbf{A}\in {\mathbb{R}}^{q\times n}$ with $q\ne n$ is derived in an $m+1$-dimensional varying affine Krylov subspace (VAKS); two minimization techniques exactly determine the $m+1$ expansion coefficients of the solution $\mathbf{x}$ in the VAKS. The minimal-norm solution can be obtained automatically regardless of whether the linear system is consistent or inconsistent. A new double optimal algorithm (DOA) is created; it is sufficiently time saving by inverting an $m\times m$ positive definite matrix at each iteration step, where $m\ll min(n,q)$. The properties of the DOA are investigated and the estimation of residual error is provided. The residual norms are proven to be strictly decreasing in the iterations; hence, the DOA is absolutely convergent. Numerical tests reveal the efficiency of the DOA for solving least-squares problems. The DOA is applicable to least-squares problems regardless of whether $q<n$ or $q>n$. The Moore–Penrose inverse matrix is also addressed by adopting the DOA; the accuracy and efficiency of the proposed method are proven. The $m+1$-dimensional VAKS is different from the traditional m-dimensional affine Krylov subspace used in the conjugate gradient (CG)-type iterative algorithms CGNR (or CGLS) and CGRE (or Craig method) for solving least-squares problems with $q>n$. We propose a variant of the Karush–Kuhn–Tucker equation, and then we apply the partial pivoting Gaussian elimination method to solve the variant, which is better than the original Karush–Kuhn–Tucker equation, the CGNR and the CGNE for solving over-determined linear systems. Our main contribution is developing a double-optimization-based iterative algorithm in a varying affine Krylov subspace for effectively and accurately solving least-squares problems, even for a dense and ill-conditioned matrix $\mathbf{A}$ with $q\ll n$ or $q\gg n$. Full article

Biomedicine is constantly evolving to ensure a significant and positive impact on healthcare, which has resulted in innovative and distinct requisites such as hydrogels. Chitosan-based formulations stand out for their versatile utilization in drug encapsulation, transport, and controlled release, which is complemented by their biocompatibility, biodegradability, and non-immunogenic nature. Stimuli-responsive hydrogels, also known as smart hydrogels, have strictly regulated release patterns since they respond and adapt based on various external stimuli. Moreover, they can imitate the intrinsic tissues’ mechanical, biological, and physicochemical properties. These characteristics allow stimuli-responsive hydrogels to provide cutting-edge, effective, and safe treatment. Constant progress in the field necessitates an up-to-date summary of current trends and breakthroughs in the biomedical application of stimuli-responsive chitosan-based hydrogels, which was the aim of this review. General data about hydrogels sensitive to ions, pH, redox potential, light, electric field, temperature, and magnetic field are recapitulated. Additionally, formulations responsive to multiple stimuli are mentioned. Focusing on chitosan-based smart hydrogels, their multifaceted utilization was thoroughly described. The vast application spectrum encompasses neurological disorders, tumors, wound healing, and dermal infections. Available data on smart chitosan hydrogels strongly support the idea that current approaches and developing novel solutions are worth improving. The present paper constitutes a valuable resource for researchers and practitioners in the currently evolving field. Full article

Mitochondria are most likely descendants of strictly aerobic prokaryotes from the class Alphaproteobacteria. The mitochondrial matrix is surrounded by two membranes according to its relationship with Gram-negative bacteria. Similar to the bacterial outer membrane, the mitochondrial outer membrane acts as a molecular sieve because it also contains diffusion pores. However, it is more actively involved in mitochondrial metabolism because it plays a functional role, whereas the bacterial outer membrane has only passive sieving properties. Mitochondrial porins, also known as eukaryotic porins or voltage-dependent anion-selective channels (VDACs) control the permeability properties of the mitochondrial outer membrane. They contrast with most bacterial porins because they are voltage-dependent. They switch at relatively small transmembrane potentials of 20 to 30 mV in closed states that exhibit different permeability properties than the open state. Whereas the open state is preferentially permeable to anionic metabolites of mitochondrial metabolism, the closed states prefer cationic solutes, in particular, calcium ions. Mitochondrial porins are encoded in the nucleus, synthesized at cytoplasmatic ribosomes, and post-translationally imported through special transport systems into mitochondria. Nineteen beta strands form the beta-barrel cylinders of mitochondrial and related porins. The pores contain in addition an α-helical structure at the N-terminal end of the protein that serves as a gate for the voltage-dependence. Similarly, they bind peripheral proteins that are involved in mitochondrial function and compartment formation. This means that mitochondrial porins are localized in a strategic position to control mitochondrial metabolism. The special features of the role of mitochondrial porins in apoptosis and cancer will also be discussed in this article. Full article

A combined experimental and molecular dynamic simulation approach was used to examine the structure and interfacial properties of solute-saturated micelles. The properties of dodecylbenzenesulfonate (DBS) micelles were examined in dodecane and benzene hydrocarbon systems. Pyrene fluorescence was used to determine the aggregation number of surfactant monomers in the micelle systems. Molecular dynamic (MD) simulations using energy minimization applying the CHARMm force field with the TIP3P model for water. Comparison of the DBS/benzene and DBS/Dodecane micelles equilibrium structures via radial distribution function (RDF) and probability distribution function (PDF) analysis indicates that the area per head group for the DBS/Benzene micelle interface is significantly larger than that of the DBS/Dodecane at the interface. It was also determined that benzene molecules can move freely within the micelle while dodecane is strictly confined in the core of the micelle. The increased interfacial area per monomer caused by the insertion of benzene also reduces the effectiveness of the surfactant, which has implications for use in various environmental applications. However, the DBS/benzene micelle can solubilize many more hydrocarbon molecules in one micelle with less surfactant monomer (i.e., lower aggregation number) per micelle due to the increased available packing positions within the micelle. This, in turn, increases the efficiency of the surfactant in real-world applications which is consistent with previous laboratory results. Understanding the differing solubilization characteristics of surfactants against various classes of hydrocarbons in single solute systems is a necessary step to beginning to understand their solubilization properties in the mixed waste systems prevalent in most surfactant enhanced remediation (SEAR) strategies. Full article

This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated–unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem’s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm’s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm’s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic. Full article

In this work, we pose and solve, in tempered distribution spaces, an open problem proposed by Schrödinger in 1925. In particular, on the Schwartz distribution spaces, we define the linear continuous quantum operators associated with relativistic Hamiltonians of massive particles—particles with rest mass different from 0 and evolving in the four-dimensional Minkowski vector space ${\mathbb{M}}_4$. In other words, upon the tempered distribution state-space ${\mathcal{S}}^{\prime }({\mathbb{M}}_4,\mathbb{C})$, we have found the most natural way to introduce the free-particle relativistic Hamiltonian operator and its corresponding Schrödinger equation (together with its conjugate equation, standing for antiparticles). We have found the entire solution space of our relativistic linear continuous evolution equation by completely solving a division problem in tempered distribution space. We define the Hamiltonian (Schwartz diagonalizable) operator as the principal square root of a strictly positive, Schwartz diagonalizable second-order differential operator (linked with the “Klein–Gordon operator” on the tempered distribution space ${\mathcal{S}}_4^{\prime }$). The principal square root of a Schwartz nondefective operator is defined in a straightforward way—following the heuristic fashion of some classic and greatly efficient quantum theoretical approach—in the paper itself. Full article

In this paper, a novel two-dimensional direction of arrival (2D-DOA) estimation method with total variation regularization is proposed to deal with the problem of sparse DOA estimation for spatially extended sources. In a general sparse framework, the sparse 2D-DOA estimation problem is formulated with the regularization of extended source characteristics including spatial position grouping, acoustic signal block sparse, and correlation features. An extended sources acoustic model, two-dimensional array manifold and its complete representation, total variation regularization penalty term, and the regularization equation are built, and are utilized to seek the solutions where the non-zero coefficients are grouped together with optimum sparseness. A total variation sparse 2D-DOA estimation model is constructed by combining total variation regularization with LASSO. The model can be easily solved by the convex optimization algorithm, and the solving process can promote the sparsity of the solution on the spatial derivatives and the solution itself. The theoretical analysis results show that the steps of decorrelation processing and angle matching of traditional 2D-DOA estimation methods could be avoided when adopting the proposed method. The proposed method has better robustness to noise, better sparsity, and faster estimation speed with higher resolution than traditional methods. It is promising to provide a coherent sources sparse representation of a non-strictly sparse field. Full article

Rare-earth-doped mixed crystals have demonstrated tunable optical properties, and it is of great importance to study the structural characteristics of the mixed-crystal hosts. Herein, Lu_xGd_1-xVO₄ (0 ≤ x ≤ 1) solid solution nanocrystals were synthesized by a modified sol–gel method, with a pure crystalline phase and element composition. The X-ray diffraction (XRD) and Rietveld refinement results showed that Lu_xGd_1−xVO₄ nanocrystals are continuous solid solutions with a tetragonal zircon phase (space group I4₁/amd) and the lattice parameters strictly follow Vegard’s law. The detailed local structures were studied by extended X-ray absorption fine structure (EXAFS) spectra, which revealed that the average bond length of Gd-O fluctuates and decreases, while the average bond length of Lu-O gradually decreases with the increase in Lu content. Furthermore, the binding energy differences of core levels indicate that the covalent V-O bond is relatively stable, while the ionicity of the Lu-O bond decreases with the increasing x value, and the ionicity of the Gd-O bond fluctuates with small amplitude. The valence band structures were further confirmed by the first-principles calculations, indicating that the valence band is contributed to by the O 2p nonbonding state, localized Gd 4f and Lu 4f states, and the hybridized states between the bonding O 2p and V 3d. The binding energies of the Lu core and the valence levels tend to decrease gradually with the increase in Lu content. This work provides insight into the structural features of mixed-crystal hosts, which have been developed in recent years to improve laser performance by providing different positions for active ions to obtain inhomogeneous broadening spectra. Full article

The next generation of wireless systems has benefits in terms of spectrum and energy inefficiencies by exploiting two promising techniques including Non-Orthogonal Multiple Access (NOMA) and Reconfigurable Intelligent Surfaces (RIS). The scenario of two legitimate users existing together with an eavesdropper is worth examining in terms of secure matter while enabling machine learning tools at the base station for expected improvement. The base station deals with a highly complicated algorithm to adjust parameters against the attack of eavesdroppers and to better improve the secure performance of mobile users. This paper suggests a better solution to allow the base station to predict performance at destinations to adjust necessary parameters such as power allocation coefficients properly. To this end, we propose a deep neural network (DNN)-based approach which also leverages the benefits of aerial RIS to achieve predictable performance and significant secure performance improvement could be enhanced. We first derive the formulations for security outage probability (SOP) in closed-form expressions and analyze the strictly positive secrecy capacity (SPSC), which are crucial performance metrics to determine how the systems are against the existence of eavesdroppers. Such eavesdroppers intend to overhear signal transmission dedicated to intended users and incur degraded system performance. The numerical simulations are expected to evaluate how the machine learning tool works with the traditional computation of system performance metrics which is able to be verified by comparing with the Monte-Carlo method. Our numerical simulations demonstrate that the design of a higher number of meta-surface elements at the RIS, as well as a higher signal-to-noise ratio (SNR) levels at the base station, are key parameters to achieving improved security performance for users. For detailed guidelines of the RIS-NOMA aided system, we provide a table of parameters samples resulting in secure performance as expected. Full article

Energy transformation in the European Union countries is progressing. Its scope is defined by formal and legal regulations and its effectiveness by the position of decision-makers, legitimised by public support for a particular type of challenge. Both issues are the focus of this article. The promotion of environmental protection measures is currently strongly promoted globally. Hence the widespread acceptance in principle of the changes associated with the implementing of the Green New Deal in the energy sector is not surprising. However, to what extent is knowledge of the solutions constituting the mainstream transition (renewable energy sources) ingrained among communities? Does the level of public awareness influence individual consumer choices, modelling the market? The threads outlined above inspired deliberations focused on analysing the assumptions behind energy transition in the EU, with particular reference to the countries directly bordering the line of the ongoing conflict in Ukraine (Poland, Lithuania), in the light of the resulting and escalating restrictions exacerbating the energy crisis. The immediate neighbourhood of the adopted countries, and their similar socio-economic conditions, provided the basis for comparisons and conclusions. The motivation for the choice of the issue and research area was to fill the clear information gap in this study area, strictly in relation to the adopted configuration of these countries. The research proceedings in the outlined area were primarily based on the methodology appropriate for capture and analysis of economic phenomena, enriched with the results of our own findings (questionnaire survey regarding general knowledge of the ZE market and consumer preferences), in order to assess the economic and environmental dimensions of energy transition in Poland and Lithuania and to assess the level of public awareness in this respect in the countries under study. The presented research is an important complementary element of the authors’ series of studies devoted to the analysis of the development of the renewable energy market in Poland and the Baltic States, related to the individual dimensions of RES. Their results give rise to the conclusion that increased social awareness in these countries determines the popularisation of RES solutions in individual use, regardless of their type, stimulating the progress of the energy transformation process. Full article