Order Terms Research Articles

On the some equations inequalities in Musielak-Orlicz spaces with measure data

Our aim in this present work is to prove the existence of a solution for the nonlinear unilateral parabolic problems associated to the equation ∂u - div a(x, t, u, ∇u) - div Φ(x, t, u) = μ in QT = Ω × (0, T), ∂t where the lower order term Φ satisfies a generalized natural growth condition and the datum μ belongs to L1(Q) + E (Q).

The role of antisymmetric functions in nonlocal equations

We use a Hopf-type lemma for antisymmetric super-solutions to the Dirichlet problem for the fractional Laplacian with zero-th order terms, in combination with the method of moving planes, to prove symmetry for the semilinear fractional parallel surface problem. That is, we prove that non-negative solutions to semilinear Dirichlet problems for the fractional Laplacian in a bounded open set Ω ⊂ R n \Omega \subset \mathbb {R}^n must be radially symmetric if one of their level surfaces is parallel to the boundary of Ω \Omega ; in turn, Ω \Omega must be a ball. Furthermore, we discuss maximum principles and the Harnack inequality for antisymmetric functions in the fractional setting and provide counter-examples to these theorems when only ‘local’ assumptions are imposed on the solutions. The construction of these counter-examples relies on an approximation result that states that ‘all antisymmetric functions are locally antisymmetric and s s -harmonic up to a small error’.

Sharp-Interface Limit of a Multi-phase Spectral Shape Optimization Problem for Elastic Structures

We consider an optimization problem for the eigenvalues of a multi-material elastic structure that was previously introduced by Garcke et al. (Adv. Nonlinear Anal. 11:159–197, 2022). There, the elastic structure is represented by a vector-valued phase-field variable, and a corresponding optimality system consisting of a state equation and a gradient inequality was derived. In the present paper, we pass to the sharp-interface limit in this optimality system by the technique of formally matched asymptotics. Therefore, we derive suitable Lagrange multipliers to formulate the gradient inequality as a pointwise equality. Afterwards, we introduce inner and outer expansions, relate them by suitable matching conditions and formally pass to the sharp-interface limit by comparing the leading order terms in the state equation and in the gradient equality. Furthermore, the relation between these formally derived first-order conditions and results of Allaire and Jouve (Comput. Methods Appl. Mech. Eng. 194:3269–3290, 2005) obtained in the framework of classical shape calculus is discussed. Eventually, we provide numerical simulations for a variety of examples. In particular, we illustrate the sharp-interface limit and also consider a joint optimization problem of simultaneous compliance and eigenvalue optimization.

Design of ion-imprinted amino-modified chitosan for selective chromium (Ⅲ) ion removal

Green ion-imprinting technique was applied to construct a Cr(III) ion-imprinted absorbent material from an amino functionalized chitosan derivative. First, nitrogenous organic compounds (GACS) as functional monomer is synthesized by a Schiff base reaction followed by a grafting reaction. In the end, imprinting was completed by cross-linking with epichlorohydrin (ECH) in aqueous media and eluting the coordinated ions with hydrochloric acid to obtain chromium-imprinted polymers (Cr(III)-IIP) with pores. The relevant parameters of the imprinting system were explored, and the superior polymer (Cr(III)-IIP9) has an excellent adsorption capacity 385.89 mg/g, wide pH range adsorption, good adsorption rates and equilibrium times (≤120 min) for Cr(III) ion. Additionally, the kinetic study is best defined in terms of pseudo-second order, while the Freundlich isotherm model fits the data well. Competitive adsorption of the quaternary system of Cr(III)/ Cd(II)/ Ni(II)/ Cu(II) were also investigated, it demonstrated a greater affinity for the Cr(III) ion than other ions. Hence, the imprinting materials prepared by amino functionalized chitosan enhances the adsorption of Cr(III) ions in the simulation of actual water sample. The adsorption mechanism accords with the hard and soft acid and base theory (HSAB), which is expected to be is utilized for the separation of Cr(III) ions in the environment.

One-level density of zeros of Dirichlet L-functions over function fields

TextWe compute the one-level density of zeros of order ℓ Dirichlet L-functions over function fields Fq[t] for ℓ=3,4 in the Kummer setting (q≡1(modℓ)) and for ℓ=3,4,6 in the non-Kummer setting (q≢1(modℓ)). In each case, we obtain a main term predicted by Random Matrix Theory (RMT) and lower order terms not predicted by RMT. We also confirm the symmetry type of the families is unitary, supporting Katz and Sarnak's philosophy. VideoFor a video summary of this paper, please visit https://youtu.be/0tGmXHvVKF0.

An efficient method for generalised Wiener series estimation of nonlinear systems using Gaussian processes

System identification of dynamical systems aims to predict the output of a system for a given input by inferring model details from data. This is particularly challenging for nonlinear vibrating systems with long memory, which often have complex dynamics for which the physics is not fully understood. However, in many engineering applications, it is important to capture as much of the nonlinearity in the response as possible. The Wiener series is a classical data-driven technique that decomposes the system response into a set of orthogonal functionals of increasing order. Unlike standard black-box algorithms, such as neural networks, the series is highly interpretable and can offer insight into the nonlinearities present. However, current methods require vast quantities of data to calculate higher order terms in the Wiener series. In this paper, a novel generalised formulation of the Wiener series is developed by framing the series explicitly as a QR decomposition. Then by placing a Gaussian process prior over the kernels, their inherent structure is exploited to significantly reduce the quantity of data required for inference. Initial investigations were carried out using two systems: first pre-defined kernels and second an idealised nonlinear oscillatory system with unknown kernels. It is demonstrated that the Gaussian Process Generalised Wiener Series (GPGWS) enables the calculation of up to and including the third order kernel for systems with long memory and improves the robustness to noise.

ZMPY3D: accelerating protein structure volume analysis through vectorized 3D Zernike moments and Python-based GPU integration.

Volumetric 3D object analyses are being applied in research fields such as structural bioinformatics, biophysics, and structural biology, with potential integration of artificial intelligence/machine learning (AI/ML) techniques. One such method, 3D Zernike moments, has proven valuable in analyzing protein structures (e.g., protein fold classification, protein-protein interaction analysis, and molecular dynamics simulations). Their compactness and efficiency make them amenable to large-scale analyses. Established methods for deriving 3D Zernike moments, however, can be inefficient, particularly when higher order terms are required, hindering broader applications. As the volume of experimental and computationally-predicted protein structure information continues to increase, structural biology has become a "big data" science requiring more efficient analysis tools. This application note presents a Python-based software package, ZMPY3D, to accelerate computation of 3D Zernike moments by vectorizing the mathematical formulae and using graphical processing units (GPUs). The package offers popular GPU-supported libraries such as CuPy and TensorFlow together with NumPy implementations, aiming to improve computational efficiency, adaptability, and flexibility in future algorithm development. The ZMPY3D package can be installed via PyPI, and the source code is available from GitHub. Volumetric-based protein 3D structural similarity scores and transform matrix of superposition functionalities have both been implemented, creating a powerful computational tool that will allow the research community to amalgamate 3D Zernike moments with existing AI/ML tools, to advance research and education in protein structure bioinformatics. ZMPY3D, implemented in Python, is available on GitHub (https://github.com/tawssie/ZMPY3D) and PyPI, released under the GPL License.

ЗЕМЕЛЬНЫЕ ОТНОШЕНИЯ В СУБЪЕКТАХ ПОВОЛЖСКОГО ЭКОНОМИЧЕСКОГО РАЙОНА

The article is devoted to the multifaceted and very different land relations of the Volga Economic Region. The cost changes in the lease, purchase and sale segments based on the results of land auctions using the grouping method according to different criteria: land rights, land area and lease term are presented and analyzed. Differences and patterns have been established between subjects in the field of land policy, in the system of land use organization, management, in particular with regard to the disposal of land resources. Proposals have been made to increase the lease terms in order to preserve soil fertility, the value of farmland, prevent land and soil degradation, and stimulate long-term, stable economic relations in the agricultural sector of production. Special attention is paid to the role and impact of industrial and economic relations on the sustainable investment development of agribusiness in rural areas.

Random dynamics for a stochastic nonlocal reaction-diffusion equation with an energy functional

<abstract><p>In this paper, the asymptotic behavior of solutions to a fractional stochastic nonlocal reaction-diffusion equation with polynomial drift terms of arbitrary order in an unbounded domain was analysed. First, the stochastic equation was transformed into a random one by using a stationary change of variable. Then, we proved the existence and uniqueness of solutions for the random problem based on pathwise uniform estimates as well as the energy method. Finally, the existence of a unique pullback attractor for the random dynamical system generated by the transformed equation is shown.</p></abstract>

On the approximation of the field of attraction of a rigid body by the field of attraction of four material points of the same mass

The problem of approximation of the gravitational potential of a rigid body by the potential of a system of four identical point masses is studied. Considering the potential in the form of expansion by a parameter characterizing the ratio of the mean body size to the distance to the test point of space, an approach is proposed to construct an approximate expression up to the terms of the third order of smallness. This approach is used to construct a model of the field of attraction for the comet nucleus (67P)Churyumov - Gerasimenko.

Pressure of a dilute spin-polarized Fermi gas: Lower bound

Abstract We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions $d\in \{1,2,3\}$ . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^d\rho ^{2+2/d}$ , where a is the p-wave scattering length of the repulsive interaction and $\rho $ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).

Degenerate singular parabolic problems with natural growth

In this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term \[\begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{|\nabla u|^{p}}{u^{\gamma}}=f & \text{ in } Q,\\ u(x,t)=0 & \text{ on } \Gamma, \\ u(x,t=0)=u_{0}(x) & \text{ in } \Omega, \end{cases}\] where \(\Omega\) is a bounded open subset of \(\mathbb{R}^{N}\), \(N\gt 2\), \(Q\) is the cylinder \(\Omega \times (0,T)\), \(T\gt 0\), \(\Gamma\) the lateral surface \(\partial \Omega \times (0,T)\), \(2\leq p\lt N\), \(a(x,t)\) and \(b(x,t)\) are positive measurable bounded functions, \(q\geq 0\), \(0\leq\gamma\lt 1\), and \(f\) non-negative function belongs to the Lebesgue space \(L^{m}(Q)\) with \(m\gt 1\), and \(u_{0}\in L^{\infty}(\Omega)\) such that \[\forall\omega\subset\subset\Omega\, \exists D_{\omega}\gt 0:\, u_{0}\geq D_{\omega}\text{ in }\omega.\] More precisely, we study the interaction between the term \(u^{q}\) (\(q>0\)) and the singular lower order term \(d(x,t)|\nabla u|^{p}u^{-\gamma}\) (\(0\lt\gamma\lt 1\)) in order to get a solution to the above problem. The regularizing effect of the term \(u^q\) on the regularity of the solution and its gradient is also analyzed.

A regularity result for nonuniformly elliptic equations with lower order terms

A regularity result for nonuniformly elliptic equations with lower order terms

테러방지법상 군(軍) 역할에 관한 법적 검토와 개정방향에 관한 제언

Today, terrorism becomes a threat in the form of megaterrorism triggering a transnational disaster that causes reckless and large damage. The Korean government dispatches troops as peace keeping force for various activities in the international society. For this reason, Korea comes to be a target of an international terrorist group. In particular, externally, since South Korea has a hostile relationship with North Korea which is equipped with an advanced ability of terrorism, it always faces the threat of terrorism. Therefore, it is more important to make preemptive prevention and responses in the comprehensive security dimension. In addition, internally, the country has frequence access of foreigners and an increased number of North Korean refugees due to its growing activities in the world; severe social discontent along with the increase in unemployment rate and the widening gap between the rich and the poor; such a structural setting as high population density suitable for new terrorism. In this circumstance, blended terrorism is likely to occur simultaneously. If these external or internal factors trigger complex megaterrorism in an urban area where important national facilities, multi-purpose facilities, or other social infrastructure are concentrated, and thereby a lot of human lives and assets are damaged, it is impossible to respond to such a disaster with limited police force. For this reason, it is inevitable to protect the security of the nation and the public and maintain public order with the use of military force. According to the counter-terrorism system of South Korea, in principle, military force is put in only if a terror is posed to military facilities. In this case, there is no controversy, because the system is well established under the leadership of the Ministry of National Defense and the Joint Chiefs of Staff. If the head of the countermeasure headquarters makes a request of support, exceptionally, it is possible to operate military force as well as military facilities. Even if the exceptional necessity to make up for insufficient police force is accepted, it is unavoidable to restrict military intervention in the private sector strictly in terms of constitutional order. Therefore, this study tries to suggest the establishment of new provisions pertinent to military presence and withdrawal procedures and the scope of work in the Act on Counter-Terrorism when counter-terrorism operation forces exceptionally intervene in a domestic situation, just as in Martial Law Act according to which military forces are allowed to intervene in such a situation as a state of national emergency in order to maintain public order. Essentially, the domestic counter-terrorism activity is use of public power for protecting social order and security. Therefore, in principle, it is required to prevent terrorism and take suppression activity with the use of police force. Exceptionally, if it is inevitable to put in the counter-terrorism operation forces under the Ministry of National Defense, it is necessary to establish new provisions suggested in this study, including ‘the limitations of the counter-terrorism of police force’, ‘the necessity of urgent support’, ‘the proposal by the director of National Counter Terrorism Committee’, ‘the approval by the President’, the control procedures of the National Assembly, such as notification to the National Assembly and the procedure of withdrawal request of the National Assembly, and the scope of work, in the Act on Counter-Terrorism.

A machine learning-based methodology for short-term kinetic energy forecasting with real-time application: Nordic Power System case

The progressive substitution of conventional synchronous generation for renewable-based generation imposes a series of challenges in many aspects of modern power systems, among which are the issues related to the low rotational inertia systems. Rotational inertia and the kinetic energy stored in the rotating masses in the power system play a fundamental role in the operation of power systems as it represents in some sort the ability of the system to withstand imbalances between generation and demand. Therefore, transmission system operators (TSOs) need tools to forecast the inertia or the kinetic energy available in the systems in the very short term (from minutes to hours) in order to take appropriate actions if the values fall below the one that ensures secure operation. This paper proposes a methodology based on machine learning (ML) techniques for short-term kinetic energy forecasting available in power systems; it focuses on the length of the moving window, which allows for obtaining a balance between the historical information needed and the horizon of forecasting. The proposed methodology aims to be as flexible as possible to apply to any power system, regardless of the data available and the software used. To illustrate the proposed methodology, time series of the kinetic energy recorded in the Nordic Power System (NPS) has been used as a case study. The results show that Linear Regression (LR) is the most suitable method for a time horizon of one hour due to its high accuracy-to-simplicity ratio, while Long Short-Term Memory (LSTM) is the most accurate for a forecasting horizon of four hours. Experimental assessment has been carried out using Typhoon HIL-404 simulator, verifying that both algorithms are suitable for real-time simulation.

Data and knowledge collaborative-driven fault identification and self-healing control action inference framework for blast furnace

The blast furnace reactor has a large volume, and smelting occurs at high temperatures and high-pressure environments. The blast furnace reactor has a large volume, and smelting occurs at high temperatures and high-pressure environments. Considering the small samples of fault data and non-stationarity of the production process with a considerable time lag, it is difficult to diagnose and eliminate the faults timely. This paper proposes for the first time a data and knowledge collaborative-driven framework to identify fault and perform self-healing control. Following the adaptive two-scale sequence division method, the prior knowledge matrix refined K2 algorithm is used to construct Bayesian networks to model the control process. When a new abnormal condition arises, the most similar historical sequence will be found, and inference on the corresponding Bayesian network can lead to fault identification results and self-healing control action. The proposed framework has achieved satisfactory results in simulation experiments and real data experiments. In the simulation data, the Bayesian network (BN) modeling achieved an accuracy of 98.75%, and the time required for structure learning of the BN was reduced by over 75.69%. In real data, the accuracy of identifying blast furnace faults reached 97.1%, and the results of self-healing control reasoning surpassed those of traditional BN reasoning methods in terms of correctness, order, completeness, and necessity.

Approximation of BPS Skyrme model using modified Lagrangian Skyrmion

One of the nuclear atomic models represented by Skyrmion was the Skyrme model. This model was a modified nonlinear sigma model with a Skyrme field where the classical solution use generalized sixth order terms and potential terms. The binding energy that will be studied in the Skyrme SU(2) model is to generalize the second order nonlinear sigma model terms with sixth order derivative terms. The Lagrangian will be obtained for these two terms to find the BPS (Bogomolny Prasad Sommerfield) solution for the profile function numerically. The result of numerical calculation will be used to calculate static energy and rotational energy, where the characteristic of the nucleus can be observed from these two energies. Furthermore, the value of the coupling constant in the Lagrangian Skyrmion will be calculated from the static energy and rotational energy obtained previously. These values are expected to help in the application of Skyrme model for many research physics field.

On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^\infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators

On Ultradifferentiable Regularity of Perturbations by Lower Order Terms of Globally $$C^\infty$$ Hypoelliptic Ultradifferentiable Pseudodifferential Operators

A universal method for constructing n-dimensional polynomial hyperchaotic systems with any desired positive Lyapunov exponents

Most existing chaotic maps have many defects in engineering applications, such as discontinuous parameter range, uneven output of chaotic sequences and dynamic degradation. Based on this, a generalized n-dimensional polynomial chaotic map is proposed in this paper. By setting the coefficient of the linear term and the order of the highest order term of the polynomial, a series of n-dimensional polynomial chaotic maps of specific Lyapunov exponents can be obtained. The system solves the defects of the above system well, in addition, one can get the desired number of positive Lyapunov exponents, and one can get the desired value of positive Lyapunov exponents. Then, the effectiveness of the map is verified by a specific numerical example, and its dynamic analysis shows that the map has complex dynamic behavior. Finally, the map is applied to secure communication technology. Compared with other chaotic maps of the same dimension, the maps can obtain a smaller bit error rate, indicating that the chaotic map is more suitable for chaotic secure communication applications.

Model detection for grey forecasting model with polynomial term

A grey forecasting model with polynomial term which includes the traditional grey model (GM (1)), the nonhomogeneous grey model (NGM(1,1,k)) and the integer order grey model with a time power term (GM(1,1,t)) as special cases is considered. In grey forecasting model with polynomial term, we need to balance the costs and benefits of using higher order term. The novel method of model detection to identify which orders of polynomial term are significant is proposed. Simulation studies prove the proposed methods can identify the true model and have good prediction performances. An empirical example about annual health expenditure in China is used to illustrate the accuracy of proposed method.