Change Of Variables Research Articles

New weighted Trudinger-Moser inequality for functions not necessarily radially symmetric and applications

In this paper, we prove some new inequality of Trudinger-Moser' type defined in some weighted Sobolev space whose norm is a combination of the norms of the N-Laplacian and the p-Laplacian with 1<p<N in RN,N≥2. The presence and the behavior of the weights prevent us to use of the symmetrization arguments. This inequality holds for functions which are not required to be radially symmetric. The strategy used in order to establish our inequality mainly consists of a proper change of variables which permits to return to the non-weighted case. Various improvements of this inequality are also proved. Finally, one of these improvements is used to study some elliptic equation involving a weighted (N,p)-Laplacian operator.

The network origins of trade comovement

I develop a production network model of the world economy that features Transcendental Logarithmic (a.k.a. translog) aggregators of varieties. This gives rise to variable substitution elasticities that consistent with the evidence are inversely related to the importer expenditure shares per exporter at the country-sector level. I quantify the model using data for 1970–2018 from 19 OECD economies and 30 sectors. Compared to the analogous constant elasticity version of the model, I find that the translog model amplifies international shock transmission between major trade partners and attenuates transmission elsewhere, which to an extent resolves the “trade comovement puzzle”.

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

Board internationalization, market competition, and corporate digital transformation

This study examines the relationship between board internationalization, market competition, and firms' digital transformation, considering the moderating role of market competition. Using variable substitution and sample time adjustment for robustness testing, the study also further analyses heterogeneity in terms of the nature of property rights and provides insights into the mediating role of factors such as technological innovation, analyst focus, and quality of internal controls in this relationship.

Decoding the influence of servitization on green transformation in manufacturing firms: The moderating effect of artificial intelligence

This research addresses three crucial dimensions in operations management: the servitization of manufacturing, the utilization of artificial intelligence (AI) platforms, and green transformation. Employing the by-production method, we construct a metric for green transformation applicable to listed firms. Our comprehensive analytical framework integrates the resource-based view and information asymmetry theories, enabling systematic investigation into the influence of manufacturing servitization on firms' green transformation. In addition, we examine the moderating effect of AI platforms on the execution of servitization strategies. The empirical foundation of our study is an annually updated dataset of 554 manufacturing firms listed on China's A-share market. Our findings reveal a strong positive correlation between the deployment of servitization strategies and the green transformation of firms. This association withstands multiple robustness tests, including core variable substitution, outlier removal, and adjustments in clustering standard errors. Our research uncovers notable nuances. The effect of servitization on green total factor productivity is more visible for eastern and central China firms. Also, state-owned enterprises demonstrate a more conspicuous influence from servitization strategies. However, we observe a slight diminishing of this effect in firms audited by the Big Four. An essential contribution of our study is the illumination of the role AI platforms play in enhancing the efficacy of servitization. These AI platforms facilitate the creation of tailored solutions that curtail resource wastage, thus amplifying the positive effect of servitization strategies on green transformation.

Exact cosmological solutions for a Chaplygin Gas in anisotropic petrov type D spacetimes in Eddington-inspired-Born-Infeld gravity: Dark Energy model

We consider a Petrov Type D physical metric g, an auxiliary metric q and a Chaplygin Gas of pressure P in Eddington-inspired-Born-Infeld theory. From the Eddington-inspired-Born-Infeld-Chaplygin Gas equations, we first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order linear ordinary differential equations for the non-vanishing components of the pressure P, the physical metric g and the auxiliary metric q. Thanks to the superposition method, we collect an analytical solution for the nonlinear system obtained, which allows to retrieve new exact cosmological solutions for the model considered. By studying the Kretschmann invariant, we see that a singularity exists at the origin of the cosmic time. By the Kruskal-like coordinates, we conclude that this solution is the counterpart of the Friedman-Lemaître-Robertson-Walker spacetime in the Eddington-inspired-Born-Infeld theory. The Hubble and deceleration parameters in both directions of the physical metric g and the auxiliary metric q, as well as their behaviours over time, are also studied. The thermodynamic behaviour of the Chaplygin Gas model is investigated and, as a result, we show that the third-law of thermodynamics is verified. This means that the value of the entropy of the Chaplygin Gas in the perfect crystal state is zero at a temperature of zero Kelvin, which yields a determined value of the entropy and not an additive constant. Finally, we show that the solutions change asymptotically to the isotropic regime of expansion of Dark Energy. With this, we infer that the Chaplygin Gas can show a unified picture of Dark Energy and Dark Matter cooling during the expansion of the Universe.

Existence of traveling wave solutions for density-dependent diffusion competitive systems

In this paper we are concerned with the existence of traveling wave solutions for two species competitive systems with density-dependent diffusion. Since the density-dependent diffusion is a kind of nonlinear diffusion and degenerates at the origin, the methods for proving the existence of traveling wave solutions for competitive systems with linear diffusion are invalid. To overcome the degeneracy of diffusion, we construct a nonlinear invariant region Ω near the origin. Then by using the method of phase plane analysis, we prove the existence of traveling wave solutions connecting the origin and the unique coexistence state, when the speed c is large than some positive value. In addition, when one species is density-dependent diffusive while the other is linear diffusive, via the change of variables and the central manifold theorem, we prove the existence of the minimal speed c∗ . And for c⩾c∗ , traveling wave solutions connecting the origin and the unique coexistence state still exist. In particular, when c=c∗ , we find that one component of the traveling wave solution is sharp type while the other component is smooth, which is a different phenomenon from linear diffusive systems and scalar equations.

State Space Representation of Jiles-Atherton Hysteresis Model and Application for Closed-Loop Control.

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles-Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.

A smartphone app-based mindfulness intervention to enhance recovery from substance use disorders: Protocol for a pilot feasibility randomized controlled trial

BackgroundPoor long-term recovery outcomes after treatment (e.g., readmission to inpatient treatment) are common among individuals with substance use disorders (SUDs). In-person mindfulness-based treatments (MBTs) are efficacious for SUDs and may improve recovery outcomes. However, existing MBTs for SUD have limited public health reach, and thus scalable delivery methods are needed. A digitally-delivered MBT for SUDs may hold promise. MethodsWe recently developed Mindful Journey, a smartphone app-based adjunctive MBT for improving long-term recovery outcomes. In this paper, we present details on the app and describe the protocol for a single-site pilot feasibility randomized controlled trial of Mindful Journey. In this trial, individuals (n = 34) in an early phase of outpatient treatment for SUDs will be randomized to either treatment-as-usual (TAU) plus Mindful Journey, or TAU only. The trial will focus on testing the feasibility (e.g., engagement) and acceptability of the app (e.g., perceived usability and helpfulness for recovery), as well as feasibility of study procedures (e.g., assessment completion). The trial will incorporate ecological momentary assessment before and after treatment to assess mechanisms in real-time, including mindfulness, craving, difficulties with negative emotion regulation, and savoring. To examine the sensitivity to change of outcomes (substance use, substance-related problems, and psychological distress) and mechanism variables (noted above), we will test within-treatment-condition changes over time. DiscussionThe proposed pilot trial will provide important preliminary data on whether Mindful Journey is feasible and acceptable among individuals with SUDs. Trial registrationClinicalTrials.gov NCT05109507.

Center Conditions for Nilpotent Singularities in the Plane Using Invariant Solutions

Recalling that at any regular point we always have a unique particular solution curve passing through it. In this work it is constructed such particular solution curve not passing through the nilpotent singularity but as close as we want to the singularity. By product the existence of such particular curve allows to use it to determine necessary conditions to have a center for nilpotent singularities in the plane. Several involve methods to solve the center problem are known all based in the existence of a change of variables and a scaling transformation of time bringing any differential system with a nilpotent center into a time-reversible system. Here we present a new algebraic method based on the existence of such particular solution curve not passing through the singular point and the involution associated to the nilpotent system with a center. The algebraic method needs the computation of this particular curve up to certain order, which can be done with the help of an algebraic manipulator. Finally a new algebraic method is derived computing the vanishing of a unique function which really gives a scalar method for computing the necessary conditions.

The influence of digital intelligence transformation on carbon emission reduction in manufacturing firms

Severe global climate change has resulted in the focus of social attention shifting to the manufacturing industry's low-carbon transformation. Digital intelligent transformation (DIT) in enterprises is identified as a crucial driver in mitigating carbon emissions. An estimation of DIT's impact on manufacturing industries' carbon emission intensity (CEI) and its underlying mechanisms was conducted using data from Chinese A-share listed companies. Research findings indicate that DIT significantly reduces corporate CEI. Robustness tests, such as the instrumental variable method and variable substitution method, confirm this conclusion. By enhancing labor productivity and accelerating capital renewal, DIT indirectly lowers CEI. Furthermore, non-state-owned enterprises with superior market competitiveness have been observed to be markedly adept at harnessing DIT for CEI. The heterogeneity test found that DIT has a considerably significant effect on reducing CEI in enterprises that are not low-carbon pilots, non-broadband pilots, smart pilots, non-provincial capitals, and eastern cities. This study provides new evidence supporting the promotion of enterprise DIT for achieving green development, offering insights for corporate policy making.

Analytical solutions for nonequilibrium bioheat transfer in tumor during magnetic nanoparticles hyperthermia

Abstract This paper presents mathematical responses for the dual-phase-lag (DPL) hypothesis, which accounts for nonequilibrium heat transfer during magnetic nanoparticle hyperthermia in tumor. To get this precision, volume averaging is used for the local instantaneous energy formulation for tissues and blood. This study proposes a hybrid numerical strategy to solve this problem by combining change of variables, improved discretization techniques, and Laplace transforms. Using the Arrhenius formulas, the range of denatured proteins is used to assess the degree of heat damages to the tumor and healthy tissues. The impacts of porosity, the blood perfusion and metabolism on the temperature and the thermal injuries are studied. The numerical estimations of temperature and the resulting of thermal injuries are shown on a graph, and a comparison with earlier research establishes the results’ validity.

Optimal Control of the Dynamics of Physical and Chemical Processes of Blending and Melting of Copper Concentrates

This paper presents the developed model of dynamics of the physicochemical processes of electromelting of copper concentrates, which was obtained taking into account the available a priori information, which makes allowance for the main features of an object and describes the change of the basic variables of the process state (quantitative aspects of material flows and power, the composition of charge, matte, and slag). Such a model can be used in the field of automation of technological processes in metallurgical and mechanical engineering, and manufacturing. Due to the complexities of the technological process, it was advisable to use classical methods.

A study of the impact of digital investment on corporate environmental performance

The improvement of corporate environmental performance is an important way to realize sustainable development.This article, based on a sample of Chinese non-financial A-share listed companies from 2013 to 2022, attempts to determine the extent to which digital investment can facilitate the improvement of corporate environmental performance. The study finds that digital investment can significantly improve corporate environmental performance. The mechanism study finds that digital investment can improve corporate environmental performance by enhancing corporate green innovation. Furthermore, the conclusions remain robust to instrumental variable substitution and endogeneity issues.

On the Convex Formulations of Robust Markov Decision Processes

Robust Markov decision processes (MDPs) are used for applications of dynamic optimization in uncertain environments and have been studied extensively. Many of the main properties and algorithms of MDPs, such as value iteration and policy iteration, extend directly to RMDPs. Surprisingly, there is no known analog of the MDP convex optimization formulation for solving RMDPs. This work describes the first convex optimization formulation of RMDPs under the classical sa-rectangularity and s-rectangularity assumptions. By using entropic regularization and exponential change of variables, we derive a convex formulation with a number of variables and constraints polynomial in the number of states and actions, but with large coefficients in the constraints. We further simplify the formulation for RMDPs with polyhedral, ellipsoidal, or entropy-based uncertainty sets, showing that, in these cases, RMDPs can be reformulated as conic programs based on exponential cones, quadratic cones, and nonnegative orthants. Our work opens a new research direction for RMDPs and can serve as a first step toward obtaining a tractable convex formulation of RMDPs. Funding: The work in the paper was supported, in part, by NSF [Grants 2144601 and 1815275]; and Agence Nationale de la Recherche [Grant 11-LABX-0047].

Joint Optimization Algorithm for Latency-Energy and Privacy Combining Discrete Differential Evolution and Convex Optimization

A privacy protection task offloading algorithm combining discrete differential evolution and convex optimization is proposed to resolve the new position privacy leakage problem for mobile terminal due to transferring tasks to multiple edge servers for computation via wireless networks. First, the privacy cost of offloading decision is defined for the characteristics of the position privacy problem combined with the standard deviation theory. Second, the objective problem is modeled as a joint optimization of position privacy protection, offloading decision and transmission power, and the total cost of task offloading is an optimization objective. Finally, to handle the objective problem efficiently, offloading decision variable is decoupled from the transmission power variable to decrease the computational complexity of the problem; the discrete differential evolution algorithm is designed to accumulate the approximate optimal offloading decision, and the optimal transmission power is efficiently solved by variable substitution method and subgradient method. Simulations reveal that the algorithm has excellent convergence; it improves the position privacy protection level of mobile terminal and reduces the total cost of task offloading while maintaining lower energy consumption and latency.

ФОРМИРОВАНИЕ СИСТЕМЫ ЭКОЛОГИЧЕСКОЙ БЕЗОПАСНОСТИ ПРОЦЕССОВ ВОДОПОДГОТОВКИ И ОЧИСТКИ СТОЧНЫХ ВОД НА ОСНОВЕ ПРИНЦИПОВ РЕСУРСОСБЕРЕЖЕНИЯ И ПРИРОДОПОДОБИЯ

Environmental safety refers to the state of protection of the natural environment and humans by ensuring an acceptable level of negative impact of natural and anthropogenic environmental hazards on the environment and humans. Based on the principles of nature similarity, resource substitution and conservation, modules and components of environmental safety of drinking water treatment and wastewater treatment processes have been formed. The functions of each module of the aquatic safety ecosystem are disclosed. Dangerous events and hazard factors in the processes of water treatment and water treatment are presented. The content of the system components of environmental safety of water treatment and wastewater treatment processes has been established: sanitary and epidemiological safety, consumer safety, technical safety, environmental safety of production and environmental and economic safety. An algorithm for the environmentally sustainable functioning of water management facilities, long-term and trouble-free operation of water treatment equipment, preservation of the health of water consumers and minimizing the impact on reservoirs, natural water sources (underground and surface) is proposed.

Environmental regulation, innovation choices, and agricultural green total factor productivity under a multi-regulatory perspective.

As environmental challenges escalate, green development is crucial for sustainability. This study analyzes China's county-level agricultural green total factor productivity using SBM and ML index, introducing a comprehensive index to quantify the impact of different types of environmental regulations on productivity. The findings reveal the following: baseline analysis reveals that comprehensive environmental regulation notably boosts agricultural green total factor productivity (AGTFP), with regulatory intensity positively linked to productivity growth. Other factors like policy intervention, industrial structure, savings levels, and per capita GDP also favorably impact productivity. All three types of regulations, command, incentive, and voluntary type, substantially enhance AGTFP. The mediating effect test results show that all three types of regulations directly and positively impact AGTFP. Indirect effects vary: command-type regulation's mediating effect through independent R&D is significant, accounting for 39% of the impact. For incentive type, both industry structure upgrading (23.79%) and independent R&D (3.1%) mediate the effect. For voluntary type, technological advancement via independent R&D mediates about 13.0% of the impact. Heterogeneity analysis reveals distinct impacts of different environmental regulations on AGTFP across regions. Command-type regulation is most effective in the west, while in the central region, both command- and incentive-type regulations have similar promotional effects. In the east, incentive- and voluntary-type regulations show stronger impacts. Robustness tests, including endogeneity testing, dependent variable substitution, sample winsorizing, and model substitution, consistently confirm the baseline finding that environmental regulation significantly boosts AGTFP.

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

Pressure Transient and Production Analysis of Fractured Vertical Wells in Tight Sand Gas Reservoirs Considering Threshold Pressure Gradient, Phase-Change Phenomenon, and Stress Sensitivity

The productivity and pressure response of the tight sand gas wells are influenced by multiple flow mechanisms, such as threshold pressure gradient, phase-change phenomena, and stress sensitivity. Understanding the sensitivity of these factors is crucial for the effective development of tight sand gas reservoirs. This study aims to clarify the sensitivity of various factors affecting the productivity and pressure response of tight sand gas wells. Based on the percolation theory of tight sand gas reservoirs, we considered stress sensitivity, threshold pressure gradient, and phase-change phenomena to derive an unsteady mathematical model of a fractured well with an infinite boundary, and a point source solution was obtained. The proposed model was solved using series function properties, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. The influence of several important parameters on pressure response and productivity is discussed in detail. The results show that the threshold pressure gradient, stress sensitivity, and skin factor significantly impact gas well production and pressure response, while the wellbore storage effect and phase-change effect primarily affect the initial production and pressure response, having little effect on the cumulative gas production. The proposed model can estimate the influence of the threshold pressure gradient and stress sensitivity on productivity and pressure, providing a guide for the development of technical measures for fractured wells in tight sand gas reservoirs.