Integral Function Research Articles

Adaptive switching control of full state constrained nonlinear systems with unknown control directions

AbstractIn this article, an adaptive switching controller is designed for the stabilization control and the tracking control of nonlinear systems suffering from full state constraints, unknown control directions, and system uncertainties. Featured with changing signs and unbounded increasing magnitudes, a switching control structure is proposed to deal with the unknown control direction problem. In order to explore and finally fix the correct control direction, an adaptive switching rule, a switching function, and a reference function are constructed. An integral Lyapunov function is adopted for the design of the control law, which ensures that full state constraints will not be violated. Using this method, the nonlinear system can be properly controlled without extra estimations or approximations. The boundedness of all the states and the stability of the system are analyzed and guaranteed. Finally, simulations are conducted to validate the proposed method, and the results illustrate its effectiveness.

On the study of double dispersive equation in the Murnaghan’s rod: Dynamics of diversity wave structures

This article secures the various wave structures of the fractional double dispersive equation, a significant nonlinear equation that describes the propagation of nonlinear waves within the elastic, uniform, and inhomogeneous Murnaghan’s rod. The model under discussion has a wide range of applications in science and engineering. Two recently developed analytical techniques known as the improved generalized Riccati equation mapping method and the multivariate generalized exponential rational integral function method have been applied to the proposed equation for the first time. A variety of solutions have been revealed such that dark, singular, bright-dark, bright, complex, and combined solitons. Furthermore, we include a diverse array of plots that illustrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. Within the context of the proposed model, these visualizations give a clear understanding of the behavior and characteristics of the solutions. This study’s results have the potential to enhance comprehension of the nonlinear dynamic characteristics exhibited by the specified system and validate the efficacy of the implemented techniques. The achieved results significantly enhance our understanding of nonlinear science and the nonlinear wave fields associated with more complex nonlinear models.

LncRNA HOTAIR and Cardiovascular diseases.

Cardiovascular diseases (CVDs) a major contributor to global mortality rates, with a steadily rising prevalence observed across the world. Understanding the molecular mechanisms that underlie the signaling pathways implicated in the pathogenesis of CVDs represents a salient and advantageous avenue toward the development of precision and targeted therapeutics. A recent development in CVDs research is the discovery of long non-coding RNAs (lncRNAs), which are now understood to have crucial roles in the onset and development of several pathophysiological processes. The distinct expression patterns exhibited by lncRNAs in various CVDs contexts, present a significant opportunity for their utilization as both biomarkers and targets for therapeutic intervention. Among the various identified lncRNAs, HOX antisense intergenic RNA (HOTAIR) functions as signaling molecules that are significantly implicated in the pathogenesis of cardiovascular disorders in response to risk factors. HOTAIR has been observed to circulate within the bloodstream and possesses an integral epigenetic regulatory function in the transcriptional pathways of many diseases. Recent studies have suggested that HOTAIR offers promise as a biomarker for the detection and treatment of CVDs. The investigation on HOTAIR's role in CVDs, however, is still in its early phases. The goal of the current study is to give a thorough overview of recent developments in the field of analyzing the molecular mechanism of HOTAIR in controlling the pathophysiological processes of CVDs as well as its possible therapeutic uses.

Oscillatory integrals for Mittag-Leffler functions with two variables

Oscillatory integrals for Mittag-Leffler functions with two variables

Streptococcus suis 5’-nucleotidases contribute to adenosine-mediated immune evasion and virulence in a mouse model

ABSTRACT Streptococcus suis (S. suis) is an important swine bacterial pathogen and causes human infections, leading to a wide range of diseases. However, the role of 5’-nucleotidases in its virulence remains to be fully elucidated. Herein, we identified four cell wall-anchored 5’-nucleotidases (Snts) within S. suis, named SntA, SntB, SntC, and SntD, each displaying similar domains yet exhibiting low sequence homology. The malachite green reagent and HPLC assays demonstrated that these recombinant enzymes are capable of hydrolysing ATP, ADP, and AMP into adenosine (Ado), with the hierarchy of catalytic efficiency being SntC>SntB>SntA>SntD. Moreover, comprehensive enzymatic activity assays illustrated slight variances in substrate specificity, pH tolerance, and metal ion requirements, yet highlighted a conserved substrate-binding pocket, His–Asp catalytic dyad, metal, and phosphate-binding sites across Snts, with the exception of SntA. Through bactericidal assays and murine infection assays involving in site-mutagenesis strains, it was demonstrated that SntB and SntC collaboratively enhance bacterial survivability within whole blood and polymorphonuclear leukocytes (PMNs) via the Ado-A2aR pathway in vitro, and within murine blood and organs in vivo. This suggests a direct correlation between enzymatic activity and enhancement of bacterial survival and virulence. Collectively, S. suis 5’-nucleotidases additively contribute to the generation of adenosine, influencing susceptibility within blood and PMNs, and enhancing survival within blood and organs in vivo. This elucidation of their integral functions in the pathogenic process of S. suis not only enhances our comprehension of bacterial virulence mechanisms, but also illuminates new avenues for therapeutic intervention aimed at curbing S. suis infections.

197 Hepatic mRNA expression of innate and adaptive immune genes in beef steers with divergent residual body weight gain

Abstract Immune function has a pivotal role in dictating the overall health and productivity of cattle. In a proficient immune system, the liver assumes an integral function in detoxification and metabolic processes and contributes substantially to overall production and immunity. In this study, we evaluated the hepatic mRNA expression of genes involved in innate and adaptive immunity in crossbred beef steers with positive or negative residual body weight (BW) gain (RADG). Positive-RADG beef steers (n = 8; RADG = 0.76 kg/d) and negative-RADG beef steers (n = 8; RADG = -0.64 kg/d) were identified from a group of 108 growing crossbred beef steers (average BW = 286 ± 380kg) after a 56-d performance testing period. At the end of the 56-d period, liver tissue samples were collected from the beef steers for RNA extraction and cDNA synthesis. The mRNA expression of 84 genes involved in innate and adaptive immunity were analyzed using pathway-focused PCR-based arrays. The mRNA expression of genes with false discovery rate-adjusted P-values (FDR) ≤ 0.05 and absolute fold change (FC) ≥ 1.2 were determined to be differentially expressed. Out of the 84 genes analyzed, four genes [interleukin (IL)-2, MYD88, CD-80, NFkB-1] were differentially expressed and were all upregulated in positive compared with negative-RADG beef steers. Gene ontology pathway enrichment analysis of the differentially expressed genes revealed that pathways related to positive regulation of IL-17 production, cellular response to lipopolysaccharide, and positive regulation of lymphocyte activation were enriched in the positive-RADG steers (P ≤ 0.05). In conclusion, our study revealed that positive-RADG beef steers had increased expression of genes and pathways involved in pathogen recognition and initiation of responses to effectively fight off infections while mitigating excess inflammatory reactions compared with negative-RADG steers, which might explain, in part, the improved feed efficiency of these beef animals

Gradient Descent Provably Escapes Saddle Points in the Training of Shallow ReLU Networks

AbstractDynamical systems theory has recently been applied in optimization to prove that gradient descent algorithms bypass so-called strict saddle points of the loss function. However, in many modern machine learning applications, the required regularity conditions are not satisfied. In this paper, we prove a variant of the relevant dynamical systems result, a center-stable manifold theorem, in which we relax some of the regularity requirements. We explore its relevance for various machine learning tasks, with a particular focus on shallow rectified linear unit (ReLU) and leaky ReLU networks with scalar input. Building on a detailed examination of critical points of the square integral loss function for shallow ReLU and leaky ReLU networks relative to an affine target function, we show that gradient descent circumvents most saddle points. Furthermore, we prove convergence to global minima under favourable initialization conditions, quantified by an explicit threshold on the limiting loss.

Impact Of Innovation and Training & Development on Operational Performance: Mediation of Green Lean Six Sigma

This research tends to discover the influence of innovation and training & development on the operational performance of an organization. Performance is an integral function of the success of any organization. Therefore, this research tends to discover the influence of innovation and training & development on the operational performance of an organization. Green lean six sigma is also an important concept that emerged in the last few years. The motive of this research is to explore the mediation of green lean six sigma among innovation, training & development, and operational performance. The current study uses a quantitative method to explore this current topic. The data utilized in this study was obtained from both customers and employees of textile and apparel manufacturing facilities located in Pakistan. Questionnaires were used to collect data from the respondents of the research. Results of the study indicate innovation and training & development are significantly associated with an organization's operational performance. Green lean six sigma also mediated the association between innovation, training & development, and operational performance. This study also includes limitations, future direction, and practical and managerial implications.

A Robust Parallel Predictive Torque Control Based on a Proportional Integral Cost Function for PMSM

A Robust Parallel Predictive Torque Control Based on a Proportional Integral Cost Function for PMSM

Integral BLF-Based Adaptive Dynamic Event-Triggered Boundary Control for a Flexible Riser System.

For the flexible riser systems modeled with partial differential equations (PDEs), this article explores the boundary control problem in depth for the first time using a dynamic event-triggered mechanism (DETM). Given the intrinsic time-space coupling characteristic inherent in PDE computations, implementing a state-dependent DETM for PDE-based flexible risers presents a significant challenge. To overcome this difficulty, a novel dynamic event-triggered control method is introduced for flexible riser systems, focusing on optimizing available control inputs. In order to save computational costs from the controller to the actuator, a dynamic event-triggered adaptive boundary controller is designed to effectively reduce boundary position vibrations. Additionally, considering external disturbances, an adaptive bounded compensation term is incorporated to counteract the influence of external disturbances on the system. Addressing boundary position constraints, a new integral barrier Lyapunov function (iBLF) tailored specifically for flexible riser systems is introduced, thereby alleviating conservatism in the controller design of flexible risers modeled by PDEs. At last, the validity of the proposed method is demonstrated through a simulation example.

Stereologically adapted Crofton formulae for tensor valuations

The classical Crofton formula explains how intrinsic volumes of a convex body K in n-dimensional Euclidean space can be obtained from integrating a measurement function at sections of K with invariantly moved affine flats. We generalize this idea by constructing stereologically adapted Crofton formulae for translation invariant Minkowski tensors, expressing a prescribed tensor valuation as an invariant integral of a measurement function of section profiles with flats. The measurement functions are weighed sums of powers of the metric tensor times Minkowski valuations. The weights are determined explicitly from known Crofton formulae using Zeilberger's algorithm. The main result is an exhaustive set of measurement functions where the invariant integration is over flats.With the main result at hand, a Blaschke-Petkantschin formula allows us to establish new measurement functions valid when the invariant integration over flats is replaced by an invariant integration over subspaces containing a fixed subspace of lower dimension. Likewise, a stereologically adapted Crofton formula valid in the scheme of vertical sections is constructed. Only some special cases of this result have been stated explicitly before, with even the three-dimensional case yielding a new stereological formula. Here, we obtain new vertical section formulae for the surface tensors of even rank.

Multiplicity and transverse momentum dependence of charge-balance functions in pPb and PbPb collisions at LHC energies

Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 8.16 TeV and lead-lead (PbPb) collisions at sNN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s_{\ extrm{NN}}} $$\\end{document} = 5.02 TeV are reported. The pPb and PbPb data sets correspond to integrated luminosities of 186 nb−1 and 0.607 nb−1, respectively, and were collected using the CMS detector at the CERN LHC. The charge-dependent correlations are characterized by balance functions of same- and opposite-sign particle pairs. The balance functions, which contain information about the creation time of charged particle pairs and the development of collectivity, are studied as functions of relative pseudorapidity (∆η) and relative azimuthal angle (∆ϕ), for various multiplicity and transverse momentum (pT) intervals. A multiplicity dependence of the balance function is observed in ∆η and ∆ϕ for both systems. The width of the balance functions decreases towards high-multiplicity collisions in the momentum region < 2 GeV, for pPb and PbPb results. Integrals of the balance functions are presented in both systems, and a mild dependence of the charge-balancing fractions on multiplicity is observed. No multiplicity dependence is observed at higher transverse momentum. The data are compared with hydjet, hijing, and ampt generator predictions, none of which capture completely the multiplicity dependence seen in the data. The comparison of results with different center-of-mass energies suggests that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.

Adaptive passive fault tolerant control of DFIG-based wind turbine using a self-tuning fractional integral sliding mode control

Controlling variable wind speed turbine (VWT) system based on a doubly-fed induction generator (DFIG) is a challenging task. It requires a control law that is both adaptable and robust enough to handle the complex dynamics of the closed control loop system. Sliding mode control (SMC) is a robust control technology that has shown good performance when employed as a passive fault-tolerant control for wind energy systems. To improve the closed control loop of VWT based on DFIG with the aim of improving energy efficiency, even in presence of nonlinearities and a certain range of bounded parametric uncertainties, whether electrically or mechanically, an adaptive passive fault tolerant control (AP-FTC) based on a self-tuning fractional integral sliding mode control law (ST-FISMC) developed from a novel hyperbolic fractional surface is proposed in this paper. ST-FISMC introduces a nonlinear hyperbolic function into the sliding manifold for self-tuning adaptation of control law, while fractional integral of the control law smooths discontinuous sign function to reduce chattering. Additionally, this work introduces an adaptive observer, developed and proved based on a chosen Lyapunov function. This observer is designed to estimate variations in electrical parameters and stator flux, ensuring sensorless decoupling in indirect field- oriented control (SI-FOC) of DFIG. Lyapunov theory is also used to prove stability of states vectors in closed control loop with presence of bounded parameters uncertainties or external disturbances. Simulation results show that the proposed approach offers better performance in capturing optimal wind energy, as well as the ability to regulate active/reactive power and high resilience in presence of occurring parameter uncertainties or external disturbances.

Can you hear the Planck mass?

For the Laplacian of an n-Riemannian manifold X, the Weyl law states that the k-th eigenvalue is asymptotically proportional to (k/V)2/n, where V is the volume of X. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification on X behaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion on X is ergodic, for large k the eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volume V, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we call weighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only for p = 6, 7, 8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory.

Propagation properties of the partially coherent radially polarized twisted beam through optical system in turbulence atmosphere

In this paper, the transmission properties of the partially coherent radially polarized twisted (PCRPT) beam propagating in the turbulence atmosphere are investigated. The analytical formulas for the components of the cross-spectral density matrix for the PCRPT beam passing through the optical system in the turbulent atmosphere are developed using the Collins integral and aperture function. Research results indicate that modifying the variable parameters and dimensions of the optical system can control the near-field and far-field distributions of the beam, while providing a more flexible choice of receivers for the PCRPT beam in the receiving plane. By utilizing the Cassegrain reflector system and adjusting the optical system parameters, it is possible to achieve collimated transmission of the PCRPT beam and significantly enhance the beam transmission efficiency in turbulent atmospheric conditions. The derivation process and the research results presented in this paper can be expanded to analyze the application of optical systems to control high-dimensional beam field variations. The envisioned utilization of the results obtained from this research investigation pertains to the fields of beam shaping and optical communications.

Acceleration Slip Regulation Control Method for Distributed Electric Drive Vehicles under Icy and Snowy Road Conditions

To achieve a rapid and stable dynamic response of the drive anti-slip system for distributed electric vehicles on low-friction surfaces, this paper proposes an adaptive acceleration slip regulation control strategy based on wheel slip rate. An attachment coefficient fusion estimation algorithm based on an improved singular value decomposition unscented Kalman filter is designed. This algorithm combines Sage–Husa with the unscented Kalman filter for adaptive improvement, allowing for the quick and accurate determination of the road friction coefficient and, subsequently, the optimal slip rate. Additionally, a slip rate control strategy based on dynamic adaptive compensation sliding mode control is designed, which introduces a dynamic weight integral function into the control rate to adaptively adjust the integral effect based on errors, with its stability proven. To verify the performance of the road estimator and slip rate controller, a model is built with vehicle simulation software, and simulations are conducted. The results show that under icy and snowy road conditions, the designed estimator can reduce estimation errors and respond rapidly to sudden changes. Compared to traditional equivalent controllers, the designed controller can effectively reduce chattering, decrease overshoot, and shorten response time. Especially during road transitions, the designed controller demonstrates better dynamic performance and stability.

Integral of Continuous Three Variable Functions

Summary In this article we continue our proofs on integrals of continuous functions of three variables in Mizar. In fact, we use similar techniques as in the case of two variables: we deal with projections of continuous function, the continuity of three variable functions in general, aiming at pure real-valued functions (not necessarily extended real-valued functions), concluding with integrability and iterated integrals of continuous functions of three variables.

Determination of the probabilistic content of organic fertilizer fractions after exposure to arch-destroying and crushing agrotechnological devices

Abstract Achieving stable and uniform dosing of organic fertilizers during local application necessitates the crushing of large lumps to a specific size range. The process of breaking down these lumps follows a random distribution. By leveraging the integral function of the normal distribution of random variables intertwined with principles of probability theory, equations are formulated to ascertain the distribution of lump sizes within organic fertilizers. Furthermore, these equations enable the calculation of the likelihood of obtaining lumps of specified sizes post the interaction of the vault-breaker-shredder’s fingers with counter-cutting ribs on the fertilizer. This analytical approach provides a systematic method to optimize the sizing and distribution of organic fertilizer particles for enhanced application efficiency and effectiveness.

Consumer heterogeneity and inefficiency in oligopoly markets

Motivated by several recent studies on oligopolistic markets with consumer heterogeneity, we characterize the geometric properties of a class of inequalities involving the product of two integrals of the probability density quantile function and its reciprocal. Through three applications, we illustrate how our characterization can help enrich our understanding of the existing findings and shed some new insights, regarding the extent to which consumer welfare and social efficiency depend on the properties of the distributions of consumer valuation heterogeneity.

An experimental and theoretical investigation on the hyper-viscoelasticity of polyamide 12 produced by selective laser sintering.

Polyamide 12 (PA12) is vastly utilized in many additive manufacturing methods, such as Selective Laser Sintering (SLS), and a better understanding of its mechanical behaviors promotes available knowledge on the behaviors of 3D-printed parts made from this polymer. In this paper, SLS-produced standard tensile specimens are studied under monotonic and cyclic tension tests, as well as stress relaxation experiments, and the obtained force-displacement responses are shown to be consistent with a hyper-viscoelastic material model. This finding is also observed in typical pantographic structures produced by the same manufacturing parameters. To propose a constitutive model for predicting these behaviors, the convolution integral of a strain-dependent function and a time-dependent function is developed where the material parameters are determined with the use of both short-term and long-term responses of the specimens. Numerical results of the presented model for standard test specimens are shown to be in good agreements with the experimental ones under various loading conditions. To prove the capabilities of the proposed model in studying any SLS-produced part, finite element implementation of the constitutive equations is shown to provide numerical results in agreement with the empirical findings for tensile loading of the 3D-printed pantographic structure.