Contraction Properties Research Articles

On the contraction properties for weak solutions to linear elliptic equations with 𝐿²-drifts of negative divergence

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with L 2 L^2 -drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the L r L^r -contraction properties of the unique weak solutions. Indeed, using the Dirichlet form theory, we construct a sub-Markovian C 0 C_0 -resolvent of contractions and identify it to the weak solutions. Furthermore, we derive an L 1 L^1 -stability result through an extended version of the L 1 L^1 -contraction property.

Legal Dogmatic Questions about the Impact of the European Union’s Digital Legislation on Hungarian Contract Law

The complexity and flexibility of contract law, and its ability to meet various social, economic and technical-technological needs, are indicated by a number of theories (approaches) that offer a new approach to the processing of contracts. Among the predominant theories one might include the following: overview of contracts from a constitutional and human rights approach2; deriving from this the contracts related to private and family life (intimate contracts)3; by connecting the concepts of contract law and property rights, exploring the specific characteristics of existing contracts4; filling the term "digital contract type" with content5; classification of different kinds of interconnection of contracts (complex contracts).6 The author dedicates the study to the topic of whether Hungarian contract law can meet the challenges created by digitalization, which have not yet been identified in all its details, and what are the critical points that require consideration and action as soon as possible. After the summary of the digital legislation of the European Union the author identifies the effects of digitalization in relation to the Hungarian contract law and the special contracts resulting from digitalization. Finally, the author makes de lege lata and de lege ferenda conclusions in light of this topic.

Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations

In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous magnetohydrodynamic equations. We first show how to specifically apply variational calculus in the quaternionic setting. To this end we explain how the mountain pass theorem can be successfully applied to guarantee the existence of (weak) solutions. To achieve this, the quaternionic integral operator calculus serves as a key ingredient allowing us to apply Schauder’s fixed point theorem. The advantage of the approach using Schauder’s fixed point theorem is that it is also applicable to large data since it does not require any kind of contraction property. These considerations will allow us to provide explicit iterative algorithms for its numerical solution. Finally to obtain more precise a-priori estimates one can use in the situations dealing with small data the Banach fixed point theorem which then also grants the uniqueness.

Foldaxane-Based Switchable [c2]Daisy Chains.

Artificial molecular muscles are highly attractive in the field of molecular machinery due to their unique properties of contraction and stretching motion. However, the synthesis of molecular muscles poses formidable challenges as it is hindered by undesirable yields and poor selectivity. Herein, we present a procedure for the dynamic assembly of foldaxane-based [c2]daisy chains, wherein the hermaphroditic sequences consisting of aromatic helices and peptide rods are interlocked through inter-strand hydrogen-bonding interactions. The binding complementarity facilitates a selective and efficient assembly of [c2]daisy chain structures, inhibiting the creation of by-products. Introducing multiple recognition sites confers the system with contraction and stretching motion actuated by chemical stimuli. The rate of this muscle-like motion is calculated to be 0.8 s-1, which is 107 times faster than that of complex dissociation.

Foldaxane‐Based Switchable [c2]Daisy Chains

AbstractArtificial molecular muscles are highly attractive in the field of molecular machinery due to their unique properties of contraction and stretching motion. However, the synthesis of molecular muscles poses formidable challenges as it is hindered by undesirable yields and poor selectivity. Herein, we present a procedure for the dynamic assembly of foldaxane‐based [c2]daisy chains, wherein the hermaphroditic sequences consisting of aromatic helices and peptide rods are interlocked through inter‐strand hydrogen‐bonding interactions. The binding complementarity facilitates a selective and efficient assembly of [c2]daisy chain structures, inhibiting the creation of by‐products. Introducing multiple recognition sites confers the system with contraction and stretching motion actuated by chemical stimuli. The rate of this muscle‐like motion is calculated to be 0.8 s−1, which is 107 times faster than that of complex dissociation.

Inflation alternative via the gravitational field of a singularity

We explore the scenario that the observable Universe emerged from the vicinity of a negative mass ring singularity, and all content of the Universe travels at the same group velocity close to the speed of light on a geodesic trajectory along the axis of rotation of the singularity. In appropriate coordinate parametrization and evaluated on the trajectory, we find that the metric tensor in the vicinity of the trajectory exhibits a conformal scale factor a(η) with contraction and subsequent expansion properties that solve the horizon problem. We then introduce a static flow of gravitating radiation along the trajectory (perturbatively with respect to the mass scale of the singularity) to model a homogeneous radiation dominated Universe. Solving the Einstein field equations with a physically motivated ansatz of metric perturbation then reveals that the effective conformal scale factor indeed grows asymptotically with the same power law as expected in a conventional radiation dominated Universe.

Optimal Dynamic Relative Performance Evaluation

ABSTRACT The theoretical prediction of a negative coefficient on positively correlated peer performance underlies much of the empirical literature on relative performance evaluation. This prediction is commonly obtained from a single period model where the variance–covariance matrix of available performance measures is exogenously restricted to be independent of the evaluee’s action. Using the dynamic approach of Holmström and Milgrom (1987), I study the properties of contracts that optimally condition an agent’s compensation both on his own performance and on how well he fares relative to a peer (group) when these restrictions are not imposed. I show that if the covariance is nonzero, the optimal contract is linear in own and peer performance as well as in their correlation. Significantly, and in line with the preponderance of the empirical evidence, in its simplest and perhaps most reasonable form, the model predicts that the expected coefficient on peer performance is exactly zero.

Evaluating the low-temperature performance of asphalt mixtures based on the contraction and relaxation properties

The thermal cracking of asphalt pavement has been the focus of research in cold regions of the world. The contraction and relaxation properties of asphalt mixtures were crucial for investigating the thermal stress of asphalt pavement based on the thermal cracking mechanism. This paper proposed a novel evaluation index for characterizing the low-temperature performance of asphalt mixtures by considering their contraction and relaxation properties. Firstly, the rank during the evaluation indexes for low-temperature performance was determined by comparative analysis of method. Secondly, the thermal contraction coefficient was used to characterize contraction properties and cumulative stress at per unit strain rate (CSSR) was used to characterize relaxation properties in this paper. According to the cumulation process of thermal stress, a novel index was constructed based on the contraction and relaxation properties. Finally, considering the correlation between the failure temperature and the novel indexes, the prediction model of low-temperature performance consistent with the order of failure temperature was established based on the multiple linear regression method. Through the standardized analysis of the prediction model, the influence of novel indexes for the low-temperature performance of asphalt mixtures under different temperature conditions was clarified. A novel evaluation index provided a theoretical basis for unifying the evaluation indexes of asphalt mixtures.

Fixed point results for almost ($ \zeta -\theta _{\rho } $)-contractions on quasi metric spaces and an application

<abstract><p>This research paper investigated fixed point results for almost ($ \zeta-\theta _{\rho } $)-contractions in the context of quasi-metric spaces. The study focused on a specific class of ($ \zeta -\theta _{\rho } $)-contractions, which exhibit a more relaxed form of contractive property than classical contractions. The research not only established the existence of fixed points under the almost ($ \zeta -\theta _{\rho } $)-contraction framework but also provided sufficient conditions for the convergence of fixed point sequences. The proposed theorems and proofs contributed to the advancement of the theory of fixed points in quasi-metric spaces, shedding light on the intricate interplay between contraction-type mappings and the underlying space's quasi-metric structure. Furthermore, an application of these results was presented, highlighting the practical significance of the established theory. The application demonstrated how the theory of almost ($ \zeta -\theta _{\rho } $)-contractions in quasi-metric spaces can be utilized to solve real-world problems.</p></abstract>

On Contractive Port-Hamiltonian Systems With State-Modulated Interconnection and Damping Matrices

In this paper, for the input-state-output class of port-Hamiltonian systems the contraction property is characterized. Recently, some results on contraction of port-Hamiltonian systems with constant interconnection and damping matrices have been published. This paper, extends these results for state-modulated interconnection and damping matrices. In this regard, the powerful method of IDA-PBC is extended for tracking designs. Controller design for under-actuated mechanical systems with non-constant mass matrices usually leads to non-constant (state-modulated) interconnection and damping matrices for the closed-loop system. Therefore, the result of this paper can be used for tracking controller design for under-actuated mechanical systems. To show the potency of proposed results, a tracking controller for cart-pole system is designed and simulated.

Les pauvres et le droit civil : essai sur la production du savoir juridique

À partir de l’analyse des sources du droit des obligations et du droit des biens, cet article examine comment les sources du droit civil, malgré la vocation universaliste de ce dernier, reflètent avant tout les enjeux juridiques vécus par les personnes morales et les personnes physiques aisées. Il propose que cette tendance s’explique principalement par des inégalités structurelles et épistémiques dans la production du savoir juridique. Effectivement, les procédés de constitution du savoir juridique, les inégalités d’accès aux tribunaux, de même que le statut social des personnes autorisées à produire les normes civilistes ainsi que le savoir sur ces normes sont des contraintes. Ces dernières façonnent considérablement le type d’enjeux, de protagonistes et de visions du monde susceptibles de percoler afin de constituer ce savoir. En découle alors une invisibilité marquée des personnes pauvres en son sein. Nous proposons ultimement une réflexion en droit civil sur les manières de mieux refléter leurs expériences en dépit des contraintes socioéconomiques et épistémiques exposées.

Automatic detection and characterization of uterine contraction using Electrohysterography

Preterm birth is the leading cause of perinatal morbidity and mortality. In clinical practice, the information of uterine contraction is an important reference for preterm delivery. The commonly used tocography method for detecting uterine contractions has low sensitivity and is not suitable for long-term measurement. The electrohysterography (EHG) can record the electrical activity of uterine muscle cells associated with contractions through electrodes on the abdomen. Therefore, this paper proposes a new automatic detection method of uterine contractions based on EHG signals. Specifically, utilizing the nonlinear property of entropy analysis, contraction and spike noise are distinguished in the complexity domain to highlight contraction activity. Then, the location of the contraction is detected by an adaptive thresholding method. Finally, the detected contractions are analyzed for pregnancy and labor. The results show that compared with the existing root mean square methods, the proposed method is less affected by spike noise, and the contraction detection rate on the Icelandic EHG database reaches 87.9%. Meanwhile, features extracted from detected contractions have significant differences between non-labor and labor categories. This demonstrates the feasibility of contraction detection by EHG signal, which can contribute to better care for high-risk pregnant women.

8-[(4-benzylpiperazin-1-yl)methyl]-3-(2-chlorophenyl)-7-hydroxy-chromen-4-one is an activator of contractile activity of intestinal smooth muscles with reversible M2 cholinomimetic properties

Background. Several pathologies (such as diabetes mellitus, Parkinson’s and Alzheimer’s diseases, multiple sclerosis, etc.) are accompanied by degeneration of cholinergic neurons, which are key regulators of the contractile function of the gastrointestinal tract walls, leading to atony and paresis. An effective strategy for normalizing the lack of contractile function of visceral SM is the use of drugs - selective agonists of muscarinic acetylcholine receptors (mAChRs) of the M2 subtype. The high similarity of the structure of the agonist-binding sites of different subtypes of mAChRs causes problems to develop selective ligands for these receptors. Nowadays, there is an urgent necessity to develop selective agonists of M2 subtype receptors as pharmacological tools for laboratory research and promising drugs. The aim of the present research was to investigate the effect of the 8-[(4-benzylpipe­razin-1-yl)methyl]-3-(2-chlorophenyl)-7-hydroxy-chromen-4-one (compound 1), which was in silico predicted to bind mAChRs, on the contractile activity of rat caecum circular smooth muscle. Materials and Methods. The research was carried out on rats. The contractile activity was studied tensometrically in the isometric mode on preparations of the circular smooth muscles of the caecum of Wistar rats. The kinetic properties of individual spontaneous contractions of SM preparations were determined in accordance with the method of multivariate mechanokinetic analysis with the calculation of mechanokinetic parameters for the phases of contraction and relaxation: time (τ0, τC and τR), force (Fmax, FC and FR), velocity (VC and VR) and impulse (Imax, IC and IR). The kinetic properties of acetylcholine-induced contractions were analyzed by calculating the normalized maximum velocities of the contraction (Vnc) and relaxation (Vnr) phases. Results. It was found that compound 1 caused an increase in the amplitude of acetylcholine-induced contractions; this effect was eliminated by preincubation of SM with the mAChRs M2 subtype inhibitor AF-DX 116. It was revealed that compound 1 (0.1–50 μM) also has the ability to significantly activate the functional activity of colonic SM in a dose-dependent manner, increasing the force and frequency of spontaneous contractions, as well as their mechanokinetic parameters. It was found that the presence of compound 1 (0.1 μM) in the solution washing the smooth muscle for a long time leads to a significant increase in the amplitude and frequency of spontaneous contractions, which tends to reach a stationary mode after 40 minutes of its action. The effect of compound 1 was stable for at least an hour of application to the caecum, and was reversible and significantly eliminated by washing the SM. Conclusions. Compound 1 stimulates the contractile activity of the cecal smooth muscle and exhibits M2 cholinergic properties.

Adaptive VEM for variable data: convergence and optimality

Abstract We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in Beirão da Veiga et al. (2023, Adaptive VEM: stabilization-free a posteriori error analysis and contraction property. SIAM J. Numer. Anal., 61, 457–494). The crucial property, which also plays a central role in this paper, is that the stabilization term can be made arbitrarily small relative to the a posteriori error estimators upon increasing the stabilization parameter. Our AVEM concatenates two modules, GALERKIN and DATA. The former deals with piecewise constant data and is shown in the above article to be a contraction between consecutive iterates. The latter approximates general data by piecewise constants to a desired accuracy. AVEM is shown to be convergent and quasi-optimal, in terms of error decay versus degrees of freedom, for solutions and data belonging to appropriate approximation classes. Numerical experiments illustrate the interplay between these two modules and provide computational evidence of optimality.

The association between human blood clot analogue computed tomography imaging, composition, contraction, and mechanical characteristics

Background Clot composition, contraction, and mechanical properties are likely determinants of endovascular thrombectomy success. A pre-interventional estimation of these properties is hypothesized to aid in selecting the most suitable treatment for different types of thrombi. Here we determined the association between the aforementioned properties and computed tomography (CT) characteristics using human blood clot analogues. Methods Clot analogues were prepared from the blood of 4 healthy human donors with 5 red blood cell (RBC) volume suspensions: 0%, 20%, 40%, 60% and 80% RBCs. Contraction was measured as the weight of the contracted clots as a percentage of the original suspension. The clots were imaged using CT with and without contrast to quantify clot density and density increase. Unconfined compression was performed to determine the high strain compressive stiffness. The RBC content was analysed using H&E staining. Results The 5 RBC suspensions formed only two groups of clots, fibrin-rich (0% RBCs) and RBC-rich (>90% RBCs), as determined by histology. The density of the fibrin-rich clots was significantly lower (31-38HU) compared to the RBC-rich clots (72-89HU), and the density increase of the fibrin-rich clots was significantly higher (82-127HU) compared to the RBC-rich clots (3-17HU). The compressive stiffness of the fibrin-rich clots was higher (178–1624 kPa) than the stiffness of the RBC-rich clots (6–526 kPa). Additionally, the degree of clot contraction was higher for the fibrin-rich clots (89–96%) compared to the RBC-rich clots (11–77%). Conclusions CT imaging clearly reflects clot RBC content and seems to be related to the clot contraction and stiffness. CT imaging might be a useful tool in predicting the thrombus characteristics. However, future studies should confirm these findings by analysing clots with intermediate RBC and platelet content.

Contracting on average iterated function systems by metric change

We study contraction conditions for an iterated function system (IFS) of continuous maps on a metric space which are chosen randomly, identically and independently. We investigate metric changes, preserving the topological structure of the space, which turn the IFS into one which is contracting on average. For the particular case of a system of C 1-diffeomorphisms of the circle which is proximal and does not have a probability measure simultaneously invariant by every map, we derive an equivalent metric which contracts on average and conclude that it carries a unique stationary probability measure. Here we strongly use local contraction properties established by Malicet in 2017, which then imply that the IFS has a negative random Lyapunov exponent and generalizes a result by Baxendale.

Contraction property of certain classes of log-[formula omitted]-subharmonic functions in the unit ball

We prove a contraction property for certain classes of smooth functions, whose absolute values of elements are log-subharmonic functions in the unit ball, thus extending the results of Kulikov to higher-dimensional space (GAFA (2022)). Moreover, by applying those results we get some new results for harmonic mappings in the complex plane.

On Contraction Analysis of Switched Systems With Mixed Contracting-Noncontracting Modes via Mode-Dependent Average Dwell Time

This paper studies contraction analysis of switched systems that are composed of a mixture of contracting and noncontracting modes. The first result pertains to the equivalence of the contraction of a switched system and the uniform global exponential stability of its variational system. Based on this equivalence property, sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive are established. Correspondingly, LMI conditions are derived that allow for numerical validation of contraction property of nonlinear switched systems, which include those with all non-contracting modes.

Comparing Parameters of Motor Potentials Recordings Evoked Transcranially with Neuroimaging Results in Patients with Incomplete Spinal Cord Injury: Assessment and Diagnostic Capabilities.

This study aimed to investigate the relationships between the different levels and degrees of incomplete spinal cord injury (iSCI) evaluated with magnetic resonance imaging (MRI) and the results of non-invasive electromyography (mcsEMG), motor-evoked potentials (MEP), and electroneurography (ENG). With a focus on patients with injuries at four different levels, C3-C5, C6-Th1, Th3-Th6, and Th7-L1, this research delved into the intricate interplay of spinal circuits and functional recovery. The study uses MEP, EMG, and ENG assessments to unveil the correlations between the MEP amplitudes and the MRI injury scores. We analysed data from 85 iSCI patients (American Spinal Injury Association-ASIA scale; ASIA C = 24, and D = 61). We compared the MRI and diagnostic neurophysiological test results performed within 1-2 months after the injury. A control group of 80 healthy volunteers was examined to establish reference values for the clinical and neurophysiological recordings. To assess the structural integrity of spinal white and grey matter on the transverse plane reconstructed from the sagittal readings, a scoring system ranging from 0 to 4 was established. The spinal cord was divided into two halves (left and right) according to the midline, and each half was further divided into two quadrants. Each quadrant was assessed separately. MEP and EMG were used to assess conduction in the corticospinal tract and the contraction properties of motor units in key muscles: abductor pollicis brevis (APB), rectus abdominis (RA), rectus femoris (RF), and extensor digitorum brevis muscles (EXT). We also used electroneurography (ENG) to assess peripheral nerve conduction and to find out whether the changes in this system significantly affect patients' scores and their neurophysiological status. The study revealed consistent positive correlations in iSCI patients between the bilateral decrease of the spinal half injury MRI scores and a decrease of the transcranially-evoked MEP amplitudes, highlighting the complex relationship between neural pathways and functional outcomes. Positive correlations are notably pronounced in the C3-C5, C6-Th1, and Th3-Th6 subgroups (mostly rs 0.5 and above with p < 0.05), while Th7-L1 presents distinct patterns (rs less than 0.5 and p being statistically insignificant) potentially influenced by unique structural compensation mechanisms. We also revealed statistically significant relationships between the decrease of the cumulative mcsEMG and MEP amplitudes and the cumulative ENG scores. These insights shed light on the multifaceted interactions between spinal cord injury levels, structural damage, neurophysiological measures, and motor function outcomes. Further research is warranted to unravel the intricate mechanisms driving these correlations and their implications for enhancing functional recovery and the rehabilitation algorithms in patients with iSCI.

Mesenchymal stem cells alleviate dexamethasone-induced muscle atrophy in mice and the involvement of ERK1/2 signalling pathway

BackgroundHigh dosage of dexamethasone (Dex) is an effective treatment for multiple diseases; however, it is often associated with severe side effects including muscle atrophy, resulting in higher risk of falls and poorer life quality of patients. Cell therapy with mesenchymal stem cells (MSCs) holds promise for regenerative medicine. In this study, we aimed to investigate the therapeutic efficacy of systemic administration of adipose-derived mesenchymal stem cells (ADSCs) in mitigating the loss of muscle mass and strength in mouse model of DEX-induced muscle atrophy.Methods3-month-old female C57BL/6 mice were treated with Dex (20 mg/kg body weight, i.p.) for 10 days to induce muscle atrophy, then subjected to intravenous injection of a single dose of ADSCs (1times {10}^{6} cells/kg body weight) or vehicle control. The mice were killed 7 days after ADSCs treatment. Body compositions were measured by animal DXA, gastrocnemius muscle was isolated for ex vivo muscle functional test, histological assessment and Western blot, while tibialis anterior muscles were isolated for RNA-sequencing and qPCR. For in vitro study, C2C12 myoblast cells were cultured under myogenic differentiation medium for 5 days following 100 muM Dex treatment with or without ADSC-conditioned medium for another 4 days. Samples were collected for qPCR analysis and Western blot analysis. Myotube morphology was measured by myosin heavy chain immunofluorescence staining.ResultsADSC treatment significantly increased body lean mass (10–20%), muscle wet weight (15–30%) and cross-sectional area (CSA) (~ 33%) in DEX-induced muscle atrophy mice model and down-regulated muscle atrophy-associated genes expression (45–65%). Hindlimb grip strength (~ 37%) and forelimb ex vivo muscle contraction property were significantly improved (~ 57%) in the treatment group. Significant increase in type I fibres (~ 77%) was found after ADSC injection. RNA-sequencing results suggested that ERK1/2 signalling pathway might be playing important role underlying the beneficial effect of ADSC treatment, which was confirmed by ERK1/2 inhibitor both in vitro and in vivo.ConclusionsADSCs restore the pathogenesis of Dex-induced muscle atrophy with an increased number of type I fibres, stronger muscle strength, faster recovery rate and more anti-fatigue ability via ERK1/2 signalling pathway. The inhibition of muscle atrophy-associated genes by ADSCs offered this treatment as an intervention option for muscle-associated diseases. Taken together, our findings suggested that adipose-derived mesenchymal stem cell therapy could be a new treatment option for patient with Dex-induced muscle atrophy.