Constant Extensions Research Articles

General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

Ранги, спектры и их динамика для семейств константных обогащений теорий

Constant or nonessential extensions of elementary theories provide a productive tool for the study and structural description of models of these theories, which is widely used in Model Theory and its applications, both for various stable and ordered theories, countable and uncountable theories, algebraic, geometric and relational structures and theories. Families of constants are used in Henkin’s classical construction of model building for consistent families of formulas, for the classification of uncountable and countable models of complete theories, and for some dynamic possibilities of countable spectra of ordered Ehrenfeucht theories. The paper describes the possibilities of ranks and degrees for families of constant extensions of theories. Rank links are established for families of theories with CantorBendixson ranks for given theories. It is shown that the 𝑒-minimality of a family of constant expansions of the theory is equivalent to the existence and uniqueness of a nonprincipal type with a given number of variables. In particular, for strongly minimal theories this means that the non-principal 1-type is unique over an appropriate tuple. Relations between 𝑒-spectra of families of constant expansions of theories and ranks and degrees are established. A model-theoretic characterization of the existence of the least generating set is obtained. It is also proved that any inessential finite expansion of an o-minimal Ehrenfeucht theory preserves the Ehrenfeucht property, and this is true for constant expansions of dense spherically ordered theories. For the expansions under consideration, the dynamics of the values of countable spectra is described.

Convergence Analysis and Numerical Studies for Linearly Elastic Peridynamics with Dirichlet-Type Boundary Conditions

The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the body. Therefore, theoretical and numerical challenges arise in order to properly formulate Dirichlet-type nonlocal boundary conditions, while connecting them to the local counterparts. While a careless imposition of local boundary conditions leads to a smaller effective material stiffness close to the boundary and an artificial softening of the material, several strategies were proposed to avoid this unphysical surface effect. In this work, we study convergence of solutions to nonlocal state-based linear elastic model to their local counterparts as the interaction horizon vanishes, under different formulations and smoothness assumptions for nonlocal Dirichlet-type boundary conditions. Our results provide explicit rates of convergence that are sensitive to the compatibility of the nonlocal boundary data and the extension of the solution for the local model. In particular, under appropriate assumptions, constant extensions yield \(\frac{1}{2}\) order convergence rates and linear extensions yield \(\frac{3}{2}\) order convergence rates. With smooth extensions, these rates are improved to quadratic convergence. We illustrate the theory for any dimension \(d\ge 2\) and numerically verify the convergence rates with a number of two-dimensional benchmarks, including linear patch tests, manufactured solutions, and domains with curvilinear surfaces. Numerical results show a first-order convergence for constant extensions and second-order convergence for linear extensions, which suggests a possible room of improvement in the future convergence analysis.

Recovering algebraic curves from L-functions of Hilbert class fields

In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its constant field extensions. As a consequence, we give a new proof of a result of Mochizuki and Tamagawa that two such curves with isomorphic fundamental groups are themselves isomorphic.

Toward a standard ontology of surgical process models.

The development of common ontologies has recently been identified as one of the key challenges in the emerging field of surgical data science (SDS). However, past and existing initiatives in the domain of surgery have mainly been focussing on individual groups and failed to achieve widespread international acceptance by the research community. To address this challenge, the authors of this paper launched a European initiative-OntoSPM Collaborative Action-with the goal of establishing a framework for joint development of ontologies in the field of SDS. This manuscript summarizes the goals and the current status of the international initiative. A workshop was organized in 2016, gathering the main European research groups having experience in developing and using ontologies in this domain. It led to the conclusion that a common ontology for surgical process models (SPM) was absolutely needed, and that the existing OntoSPM ontology could provide a good starting point toward the collaborative design and promotion of common, standard ontologies on SPM. The workshop led to the OntoSPM Collaborative Action-launched in mid-2016-with the objective to develop, maintain and promote the use of common ontologies of SPM relevant to the whole domain of SDS. The fundamental concept, the architecture, the management and curation of the common ontology have been established, making it ready for wider public use. The OntoSPM Collaborative Action has been in operation for 24months, with a growing dedicated membership. Its main result is a modular ontology, undergoing constant updates and extensions, based on the experts' suggestions. It remains an open collaborative action, which always welcomes new contributors and applications.

Changes in electromechanical delay during fatiguing dynamic muscle actions.

The onsets of the electromyographic (EMG) signal, mechanomyographic (MMG) signal, and force production were used to identify voluntary electromechanical delay (EMD) during maximal and submaximal leg extensions. Twelve men performed 30% 1-repetition-maximum concentric, dynamic constant external resistance leg extensions to failure. The time periods for the onsets of EMG to MMG (EMDE-M ), MMG to force (EMDM-F ), and EMG to force (EMDE-F ) were assessed before, during, and after testing. Pretest vs. posttest assessments indicated approximately equal contributions from excitation-contraction coupling (EMDE-M ) and series elastic component (EMDM-F ) to the overall EMDE-F . During the workbout, excitation-contraction coupling failure and increases in the compliance of the series elastic component began at 40% and 30% of the repetitions to failure, respectively, and continued to failure. Increases in the series elastic component (EMDM-F ) began to affect EMDE-F before excitation-contraction coupling failure (EMDE-M ), and both contributed to EMDE-F throughout the remainder of the fatiguing workbout. Muscle Nerve 56: 315-320, 2017.

Time Course of Changes in Neuromuscular Responses at 30% versus 70% 1 Repetition Maximum during Dynamic Constant External Resistance Leg Extensions to Failure

Time Course of Changes in Neuromuscular Responses at 30% versus 70% 1 Repetition Maximum during Dynamic Constant External Resistance Leg Extensions to Failure

Effect of neuromuscular electrical stimulation on motor cortex excitability upon release of tonic muscle contraction

The aim of the present study was to investigate the neurophysiological triggers underlying muscle relaxation from the contracted state, and to examine the mechanisms involved in this process and their subsequent modification by neuromuscular electrical stimulation (NMES). Single-pulse transcranial magnetic stimulation (TMS) was used to produce motor-evoked potentials (MEPs) and short-interval intracortical inhibition (SICI) in 23 healthy participants, wherein motor cortex excitability was examined at the onset of voluntary muscle relaxation following a period of voluntary tonic muscle contraction. In addition, the effects of afferent input on motor cortex excitability, as produced by NMES during muscle contraction, were examined. In particular, two NMES intensities were used for analysis: 1.2 times the sensory threshold and 1.2 times the motor threshold (MT). Participants were directed to execute constant wrist extensions and to release muscle contraction in response to an auditory “GO” signal. MEPs were recorded from the flexor carpi radialis (FCR) and extensor carpi radialis (ECR) muscles, and TMS was applied at three different time intervals (30, 60, and 90 ms) after the “GO” signal. Motor cortex excitability was greater during voluntary ECR and FCR relaxation using high-intensity NMES, and relaxation time was decreased. Each parameter differed significantly between 30 and 60 ms. Moreover, in both muscles, SICI was larger in the presence than in the absence of NMES. Therefore, the present findings suggest that terminating a muscle contraction triggers transient neurophysiological mechanisms that facilitate the NMES-induced modulation of cortical motor excitability in the period prior to muscle relaxation. High-intensity NMES might facilitate motor cortical excitability as a function of increased inhibitory intracortical activity, and therefore serve as a transient trigger for the relaxation of prime mover muscles in a therapeutic context.

Will Publons Popularize the Scientific Peer-Review Process?

Will Publons Popularize the Scientific Peer-Review Process?

Transparency in agency: The constant elasticity case and extensions

This paper considers a hidden action agency problem where the principal has a single source of hidden information concerning the agent's utility, the agent's effort productivity, or the agent's cost of effort. We examine whether the principal should precommit to disclosing these different single sources of information to the agent. If the optimal contract is invariant over the hidden information and, thus, the disclosure rules (constant elasticity case), such disclosure increases the agent's utility, it can raise or lower profit and total surplus depending on the source of hidden information, and non-disclosure can be optimal if disclosure affects the agent's motivation. If the contract varies with the hidden information and, thus, disclosure rule, disclosure or non-disclosure can be optimal depending on whether the party's payoff is convex or concave in the information variable, respectively.

ON THE RELATIVE ZETA FUNCTION IN FUNCTION FIELDS

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

Fatigue crack growth and closure behaviour under multiaxial loading

The three dimensional finite- element analysis of fatigue crack growth and closure was used to investigate crack- opening and closure stresses of elastic-perfectly plastic Aluminium 2024 alloy under constant amplitude crack extensions.. The 3D analysis was applied to the middle-crack specimen with a specified thickness value under multiaxial and uniaxial loadings. Then, crackopening and closure stresses and the v-displacements of nodes on the crack surface plane for both multiaxial and uniaxial cases were investigated.The finite element analysis was developed using isoparametric eight nodded hexahedron elements. The plasticity part of the program uses initial stress approach. In the analysis, the crack was advanced one element size as the applied load reached the maximum Value of each load cycle.

A Note on Optimal Towers over Finite Fields

Recently, under the influence of Elkies' conjecture [2], the optimal recursive towers of algebraic function fields (of one variable) over the finite fields with square cardinality are studied [3, 5, 6]. In this paper, we define the limit $$ \lim_{i \to \infty} \text{(the number of places of degree $n$ in $F_{i}/\mathbf{F}_{q}$)/(genus of $F_{i}$)} $$ of a tower $F_{0} \subseteq F_{1} \subseteq F_{2} \subseteq \cdots$ over the finite field $\F_{q}$. Using this limit, we prove that all the proper constant field extensions of all the optimal towers over the finite fields with square cardinality are not optimal, and we show a simple criterion whether a tower is optimal or not. Moreover, we give many new recursive towers of finite ramification type.

Multijoint reflexes of the stroke arm: Neural coupling of the elbow and shoulder

The reflex torque responses of the elbow and shoulder to constant velocity angular extensions of the full comfortable range of the spastic elbow were measured in 16 people with unilateral stroke and 6 neurologically intact controls in order to identify the interjoint reflex coupling that occurs after stroke. The resulting responses showed a substantial reflex torque at the elbow and shoulder in subjects with stroke, with 12 of the 16 subjects producing adduction of the shoulder in response to passive extension of the elbow. The presence of simultaneous shoulder flexion torque with elbow flexion torque and with an identical waveform indicated an active role of biarticular elbow/shoulder flexors, such as the biceps. As the biceps muscle produces a shoulder abduction moment, shoulder adduction produced during elbow extension was thought to be associated with neural rather than biomechanical coupling. These results suggest that spasticity in people with stroke is more complex than its traditional perception as a hyperexcitable stretch reflex, and includes potent heteronymous reflex pathways. The reflex coupling observed between the shoulder and elbow should be considered in the diagnosis and clinical management of spasticity. The potential impact of this reflex on the coordination of volitional arm movements will be examined in future studies.

Process modeling of composites by resin transfer molding

PurposeThe purpose of the present paper is to describe the modeling, analysis and simulations for the resin transfer molding (RTM), manufacturing process with particular emphasis on the sensitivity analysis for non‐isothermal applications.Design/methodology/approachFor the manufacturing of advanced composites via RTM, besides the tracking of the resin flow fronts through a porous fiber perform, the heat transfer and the resin cure kinetics play an important role. The computational modeling is coupled multi‐disciplinary problem of flow‐thermal‐cure. The paper describes the so‐called continuous sensitivity formulation via the finite element method for this multi‐disciplinary problem for process modeling of composites manufactured by RTM to predict, analyze and optimize the manufacturing process.FindingsIllustrative numerical examples are presented for two sample problems which include examination of sensitivity parameters for the case of material and geometric properties, and boundary conditions including fill time sensitivity analysis. The results indicate that the proposed formulations serve a useful role for the design and optimization of the RTM manufacturing process, thereby, avoiding heuristic trial‐and‐error methods.Research limitations/implicationsThe paper restricts attention to constant properties and extensions to non‐linear thermophysical properties will serve as an added benefit.Practical implicationsThe present efforts significantly impact the design/optimization process in the process modeling of composites manufactured by RTM.Originality/valueTo the authors' knowledge, this is the first time that continuous sensitivity analysis is done for non‐isothermal considerations in RTM.

Linear spring-damper model of the hypertonic elbow: reliability and validity

Hypertonia of the elbow joint complex is common in individuals with stroke and is related to the magnitude of the torque response (described by position dependent parameters) during constant velocity extensions. The objective of this study was to model position and velocity dependent characteristics of hypertonia. For both the more and less affected arms in 17 persons with chronic stroke, we measured the torque response to constant velocity stretches (30–180°/s). The responses were combined in position–velocity space and parameters of stiffness, damping, and offset angle were determined from a linear spring-damper model of the torque profile. The model was assessed at three levels: (1) ability to describe the combined torque profile variance, (2) reliability of parameters, and (3) validity of parameters (i.e. clinical correlation). Model parameters fit the torque profiles of both arm groups well and exhibited day-to-day reliability. Stiffness (r=0.820), damping (r=0.816), and ‘viscoelasticity’ (r=0.909), a composite parameter index developed posthoc, were highly correlated to a manual assessment of hypertonia (Modified Ashworth Scale). Mechanically determined parameters of hypertonia graded along a continuum may have better discriminatory power than manual assessments and thus, may be better at tracking recovery and evaluating interventions.

Effect of the rate of deformation on the crystallization behavior of polymers

Deformation has a significant influence on the crystallization process in a number of polymers. In this paper, the response of a recently developed model for crystallizing polymers is investigated when subject to uni-, bi-axial and constant width extensions for a range of strain rates. Both the loading and unloading behavior are examined for these deformations. The particular model studied here was developed to capture the effect of strain induced crystallization in polymers and has been applied to model crystallization in polyethylene terephthalate at temperatures just above its glass transition temperature. The model has been formulated using the notion of multiple natural configurations within a full thermodynamic framework. The connection between micro-structural changes taking place in the polymer and the form of the model are elucidated. The interplay between the relaxation processes, the rate of deformation and their combined effect on crystallization is illustrated. The results show an earlier onset of crystallization for high strain rates due to stretching of the polymer network. At low strain rates however, crystallization is not observed as the polymer network is able to relax during the deformation. A sharp upturn in the stress is observed after the onset of crystallization due to the formation of a rigid crystalline phase. The unloading curves clearly show a hysteric behavior with the amount of dissipation increasing for increasing values of strain rate. These results compare favorably with experimental observations available in literature.

Improved Bounds for Laue's Constant and Multivariate Extensions

Denote by 𝒫 the class of probability density functions on ℝ with a nonnegative and integrable characteristic function. For each p ∈ 𝒫, there exists an adjoint density , which is proportional to the characteristic function of p. The products λ(p) = Var(p) Var() have a greatest lower bound Λ known as Laue's constant. In this paper we improve the previous estimates of Λ, proving that 0.543 < 0.85024. Further results and related estimates are also obtained for a multivariate version of the uncertainty relation which is based on univariate projections.

On a Refined Stark Conjecture for Function Fields

We prove that a refinement of Stark's Conjecture formulated by Rubin in Ann. Inst Fourier 4 (1996) is true up to primes dividing the order of the Galois group, for finite, Abelian extensions of function fields over finite fields. We also show that in the case of constant field extensions, a statement stronger than Rubin's holds true.

Mechanical properties of human tendon and their age dependence.

There are no previously published data on changes in the mechanical behaviors of human tendon from maturation in the second decade to senectitude in the seventh decade or thereafter. In this study, 44 tendons from individuals ranging in age from 16 to 88 yr were subjected to an extensive series of mechanical tests which included preconditioning, extensions at strain rates of 100 percent/s, 1 percent/s, and 0.01 percent/s, and stress relaxation with cyclic and constant extensions. Pairs of extensions at 1 percent/s were run throughout the protocol to evaluate the repeatability of tissue response. It was found that these responses changed little for any single sample within a pair of such tests; however, throughout the protocol, the peak stresses and moduli decreased. Extensions at different rates revealed a definite rate dependency of tendon responses with sample modulus being directly related to extension rate and slightly less hysteresis at 1 percent/s than at 100 percent/s or 0.01 percent/s. The load relaxation in samples subjected to either cyclic or constant extensions was generally best described by a linear function of the logarithm of time. The rate of relaxation with constant extension varied little with extension magnitude. The rate of relaxation in the cyclic tests was greater at 10 Hz than at 0.1 Hz. The results indicate that subject age has no effect on tendon modulus and a very small effect on hysteresis and relaxation. Extensive information on subject history was not available in this study for correlation with mechanical responses so that an age effect may have been masked by other variables, possibly health, diet, disease, or exercise.