Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs.

Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.

There is ample psycholinguistic evidence that speakers behave efficiently, using shorter and less effortful constructions when the meaning is more predictable, and longer and more effortful ones when it is less predictable. However, the Principle of No Synonymy requires that all formally distinct variants should also be functionally different. The question is how much two related constructions should overlap semantically and pragmatically in order to be used for the purposes of efficient communication. The case study focuses on want to + Infinitive and its reduced variant with wanna, which have different stylistic and sociolinguistic connotations. Bayesian mixed-effects regression modelling based on the spoken part of the British National Corpus reveals a very limited effect of efficiency: predictability increases the chances of the reduced variant only in fast speech. We conclude that efficient use of more and less effortful variants is restricted when two variants are associated with different registers or styles. This paper also pursues a methodological goal regarding missing values in speech corpora. We impute missing data based on the existing values. A comparison of regression models with and without imputed values reveals similar tendencies. This means that imputation is useful for dealing with missing values in corpora.

We prove the existence of common fixed points for monotone contractive and monotone nonexpansive semigroups of nonlinear mappings acting in Banach spaces equipped with partial order. We also discuss some applications to differential equations and dynamical systems.

In this paper we investigate gradient estimation for a class of contracting stochastic systems on a continuous state space. We find conditions on the one-step transitions, namely differentiability and contraction in a Wasserstein distance, that guarantee differentiability of stationary costs. Then we show how to estimate the derivatives, deriving an estimator that can be seen as a generalization of the forward sensitivity analysis method used in deterministic systems. We apply the results to examples, including a neural network model.

In 1968 Emmerick proposed the existence of a present stem type D. It is shown here from morphophonological patterning that his category contains two subtypes, temporarily labelled D1 and D2. By comparing vocalic contractions from the nominals with the D1 endings, it is clear that the D1 stems end synchronically in -a- and take the regular type A endings. The D2 stem vowel in contrast, behaves partly like nominal stems in -a-, and partly like stems in -i-. By reviewing contraction evidence relating to all vowels, it is shown that the D2 stems end synchronically, albeit abstractly, in -e- and take the regular type A endings. Two further verbs from Emmerick's type C are shown also to end in -e- and take the regular endings.

In this paper we prove Caristi’s fixed point theorem using only purely metric techniques.

Background: Short- (SICI) and long-interval intracortical inhibition (LICI) are involved in the control of movement and movement initiation. Alterations to the two circuits can result in direct alterations to the physiology of the muscles and can be used to explain the physiological changes to individuals with spinal cord injury (SCI). Objective: To probe changes in GABAergic function by characterizing the recruitment curves of SICI and LICI interval intracortical inhibition in an upper limb muscle in chronic SCI participants with injury between C3 and C7. Methods: Recruitment curves were elicited with conditioning stimulus intensities determined as a percentage of active motor threshold (AMT) (SICI, 60% to 110% AMT; LICI, 90% to 130% AMT) and recorded from the flexor carpi radialis muscle during an isometric contraction equal to 15% to 20% of maximum voluntary contraction. Results: AMT was greater and motor-evoked potential sizes were lower in SCI compared with uninjured controls. SICI magnitude was not different between groups, although the range of conditioning stimulus intensities to evoke SICI was unique to each group. LICI was reduced in the control group during active contraction and remained present in SCI. Discussion: LICI was increased in the actively contracted flexor carpi radialis muscle in individuals with SCI compared with age-matched controls. These findings indicate that GABAB function mediating LICI is different in SCI versus controls. Conclusions: Increased LICI in SCI may be attributed to the medication baclofen or to changes in the neural mechanisms controlling contraction-related modulation of the LICI circuit.

In this article, we prove convergence of the weakly penalized adaptive discontinuousGalerkin methods. Unlike other works, we derive the contraction property for variousdiscontinuous Galerkin methods only assuming the stabilizing parameters are large enoughto stabilize the method. A central idea in the analysis is to construct an auxiliarysolution from the discontinuous Galerkin solution by a simple post processing. Based onthe auxiliary solution, we define the adaptive algorithm which guides to the convergenceof adaptive discontinuous Galerkin methods.

Let $T$ be a contraction on a complex, separable, infinite dimensional Hilbert space and let $\sigma (T)\,(\text{resp}\text{.}\,{{\sigma }_{e}}(T))$ be its spectrum (resp. essential spectrum). We assume that $T$ is an essentially isometric operator; that is, ${{I}_{H}}\,-\,T*T$ is compact. We show that if $D\backslash \sigma (T)\,\ne \,\varnothing $, then for every $f$ from the disc-algebra

$${{\sigma }_{e}}\left( f\left( T \right) \right)\,=\,f\left( {{\sigma }_{e}}\left( T \right) \right),$$

where $D$ is the open unit disc. In addition, if $T$ lies in the class ${{C}_{0}}.\,\bigcup \,C{{.}_{0}}$, then

$${{\sigma }_{e}}\left( f\left( T \right) \right)\,=\,f\left( \sigma \left( T \right)\,\bigcap \,\Gamma \right),$$

where $\Gamma $ is the unit circle. Some related problems are also discussed.

The mechanism of anthelmintic resistance against the widely used macrocyclic lactones (MLs) is still not fully understood. Pharyngeal, somatic body muscles and the ovijector have been proposed as putative sites of action as well as resistance. In the present study the effects of three avermectins and three milbemycins on adult parasitic nematodes were evaluated in vitro. The Muscle Transducer system was used to investigate the effects of MLs on muscle contraction in female Haemonchus contortus and effects on motility were measured in Ostertagia (Teladorsagia) circumcincta using the Micromotility Meter. Concentration-response curves for all substances in both systems shifted to the right in the resistant isolates. Resistance was present to ivermectin (IVM) and its components IVM B1a and IVM B1b, suggesting that both components are involved in the mode of action and resistance. No consistent patterns of potency and resistance of the substances were observed except that milbemycins generally showed lower resistance ratios (RRs) than IVM. IVM and IVM B1b were the most potent inhibitors of contraction and motility in both susceptible isolates and also showed the highest RR in both species. Low RRs for milbemycins recorded in vitro for highly resistant isolates in vivo suggest that other factors such as pharmacokinetics influence drug potency in vivo.

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a prioriL∞ estimates. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEMalgorithmis also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.

We study the problem of breakup of an air bubble in a Hele-Shaw cell. In particular, we propose some sufficient conditions of breakup of the bubble, and ways to find the contraction points of its parts. We also study regulated contraction of a pair of bubbles (in which the rates of air extraction from the bubbles are controlled) and study various asymptotic questions (such as the asymptotics of contraction of a bubble to a degenerate critical point, and asymptotics of contraction of a small bubble in the presence of a big bubble)

We give an explicit Krasnoselski–Mann type method for finding common solutions of the following system of equilibrium and hierarchical fixed points: where C is a closed convex subset of a Hilbert space H, G:C×C→ℝ is an equilibrium function, T:C→C is a nonexpansive mapping with Fix(T) its set of fixed points and f:C→C is a ρ-contraction. Our algorithm is constructed and proved using the idea of the paper of [Y. Yao and Y.-C. Liou, ‘Weak and strong convergence of Krasnosel’skiĭ–Mann iteration for hierarchical fixed point problems’, Inverse Problems24 (2008), 501–508], in which only the variational inequality problem of finding hierarchically a fixed point of a nonexpansive mapping T with respect to a ρ-contraction f was considered. The paper follows the lines of research of corresponding results of Moudafi and Théra.

As the amphibian oocyte becomes the fertilisation-competent egg an actin-myosin assembles in the cortex which provides for the cortical contraction that accompanies the fertilisation. A number of recent investigations provide data for development of a model detailing the structural changes which should accompany the development of this contractile network as well as the signalling mechanisms which regular assembly and contraction.