Ball Condition Research Articles

Weak solutions of anisotropic (and crystalline) inverse mean curvature flow as limits of p-capacitary potentials

We construct weak solutions of the anisotropic inverse mean curvature flow (A-IMCF) under very mild assumptions both on the anisotropy (which is simply a norm in RN with no ellipticity nor smoothness requirements, in order to include the crystalline case) and on the initial data. By means of an approximation procedure introduced by Moser, our solutions are limits of anisotropic p-harmonic functions or p-capacitary functions (after a change of variable), and we get uniqueness both for the approximating solutions (i.e., uniqueness of p-capacitary functions) and the limiting ones. Our notion of weak solution still recovers variational and geometric definitions similar to those introduced by Huisken-Ilmanen, but requires to work within the broader setting of BV-functions. Despite of this, we still reach classical results like the continuity and exponential growth of perimeter, as well as outward minimizing properties of the sublevel sets. Moreover, by assuming the extra regularity given by an interior rolling ball condition (where a sliding Wulff shape plays the role of a ball), the solutions are shown to be continuous and satisfy Harnack inequalities. Finally, examples of explicit solutions are built.

Adjustment of segmental rotations to achieve both racket speed and accuracy at various impact heights during a two-handed backhand stroke

ABSTRACT This study investigated the influence of impact height and competitive level on racket speed and stroke accuracy by analysing segmental angular kinematics under a random ball condition. High- (HQ, n = 7) and low-quality (LQ, n = 7) groups were determined by k-means clustering of the ratio of ball landing in the target (accuracy) and racket speed decrease. HQ showed higher accuracy (48.3% vs. 32.4%), less speed decrease at lower impact heights (−4.4% vs. −10.3%) and better competitive level ranking [median (1st–3rd quartiles); 4 (2–7)] than LQ [10 (8–13)]. HQ produced greater racket speed (24.4 vs. 21.6 m/s), especially with a notable horizontal velocity (23.8 vs. 20.8 m/s) of the racket at lower impact height, which was attributed to the central role of greater angular velocity of pelvis and thorax in the hitting direction. Both groups showed similar adjustment mechanisms that due to the decrease in angular velocity of pelvis, players increased the relative rotation angle between pelvis and thorax to maintain angular velocity of thorax when transitioning from low to high impact heights. Our findings suggest that players should emphasise the coordination between pelvic and thoracic rotations according to impact heights to maintain racket speed while controlling ball landing position.

Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition

In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of C1,1-regular domains satisfying a uniform ball condition as long as the desired objective function satisfies certain properties. We then verify that the helicity isoperimetric problem studied in [Cantarella et al., J. Math. Phys. 41, 5615 (2000)] satisfies the conditions of our framework and hence establish the existence of optimal domains within the given class of domains. We additionally use the same framework to prove the existence of optimal domains among uniform C1,1-domains for a first curl eigenvalue problem which has been studied recently for other classes of domains in [Enciso et al., Trans. Am. Math. Soc. 377, 4519–4540 (2024)].

Characterization of the subdifferential and minimizers for the anisotropic p-capacity

Abstract We obtain existence of minimizers for the p-capacity functional defined with respect to a centrally symmetric anisotropy for 1 < p < ∞ {1<p<\infty} , including the case of a crystalline norm in ℝ N {\mathbb{R}^{N}} . The result is obtained by a characterization of the corresponding subdifferential and it applies to unbounded domains of the form ℝ N ∖ Ω ¯ {\mathbb{R}^{N}\setminus\overline{\Omega}} under mild regularity assumptions (Lipschitz-continuous boundary) and no convexity requirements on the bounded domain Ω. If we further assume an interior ball condition (where the Wulff shape plays the role of a ball), then any minimizer is shown to be Lipschitz continuous.

Trunk Muscle Activity and Ratio of Local Muscle to Global Muscle Activity during Supine Bridge Exercises under Unstable Conditions in Young Participants with and without Chronic Low Back Pain.

Core exercises on an unstable surface increase trunk muscle activity, especially for local muscle groups. Therefore, there is a possibility that exercises on an unstable surface would be effective in the rehabilitation of non-specific chronic low back pain (NSCLBP). The present study assessed trunk muscle activities during bridge exercise on the floor and two kinds of unstable surfaces, i.e., a balance ball and the BOSU, for individuals with and without NSCLBP. This study enrolled 17 and 18 young participants with and without NSCLBP, respectively. In the balance ball condition, both groups showed a significant increase in erector spinae activity compared to the floor condition, and the increase in activity was significantly greater in the NSCLBP group than in the control group (p = 0.038). On the other hand, neither group showed significant changes in trunk muscle activities in the BOSU condition compared to those in the floor condition. The control group showed a significant increase in internal oblique/transversus abdominis activity under the balance ball condition (p = 0.020), whereas there were no significant changes in these muscle activities between the balance ball and floor conditions in the NSCLBP group. The present study showed that participants with NSCLBP significantly increased muscle activity of the erector spinae, one of the global back muscles, on the balance ball in spite of small effects on muscle activity of the internal oblique/transversus abdominis, which is one of the local abdominal muscles. Therefore, attention should be paid to the application of bridge exercises on the balance ball for individuals with NSCLBP.

Effect of Ball Inclusion in Drop Vertical Jump Test on Performance and Movement Variability in Basketball Players

The aim of this study was to assess and compare performance and movement variability (MV) in both bilateral and unilateral vertical drop jumps (DVJs) under conditions involving the incorporation or exclusion of ball catching. Twelve amateur basketball players were recruited for participation in the study (seven females and five males). Participants performed three jumps in each of the six conditions analyzed in randomized order: bilateral DVJ without (BNB) and with ball (BB); unilateral DVJ right leg without (RNB) and with ball (RB); and unilateral DVJ left leg without (LNB) and with ball (LB). MV and DVJ performance parameters were analyzed with an accelerometer and a force platform. MV was quantified using the sample entropy (sample entropy; SampEn) derived from the acceleration of the lower back. Differences between the different DVJ conditions were determined with the Wilcoxon test, with a significance level set at p < 0.05. The comparisons were also assessed via standardized mean differences (Cohen’s d). No significant differences were observed in jump height, contact time and reactive strength index between conditions. However, the RB condition reported higher MV compared to RNB (effect size = 0.79; p = 0.016). Similarly, LNB showed greater MV compared to RNB (effect size = −0.62; p = 0.042). The inclusion of the ball in the DVJ increased the MV in the bilateral condition and in the right leg, but not in the unilateral condition with the left leg. The asymmetry between legs (right vs. left) in MV values in NOBALL conditions was higher (≈15%) compared to the BALL condition (≈5%).

The effect of ball pressure and maximal isometric neck strength on head acceleration during purposeful heading in adult football players during heading drills

ObjectiveThis randomised repeated measures study explored the effect of ball pressure and maximal isometric neck strength on head acceleration during purposeful heading in adult football players during heading drills within a laboratory environment. MethodsRecreational football players (n ​= ​17) attended one familiarisation session to determine baseline maximal isometric neck strength, followed by two experimental sessions where they randomly trialled two conditions (>72-h apart). The first condition included 20 rotational headers with a match-ball at low-pressure (58.6 ​kPa; 8.5 psi) and the second included 20 rotational headers with a match-ball at high-pressure (103.4 ​kPa; 15.0 psi) whilst instrumented with an inertial measurement unit. ResultsA statistically significant difference between conditions for both peak linear head acceleration (F ​= ​15.2; p= ​ < ​ 0.001) and peak angular head velocity (F ​= ​5.71; p ​= ​0.018) during purposeful heading. The low-pressure ball condition demonstrated a 12 ​% reduction in peak linear acceleration and 6 ​% reduction in peak angular velocity when compared with high-pressure ball condition. Additionally, neck strength significantly predicted head acceleration during purposeful heading (p ​ = ​ <0.05). ConclusionThese findings suggest that lower ball pressure and higher neck strength can lower head acceleration during heading in adult football players during heading drills within a laboratory environment.

Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy

We consider nonlinear viscoelastic materials of Kelvin–Voigt-type with stored energies satisfying an Andrews–Ball condition, allowing for nonconvexity in a compact set. Existence of weak solutions with deformation gradients in [Formula: see text] is established for energies of any superquadratic growth. In two space dimensions, weak solutions notably turn out to be unique in this class. Conservation of energy for weak solutions in two and three dimensions, as well as global regularity for smooth initial data in two dimensions are established under additional mild restrictions on the growth of the stored energy.

On fractional Poincaré inequality for unbounded domains with finite ball conditions: Counter example

In this paper we investigate the fractional Poincaré inequality on unbounded domains. In the local case, Mancini and Sandeep (2010) showed that in the class of simply connected domains, Poincaré inequality holds if and only if the domain satisfies finite ball condition. We prove that such a result cannot be true in the ‘nonlocal/fractional’ setting even if finite ball condition is replaced by a related stronger condition. We further provide some sufficient criterions on domains for fractional Poincaré inequality to hold. In the end, asymptotic behaviour of all eigenvalues of fractional Dirichlet problems on long cylindrical domains is addressed.

Sensorimotor processing is dependent on observed speed during the observation of hand-hand and hand-object interactions.

Observing a physical interaction between individuals (e.g., observing friends shaking hands) or between an object and an individual (e.g., observing a teammate striking or being struck with a ball) can lead to somatosensory activation in the observer. However, it is not known whether the speed of the observed interaction modulates such somatosensory activation (e.g., observing a teammate being struck with a slow vs. a fast-moving ball). In three experiments, participants observed a hand or object interact with another hand or object, all presented with a slow- or fast-moving effector. To probe sensorimotor processes during observation, participants were asked to react to an auditory beep (i.e., response time [RT] task) at the moment of observed contact. If observed contact led to increased somatosensory activation, RTs would decrease due to statistical and/ or intersensory facilitation. In all three experiments, RTs were lower when observing fast compared to slow motion stimuli, regardless of the moving (i.e., hand or ball) and target stimulus (i.e., hand or leaf). Further, when only an object (i.e., leaf) was the target, RTs did not differ between the moving hand and moving ball condition. In contrast, when an object (i.e., ball) was used as the moving stimulus, the magnitude of the speed effect (i.e., fast - slow RT difference) was significantly larger when the ball contacted a hand as compared to a leaf. Overall, these results provide novel evidence for a relationship between the observed kinematics of an object-human interaction and the sensorimotor processing in the observer.

Reachable set for Hamilton–Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

We give a full characterization of the range of the operator which associates, to any initial condition, the viscosity solution at time T of a Hamilton–Jacobi equation with convex Hamiltonian. Our main motivation is to be able to treat the case of convex Hamiltonians with no further regularity assumptions. We give special attention to the case H(p)=|p|, for which we provide a rather geometrical description of the range of the viscosity operator by means of an interior ball condition on the sublevel sets. From our characterization of the reachable set, we are able to deduce further results concerning, for instance, sharp regularity estimates for the reachable functions, as well as structural properties of the reachable set. The results are finally adapted to the case of scalar conservation laws in dimension one.

Foot dominance and ball approach angle affect whole-body instep kick kinematics in soccer players

ABSTRACT Past investigations provided limited information regarding instep kicking kinematics in soccer. It is unclear how foot dominance and ball approach angle impact whole-body kinematics and consequently the ball velocity. We aimed to analyse the effects of the ball approach angle and the foot used on the whole-body kinematics of soccer players performing an instep kick. Twenty-four soccer players performed maximal instep kicks, using the dominant and non-dominant feet, with the ball stationary or rolling from four different directions. Whole-body motion was recorded during the kicking action and kinematic time-series were extracted and resampled to 200 points equally divided into kicking and follow-through phases. 1-D statistical parametric mapping two-way ANOVA tested for the effect of ball condition and foot dominance. Ball approach angle affected most of the swinging and support limb variables and some upper body variables. Performance-related variables such as CoM, foot, and shank velocities were reduced when the ball approached posteriorly. The linear and angular velocities of the swinging limb, and CoM vertical position, were higher when kicking with dominant foot. Based on these findings, as a practical implication, coaches should vary ball approach angles and the foot used during kicking drills to improve technical effectiveness in various situations.

Connes spectral distance and nonlocality of generalized noncommutative phase spaces

We study the Connes spectral distance of quantum states and analyse the nonlocality of a 4D generalized noncommutative phase space. By virtue of the Hilbert–Schmidt operatorial formulation, we obtain the Dirac operator and construct a spectral triple corresponding to the noncommutative phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements, and then calculate the Connes spectral distance between two Fock states. Due to the noncommutativity, the spectral distances between Fock states in generalized noncommutative phase spaces are shorter than those in normal phase spaces. This shortening of distances implies some type of nonlocality caused by the noncommutativity. These spectral distances in the 4D generalized noncommutative phase space are additive and satisfy the normal Pythagoras theorem. When the noncommutative parameters go to zero, the results return to those in normal quantum phase spaces.

Connes distance of 2D harmonic oscillators in quantum phase space* *Project supported by the Key Research and Development Project of Guangdong Province, China (Grant No. 2020B0303300001), the National Natural Science Foundation of China (Grant No. 11911530750), the Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2019A1515011703), the Fundamental Research Funds for the Central Universities, China (Grant No. 2019MS109),

We study the Connes distance of quantum states of two-dimensional (2D) harmonic oscillators in phase space. Using the Hilbert–Schmidt operatorial formulation, we construct a boson Fock space and a quantum Hilbert space, and obtain the Dirac operator and a spectral triple corresponding to a four-dimensional (4D) quantum phase space. Based on the ball condition, we obtain some constraint relations about the optimal elements. We construct the corresponding optimal elements and then derive the Connes distance between two arbitrary Fock states of 2D quantum harmonic oscillators. We prove that these two-dimensional distances satisfy the Pythagoras theorem. These results are significant for the study of geometric structures of noncommutative spaces, and it can also help us to study the physical properties of quantum systems in some kinds of noncommutative spaces.

Lower limbs muscle activation during instep kick in soccer: effects of dominance and ball condition

ABSTRACT Muscle activation has been studied in soccer players kicking stationary balls with the dominant foot. This study evaluated swinging and support limb muscle activation during the instep kick using different feet and ball approach conditions.Vastus medialis (VM), biceps femoris (BF), gastrocnemius medialis (GM) and tibialis anterior (TA) activations were evaluated during maximal instep kicks with both feet and the ball in five conditions (n = 18): stationary (STAT), approaching anteriorly (ANT), posteriorly (POST), laterally (LAT) and medially (MED). A repeated-measures two-way ANOVA compared activations between feet and ball conditions throughout the kicking (0–100%) and follow-through phases (101–200%). Close to ball contact (81–124%), non-dominant support GM had greater activation than the dominant one. The LAT and MED conditions differed within the cycle in the swinging VM (0–21%; 191–200%), BF (13–70%; 121–161%), GM (22–82%; 121–143%) and TA (0–32%; 55–97%; 186–200%) and in support VM (0–81%), BF (6–24%; 121–161%) and GM (24–87%). Players require greater support GM activation to stabilize the ankle during non-dominant kicks. Muscle activation differences between LAT and MED indicate that the kicking strategies are altered when kicking balls approaching from different directions.

Distance functions with dense singular sets

We characterize the denseness of the singular set of the distance function from a -hypersurface in terms of an inner ball condition and we address the problem of the existence of viscosity solutions of the Eikonal equation whose singular set (i.e. set of non-differentiability points) is not no-where dense.

Study of fractional Poincaré inequalities on unbounded domains

The central aim of this paper is to study (regional) fractional Poincar\'e type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various conditions on domains and on the range of $s \in (0,1)$. The best constant in both regional fractional and fractional Poincar\'e inequality is characterized for strip like domains $(\omega \times \mathbb{R}^{n-1})$, and the results obtained in this direction are analogous to those of the local case. This settles one of the natural questions raised by K. Yeressian in [\textit{Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89, (2014), no 1-2}].

Exit times for semimartingales under nonlinear expectation

Let Eˆ be the upper expectation of a weakly compact but possibly non-dominated family P of probability measures. Assume that Y is a d-dimensional P-semimartingale under Eˆ. Given an open set Q⊂Rd, the exit time of Y from Q is defined by τQ≔inf{t≥0:Yt∈Qc}.The main objective of this paper is to study the quasi-continuity properties of τQ under the nonlinear expectation Eˆ. Under some additional assumptions on the growth and regularity of Y, we prove that τQ∧t is quasi-continuous if Q satisfies the exterior ball condition. We also give the characterization of quasi-continuous processes and related properties on stopped processes. In particular, we obtain the quasi-continuity of exit times for multi-dimensional G-martingales, which nontrivially generalizes the previous one-dimensional result of Song (2011).

The Influence of Functional Flywheel Resistance Training on Movement Variability and Movement Velocity in Elite Rugby Players.

The aim of this study was to identify the changes in movement variability and movement velocity during a six-week training period using a resistance horizontal forward–backward task without (NOBALL) or with (BALL) the constraint of catching and throwing a rugby ball in the forward phase. Eleven elite male rugby union players (mean ± SD: age 25.5 ± 2.0 years, height 1.83 ± 0.06 m, body mass 95 ± 18 kg, rugby practice 14 ± 3 years) performed eight repetitions of NOBALL and BALL conditions once a week in a rotational flywheel device. Velocity was recorded by an attached rotary encoder while acceleration data were used to calculate sample entropy (SampEn), multiscale entropy, and the complexity index. SampEn showed no significant decrease for NOBALL (ES = -0.64 ± 1.02) and significant decrease for BALL (ES = -1.71 ± 1.16; p < 0.007) conditions. Additionally, movement velocity showed a significant increase for NOBALL (ES = 1.02 ± 1.05; p < 0.047) and significant increase for BALL (ES = 1.25 ± 1.08; p < 0.025) between weeks 1 and 6. The complexity index showed higher levels of complexity in the BALL condition, specifically in the first three weeks. Movement velocity and complex dynamics were adapted to the constraints of the task after a four-week training period. Entropy measures seem a promising processing signal technique to identify when these exercise tasks should be changed.

Existence of optimal shapes under a uniform ball condition for geometric functionals involving boundary value problems

In this article, we are interested in shape optimization problems where the functional is defined on the boundary of the domain, involving the geometry of the associated hypersurface (normal vector n, scalar mean curvature H) and the boundary values of the solution uΩ related to the Laplacian posed on the inner domain Ω enclosed by the shape. For this purpose, given ε &gt; 0 and a large hold-all B ⊂ ℝn, n ≥ 2, we consider the class Oε(B) of admissible shapes Ω ⊂ B satisfying an ε-ball condition. The main contribution of this paper is to prove the existence of a minimizer in this class for problems of the form infΩ∈Oε(B) ∫ ∂Ωj[uΩ(x),∇uΩ(x),x,n(x),H(x)]dA(x). We assume the continuity of j in the set of variables, convexity in the last variable, and quadratic growth for the first two variables. Then, we give various applications such as existence results for the configuration of fluid membranes or vesicles, the optimization of wing profiles, and the inverse obstacle problem.