The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Optic variables used to judge future ball arrival position in expert and novice soccer players

Although many studies have looked at the perceptual-cognitive strategies used to make anticipatory judgments in sport, few have examined the informational invariants that our visual system may be attuned to. Using immersive interactive virtual reality to simulate the aerodynamics of the trajectory of a ball with and without sidespin, the present study examined the ability of expert and novice soccer players to make judgments about the ball's future arrival position. An analysis of their judgment responses showed how participants were strongly influenced by the ball's trajectory. The changes in trajectory caused by sidespin led to erroneous predictions about the ball's future arrival position. An analysis of potential informational variables that could explain these results points to the use of a first-order compound variable combining optical expansion and optical displacement.

(From) The Mill for Grinding Old People Young

Chapter one of novel in progress

The application of colloidal gas aphrons in the recovery of fine cellulose fibres from paper mill wastewater

Colloidal gas aphrons (CGAs) are micron-sized gas bubbles of 25–30 µm in diameter produced by a high-speed stirrer in a vessel containing dilute surfactant solution. These bubbles, because of their small size, exhibit some colloidal properties. In this work, CGAs were used to separate fine fibres from a lean slurry of cellulosic pulp in a flotation column. The pulp fibres were recovered as foamate from the top. Sodium dodecyl sulphate at a concentration of 2.0 kg/m3 was used as a surfactant to generate the CGAs in a spinning disc apparatus. The results indicated that up to 70% flotation efficiency could be obtained within a short column height of 0.3–0.35 m. This technique can be applied to recover fine cellulosic pulp from paper-machine backwater.

Pattern stability and error correction during in-phase and antiphase four-ball juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.

Synthesis of caffeic acid and p-hydroxybenzoic acid molecularly imprinted polymers and their application for the selective extraction of polyphenols from olive mill waste waters

Using caffeic acid and p-hydroxybenzoic acid as templates, two molecularly imprinted polymers (MIPs) were prepared that were used for isolation of polyphenols from olive mill waste water samples (OMWWs) without previous pre-treatment. For the preparation of the caffeic acid MIPs 4-vinylpyridine, allylurea, allylaniline and methacrylic acid were tested as functional monomers, ethylene glycol dimethylacrylate (EDMA), pentaerythritol trimethylacrylate (PETRA) and divinylbenzene 80 (DVB80) as cross-linkers and tetrahydrofuran as porogen. For p-hydroxybenzoic acid 4-vinylpyridine, allylurea and allylaniline were tested as functional monomers, EDMA and PETRA as cross-linkers and acetonitrile as porogen. The performance of the synthesized polymers was evaluated against seven structurally related compounds by means of polymer-based HPLC. The two polymers that presented the most interesting properties were further evaluated by batch rebinding and from the derived isotherms their capacity and binding strength were determined. Using solid-phase extraction (SPE), their ability to recognize and bind the template molecule from an aqueous solution as well as the pH dependence of the binding strength were explored. After establishing the best SPE protocol, an aqueous model mixture of compounds and a raw OMWWs sample were loaded on the two best polymers. The result of the consecutive use of the two polymers on the same sample was explored. It was concluded that acidic conditions favour the recognition abilities of both polymers and that they can be used for a quick and efficient isolation of the polyphenol fraction directly from raw OMWW.

Clarification of rubber mill wastewater by a plant based biopolymer- comparison with common inorganic coagulants

Background: In this study, the efficiency of Guar gum as a biopolymer has been compared with two other widely used inorganic coagulants, ferric chloride (FeCl3) and aluminum chloride (AlCl3), for the treatment of effluent collected from the rubber-washing tanks of a rubber concentrate factory. Settling velocity distribution curves were plotted to demonstrate the flocculating effect of FeCl3, AlCl3 and Guar gum. FeCl3 and AlCl3 displayed better turbidity removal than Guar gum at all settling velocities.

Result: FeCl3, AlCl3 and Guar gum removed 92.8%, 88.2% and 88.1% turbidity, respectively, of raw wastewater at a settling velocity of 0.1 cm min-1, respectively. Scanning electron microscopic (SEM) study conducted on the flocs revealed that Guar gum and FeCl3produced strong intercoiled honeycomb patterned floc structure capable of entrapping suspended particulate matter. Statistical experimental design Response Surface Methodology (RSM) was used to design all experiments, where the type and dosage of flocculant, pH and mixing speed were taken as control factors and, an optimum operational setting was proposed.

Conclusion: Due to biodegradability issues, the use of Guar gum as a flocculating agent for wastewater treatment in industry is highly recommended.

Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm

The Richardson-Lucy algorithm is one of the most important algorithms in the image deconvolution area. However, one of its drawbacks is slow convergence. A very significant acceleration is obtained by the technique proposed by Biggs and Andrews (BA), which is implemented in the deconvlucy function of the Image Processing MATLAB toolbox. The BA method was developed heuristically with no proof of convergence. In this paper, we introduce the Heavy-Ball (H-B) method for Poisson data optimization and extend it to a scaled H-B method, which includes the BA method as a special case. The method has proof of the convergence rate of O(k-2), where k is the number of iterations. We demonstrate the superior convergence performance of the scaled H-B method on both synthetic and real 3D images.

A comparative study of biopolymers and alum in the separation and recovery of pulp fibres from paper mill effluent by flocculation

Recovery of cellulose fibres from paper mill effluent has been studied using common polysaccharides or biopolymers such as Guar gum, Xanthan gum and Locust bean gum as flocculent. Guar gum is commonly used in sizing paper and routinely used in paper making. The results have been compared with the performance of alum, which is a common coagulant and a key ingredient of the paper industry. Guar gum recovered about 3.86 mg/L of fibre and was most effective among the biopolymers. Settling velocity distribution curves demonstrated that Guar gum was able to settle the fibres faster than the other biopolymers; however, alum displayed the highest particle removal rate than all the biopolymers at any of the settling velocities. Alum, Guar gum, Xanthan gum and Locust bean gum removed 97.46%, 94.68%, 92.39% and 92.46% turbidity of raw effluent at a settling velocity of 0.5 cm/min, respectively. The conditions for obtaining the lowest sludge volume index such as pH, dose and mixing speed were optimised for guar gum which was the most effective among the biopolymers. Response surface methodology was used to design all experiments, and an optimum operational setting was proposed. The test results indicate similar performance of alum and Guar gum in terms of floc settling velocities and sludge volume index. Since Guar gum is a plant derived natural substance, it is environmentally benign and offers a green treatment option to the paper mills for pulp recycling.

Better understanding of mechanochemical reactions: Raman monitoring reveals surprisingly simple 'pseudo-fluid' model for a ball milling reaction

Quantitative monitoring of a mechanochemical reaction by Raman spectroscopy leads to a surprisingly straightforward second-order kinetic model in which the rate is determined simply by the frequency of reactive collisions between reactant particles.

Balls to the wall: How acoustic information from a ball in motion guides interceptive movement in people with Parkinson’s disease

Previous research has shown that Parkinson's disease (PD) patients can increase the speed of their movement when catching a moving ball compared to when reaching for a static ball (Majsak et al., 1998). A recent model proposed by Redgrave et al. (2010) explains this phenomenon with regard to the dichotomic organization of motor loops in the basal ganglia circuitry and the role of sensory micro-circuitries in the control of goal-directed actions. According to this model, external visual information that is relevant to the required movement can induce a switch from a habitual control of movement toward an externally-paced, goal-directed form of guidance, resulting in augmented motor performance (Bienkiewicz et al., 2013). In the current study, we investigated whether continuous acoustic information generated by an object in motion can enhance motor performance in an arm reaching task in a similar way to that observed in the studies of Majsak et al. (1998, 2008). In addition, we explored whether the kinematic aspects of the movement are regulated in accordance with time to arrival information generated by the ball's motion as it reaches the catching zone. A group of 7 idiopathic PD (6 male, 1 female) patients performed a ball-catching task where the acceleration (and hence ball velocity) was manipulated by adjusting the angle of the ramp. The type of sensory information (visual and/or auditory) specifying the ball's arrival at the catching zone was also manipulated. Our results showed that patients with PD demonstrate improved motor performance when reaching for a ball in motion, compared to when stationary. We observed how PD patients can adjust their movement kinematics in accordance with the speed of a moving target, even if vision of the target is occluded and patients have to rely solely on auditory information. We demonstrate that the availability of dynamic temporal information is crucial for eliciting motor improvements in PD. Furthermore, these effects appear independent from the sensory modality through-which the information is conveyed.