scholarly journals Freely Solvable Graphs in Peg Solitaire

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Robert A. Beeler ◽  
Aaron D. Gray

In a 2011 paper, the game of peg solitaire is generalized to arbitrary boards, which are treated as graphs in the combinatorial sense. Of particular interest are graphs that are freely solvable, that is, graphs that can be solved from any starting position. In this paper we give several examples of freely solvable graphs including all such trees with ten vertices or less, numerous cycles with a subdivided chord, meshes, and generalizations of the wheel, helm, and web.

2000 ◽  
Vol 81 (5) ◽  
pp. 592-597
Author(s):  
Johan L[ouml ]nn ◽  
Albert G. Crenshaw ◽  
Mats Djupsj[ouml ]backa ◽  
Jonas Pedersen ◽  
H[aring ]kan Johansson

2018 ◽  
Vol 1 (84) ◽  
Author(s):  
Vilma Jurevičienė ◽  
Albertas Skurvydas ◽  
Juozas Belickas ◽  
Giedra Bušmanienė ◽  
Dovilė Kielė ◽  
...  

Research  background  and  hypothesis.  Proprioception  is  important  in  the  prevention  of  injuries  as  reduced proprioception  is  one  of  the  factors  contributing  to  injury  in  the  knee  joint,  particularly  the  ACL.  Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores  to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation.  After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was  independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.


ROBOT ◽  
2013 ◽  
Vol 35 (1) ◽  
pp. 90 ◽  
Author(s):  
Haiyong CHEN ◽  
Zaojun FANG ◽  
De XU ◽  
Hexu SUN

1980 ◽  
Vol 50 (1) ◽  
pp. 171-182
Author(s):  
H. D. Day ◽  
L. F. Shelly

The effects of varying conditions of unilateral auditory stimulation on the visual perception of verticality were examined in two experiments using 18 and 42 subjects, respectively. Significant effects of auditory stimulation and hand used to make the verticality adjustments were not found. With only one exception in Exp. 2, the starting position of the rod also had no influence on the ability of the subjects to adjust a rod to its vertical position. The literature pertaining to sensory-tonic field theory of perception was critically reviewed.


Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 581
Author(s):  
Kai Li ◽  
Zhenyu Zhao ◽  
Houming Zhou ◽  
Hao Zhou ◽  
Jie Yin ◽  
...  

As a surface finishing technique for rapid remelting and re-solidification, laser polishing can effectively eliminate the asperities so as to approach the feature size. Nevertheless, the polished surface quality is significantly sensitive to the processing parameters, especially with respect to melt hydrodynamics. In this paper, a transient two-dimensional model was developed to demonstrate the molten flow behavior for different surface morphologies of the Ti6Al4V alloy. It is illustrated that the complex evolution of the melt hydrodynamics involving heat conduction, thermal convection, thermal radiation, melting and solidification during laser polishing. Results show that the uniformity of the distribution of surface peaks and valleys can improve the molten flow stability and obtain better smoothing effect. The high cooling rate of the molten pool resulting in a shortening of the molten lifetime, which prevents the peaks from being removed by capillary and thermocapillary forces. It is revealed that the mechanism of secondary roughness formation on polished surface. Moreover, the double spiral nest Marangoni convection extrudes the molten to the outsides. It results in the formation of expansion and depression, corresponding to nearby the starting position and at the edges of the polished surface. It is further found that the difference between the simulation and experimental depression depths is only about 2 μm. Correspondingly, the errors are approximately 8.3%, 14.3% and 13.3%, corresponding to Models 1, 2 and 3, respectively. The aforementioned results illustrated that the predicted surface profiles agree reasonably well with the experimentally measured surface height data.


2021 ◽  
Vol 11 (15) ◽  
pp. 6774
Author(s):  
Fan Yang ◽  
Dongjin Jiang ◽  
Tieli Wang ◽  
Pengcheng Chang ◽  
Chao Liu ◽  
...  

The outlet conduit is an important construction connecting the outlet of the pump guide vane and the outlet pool; in order to study the hydraulic performance of the straight outlet conduit of the axial-flow pump device, this paper adopts the method of numerical simulation and analyzes the influence of the division pier on the pressure and velocity distribution inside and near the wall of the straight outlet conduit based on three design schemes. Four pressure pulsation measuring points were arranged in the straight outlet conduit, and the low-frequency pulsation characteristic information inside the straight outlet conduit with and without the division pier was extracted by wavelet packet reconstruction. The results show that the addition of a division pier has an effect on the hydraulic loss, near-wall pressure and velocity distribution in the straight outlet conduit. A small high-pressure zone is formed near the wall at the starting position of the division pier, and a large high-speed zone is formed on the left side at the starting position of the division pier. The length of the division pier has no significant effect on the flow distribution of the straight outlet conduit and the pressure and velocity distribution near the wall. Under different working conditions, each monitoring point has the maximum energy in the sub-band (0~31.25 Hz). With the increase of the flow rate, the total pressure energy of the straight outlet conduit decreases gradually. Under each condition, the difference of the energy proportion of the horizontal monitoring points of the straight outlet conduit is small, and the difference of the energy proportion of the two monitoring points at the top and bottom of the outlet channel is relatively large. The energy of the two monitoring points in the straight outlet conduit with a division pier is smaller than that of the two monitoring points in the straight outlet conduit without a division pier. There are differences in the main frequency and the power spectrum corresponding to the main frequency of the monitoring points in the straight outlet conduit, and the reasonable setting of the division pier is conducive to reducing the pressure pulsation of the flow in the straight outlet conduit and is beneficial to the safe and stable operation of the pump device.


1974 ◽  
Vol 39 (1) ◽  
pp. 523-528 ◽  
Author(s):  
Philip H. Marshall ◽  
Diana Jo Smith ◽  
Thomas T. Jackson

The effects of information sequencing and variations in interstimulus interval were investigated in a metered-memory-search paradigm where S responded with a rule-defined letter belonging to a memory set. If information concerning the starting point of the search was presented before the defining rule, the over-all latency was shorter than if the reverse was the case, supporting the notion that isolation of the starting position is an integral component of the metered-memory-search task. Increasing the interstimulus interval between information about the starting position and rule-defining transformation resulted over-all in a longer latency but had no effect on rate of search.


1994 ◽  
Vol 71 (4) ◽  
pp. 1390-1402 ◽  
Author(s):  
A. J. Van Soest ◽  
M. F. Bobbert ◽  
G. J. Van Ingen Schenau

1. Humans can execute explosive movements such as jumping and hitting an object irrespective of the starting position from which these movements have to be initiated; in fact, variability of kinematic parameters has been shown to decrease in the course of the movement. 2. We address the question of whether it is necessary to adapt the stimulation pattern of the muscles to such variations in starting position or whether the stabilizing effect of intrinsic muscle properties is such that one single muscle stimulation pattern might be used for a wide range of starting positions. 3. Specifically, we address this question for maximum-height human vertical squat jumping, using an approach based on mathematical modeling and computer simulation. The stimulation pattern of the muscles is the input of the model and the resulting movement is the output. 4. The optimal stimulation pattern for a starting position in the middle of the range of starting positions considered does not lead to adequate performance for other starting positions in that range. 5. However, a muscle stimulation pattern can be found that does result in close to optimal achievement for a wide range of starting positions. This muscle stimulation pattern, which is not optimal for any specific starting position, may be considered as "control that works" as opposed to "optimal control." 6. The latter muscle stimulation pattern also leads to adequate behavior for "new" starting positions both within and outside the range considered.


2000 ◽  
Vol 83 (5) ◽  
pp. 2791-2801 ◽  
Author(s):  
Jed A. Hartings ◽  
Simona Temereanca ◽  
Daniel J. Simons

The thalamic reticular nucleus (Rt) is strategically positioned to integrate descending and ascending signals in the control of sensorimotor and other thalamocortical activity. Its prominent role in the generation of sleep spindles notwithstanding, relatively little is known of Rt function in regulating interactions with the sensory environment. We recorded and compared the responses of individual Rt and thalamocortical neurons in the ventroposterior medial (VPm) nucleus of the rat to controlled deflections of mystacial vibrissae. Transient Rt responses to the onset (on) and offset (off) of vibrissa deflection are larger and longer in duration than those of VPm and of all other populations studied in the whisker/barrel pathway. Magnitudes of on and off responses in Rt were negatively correlated with immediately preceding activities, suggesting a contribution of low-threshold T-type Ca2+ channels. Rt neurons also respond with high tonic firing rates during sustained vibrissa deflections. By comparison, VPm neurons are less likely to respond tonically and are more likely to exhibit tonic suppression. Rt and VPm populations are similar to each other, however, in that they retain properties of directional sensitivity established in primary afferent neurons. In both populations neurons are selective for deflection angle and exhibit directional consistency, responding best to a particular direction of movement regardless of the starting position of the vibrissal hair. These findings suggest a role for Rt in the processing of detailed sensory information. Temporally, Rt may function to limit the duration of stimulus-evoked VPm responses and to focus them on rapid vibrissa perturbations. Moreover, by regulating the baseline activity of VPm neurons, Rt may indirectly enhance the response selectivity of layer IV barrel neurons to synchronous VPm firing.


2000 ◽  
Vol 81 (5) ◽  
pp. 592-597 ◽  
Author(s):  
Johan Lönn ◽  
Albert G. Crenshaw ◽  
Mats Djupsjöbacka ◽  
Jonas Pedersen ◽  
Håkan Johansson

Sign in / Sign up

Export Citation Format

Share Document