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Counting Hecke eigenforms with nonvanishing value
No full textWe develop some asymptotics for a kernel function introduced by Kohnen and use them to
estimate the number of normalised Hecke eigenforms in whose -values
are simultaneously non-vanishing at a given pair of points each of which lies inside the critical strip
A note on Girstmair's irreducibility criterion
No full textGirstmair in \cite[Theorem 1]{G} gave a generalization of Murty's irreducibility criterion (see \cite[Theorem 1]{Mu}). In this article, we further generalize these criteria
Toughness, isolated toughness and path factors in graphs
No full texthttp://dx.doi.org/10.1017/S000497271200033
Elliptic curves and -adic elliptic transcendence
No full texthttp://dx.doi.org/10.1017/S000497271200033
An elementary expression in five variables relevant to many road accidents
Get PDFThis article suggests a model for many road accidents, namely, those in which a vehicle being driven forwards encounters an obstacle such as a pedestrian, a vehicle, or a tree. An equation for speed of impact is obtained from the model. (Speed of impact is very important in determining severity of injury.) The equation is an expression in five variables. As it is elementary, it will be of interest to educators in mathematics and other subjects, as well as to road safety specialists. Two of the five variables (speed of vehicle, and distance of the obstacle) are conditions existing at the initiation of the emergency; and three are approximately termed: range of the sensing system; reaction time; and deceleration; and are properties of the system of driver and vehicle. Thus the focus is on the moment the emergency is appreciated, a few seconds before impact. The model and equation may be relevant to some railway accidents, also. In addition, the article discusses how to push our understanding to a point some seconds earlier, in the hope of throwing light on accident causation.
References
T. P. Hutchinson. A method of constructing models of reaction to an imminent road crash. Traf. Eng. Control 57 (2016), pp. 97–103
T. P. Hutchinson. Road Safety Theory. Published online. 2018. url: http://RoadSafetyTheory.com
T. P. Hutchinson. The theory of reduction of impact speeds. Traf. Eng. Control 56 (2015), pp. 177–180
D. N. Lee. A theory of visual control of braking based on information about time-to-collision. Perception 5 (1976), pp. 437–459. doi: 10.1068/p050437
D. F. Moore. Minimization of occupant injury by optimum front-end design. Society of Automotive Engineers Technical Report No. 700416 (1970). doi: 10.4271/700416
D. Stewart, C. J. Cudworth, and J. R. Lishman. Misperception of time-to-collision by drivers in pedestrian accidents. Perception 22 (1993), pp. 1227–1244. doi: 10.1068/p221227
K. Suzuki, H. Tanaka, Y. Miichi, and M. Aga. Collision-mitigation level of collision-avoidance braking system. Int. J. Vehicle Safety 7 (2014), pp. 1–16. doi: 10.1504/IJVS.2014.058238
J. Wooller. Road traffic accidents in Adelaide and Brisbane, Australia—Excerpts from a report in preparation. Proceedings, 4th Conference, Australian Road Research Board 4 (1968), pp. 976–994. url: http://155.212.5.248/Presto/content/Detail.aspx?ctID=MjE1ZTI4YzctZjc1YS00MzQ4LTkyY2UtMDJmNTgxYjg2ZDA5&rID=OTAx&qrs=RmFsc2U=&ph=VHJ1ZQ==&bckToL=VHJ1ZQ==&rrtc=VHJ1ZQ=
On the increasing partial quotients of continued fractions of points in the plane
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the modularity of solutions to certain differential equations of hypergeometric type
No full texthttp://dx.doi.org/10.1017/S000497271200033
On quotients of values of Euler's function on factorials
No full texthttp://dx.doi.org/10.1017/S000497271200033
Second Hankel determinant of logarithmic coefficients of convex and starlike functions
No full texthttp://dx.doi.org/10.1017/S000497271200033
