Mahler Measure of "Almost" Reciprocal Polynomials

Here we give a lower bound of the Mahler measure on a set of polynomials that are "almost" reciprocal. Here "almost" reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern breaks down for the innermost coefficients

The quest for extreme water repellency: Superhydrophobicity made easy

In his seminal work On Floating Bodies I Archimedes of Syracuse provided an explanation of the action of solid bodies on water. Although his thesis immediately benefitted King Heiro II² and has continued to serve mankind well, it ignores the effect of the interfacial interactions between the solid, water and air (surface tension). These interactions are negligible, or at least are considered negligible, compared to forces arising from the effect of gravity on large bodies. However, as the mass of the body decreases, the surface interactions become increasingly important leading to some unusual and potentially useful phenomena. The understanding and application of these effects is currently driving much fundamental research by physicists, chemical engineers, material scientists, and chemists into surfaces that display extreme properties, in particular extreme water repellency, or superhydrophobicitv. It is only comparatively recently that detailed mathematical expressions for the interaction between a liquid, solid and gas at these extremes have been developed, making progress that parallels that for the fabrication of these surfaces

On the importance of π–π stacking and cation–anion interactions in the construction of non-centrosymmetric networks of bromide salts of imidazolium cations bearing arene and polyfluoroarene rings

The salt 1-(2,3,5,6-tetrafluoropyridyl)-3-benzylimidazolium bromide crystallizes in the non-centrosymmetric space group Pna2₁. The structure arises from π–π stacking between the benzyl and tetrafluoropyridyl groups of the cations and cation–bromide interactions. It is the latter that gives rise to the non-centrosymmetry

The number of k-tons in the coupon collector problem

Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is $1/n$ and that we keep buying boxes until we collect at least $m$ coupons of each type. For $k\geq m$ call a certain coupon a $k$-ton if we see it $k$ times by the time we have seen $m$ copies of all of the coupons. Here we determine the asymptotic distribution of the number of $k$-tons after we have collected $m$ copies of each coupon for any $k$ in a restricted range, given any fixed $m$. We also determine the asymptotic joint probability distribution over such values of $k$ and the total number of coupons collected

Half-time and high-speed running in the second half of soccer

This study investigated if the quantity of high-speed running (movements >15 km.h-1) completed in the first 15 minutes of competitive football matches differed from that completed in the corresponding 15 minutes of the second half. Twenty semi-professional soccer players (age 21.2 ± 3.6 years, body mass 76.4 ± 3.8 kg, height 1.89 ± 0.05 m) participated in the study. Fifty competitive soccer matches and 192 data files were analysed (4 ± 2 files per match) using Global Positioning Satellite technology. Data were analysed using 2-way repeated measures ANOVA and Pearson correlations. No differences were found between the first 15 min of each half for the distance completed at high-speed (>15 km.h-1) or sprinting (>21 km.h-1), or in the number of sprints undertaken (p>0.05). However, total distance covered was shorter (1st half vs. 2nd half: 1746 ± 220 vs. 1644 ± 224 m; p<0.001) and mean speed lower (1st half vs. 2nd half: 7.0 ± 0.9 vs. 6.6 ± 0.9 km.h-1; p<0.001) in the first 15 min of the second half compared to the first. The correlations between the duration of the half-time interval and the difference in the high-speed running or sprinting between first and second halves (0-15 min) were very small (r=0.08 [p=0.25] and r=0.04 [p=0.61] respectively). Therefore, this study did not find any difference between the amount of high-speed running and sprinting completed by semi-professional soccer players when the first 15 minutes of the first and second half of competitive matches were compared The maintenance of high-speed running and sprinting, as total distance and mean speed declined, may be a function of the pacing strategies adopted by players in competitive matches

Remote Camera and Trapping Survey of the Deep-water Shrimps Heterocarpus laevigatus and H. ensifer and the Geryonid Crab Chaceon granulatus in Palau

Time-lapse remote photo-sequences at 73-700 m depth off Palau, Western Caroline Islands, show that the caridean shrimp Heterocarpus laevigatus tends to be a solitary animal, occurring below ~350 m, that gradually accumulates around bait sites over a prolonged period. A smaller speies, H. ensifer, tends to move erratically in swarms, appearing in large numbers in the upper part of its range (<250 m) during the evening crepuscular period and disappearing at dawn. Trapping and photsequence data indicate the depth range of H. ensifer (during daylight) is ~250-550 M, while H. laevigatus ranges from 350 m to at least 800 m, along with the geryonid crab Chaceon granulatus. Combined trapping for Heterocarpus laevigatus and Chaceon granulatus, using a three-chamber box-trap and extended soak times (48-72 hr), may be an appropriate technique for small-scale deep-water fisheries along forereef slopes of Indo-Pacific archipelagoes

Orbital debris removal with solar concentrators

In 1993 solar concentrators were first proposed to deflect asteroids away from a collision course with the Earth. The original concept was expanded by the authors, and proved to be effective and technologically feasible. One way to deflect the asteroid is to produce a slow decay of its orbit by inducing a thrust via concentrated solar light. Two mechanisms have been investigated: the sublimation of the surface of the asteroid to generate a jet of gas and the induced thrust by light pressure and enhanced Yarkovsky effect. If the concentrators are reduced in size, a similar concept can be adopted to remove orbital debris and inert satellites. In this paper, we present an orbital debris removal system based on concentrated solar light. We will show how enhanced solar pressure, generated by a formation of solar concentrators, can be used to accelerate the decay of small inert objects orbiting the Earth. A set of modified proximal motion equations is proposed to describe the relative dynamics of the solar concentrators with respect to the target piece of debris. The paper will provide an analysis of the cost of the optimal control of the concentrators during the deflection of the debris and a system engineering analysis. In particular, we will show that the concentrator acts as an active solar sail while not deflecting, and as a hybrid solar sail (i.e. the orbit is maintained with an auxiliary low-thrust engine) while deflecting the debris. The results will show that objects with even a small area-to-mass ratio (down to 0.01) can be brought from an 800 km to a 200 km altitude orbit in few hundred days of constant operation. The paper will discuss also the possibility to vaporize some small size targets with high power solar pumped laser

A mediator in Matthew: an analysis of the Son of Man’s function in the first Gospel

The function of the Son of Man in the Gospel of Matthew is not settled. The majority of the research on the Son of Man in Matthew has been focused on the latter part of the Gospel, that is, Matt 21‒25. A gap still needs to be filled in the research—a consistent, theological understanding of the role of the Son of Man throughout the entire Gospel. This thesis argues that Jesus the Son of Man serves as the mediator of God’s will to his genuine disciples. The primary research method used is new redaction criticism, together with literary and social-scientific emphases. All thirty Son of Man logia are studied in their respective literary contexts and in relationship to the entire Gospel. In chapter one, a general review of Son of Man research is provided along with a sketch of representative literature on the Son of Man in Matthew. In chapter two, the Son of Man logia that relate to Jesus’ earthly life are studied (Matt 8‒12). In these passages, the Son of Man mediates God’s revealed will to his genuine disciples through his message and works. In chapter three, the Son of Man logia that relate to the Son of Man’s suffering, death, and resurrection are analyzed. The Son of Man’s journey to the cross demonstrates his obedient response to his Father’s will, which mediates for his disciples the self-denial and sacrificial allegiance to God’s plan necessary in genuine followership. In chapter four, the Son of Man logia that relate to Jesus’ parousia are investigated. The purpose of the Son of Man’s parousia will be to mediate promised vindication and reward disciples who have proven their fidelity to Jesus and God’s will. In chapter five a conclusion of research findings are addressed