25,092 research outputs found
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 IIĀ² 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 ĻāĻ stacking and cationāanion 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 Pna2ā. The structure arises from ĻāĻ stacking between the benzyl and tetrafluoropyridyl groups of the cations and cationābromide 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 and that
we keep buying boxes until we collect at least coupons of each type. For
call a certain coupon a -ton if we see it times by the time we
have seen copies of all of the coupons. Here we determine the asymptotic
distribution of the number of -tons after we have collected copies of
each coupon for any in a restricted range, given any fixed . We also
determine the asymptotic joint probability distribution over such values of
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 Ā± 3.6 years, body mass 76.4 Ā± 3.8 kg, height 1.89 Ā± 0.05 m) participated in the study. Fifty competitive soccer matches and 192 data files were analysed (4 Ā± 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 Ā± 220 vs. 1644 Ā± 224 m; p<0.001) and mean speed lower (1st half vs. 2nd half: 7.0 Ā± 0.9 vs. 6.6 Ā± 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 Manās 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 21ā25. A gap still needs to be filled in the researchāa 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 Godās 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 Jesusā earthly life are studied (Matt 8ā12). In these passages, the Son of Man mediates Godās 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 Manās suffering, death, and resurrection are analyzed. The Son of Manās journey to the cross demonstrates his obedient response to his Fatherās will, which mediates for his disciples the self-denial and sacrificial allegiance to Godās plan necessary in genuine followership. In chapter four, the Son of Man logia that relate to Jesusā parousia are investigated. The purpose of the Son of Manās parousia will be to mediate promised vindication and reward disciples who have proven their fidelity to Jesus and Godās will. In chapter five a conclusion of research findings are addressed
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