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The aerodynamic performance of a deployable and low-cost unmanned aerial vehicle (UAV) is investigated and improved in present work. The parameters of configuration, such as airfoil and winglet, are determined via an optimising process based on a discrete adjoint method. The optimised target is locked on an increasing lift-to-drag ratio with a limited variation of pitching moments. The separation that will lead to a stall is delayed after optimisation. Up to 128 design variables are used by the optimised solver to give enough flexibility of the geometrical transformation. As much as 20% enhancement of lift-to-drag ratio is gained at the cruise angle-of-attack, that is, a significant improvement in the lift-to-drag ratio adhering to the preferred configuration is obtained with increasing lift and decreasing drag coefficients, essentially entailing an improved aerodynamic performance.

We can obtain a two-fold symmetric figure by folding a square sheet of paper in the middle and then cutting along some curves drawn on the paper. By making two perpendicular folds through the centre of the paper and then cutting, we can obtain a four-fold symmetric figure. We can also get an eight-fold symmetric figure by making a fold bisecting an angle made by the two perpendicular folds before cutting. But it is not possible to obtain a three-fold, five-fold or six-fold symmetric figure in this way; we need to make more folds before cutting. Making a three-fold (respectively five-fold and six-fold) figure involves the division of the angle at the centre (360°) of a square sheet of a paper into six (respectively ten and twelve) equal parts. In other words, we need to construct the angles 60°, 36° and 30°. But these angles cannot be obtained by repeated bisections of 180° by simple folding as in the making of two-fold, four-fold and eight-fold figures. In [1], we see that each of the constructions of 60° and 30° applies the fact that sin 30° = ½ and takes only a few simple folding steps. The construction of 36° is more tedious (see, for example, [2] and [3]) as sin 36° is not a simple fraction but an irrational number. In this Article, we show how to make, by paper-folding and cutting a regular pentagon, a five-pointed star and create any five-fold figure as we want. The construction obtained by dividing the angle at the centre of a square paper into ten equal parts is called a pentagon base. We gained much insight from [2] and [3] when developing the method for making the pentagon base to be presented below.

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some counterexamples are presented and alternative formulations are discussed., Comment: To appear in Journal of Applied Probability, 11 pages

What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin (1894–1959) (see fig. 1) wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov (1903–1987), who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by introducing the modern measure-theoretic approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide.

The concept of a metaplectic form was introduced about 40 years ago by T. Kubota. He showed how Jacobi-Legendre symbols of arbitrary order give rise to characters of arithmetic groups. Metaplectic forms are the automorphic forms with these characters. Kubota also showed how higher analogues of the classical theta functions could be constructed using Selberg's theory of Eisenstein series. Unfortunately many aspects of these generalized theta series are still unknown, for example, their Fourier coefficients. The analogues in the case of function fields over finite fields can in principle be calculated explicitly and this was done first by J. Hoffstein in the case of a rational function field. Here we shall return to his calculations and clarify a number of aspects of them, some of which are important for recent developments.

AbsrtactStaring form a probability σ on the half-line moments of any order A. G. Pakes has defined probabilities σr, by length biasing order r and gr, by the stationary-excess operation of order r, r = 1, 2,…Examples are given to show that σ can bt determined in the Stieltjes sence while σ1 and g1 are indeterminate in the Stieltjes sence. This shows that a statement in a recent paper by Pakes does not hold.

This paper discusses the stationarity conditions proposed by M. Yang (2000, Econometric Theory 16, 23–43), in the framework of Markov-switching first-order autoregressions. A weaker second-order stationarity assumption is proposed.

This paper presents a sufficient condition for a one-dimensional Dirac operator with a potential tending to infinity at infinity to have no eigenvalues. It also provides a quick proof (and suggests variations) of a related criterion given by Evans and Harris.

In the present paper we give a short proof of a result of Zaks, Frostig and Levikson [2006] on the solution of an optimization problem which is related to the problem of optimal pricing of a heterogeneous portfolio. Following Zaks, Frostig and Levikson [2006], we consider a heterogeneous portfolio which is composed by k risk classes such that for each j ! {1, …, k} the risk class j contains nj risks Xj,1 ,… ,Xj,nj which are assumed to be i.i.d. with finite first and second moments and non-zero variance. Then the total risk of risk class j is defined as

This note discusses the concept of aliasing and its use in the paper by H.J. Bierens (2001, Econometric Theory 17, 962–983), in the framework of a second-order autoregression with complex unit roots. The condition on the range of the angular frequency I† is extended to I† ∈ (0,2I€) − {I€}.Financial support from UPV-EHU research project 9/UPV-00038.321-13503/2001, Basque Government project PI9970 and Ministerio de ciencia y tecnologA­a BEC2003-02028 is gratefully acknowledged.

Grosch & Salwen (1978) discuss the continuous-spectrum contribution in both temporal and spatial stability problems that are governed by the linear Orr–Sommerfeld equation. Their computed temporal continuum eigenfunctions for the Blasius boundary layer and for a laminar jet profile show surprising differences. This note provides an improved physical understanding of the results through a simple model, and shows that these differences are more apparent than real.

SynopsisSome disparate ideas in the literature are drawn together. The work of P. J. Olver and his associates on Lagrangians which vanish for arbitrary variations, the so-called null Lagrangians, is viewed as a parallel development to Witten's study of topological field theories. A theorem of Olver, that all hyperjacobians are expressible as divergences, and are thus candidates for the construction of null Lagrangians, is shown to follow directly from the observation that such entities appear in a power series development of the general associative product, and this technique facilitates the construction of multi-dimensional examples.

In the second paragraph on page 30 [ 1 ], we wrote ‘Making a critical point precritical decreases the number of points about which we have to worry’. Indeed, we stopped worrying about these points so much, that we forgot to mention them in several statements. This includes Lemma 3.13, Theorem 3.14 and the Main Theorem. Thus, the possibility of critical points being precritical (not only sinking or recurrent) has to be added to those statements. In particular, the Main Theorem should read as follows.

It is shown that an immersion of n dimensional compact oriented manifold without boundary into the n+1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilic immersion if one of the mean curvature function H_l does not vanish and the ratio H_k/H_l is constant, 1\leq k, l \leq n, k\ne l.

The possible risks of infection associated with the practice of licking envelopes, stamps and labels were investigated. Although pathogenic bacteria and viruses were not isolated from sample envelopes obtained from various sources, the gums used in manufacture were found to exert a protective effect against death from desiccation on the bacteria and viruses which had been introduced into them.Staph. aureus and Salm. paratyphi Bremained viable for several months in dried films of two out of four gums tested. An echovirus could be recovered from similar films for up to 30 days, and an adenovirus for up to 10 days.Bacterial multiplication occurred in the gum used for the manufacture of postage stamps. The comparison is drawn between the possible consequences of minimal contamination of this gum and of cans of corned beef in the light of recent studies.

In our paper [1], in the proof of Proposition 1, we implicitly assume that the polynomial P is monic, although later we apply this proposition to polynomials which are not monic. The following corrections should be made in the proof of Proposition 1.

Recently, Saleh claimed to have solved `a long standing open question' in Topology; namely, he proved that every almost continuous function is closure continuous (= $\theta$-continuous). Unfortunately, this problem was settled long time ago and even a better result is known., Comment: 2 pages, to appear in "Glasgow Math. J."

Peter Morriss's attack on R. J. Johnston's Note takes some side-swipes at us. We are allegedly ‘not quite up to par’, because (i) we are said to advocate the Banzhaf index; (ii) we are accused of ignoring a simpler route to our conclusion.

A well known observation of Lov\'asz is that if a hypergraph is not $2$-colorable, then at least one pair of its edges intersect at a single vertex. %This very simple criterion turned out to be extremly useful . In this short paper we consider the quantitative version of Lov\'asz's criterion. That is, we ask how many pairs of edges intersecting at a single vertex, should belong to a non $2$-colorable $n$-uniform hypergraph? Our main result is an {\em exact} answer to this question, which further characterizes all the extremal hypergraphs. The proof combines Bollob\'as's two families theorem with Pluhar's randomized coloring algorithm., Comment: A note on Property B

The mechanical procedure of paper folding generates an uncountable family of infinite sequences of fold patterns. We obtain the associated Fourier series and show that the sequences are almost periodic and hence deterministic. Further, we show that paper folding numbers defined by the sequences are all transcendental.

Consider the first order differential equation (1) , where pi, and τi, for i = 1,…,n, are positive constants. To find necessary and sufficient conditions, in terms of the coefficients and the delays only, under which all solutions of (1) oscillate, is a problem of great importence. In a recent paper, Bowcock and Yu claimed that is a necessary and sufficient condition for all solutions of (1) to be oscillatory. In this paper a counterexample shows that the above result is not valid and the error in this paper is indicated.