Spread-F in the ionosphere over ahmedabad during the years 1954–57

From a study of spread-F or F-scatter at Ahmedabad during the four years 1954–57 of increasing sunspot activity, it was found that the time of its maximum occurrence receded from 03 hr. in low sunspot years to an hour or two before midnight in high sunspot years. This was particularly well seen in the winter and equinoctial months. Also, maximum spread-F activity which was found in summer in sunspot minimum mum years, occurred in equinoxes in maximum sunspot years. The frequency of occurrence of spread-F was found to be a maximum whenhpF₂ was in the range 300–350 km. F-scatter and F₂-stratification were found to be anti-correlated both in their diurnal and seasonal variations. The general trend was towards decreased spread-F with increased sunspot activity. It is concluded that (1) spread-F at Ahmedabad geomagnetic latitude (Φ=13·6° N) undergoes variations similar to those at equatorial stations, more so in high sunspot years, (2) the change-over from low-latitude type to middle-latitude type of variation of spread-F takes place at about geomagnetic latitude 22°, and (3) spread-F at Ahmedabad decreases with increase in magnetic activity, which is the reverse of that observed at high latitudes.     

Should European gamblers play lotto in the USA?

Any jackpot building game is designed to have a negative expected return for the gambler, but it can be profitable under certain circumstances. Previous studies have shown that the purchase of a single ticket of US-American state lotteries is sometimes a gamble with a positive expected value. Lottery winnings are not taxed in Europe, which suggests that the profitability of European games may be even higher. We present an exact formula for the calculation of the expected value of a single lotto ticket and find European lottery drawings to be far less profitable for the gambler compared to the US-American lotto market. Those US lotteries that generate profitable drawings are not characterized by higher redistribution rates or by their specific rules, but by the purchasing behavior of the gamblers. These gamblers buy far fewer tickets (per capita) and they barely react to increasing jackpots, even though the jackpots are large enough to cause positive expected winnings.     

Imaginary Modules over the Affine Nappi–Witten Algebra

In this paper,we consider the imaginary highest weight modules and the imaginary Whittaker modules for the affine Nappi-Witten algebra.We show that simple singular imaginary Whittaker modules at level(κ、c)(κ∈C~*) are simple imaginary highest weight modules.The necessary and sufficient conditions for these imaginary modules to be simple are given.All simple imaginary modules are classified.     

The linear flows in the space of Krichever–Lax matrices over an algebraic curve

Krichever (Commun Math Phys 229(2):229–269, 2002) invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation (Hitchin, Duke Math J 54(1):91–114, 1987). We study a necessary and sufficient condition for the linearity of flows on the space of Krichever–Lax matrices in a Lax representation in terms of cohomological classes using the similar technique and analysis from the work by Griffiths (Am J Math 107(6):1445–1484, 1985).      

Partial Orderings in the Category of Matrices over the Quaternion Field

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Yetter–Drinfeld Modules over the Hopf–Ore Extension of the Group Algebra of Dihedral Group

Let k be an algebraically closed field of characteristic zero, and D _n be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD _n . We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0).     

On the Tate–Shafarevich group of Abelian schemes over higher dimensional bases over finite fields

We study analogues for the Tate–Shafarevich group for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields.     

Toeplitz Products on Bergman–Sobolev Spaces over the Unit Polydisk

In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.     

Determinantal representation of the Moore–Penrose inverse matrix over the quaternion skew field

Within the framework of the theory of column and row determinants, we have obtained the determinantal representation of the Moore–Penrose inverse matrix over the quaternion skew field.     

Poletsky–Stessin–Hardy Spaces in the Plane

In this paper we give two characterizations of the Poletsky–Stessin–Hardy spaces in the complex plane: First we completely describe functions in these spaces by having a harmonic majorant with a certain growth condition and we prove some basic results about these spaces. Second we describe these functions in terms of their boundary values as a weighted subclass of the usual $L^p$ class with respect to the arclength measure on the boundary, when the boundary is $C^2$ . In particular, we extend the classical result of Beurling which describes the invariant subspaces of the shift operator. Additionally we provide non-trivial examples.     

Gender Differences in Mathematics Achievement Among High School Students in the United Arab Emirates, 1991–2000

This study explored gender differences in mathematics achievement of students in the last grade of high school and changes in these differences over a 10-year period in United Arab Emirates. A random sample of 2,000 students, 100 males and 100 females for each of the 10 academic years, was taken from Ministry of Education records, and achievement results for males and females were compared. Findings indicated no significant overall differences. In the last 6 years, females scored higher, although effect sizes were small. Results are discussed in the light of cultural differences.     

Effects of prey over–undercrowding in predator–prey systems with prey-dependent trophic functions

The local dynamics of a two-trophic chain in the presence of both overcrowding and undercrowding effects on prey growth is investigated. The starting point is given by a general predator–prey system, in which the prey growth rate and the trophic interaction function are defined only by some properties determining their shapes; in particular, the prey growth function is assumed to model a strong Allee effect. A stability analysis of the system using the predation efficiency as bifurcation parameter is performed; conditions for the existence and stability of extinction and coexistence equilibrium states are determined, and peculiar features of the dynamics exhibited by the system are presented, with particular attention to limit cycles and bistability situations. Results are compared with those obtained when overcrowding and undercrowding effects are considered separately.     

Cuspidal representations in the cohomology of Deligne–Lusztig varieties for GL(2) over finite rings

We define closed subvarieties of some Deligne–Lusztig varieties for GL(2) over finite rings and study their ´etale cohomology. As a result, we show that cuspidal representations appear in it. Such closed varieties are studied in [Lus2] in a special case. We can do the same things for a Deligne–Lusztig variety associated to a quaternion division algebra over a non-archimedean local field. A product of such varieties can be regarded as an affine bundle over a curve. The base curve appears as an open subscheme of a union of irreducible components of the stable reduction of the Lubin–Tate curve in a special case. Finally, we state some conjecture on a part of the stable reduction using the above varieties. This is an attempt to understand bad reduction of Lubin–Tate curves via Deligne–Lusztig varieties.     

Propagation of chaos for the Keller–Segel equation over bounded domains

In this paper we rigorously justify the propagation of chaos for the parabolic–elliptic Keller–Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller–Segel equation for bounded weak solutions.