We study the arithmetic properties of hyperelliptic curves given by the affine equation y^{2} = x^{n} + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps)., Kevser Aktaş, Hasan Şenay., and Obsahuje seznam literatury
Empirical protocols for assessing the suitability of prey for aphidophagous coccinellids are examined and a modified scheme of categorization is presented. It is argued that prey suitability should be assessed independently for larval development and adult reproduction because of potentially divergent nutritional requirements between these life stages. A scheme is proposed for assessing prey suitability for larval development using conspecific eggs as a reference diet against which diets of various prey types can be compared both within and among coccinellid species. Among suitable prey (those that support ca. 100% survival of larvae to the adult stage), those that promote faster development and yield larger adults relative to a conspecific egg diet are considered "optimal" for larvae. Prey that yield viable adults with similar or reduced adult weight after a similar or extended period of development relative to a diet of conspecific eggs are classified as "adequate". Prey are "marginal" if they support the survival of some larvae, but significantly less than 100%. Supplementary water should be provided with any non-aphid diet (e.g. pollen and alternative sources of animal protein) given the potential for food-specific diet-drought stress interactions. For adults, suitable prey are classified as "adequate" if they support the production of viable eggs when fed as a monotypic diet, or "marginal" if they merely prolong adult life relative to a water source. Prey that comprise an optimal or adequate diet for both larval development and adult reproduction are termed "complete" and these can be indexed for relative suitability according to derived estimates of rm. Potential sources of error in diet evaluation studies are identified and discussed.
In this paper, we describe an alternative methodology for the assessment of global Terrestrial Reference Frames (TRFs), called the Velocity Decomposition Analysis (VEDA). Although it is related to the well-known Helmert transformation, a new conceptual manner is presented and discussed. All the necessary mathematical formulas for the adjustment and the quality assessment are provided, as well as a discussion of the similarities and differences to the existing approaches. The core of the VEDA concept lays on the separation of the velocities in two parts: the transformation related one and the optimal velocities, respectively. Using the suggested strategy, we test the global TRFs, the ITRF2008 and the DTRF2008. Their comparison in terms of Helmert transformation parameters reveals discrepancies reaching 0.83 mm/yr for the orientation rates, 0.97 mm/yr for the translation rates and 0.32 mm/yr for the scale rate. The comparison between the new approach and the classical Helmert transformation shows a consistency at the level of 0.66 mm/yr in a mean sense. In addition, we find a relative bias between the two frames reaching 0.44 mm/yr. The new approach also allows quantifying the geometric effect which corresponds to the impact of the systematic inconsistencies and the effect of the set of stations global distribution.
Sufficient conditions are formulated for existence of non-oscillatory solutions to the equation y (n) + ∑ n−1 j=0 aj (x)y (j) + p(x)|y| k sgn y = 0 with n > 1, real (not necessarily natural) k > 1, and continuous functions p(x) and aj (x) defined in a neighborhood of +∞. For this equation with positive potential p(x) a criterion is formulated for existence of non-oscillatory solutions with non-zero limit at infinity. In the case of even order, a criterion is obtained for all solutions of this equation at infinity to be oscillatory. Sufficient conditions are obtained for existence of solution to this equation which is equivalent to a polynomial.
Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification for ties of a class of multisample location and scale test statistics, based on ranks and including the proposed test statistics, is presented. It is shown that under the validity of the null hypothesis these modified test statistics are asymptotically chi-square distributed provided that the score generating functions fulfill the imposed regularity conditions. An essential assumption is that the matrix, appearing in these conditions, is regular. Conditions sufficient for the validity of this assumption are also included.
In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients ak,l satisfy certain conditions) the following order equality is proved g(x,y) ∼ mnam,n + m⁄ n ∑ n−1 l=1 lam,l + n⁄ m ∑mX−1 k=1 kak,n + 1 m ⁄n ∑ n−1 l=1 ∑ m−1 k=1 klak,l, where x ∈ ( π⁄ m+1 , π ⁄ m ], y ∈ ( π ⁄ n+1 , π ⁄ n ], m, n = 1, 2, . . ..
In this paper we study the relationship between one-sided reverse Hölder classes $RH_r^+$ and the $A_p^+$ classes. We find the best possible range of $RH_r^+$ to which an $A_1^+$ weight belongs, in terms of the $A_1^+$ constant. Conversely, we also find the best range of $A_p^+$ to which a $RH_\infty ^+$ weight belongs, in terms of the $RH_\infty ^+$ constant. Similar problems for $A_p^+$, $1<p<\infty $ and $RH_r^+$, $1<r<\infty $ are solved using factorization.
Motivated by [10], we prove that the upper bound of the density function $\rho $ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.