In the book which accompanies the stencils various methods of finding quadratic residues are discussed and the method by means of the expansion of the square root of the number in a continued fraction is found to be by far the most effective. Various examples are given illustrating the power of the stencils, and a reproduction of the first page of the list of primes accompanies the work. The pl...

The ability of the gut epithelium to defend against pathogens while tolerating harmless commensal organisms remains an important puzzle. In this issue of Cell Host & Microbe, Lee et al. (2015) reveal how pathogen-secreted uracil acts at two steps to induce ROS via the Hedgehog pathway.

In [1] a proof was given of Fermat’s Two-Square Theorem using the group theoretical structure of the classical modular group. This has been extended in many directions and to other square properties in general rings. In particular in [2] a two-square theorem was given for the Gaussian integers in terms of when ii is a quadratic residue. In this note we examine and survey this technique and the ...

Let π(x; d, a) denote the number of primes p ≤ x with p ≡ a(mod d). Chebyshev’s bias is the phenomenon that ‘more often’ π(x; d, n) > π(x; d, r), than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If π(x; d, n) ≥ π(x; d, r) for every x up to some large number, then one expects that N(x; d, n) ≥ N(x; d, r) for every x. Here N(x; d, a) denotes ...

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to study the effects of two irrigation regimes and application of barley residue, zeolite and superabsorbent polymer on forage yield and some physiological traits of maize and sorghum, an experiment was conducted over two years in kerman, iran. a randomized complete block design arranged in a factorial split was used with three replications. two irrigation regimes of normal irrigation and water...

abstract in order to study the sensitivity of seven crops to total herbicide soil residue, an experiment was carried out under controlled conditions in 2009 at the college of agriculture, ferdowsi university of mashhad-iran. in this study 7 crops (pea, bean, lentil, corn, rape, beet and tomato), across 7 simulated soil residual concentration of total herbicide (0, 0.0002, 0.0005, 0.001, 0.002, ...

background isolated small gut mesentery injury after blunt abdominal trauma from the steering wheel in road traffic accidents is rare. these are always challenging to diagnose and pose a diagnostic dilemma. objectives to study the pattern of small gut mesenteric injury by steering wheel blunt abdominal trauma in road traffic accidents in patients who had laparotomy. patients and methods a 10-ye...