Edwards’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose that designers specify Edwards curves, but implement scalar multiplications and the like using an ...

Antiviral interferon activity in any one species can be exhibited by a variety of substances that differ in their physical and chemical properties, but the nature of these differences is not understood. Conditions that can lead to the formation of diverse types of interferons have been outlined. Reasons have been adduced why, for certain purposes, purification of interferons is desirable or eve...

Water is a major component of all living things. It is anomalous in many of its physical and chemical properties. Some are essential for life while others have profound effects on the size and shape of living organisms, how they work, and the constraints within which they must operate. Many of water’s basic physical properties can now be explained, at least semiquantitatively, in molecular and ...

Microbial functional diversity in four soils sampled in the vicinity of Wanda Glacier, Antarctic Peninsula, was determined using Biolog EcoPlates at 5°C and 25°C. Comparisons of the patterns of substrate utilization and the diversity index showed differences in community composition, reflecting the heterogeneous distribution of microorganisms in this environment. Differences in microbial divers...

This study evaluates the spatial heterogeneity of the soil chemical properties of surface soils across a 1 ha old-growth subtropical karst forest in southwest China.

Phosphasilenes, P=Si doubly bonded compounds, have received considerable attention due to their unique physical and chemical properties. We report on the synthesis and structure of a chlorophosphasilene coordinated by an N-heterocyclic carbene (NHC), which has the potential of functionalization at the Si-Cl moiety. Treatment of a silylphosphine, ArPH-SiCl₂RSi (Ar = bulky aryl group, RSi = Si(Si...

Symmetry has been dealt with in a wide variety of elds in both art and science. Symmetry and asymmetry as aesthetic features have been used in architecture, sculptures and paintings. Symmetry and symmetric groups have been de ned in mathematics [31]. Symmetry and it's compliment feature Chirality are basic properties of molecular structure that mediate chemical properties [29]. Though symmetry ...

Since the late 1970's, dozens of researchers, scholars, skeptics and "professional debunkers" have presented their theories on how the image on the Shroud of Turin was formed. Some are based on serious science while others show a complete lack of understanding of the Shroud image or its properties. In this paper, I will review the "proto-photography" theory proposed by Prof. Nicholas Allen of S...

Freshly prepared 2% acid and alkaline glutaraldehyde solutions were stored at 4, 20, and 37 C. At intervals, samples were removed and changes in pH, ultraviolet spectrum, and sporicidal activity (against Bacillus pumilus spores) were recorded. Alkaline solutions stored at 4 C showed little changes in these properties, whereas such solutions stored at 37 C became turbid and showed a decrease in ...

1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show that Mazur's example is in fact a true 4-sphere after all. This raises the odds in favour of the 4-dimensional Poincaré Conjecture. The proof involves a smooth knot of S2 in S4 with unusual properties.