A one line factoring algorithm

We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package

Class invariants from a new kind of Weber-like modular equation

A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method. They are obtained by means of specialising certain modular equations related to Weber's modular equations of `irrational type'. The technique works for certain eta quotients evaluated at points in an imaginary quadratic field with discriminant d1 (mod 8)

Dispersal of \u3ci\u3eFenusa Dohrnii\u3c/i\u3e (Hymenoptera: Tenthredinidae) From an \u3ci\u3eAlnus\u3c/i\u3e Short-Rotation Forest Plantation

The European alder leafminer, Fenusa dohrnii, is a defoliating insect pest of Alnus in short-rotation forest plantations. A 2-year study was performed to quantify movement from infested stands to uninfested areas. Sticky traps and potted monitor trees were installed at different locations within and at various distances from (0,5, 10, and 20 m) an infested stand to measure adult flight and oviposition activity, respectively. Trap catch and oviposition activity fell off sharply with distance, few insects being trapped or eggs laid at distances of 5 m or greater from the infestation

Involution products in Coxeter groups

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero

The effect of different solar simulators on the measurement of short-circuit current temperature coefficients

Gallium arsenide solar cells are considered for several high temperature missions in space. Both near-Sun and concentrator missions could involve cell temperatures on the order of 200 C. Performance measurements of cells at elevated temperatures are usually made using simulated sunlight and a matched reference cell. Due to the change in bandgap with increasing temperature at portions of the spectrum where considerable simulated irradiance is present, there are significant differences in measured short circuit current at elevated temperatures among different simulators. To illustrate this, both experimental and theoretical data are presented for gallium arsenide cells

A high-throughput ab initio review of platinum-group alloy systems

We report a comprehensive study of the binary systems of the platinum group metals with the transition metals, using high-throughput first-principles calculations. These computations predict stability of new compounds in 38 binary systems where no compounds have been reported in the literature experimentally, and a few dozen of as yet unreported compounds in additional systems. Our calculations also identify stable structures at compound compositions that have been previously reported without detailed structural data and indicate that some experimentally reported compounds may actually be unstable at low temperatures. With these results we construct enhanced structure maps for the binary alloys of platinum group metals. These are much more complete, systematic and predictive than those based on empirical results alone.Comment: 24 pages, 12 figure