We find the minimal weighted energy ∫ Ω a(x)∣Du∣ of maps u ∶ Ω ⊂ Rm+n → S with prescribed singularities, where a(⋅) is a continuous positive weight. Our result extends previous ones of H. Brezis, J-M. Coron and E.H. Lieb (1986), G. Alberti, S. Baldo and G. Orlandi (2003), and V. Millot (2005).

This publication gives an introductory overview of the role fire in forest systems, benefits using prescribed as a part management, and necessary safety regulatory precautions that landowners land managers need to adhere fire.

Prescribed fire is a management tool used to reduce fuel loads on public lands in forested areas in the western United States. Identifying the impacts of prescribed fire on bird communities in ponderosa pine (Pinus ponderosa) forests is necessary for providing land management agencies with information regarding the effects of fuel reduction on sensitive, threatened, and migratory bird species. ...

The distributional k-dimensional Jacobian of a map u in the Sobolev space W 1,k−1 which takes values in the the sphere S can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary M o...

AIM To determine the best method of estimating the optimum magnification needed by visually impaired patients. METHODS The magnification of low vision aids prescribed to 187 presbyopic visually impaired patients for reading newspapers or books was compared with logMAR distance and near acuity (at 25 cm) and magnification predicted by +4 D step near additions. RESULTS Distance letter (r = 0....

We had found functions can be used to fix bits [2] by given differences. We use these functions build a message expansion function. In the message expansion function, there are some bits include message bits and incremental bits produced from message bits, these bits will be used as parameter of date-depend function. This message expansion function will fixed at lease n × 5 . 5 bits with given ...

the aim of the present study was to provide a clear picture of the prescribing pattern of corticosteroids in zanjan, iran. a retrospective and cross-sectional study was conducted to describe the pattern of corticosteroids prescription at beheshti pharmacy (zanjan, iran) over a period of six months between march 21 and september 22 of 2013. descriptive analyses were stratified by gender, age, typ...

We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in flight time. prove that, putting aside "opposition case" where infinitely many planes of motion are possible, there at most such each "type". There is bilinear quantity that we call b which all cases good parameter for positions. The time satisfies "variational" differential equation b, a...