PURPOSE To accelerate dose calculation to interactive rates using highly parallel graphics processing units (GPUs). METHODS The authors have extended their prior work in GPU-accelerated superposition/ convolution with a modern dual-source model and have enhanced performance. The primary source algorithm supports both focused leaf ends and asymmetric rounded leaf ends. The extra-focal algorith...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

‎in this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by zou [operator inequalities associated with tsallis relative operator entropy‎, ‎{em math‎. ‎inequal‎. ‎appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and tsallis relative o...

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...