Introduction Radiotherapy with small fields is used widely in newly developed techniques. Additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. In the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against Monte Carlo method. Materials and Methods Siemens Once or linea...

in the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.

Students often have a difficult time understanding what convolution is. Students can often evaluate the convolution integral (continuous time case), convolution sum (discrete-time case), or perform graphical convolution but may not have a good grasp of what is happening. In other words, students can solve the formula but often do not understand the result or why they get that result. Most engin...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

Convolution is a critical component in modern deep neural networks, thus several algorithms for convolution have been developed. Direct convolution is simple but suffers from poor performance. As an alternative, multiple indirect methods have been proposed including im2colbased convolution, FFT-based convolution, or Winograd-based algorithm. However, all these indirect methods have high memory-...

In an earlier paper [1], the author introduced the notion of convolution of Riemannian manifolds. In [1] he also provided some examples and applications of convolution manifolds. In this paper we use tensor product to construct more examples of convolution manifolds and investigate fundamental properties of convolution manifolds. In particular, we study the relationship between convolution mani...

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

Recursive inverse filtering with non-stationary filters is becoming a useful tool in a range of applications, from multi-dimensional inverse problems to wave extrapolation. I formulate causal non-stationary convolution and combination and their adjoints in such a way that it is apparent that the corresponding non-stationary recursive filters are true inverse processes. Stationary recursive inve...

The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...