Introduction: Physical wedge by modify photon beam shape and intensity has been utilized in radiotherapy to obtain uniformly dose distribution in tumor site with reduced hot spots. Calculation of dosimetric parameters for both symmetric and asymmetric wedged fields is proved necessary during linear accelerator (Linac) commissioning. The present study aimed to achieve o...

in this paper, we prove the hyers-ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. as a consequence, weobtain some random stability results in the sense of hyers-ulam-rassias.

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

The central mathematical problem studied in this work is the estimation of quadratic form $x^TA^{-1}x$ for a given symmetric positive definite matrix $A \in \mathbb{R}^{n \times n}$ and vector $x \mathbb{R}^n$. Several methods to estimate without computing inverse are proposed. precision estimates analyzed both analytically numerically.

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

The reactions here explored are microscopic analogs of Newton cradle: left thing attack, right leaves and central remains unaffected. We have studied symmetric SX2 reactions, X = N or E, where the attacking leaving molecules same: H3N, H3B, H3C(–) H3B (SN[email protected]), H3N (SE2) H3C protected]). Non-symmetric with different initial final complexes were also examples elements lateral differ...

Winds from massive stars supply ≈ 10 −3 M ⊙ yr −1 of gas to the central parsec of the Galactic Center. Spherically symmetric hydrodynamic calculations show that ≈ 1% of this gas, or ≈ 10 −5 M ⊙ yr −1 , flows in towards the central massive black hole Sgr A*; the remaining gas, ≈ 10 −3 M ⊙ yr −1 , is thermally driven out of the central star cluster in a wind. This dynamical model accounts for the...

We have chosen an Ising ASYNNNI (ASYmmetric Next Nearest Neighbor Interaction)   model under a grand canonical regime to investigate structural phase transition from a high symmetric tetragonal (Tet) to a low symmetric orthorhombic in YBa2Cu3O6+x , 0<x<1,  HTc system. Ordering process for absorbed oxygens from an external gas bath into the basal plane of the layered system is studied by Monte C...

We characterize noncommutative Frobenius algebras A in terms of the existence of a coproduct which is a map of left A-modules. We show that the category of right (left) comodules over A, relative to this coproduct, is isomorphic to the category of right (left) modules. This isomorphism enables a reformulation of the cotensor product of Eilenberg and Moore as a functor of modules rather than com...

In this paper, we prove the Hyers-Ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. As a consequence, weobtain some random stability results in the sense of Hyers-Ulam-Rassias.