Fairness properties, which state that a sequence of bad events cannot happen infinitely before good event takes place, are often crucial in program verification. However, general methods for expressing and reasoning about various kinds fairness properties relatively underdeveloped compared to those safety properties. This paper proposes FOS (Fair Operational Semantics), theory capable arbitrary...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

a  convenient  and  efficient  one-pot  four-component  synthesis  of  1,  2,  4,  5-tetrasubstituted  imidazoles  using  nano  tio2  as  a  recyclable  catalyst  is  reported.  the results  show  that  the  methodology  has  several  advantages  such  as  low  loading  of catalyst,  excellent  yield,  short  reaction  time,  operational  simplicity  and  solvent-free conditions.

this study presents a comparison between aluminum and iron plate electrodes on phosphate removal from aqueous solutions by electrocoagulation process. the effectiveness of main operational parameters such as initial ph, initial phosphate concentration and current density were examined. in addition, treated solution and sludge characteristics, energy consumption and electrode mass depletion w...

‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...