The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is effective and appropriate for obtaining the numerical solution of the timefractional Modified Camassa-Holm equation and Time fractional Modified Degasperis-Procesi equation.

Background: Nonunions with large defect is a problem, especially in large defects with infection this problem is more serious. Due to war and grave accidents in our country, we have encountered with these difficulties and in future time will also.Methods: We modified D.O.B.G by using plate in one side of large defect and metal plate on another side, and fixed these plates using screws anchoring the distal and proximal segments of nonunion sites rigidly. The technique is very simple, reliable, less morbidity in donor site, short operation time and needn's especial instruments and equipments. We use this technique in 146 patients and follow one hundred of thems for 2.5 yrs (mean time) clinically and radiological.Results: Union rate was ninety percent. Due to rigid fixation and early R.O.M of joints the final limbs function were excellent (comparison with others technique).Discussion: Modified D.O.B.G is the choice technique for nonunion with lange defect especially in metaphysis. because of rigid fixation results early R.O.M and good limb function, high union rate, short operation time, simple technique and less morbidity in donor site.

In the AdS/CFT correspondence, the space-time metric can be modified by a dilaton background with a positive sign. Modifying the metric and action with the dilaton field in the non-Abelian sector of Quantum Field Theory, such as Quantum Chromodynamics (QCD), produces an analytical running coupling constant applicable in the non-perturbative domain of the theory. The computed running coupling constant aligns closely with experimental results at low energy levels. The Burkert-Ioffe model can additionally modify this $\alpha _s^{Ads}({Q^2})$ to more closely align with experimental results at high energy scales. Consequently, utilizing the AdS/CFT correspondence, we analyze specific QCD observables including the Bjorken sum rule, electron-positron annihilation into hadrons, and hadronic tau decay at low energy scales, below the QCD cut-off parameter, and we compare the outcomes with experimental data that match them closely.

Permanent deformation is an important factor in flexible pavement design. Through increasing traffic load and tire pressure most permanent deformation occurs in the upper layer rather than in subgrade Wheel tracking is a popular HMA test, since it simu- lates the permanent deformation resistance of mixtures. The basic similarity of these devices is in using a cyclic wheel passing through the surface of specimens, and the cumulative rut after the proposed cycles is used as a measure of rutting potential. The wheel tracking test is undertaken using the Iran University of Science and Technology, ABRC Wheel Track machine, by applying 8000 cycles of wheel load of 50kg that turns around an axis and applies the wheel load to specimens. The test was done at 60 oC.In this study, the rutting performance of hot mix as- phalt specimens made with bentonite as bitumen mod- ifiers were studied. 10%, 15%, 20%, 25% and 30% ben- tonite content by weight of asphalt cement were used as its modifier. A propeller mixer was used for blend- ing the bentonite and asphalt cement. In this study, the rutting performance of modified asphalt mixtures was evaluated through various laboratory tests, such as Marshall stability and permanent deformation The test methods used in this evaluation were the dynamic creep test and wheel tracking tests. The results demonstrated that the use of bentonite can enhance Marshall stabil- ity and resistance to permanent deformation of mix- tures. The mixtures also show good resistance to perma- nent deformation, evaluated by means of wheel tracking tests.