In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference e...

‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

Differential privacy is becoming one gold standard for protecting the of publicly shared data. It has been widely used in social science, data public health, information technology, and U.S. decennial census. Nevertheless, to guarantee differential privacy, existing methods may unavoidably alter conclusion original analysis, as privatization often changes sample distribution. This phenomenon kn...

I classified bilinear differential operators acting in the spaces of tensor fields on any real or complex manifold and invariant with respect to diffeomorphisms 1980. Here give details proof.

In addition to optimal conditions, invariant laws of Lorentz, parity and time reversal are imposed to find the relation between observables (spin rotation parameters) and bilinear combination of helicity amplitudes in pion-proton elastic scattering at 6.0 GeV/c. By normalizing the differential cross-section to unity, the magnitudes of helicity amplitudes and the angle between them are dete...