Variational principle(S) are very important for a lot of (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR problem(S) to be analyzed theoretically or (S)olved numerically. By the popular (S)emi-inver(S)e method and de(S)igning trial-Lagrange functional(S) (S)killfully, new variational principle(S) are con(S)tructed (S)ucce(S)(S)fully for the Kuramoto-(S)iva(S)hin(S)ky (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION and the Coupled KdV (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION(S), re(S)pectively, which can model a lot of (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR wave(S) in (S)hallow water. The e(S)tabli(S)hed variational principle(S) are al(S)o proved correct. The procedure reveal(S) that the u(S)ed technologie(S) are very powerful and applicable, and can be extended to other (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR phy(S)ical and mathematical model(S).

In thi(S) paper, a novel device, namely heterojunction electron-hole bilayer tunnel field effect tran(S)i(S)tor (HJ-EHBTFET), i(S) propo(S)ed which outperform(S) conventional tunnel field effect tran(S)i(S)tor (TFET) in term(S) of electrical performance. The u(S)e of lattice matched InA(S)/Al0.6Ga0.4(S)b material combination re(S)ult(S) in a broken band gap configuration, making it highly (S)uitable for high (S)peed ultra-low application(S), a(S) it require(S) (S)maller gate bia(S) for the on(S)et of tunneling. The impact of critical de(S)ign parameter(S) on the device performance i(S) comprehen(S)ively inve(S)tigated. The propo(S)ed device utilize(S) electrical doping in(S)tead of phy(S)ical doping for the creation of tunneling junction, which effectively addre(S)(S)e(S) the problem of low (S)olubility of dopant(S) in heavily doped III-V material(S). The top gate and bottom gate workfunction are critical de(S)ign parameter(S) that effectively modulated the electrically induced charge(S) at the tunneling junction and con(S)equently, affect the tunneling rate. In order to obtain the lowe(S)t po(S)(S)ible tran(S)ition voltage for the on(S)et of tunneling, a variation matrix of thre(S)hold voltage variation i(S) computed a(S) a function of gate electrode workfunction. Through thi(S) proce(S)(S), a (S)tep-like behavior from off-(S)tate to on-(S)tate ha(S) been achieved, with a (S)ubthre(S)hold (S)wing of 3 mV/dec and on/off current ratio of 5.8&time(S);1012, thereby paving the way for the de(S)ign of low-power high-(S)peed digital computing (S)y(S)tem(S).

In thi(S) paper a method i(S) pre(S)ented in detail(S) to (S)olve a (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION which ha(S) many application(S) in engineering field(S). The boundary condition i(S) mixed to be able to define the value of function on it(S) variation on the boundary. Example(S) are given to demon(S)trate the accuracy and efficiency of the method.

In thi(S) paper, an exten(S)ion of (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL Tran(S)formation Method (DTM) which i(S) an analytical-numerical method for (S)olving the fuzzy (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION (FPDE) by u(S)ing the (S)trongly generalized differentiability concept i(S) inve(S)tigated. The propo(S)ed algorithm i(S) illu(S)trated by numerical example.

In thi(S) paper, an approximate (S)olution of a (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR parabolic (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION i(S) obtained for a non-uniform me(S)h. The (S)cheme for (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION (S)ubject to Neumann boundary condition(S) i(S) ba(S)ed on cubic B-(S)pline collocation method. Modi, ed cubic B-(S)pline(S) are propo(S)ed over non-uniform me(S)h to deal with the Dirichlet boundary condition(S). Thi(S) (S)cheme produce(S) a (S)y(S)tem of , r(S)t order ordinary (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION(S). Thi(S) (S)y(S)tem i(S) (S)olved by Crank Nichol(S)on method. The (S)tability i(S) al(S)o di(S)cu(S)(S)ed u(S)ing Von Neumann (S)tability analy(S)i(S). The accuracy and efficiency of the (S)cheme are (S)hown by numerical experiment(S). We have compared the approximate (S)olution(S) with that in the literature.

The main i(S)(S)ue in any image zooming technique(S) i(S) to pre(S)erve the (S)tructure of the zoomed image. The zoomed image may (S)uffer from the di(S)continuitie(S) in the (S)oft region(S) and edge(S); it may contain artifact(S), (S)uch a(S) image blurring and blocky, and (S)tairca(S)e effect(S). Thi(S) paper pre(S)ent(S) a novel image zooming technique u(S)ing (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION(S) (PDE(S)). It combine(S) a non-linear Fourth-order PDE method with the Locally Adaptive Zooming (LAZ) algorithm. The propo(S)ed method u(S)e(S) high-re(S)olution image obtained from LAZ algorithm to con(S)truct zoomed image by Fourth-order PDE. Thi(S) propo(S)ed method pre(S)erve(S) edge(S) and minimize(S) blurring and (S)tairca(S)e effect(S) in the zoomed image. In order to evaluate image quality obtained from the propo(S)ed method, thi(S) paper focu(S)e(S) on both (S)ubjective and objective a(S)(S)e(S)(S)ment(S). The re(S)ult(S) of the(S)e mea(S)ure(S) on a variety of image(S) (S)how that the propo(S)ed method i(S) (S)uperior over the other image zooming method(S).

In thi(S) work, we extend the exi(S)ting local fractional (S)umudu decompo(S)ition method to (S)olve the (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR local fractional (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">PARTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">DIFFERENTIAL (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION(S). Then, we apply thi(S) new algorithm to re(S)olve the (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR local fractional ga(S) dynamic(S) (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION and (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">NONLINEAR local fractional Klein-Gordon (S)tyle="font-(S)tyle:inherit;color:rgb(255,0,120);">EQUATION, (S)o we get the de(S)ired non-differentiable exact (S)olution(S). The (S)tep(S) to (S)olve the example(S) and the re(S)ult(S) obtained, (S)howed the flexibility of applying thi(S) algorithm, and therefore, it can be applied to (S)imilar example(S).