Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs

In this paper, we start with the consideration of direct collocation-based Runge-Kutta-Nyström (RKN) methods with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y″(t) = f(t, y(t)). At nth step, the continuous output formulas can be used for calculating the step values at (n + 2)th step and the integration processes can be proceeded twostep-by-twostep. In this case, we obtain twostep-by-twostep RKN methods with continuous output formulas (continuous TBTRKN methods). Furthermore, we consider a parallel predictor-corrector (PC) iteration scheme using the continuous TBTRKN methods as corrector methods with predictor methods defined by the continuous output formulas. The resulting twostep-by-twostep parallel-iterated RKN-type PC methods with continuous output formulas (twostep-by-twostep continuous PIRKN-type PC methods or TBTCPIRKN methods) give us a faster integration processes. Numerical comparisons based on the solution of a few widely-used test problems show that the new TBTCPIRKN methods are much more efficient than the well-known PIRKN methods, the famous nonstiff sequential ODEX2, DOP853 codes and comparable with the CPIRKN methods.     

A Solution‐Processed Air‐Stable Perylene Diimide Derivative for N‐type Organic Thin Film Transistors

For future all‐soluble organic thin film transistor (OTFT) applications, a new soluble n‐type air‐stable perylene diimide derivative semiconductor material with (trifluoromethyl)benzyl groups (TC–PDI–F) is synthesized. The film is formed by spin‐coating in air and optimized for OTFT fabrications. The transistor characteristics and air‐stability of the TC–PDI–F OTFTs is measured to investigate the feasibility of using solution‐processed TC–PDI–F for future OTFT applications. For all‐solution OTFT process applications, the transistor characteristics are demonstrated by using TC–PDI–F as an n‐type semiconductor material and liquid‐phase‐deposited SiO₂ (LPD–SiO₂) as a gate dielectric material. All processes (except material synthesis and electrode deposition) and electrical measurements are conducted in air.     

Hardy－Littlewood Theorems in Mixed Norm Spaces on Bounded Symmetric Domain of C~n

Ｈａｒｄｙ－ＬｉｔｔｌｅｗｏｏｄＴｈｅｏｒｅｍｓｉｎＭｉｘｅｄＮｏｒｍＳｐａｃｅｓｏｎＢｏｕｎｄｅｄＳｙｍｍｅｔｒｉｃＤｏｍａｉｎｏｆＣ~ｎ￥（乌兰哈斯）ＷｕｌａｎＨａｓｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｎｅｒＭｏｎｇｏｌｉａＮ?..     

Some Examples of Nonhypoelliptic Infinitely Degenerate Elliptic Differential Operators

This paper contains examples of nonhypoelliptic infinitely degenerate elliptic differential operators. Global nonsmooth solutions of the corresponding homogeneous equations are constructed.     

Semilinear perturbation of powers of the mizohata operators

ABSTRACT

We study the Cauchy Problem associated to a class of quasilinear Schrödinger equations which have been derived as models of several physical phenomenas. We prove local existence in arbitrary space dimension N without any smallness condition on the initial data.