摘要：The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

摘要：Two classes of superconvergence points for L 2 projection u\-n in n degree finite elements on uniform grids are shown by element analysis method. Superconvergence points of u n are n+1 order Gauss point G n+1 for odd d≥1 (so the endpoint of each element is of superconvergent), and n+1 order pointset Z n+1 for even n ≥2 (which includes the endpoints and midpoint), respectively. Symmetry point is only an important part of them.

摘要：The concept if t-PBIB design was introduced by Wei Wandi and Yang Benfu as a generalization of t-design and PBIB design. In this paper, a number of 3-association schemes and 3-PBIB(2) designs are constructed on the bases of the finite vector space over Fq and the finite unitary geometry over Fq2. Then a number of 3-designs are constructed on the bases of the finite orthogonal geometries over Fq. The parameters of all these designs are computed.

摘要：RECENTLY, frequency selective excitation was extensively studied and applied successfullyto various types of nuclear magnetic resonance (NMR) experiments. Solvent suppression,double resonance, multiple quantum coherence, as well as multi-dimensional NMR are all re-lated to selective excitation. Probably, its most important application is in NMR ***, selective excitation unit (SEU) has become an important accessory in modernNMR spectrometer.

摘要：A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a numeric example.

摘要：Aim: This paper discusses the design and finite Element Analysis (FEA) of a Percutaneous Aor-tic Valve Stent. The aim of this study was to model a percutaneous aortic valve stent and subject it to finite element analysis. The design process was carried out to meet the functional and surgical requirements. Methods and Results: Analysis was done with different materials with loads ranging from 50 kgf/mm²to 73 kgf/mm². These forces were selected because these val-ues are far greater than the normal human blood pressure which ranges from 10kPa to 16kPa. It was also to understand the mechanical behavior of different stent materials under such high pressures. A stent model was generated and its physical, mechanical and behavioral properties were studied. finite element analysis and simulation of the model enhanced the designer to optimize the geometry suitable for perform-ance during and after implantation. The design objective for the stent is to have long term du-rability, low thrombogenicity, resistance to mi-gration and paravalvular leak. Conclusion: The analysis performed in this paper may aid in understanding the stent’s tolerable pressures ranges in comparison with the physiological pressures exerted by the heart and cardiac blood flow during abnormal cardiovascular conditions.

摘要：It is widely known that a finite verb phrase(fVP)of a clause in English consists of three components:tense,aspect and *** the two tenses,present and past,and the two voices,active and passive,are recognized and generally agreed,the number and constituents of aspects may not be so simple and they are open to *** paper proposes that a new aspect,the“modal”aspect,be included in addition to the commonly recognized ones,namely“simple”,“perfect”and“continuous”(also known as“progressive”).With the inclusion of the“modal”aspect,there are four single aspects:“simple”,“modal”,“perfect”and“continuous”.They can be combined to form multiple aspects according to the aforesaid ***“modal”aspect is realized with a modal verb(any ofthe modal verbs will/would,shall/should,can/could,may/might,must,ought to,used to and the two semi-modals,“need”and“dare”in interrogative and negative structures).Whenever a modal verb is used,the verb phrase is in the modal *** modal verb to be used is for the interlocutor to decide and falls beyond this discussion,which focuses on the structure of the fVP of the English *** two tenses,eight aspects and two voices(active and passive)make up the 32 TAVs(an acronym formed with“Tense”,“Aspect”and“Voice”)of the English ***“discovery”of the“modal”aspect and its incorporation in the aspect system of English might have a significant impact on the learning of English for non-native speakers as they would have a clearer and more precise concept about the“TAVs”of the English fVP.

摘要：In this paper, a biosensor based on photonic crystal fiber (PCF) is proposed and designed using Full-Vectorial finite Element Method (FVFEM). The proposed PCF sensor consists of three concentric circles surrounding the core. The key optical sensor characteristics such as sensitivity, the field profiles and real part of the refractive index of the proposed PCF structure are investigated by employing the FVFEM. The proposed sensor can be deployed for environmental sensing when the PCF active region is filled with either analytes such as liquids or gas. By careful selection of the design parameters such as the radius of the sensing circle, the diameter of air holes in the core region and hole to hole spacing, Λ, the sensitivity analytes is determined. Our simulation results show that, the electric field distribution is primary localized in the third concentric circle with a radius of 16 μm. Effects of PCF bending on the sensitivity is also studied and reported.

摘要：Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.

摘要：It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.