《辞海》“几何”条漏收“怎么”义及给文选注释带来的失误

论证了《辞海》"几何"条漏列"怎么、为什么"义项与对"几何不从汝而死也"的错误疏解,纠正了因依据《辞海》释义的各相应选本的误注。

On Simultaneous Exact Controllability

We consider a mixed problem for a system describing the evolution of sound in a compressible fluid. We describe how to treat a simultaneous exact boundary controllability problem in the sense proposed by J.L. Lions as well as D. Russell. By using convenient modified multipliers we obtain an observability inequality provided suitable geometric condition on the domain is valid and the speed velocity of the models are related.

Alignments, Topologies, Convex Geometries and Higgs Spaces

Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary （that is, not necessarily finite） aligned, topological and Higgs spaces.

Mutual Interference of Two Debris Flow Deposits Delivered in a Downstream River Reach

We investigate experimentally the depositions of two contiguous debris flows flowing into a main river reach.The aim of the present experimental research is to analyze the geometry and the mutual interactions of debris flow deposits conveyed by these tributaries in the main channel.A set of 19 experiments has been conducted considering three values of the confluence angle,two slopes of the tributary,and three different triggering conditions(debris flows occurring simultaneously in the tributaries,or occurring first either in the upstream or in the downstream tributary).The flow rate along the main channel was always kept constant.During each experiment the two tributaries had the same slope and confluence angle.The analysis of the data collected during the experimental tests indicates that the volume of the debris fan is mainly controlled by the slope angle,as expected,while the shape of the debris deposit is strongly influenced by the confluence angle.Moreover,in the case of multiple debris flows,the deposit shape is sensitive to the triggering conditions.Critical index for damming formation available in literature has been considered and applied to the present case,and,on the basis of the collected data,considerations about possible extension of such indexes to the case of multiple confluences are finally proposed.

Recombinants for Enhanced Productivity and Drought Tolerance in Barley （Hordeum vulgare L.）

In an attempt to enhance productivity as well as drought tolerance of barley cultivar, a 5 × 5 diallel cross involving rainfed cultivars was made. Of the 10 crosses, cross K603 x K560 was most promising as it yielded highest number of recombinants （21 in irrigated and 36 in rainfed conditions）; the cultivar K506 was considered as drought resistant （drought susceptibility index 〈 1）. A total of 22 out of 64 and 18 out of 59 most promising F2 recombinants in irrigated and rainfed conditions, respectively from 6 crosses were evaluated for yield, harvest index as well as proline content. All the recombinants selected under rainfed condition （including a few from irrigated condition） showed enhanced level of proline content coupled with high grain yield and harvest index. Further, a total of twenty-nine segregants （12 rainfed and 17 irrigated derived cultures） showing significantly higher values of proline content and grain yield were grown during 2007-2008 under both the environments, rainfed and irrigated to determine the geometric mean （GM） and drought susceptibility index （S）. The segregants （Culture No. 8, 10 ＆ 13） derived from cross K 603 × K 560 and culture No. 5 from K 560 × RD 2508 gave maximum mean yield under rainfed and geometric mean coupled with lower drought susceptibility index （S）. Also, it has been observed that the transgressive segregants selected from limited water environment （rainfed） performed better than those selected from irrigated environment for higher grain yield and drought tolerance.

The Geometry Effect in a Pioneering Experimental Study on the Batch Crystallization of the CAM

Far from being equivalent to host the process, the vessels play an active role in the crystallization thanks to their differently shaped bottoms. It was clearly pointed out through a meticulous experimental research on the batch crystallization of CAM （citric acid monohydrate） carried out in the years 1997-1998 by the author at the historic laboratories of＂La Sapienza＂ University of Rome. Such pioneering M.Sc. thesis, supervised by Prof. Barbara Mazzarotta （Department of Chemical Engineering）, was already summarized in an informative essay but, since the crystallization operating conditions to optimize were illustrated ＂collectively＂, it seemed necessary a further paper expounding uniquely the geometry effect. Our aim is to use all the data, collected and simulated, in order to show why the round-bottomed crystallizer performed better than the conical-bottomed one with the CAM from aqueous solutions, and why we should discard the flat-bottomed crystallizers.

G^1 Continuous Condition of B-Spline Surfaces with Double Knots

The conditions for G1 continuity between two adjacent bicubic B-spline surfaces with double interior knots along their common boundary curve are obtained in this paper, which are directly represented by the control points of the two B-spline surfaces. As stated by Shi Xi-quan and Zhao Yan, a local scheme of constructing G1 continuous B-spline surface models with single interior knots does not exist; we may achieve a local scheme of (true) G1 continuity over an arbitrary B-spline surface network using these conditions.

Geometry and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss

It is known that the space of homogeneous type introduced by Coifman and Weiss(1971) provides a very natural setting for establishing a theory of Hardy spaces. This paper concentrates on how the geometrical conditions of the space of homogeneous type play a crucial role in building a theory of Hardy spaces via the Littlewood-Paley functions.

A Review of Heat Transfer Enhancement through Flow Disruption in a Microchannel

In this paper a comprehensive review of heat transfer enhancement through microchannels has been presented. Over the past few years due to multifunetion, shrinking package size and high power dissipation, the heat flux per unit area has increased significantly. Microchannels, with their large heat transfer surface to volume ratio and their small volumes, have shown a good thermal performance. Microchannels have been proven to be a high per- formaace cooling technique which is able to dissipate heat flux effectively from localized hot spots over small surface area. A good amount of heat transfer augmentation techniques have been reported on flow disruption through microchannel. These techniques promote free stream separation at the leading edge which results in boundary layer development and enhanced mixing leading to increased heat transfer. Flow disruption can be achieved through passive surface modifications, such as, shape of channel, dimple surfaces, ribs, cavities, groove structures, porous medium, etc. Combined effects of these geometrical configurations in heat transfer augmenta- tion are also reported in the literature. In this paper recent developments in experimental and numerical simula- tions of single-phase liquid cooled microchannel have been discussed to analyze the pressure drop, friction and heat transfer characteristics due to different flow conditions, roughness structure and passive surface modifica- tions. It has been observed that the flow disruption techniques are effective for heat transfer enhancement with lower penalties of increased pressure drop. The review concludes with suggestions for future research in this area.

Porosity of Self-affine Sets

In this paper, it is proved that any self-affine set satisfying the strong separation condition is uniformly porous. The author constructs a self-affine set which is not porous, although the open set condition holds. Besides, the author also gives a C^1 iterated function system such that its invariant set is not porous.

IDEAL STRUCTURE OF UNIFORM ROE ALGEBRAS OVER SIMPLE CORES

This paper characterizes ideal structure of the uniform Roe algebra B*(X) over simple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B*(X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B*(X) are completely described by the corona of the Stone-Cech compactification of X.

A survey on the local refinable splines

This paper provides a survey of local refinable splines,including hierarchical B-splines,T-splines,polynomial splines over T-meshes,etc.,with a view to applications in geometric modeling and iso-geometric analysis.We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis.

Non-Geometric Conditional Phase Gate by Quantum Zeno Dynamics in Laser-Excited Nitrogen-Vacancy Centers

Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.

Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents

A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.

Numerical manifold method based on isogeometric analysis

In this study, numerical manifold method(NMM) coupled with non-uniform rational B-splines(NURBS) and T-splines in the context of isogeometric analysis is proposed to allow for the treatments of complex geometries and local refinement. Computational formula for a 9-node NMM based on quadratic B-splines is derived. In order to exactly represent some common free-form shapes such as circles, arcs, and ellipsoids, quadratic non-uniform rational B-splines(NURBS) are introduced into NMM. The coordinate transformation based on the basis function of NURBS is established to enable exact integration for the manifold elements containing those shapes. For the case of crack propagation problems where singular fields around crack tips exist, local refinement technique by the application of T-spline discretizations is incorporated into NMM, which facilitates a truly local refinement without extending the entire row of control points. A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed. Results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies. The coordinate transformation based on the NURBS basis function improves the accuracy of NMM by exact integration. The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.

Automatic recognition of intersecting features of freeform sheet metal parts

This paper presents an approach for recognizing both isolated and intersecting geometric features of freeform surface models of parts,for the purpose of automating the process planning of sheet metal forming.The developed methodology has three major steps:subdivision of B-spline surfaces,detection of protrusions and depressions,and recognition of geometric features for sheet metal forming domain.The input geometry data format of the part is based on an IGES CAD surface model represented in the form of trimmed B-spline surfaces.Each surface is classified or subdivided into different curvature regions with the aid of curvature property surfaces obtained by using symbolic computation of B-spline surfaces.Those regions satisfying a particular geometry and topology relation are recognized as protrusion and depression(DP) shapes.The DP shapes are then classified into different geometric features using a rule-based approach.A verified feasibility study of the developed method is also presented.

Boundary Shape Control of the Navier-Stokes Equations and Applications

In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

FUNCTIONAL COEFFICIENT AUTOREGRESSIVE CONDITIONAL ROOT MODEL

This paper proposes an extended model based on ACR nmdel： Functional coefficient autoregressive conditional root model （FCACR）. Under some assumptions, the authors show that the process is geometrically ergodic, stationary and all moments of the process exist. The authors use the polynomial spline function to approximate the functional coefficient, and show that the estimate is consistent with the rate of convergence Op（hv＋1 ＋ n-1/3）. By simulation study, the authors discover the proposed method can approximate well the real model. Furthermore, the authors apply the model to real exchange rate data analysis.

THE MIMIc QUEUE WITH (e, d) SETUP TIME

The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

In the present paper system and the solutions to the the solvability condition of the linearized Gauss-Codazzi homogenous system are given. In the meantime, the ＇solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov＇s positive annulus in R^3.