Equipment effectiveness: OEE revisited

Overall equipment effectiveness (OEE) is a metric that has been accepted completely in the semiconductor industry. OEE is simple and clear, and standards and guidelines have been developed. Nonetheless, literature indicates imperfections in applying OEE with regard to time base and rate efficiency. As literature lacks a basic framework for OEE, effectiveness has been approached systematically that resulted in a new equipment effectiveness E. The main difference between OEE and E concerns the choice of the time base. OEE does include equipment-independent conditions, such as lack of input items. This condition is not caused by the equipment but by the environment of the equipment. E has been defined to get a performance measure that is related to equipment-dependent states only, viz. effective state consisting of productive state, scheduled down state, and unscheduled down state. Because of the stand-alone condition, the equipment effectiveness expresses the (equipment) internal losses, while utilization expresses the external losses. By using E, equipment can be compared and improved. It can be concluded that the advantage of E over OEE is that real equipment effectiveness is measured as the influence of utilization (equipment-independent conditions) is eliminated.     

The wavelet dimension function is the trace function of a shift-invariant system

In this note, we observe that the dimension function associated with a wavelet system is the trace of the Gramian fibers of the shift-invariant system generated by the negative dilations of the mother wavelets. When this shift-invariant system is a tight frame, each of the Gramian fibers is an orthogonal projector, and its trace, then, coincides with its rank. This connection leads to simple proofs of several results concerning the dimension function, and the arguments extend to the bi-frame case.

     

利用电场感应器件MC33794测定液体高度

电场成像器件IC（MC33794）：Motorola公司提供行业内惟一可产生及检测低水平电场和功率并支持微控制器(MCU)的集成电路(IC)，所有这些功能均集成在单个芯片中。     

Optimal fractional matchings and covers in infinite hypergraphs: Existence and duality

We study fractional matchings and covers in infinite hypergraphs, paying particular attention to the following questions: Do fractional matchings (resp. covers) of maximal (resp. minimal) size exist? Is there equality between the supremum of the sizes of fractional matchings and the infimum of the sizes of fractional covers? (This is called weak duality.) Are there a fractional matching and a fractional cover that satisfy the complementary slackness conditions of linear programming? (This is called strong duality.) In general, the answers to all these questions are negative, but for certain classes of infinite hypergraphs (classified according to edge cardinalities and vertex degrees) we obtain positive results. We also consider the question of the existence of optimal fractional matchings and covers that assume rational values.     

适度集成有助于汽车功率驱动系统设计

汽车电子系统设计人员在选择MOSFET器件时以前只有两种选择:没有任何保护措施的“简单”PowerMOS或具有完全保护的器件,后者在环境条件超出规定范围时会自动关闭,然而带有额外逻辑和保护电路的完全保护器件成本较高。因此,有些供应商开发了一种介于两者之间的适度集成的新型器件,在单芯片中结合了TrenchMOS技术以及温度和电流传感元件。其优点是不需要昂贵的智能功率器件即可为系统提供保护并节约空间。     

Teacher and students’ joint production of a reversible fraction conception

Within a constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative reasoning about fractions. The study articulates a conception in a developmental sequence of iteration-based fraction conceptions and the teacher’s role in fostering such a conception in students.     

Application of a Mickens finite‐difference scheme to the cylindrical Bratu‐Gelfand problem

The boundary value problem Δu + λe^u = 0 where u = 0 on the boundary is often referred to as “the Bratu problem.” The Bratu problem with cylindrical radial operators, also known as the cylindrical Bratu‐Gelfand problem, is considered here. It is a nonlinear eigenvalue problem with two known bifurcated solutions for λ < λ_c, no solutions for λ > λ_c and a unique solution when λ = λ_c. Numerical solutions to the Bratu‐Gelfand problem at the critical value of λ_c = 2 are computed using nonstandard finite‐difference schemes known as Mickens finite differences. Comparison of numerical results obtained by solving the Bratu‐Gelfand problem using a Mickens discretization with results obtained using standard finite differences for λ < 2 are given, which illustrate the superiority of the nonstandard scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 327–337, 2004     

Counting 1-factors in infinite graphs

F. Bry (J. Combin. Theory Ser. B 34 (1983), 48–57) proved that a locally finite infinite n-connected factorizable graph has at least (n−1)! 1-factors and showed that for n = 2 this lower bound is sharp. We prove that for n≥3 any infinite n-connected factorizable graph has at least n! 1-factors (which is a sharp lower bound).