Grey relational analysis for optimization of wear parameters and surface roughness on nano composite coating

The higher wear resistance of Ni based nano composite coatings makes them potential replacement in protecting the substrate materials. The role of surface roughness of the coating along with wear parameters on the specific wear rate, pin temperature, and COF are addressed in the present study. The use of hard nano Al₂O₃ particles found significant role in increasing the resistance to wear for Ni matrix coatings on Al6061 material. The resistance to dislocation offered by these nano Al₂O₃ particles and smear out of debris with plastic deformation indicated abrasive and adhesive nature of wear mechanism in combination. The optimization of wear parameters are carried out by surface response method based grey relation analysis. The normal load applied onto the pin has significant influence on the specific wear rate and temperature rise in the pin. The surface roughness of the coating has also found instrumental in the higher pin temperature and friction coefficient.     

Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

A new high frequency dynamic mechanical analysis system: An approach to direct high frequency testing of tire tread rubber

Dynamic Mechanical Analysis (DMA) systems are measurement devices for obtaining master curves and complex modules of viscoelastic materials, such as rubbers. The conventional DMAs measurement systems in market have several limitations, which restrict their ability for operating at high frequencies. Thus, Williams, Landel and Ferry (WLF) relation is used to produce master curves and predict the material properties at high frequencies. In conventional DMAs, experiments are done in a range of temperatures, and then a master curve is made for a chosen reference temperature by shifting the measurements data to high frequencies. Therefore, the obtained results, which are not based on direct measurements, can be inaccurate. In order to overcome this problem a new simple shear high-frequency DMA (HFDMA) system is designed and built to directly measure the dynamic mechanical properties of viscoelastic material at high frequencies and the strain levels sufficient for tire manufacturers. The new HFDMA can be used to test any viscoelastic materials which have glass transmission temperature (Tg) lower than room temperature (about 23 °C) such as the Styrene-butadiene rubber (SBR). The SBR is the base material for tire tread. The designing process of this new HFDMA is presented in this paper. The rubber specimen shape is chosen by taking into account the shear elastic wave effect, bending, buckling effect and heat generation in the specimen. The repeatability test is accomplished to ensure that the results obtained from the new HFDMA are repeatable and the repeatability uncertainty is about 0.04%. The new HFDMA is validated by comparing to the direct test results of conventional DMA at 100 Hz. The direct high frequency (5 kHz) complex shear modulus and damping factor are compared with the master curve of the conventional DMA developed by the use of WLF relation for SBR. This comparison revealed that the complex shear modulus and damping factor of the SBR obtained from the HFDMA at 5 kHz and 0.05% strain amplitude are about 7% and 6.5% higher than those obtained from the conventional DMA, respectively.     

On Regular Orbits of Elements of Classical Groups in Their Permutation Representations

Let H be a simple finite classical group not isomorphic to PSL(n, q) for any n, q. We prove that every cyclic subgroup of H has a regular orbit on every nontrivial permutation H-set.     

Extremal maximal sectorial extensions of sectorial relations

The extremal maximal sectorial extensions of a not necessarily densely defined sectorial relation (multivalued linear operator) in a Hilbert space are characterized in terms of a construction which goes back to Sebestyén and Stochel. In particular the two extreme maximal sectorial extensions, namely the Friedrichs extension and the Kreĭn extension, are characterized. For this purpose a survey is given of the connection between closed sectorial forms and maximal sectorial relations.     

On the Padé table for e x and the simple continued fractions for e and e L/M

A recently observed connection between some Padé approximants for the exponential series and the convergents of the simple continued fraction for e is established, leading to an alternative proof of the latter. Similar results for the simple continued fraction e ²,e ^1/M and e ^2/M , when M is a natural number greater than one, are derived.      

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

基于可拓变换的二维随机变量分布律的研究

建立了随机事元之间的关系事元,研究随机事件之间的关系.利用关系元刻画了两个随机事件之间的关系.运用可拓变换初步研究了二维离散型随机变量的分布律和边缘分布律的传导分布.     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.