integral

摘要： Wood has been an integral part of people's life for thousands of years.It hasbeen not only used for constructions,furniture,and daily necessities,but alsoserved as a main pillar for the economic and social development.Wood industryis a long-established business in China.

摘要： In this paper, we consider an integral basis for affine vertex algebra Vk (sl2) when the level k is integral by a direct calculation, then use the similar way to analyze an integral basis for Virasoro vertex algebra Vvir (2k,0). Finally, we take the combination of affine algebras and Virasoro Lie algebras into consideration. By analogy with the construction of Lie algebras over Z using Chevalley bases, we utilize the Z-basis of Lav whose structure constants are integral to find an integral basis for the universal enveloping algebra of it.

摘要： Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

摘要： With rising awareness about health,physical exercise has become an integral part of many people’s daily routine.However,in many cities,especially in the old urban areas,there are limited places for residents to do exercise.A small number of fitness equipment installed in public places can no longer meet the exercise needs of the whole community.

摘要： Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.

摘要： A novel geometric approach is proposed for the development of the wave-particle notions. This approach is based on a comparison of the two geometries with different sizes of an infinitesimal point. It is assumed that the smaller is object mass, the larger is the size of the infinitesimal point in comparison with the point of the geometry of macro world. Within this approach, the smaller is object mass, the larger is the uncertainty of its position from the viewpoint of macro objects (macro geometry). This approach provides a natural ex-planation of Heisenberg’s indeterminancy principle. Formally, this approach appears as an unusual operation with an infinitesimal value (point). However, it should be noted that unusual operations (though with infinitely large values) are already known in physics. These are unattainability of the absolute zero of temperature and unattainability of the maximal velocity of movement. Interconnection of the two geometries with different sizes of infinitesimal values is possible with the help of the direct and inverse Weierstrass transformation. At present, diffraction effects are described using the wave notions about the light and Fourier transform. The diffraction of light is usually registered at a distance not less than 1 - 3 metres between the screens in one of which there is a slit or several slits. This distance is about 106 times longer than the wavelength of the radiation. In the present work, an approach is proposed that allows one to describe the light fluxes at short distances between the screens with the help of Fourier and Weierstrass transforms.

摘要： An experimental study of the gas-solid flow dynamics in the high-flux CFB riser was accomplished by analysing the scaling regions from solid concentration signals collected from a 76 mm internal diameters and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s gas velocity and 50 to 550 kg/m2s solids flux. Spent fluid catalytic cracking (FCC) catalyst particles of 67 μm mean diameter and 1500 kg/m3 density together with 70% to 80% humid air was used. Solid concentration data were analysed using codes prepared in FORTRAN 2008 to get correlation integrals at different embedding dimensions and operating conditions and plot their profiles. Scaling regions were identified by visual inspection method and their location on planes determined. Scaling regions were analysed based on operating conditions and riser spatial locations. It was found that scaling regions occupy different locations on the plane depending on the number of embedding dimensions and operating conditions. As the number of embedding dimensions increases the spacing between scaling regions decreases until it saturates towards higher embedding dimensions. Slopes of scaling regions increases with embedding dimensions until saturation where they become constant. Slopes of scaling regions towards the wall decrease while the number of scaling regions for a particular profile increases. The span of the scaling region is wider at the initial values of hyperspherical radius than its final values. The scaling regions in some flow development sections show multifractal behaviour for each embedding dimension which manifests into visible basin which is defined in this study as multifractal basin. Further, the end points of the scaling region for each correlation integral profile differ from each other as the embedding dimension changes. This study suggests that identification of scaling region by visual inspection method is useful in understanding the gas-solid flow dynamics in the High-Flux CFB riser system. Further studies are recommended on risers of different diameters and heights operated at low and high solid fluxes and different gas velocities for comparison or usage of time series of different signal types like pressure fluctuations.

摘要： A robust topology optimization design framework is developed to solve lightweight structural design problems under uncertain conditions. To enhance the calculation accuracy and flexibility of the statistical moments of robust analysis, number theory integral method is applied to sample point selection and weight assignment. Both the structure topology optimization and number theory integral methods are combined to form a new robust topology optimization method. A suspension control arm problem is provided as a demonstration of robust topology optimization methods under loading uncertainties. Based on the results of deterministic and robust topology optimization, it is demonstrated that the proposed robust topology optimization method can produce a more robust design than that obtained by deterministic topology optimization. It is also found that this new approach is easy to apply in the existing commercial topology optimization software and thus feasible in practical engineering problems.

摘要： In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.

摘要： Short Retraction Notice? The paper does not meet the standards of "Advances in Pure Mathematics".? This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.? Editor guiding this retraction: Editorial Board (EIC of APM).? Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".