Triglyceride Composition Seed Oils from Certain Plants

The type compositions of triglycerides (TAG) from seed oils of various plants were presented. The possibility of using a statistical model to estimate the ratio of TAG types formed by oleic, linoleic, and -linolenic acids was discussed. The greatest deviations from the statistical model were observed in oils for which the TAG contained -linolenic, -eleostearic, and ranunculeic acids.     

Uniform Continuity of a Family of Weakly Regular Set Functions on Topological Spaces

Conditions for the uniform continuity of a family of weakly regular set functions defined on an algebra of subsets of a -topological space (T,) and taking values in an arbitrary topological space are found.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.     

On the Growth of Entire Functions of Exponential Type near a Straight Line

Let be a sequence of complex numbers such that as . For close to the imaginary axis, upper bounds of the indicator of a nonzero entire function of exponential type with minimal growth vanishing on is obtained. These bounds give sufficient conditions for the system of exponents to be incomplete in an unbounded domain in .     

On the N-exciton normalization factor

The N-ground-state-exciton normalization factor, namely 〈v| B ₀ ^N B ₀ ^dagN| v〉 = N!F _N, with B ₀ ^d ag the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity F_N turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution exists in their many-body effects, which relies directly on F_N. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and in the BCS theory of superconductivity, we rederive important relations verified by the F_N's. We also give new explicit expressions of F_N valid for η = Na _x ³/ small but N ² a _x ³/ large, as F_N does not read in terms of η but Nη, the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, F_N does not appear alone in physical quantities, but through ratios like F _{N + p}/F _N. We end this work by giving the η expansion of these ratios, useful for all purely Pauli many-body effects. Received 30 May 2002 / Received in final form 12 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

The structure of XLPE and the distribution of space charge

The formation and accumulation of space charge under charge treatment are investigated using PWP method. The interaction between space charge and the structure of XLPE is measured using infrared spectroscopy (IR) method. The related mechanism about space charge distribution and the structure of XLPE are discussed.     

Unconventional Hamilton-type variational principle in phase space and symplectic algorithm

By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance.     

Infinite order differential operators in spaces of entire functions

Differential operators ?(Δ_θ,ω), where ? is an exponential type entire function of a single complex variable and Δ_θ,ω=(θ+ωz)D+zD², D=∂/∂z, , θ?0, , acting in the spaces of exponential type entire function are studied. It is shown that, for ω?0, such operators preserve the set of Laguerre entire functions provided the function ? also belongs to this set. The latter consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane . The operator exp(aΔ_θ,ω), a?0 is studied in more details. In particular, it is shown that it preserves the set of Laguerre entire functions for all . An integral representation of exp(aΔ_θ,ω), a>0 is obtained. These results are used to obtain the solutions to certain Cauchy problems employing Δ_θ,ω.