Permanents of cyclic (0,1) matrices

AbstractAn efficient method is presented for evaluating the permanents Pnk of cyclic (0,1) matrices of dimension n and common row and column sum k. A general method is developed for finding recurrence rules for Pnk (k fixed); the recurrence rules are given in semiexplicit form for the range 4≤k≤9. A table of Pnk is included for the range 4≤k≤9, k≤n≤80. The Pnk are calculated in the formPnk=2+∑τ−1[k−12]Tτk(n)where the Ttk(n) satisfy recurrence rules given symbolically by the characteristic equations of certain (0, 1) matrices Πrk; the latter turn out to be identical with the r-th permanental compounds of certain simpler matrices Π1k. Finally, formal expressions for Pnk are given which allow one to write down the solution to the generalized Ménage Problem in terms of sums over scalar products of the iterates of a set of unit vectors

On finite limit sets for transformations on the unit interval

AbstractAn infinite sequence of finite or denumerable limit sets is found for a class of many-to-one transformations of the unit interval into itself. Examples of four different types are studied in some detail; tables of numerical results are included. The limit sets are characterized by certain patterns; an algorithm for their generation is described and established. The structure and order of occurrence of these patterns is universal for the class

Cohort profile: the Siyakhula cohort, rural South Africa

No abstract available

Iron dextran in the treatment of iron-deficiency anaemia of pregnancy - Haematological response and incidence of side-effects

Sixty pregnant patients with a haemoglobin (Hb) < 8 g/dl arid proven iron-deficiency anaemia were randomly allocated to two treatment groups. Group A received the usual recommended dose of iron dextran (Imferon; Fisons) and group 8 received two-thirds of the recommended dose. A further 30 patients received oral iron (group C). There was no difference in Hb value between the three groups 4 weeks after treatment or 3 months after delivery. At 6 months after delivery, a higher mean Hb value was found in the patients in group A than those in groups 8 and C. Significantly higher serum ferritin levels were found in group A and this difference was still present 6 months postnatally. There was no significant difference in the incidence of delayed reactions between the two groups who received iron dextran

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Emissions Savings in the Corn-Ethanol Life Cycle from Feeding Coproducts to Livestock

Environmental regulations on greenhouse gas (GHG) emissions from corn (Zea mays L.)-ethanol production require accurate assessment methods to determine emissions savings from coproducts that are fed to livestock. We investigated current use of coproducts in livestock diets and estimated the magnitude and variability in the GHG emissions credit for coproducts in the corn-ethanol life cycle. The coproduct GHG emissions credit varied by more than twofold, from 11.5 to 28.3 g CO2e per MJ of ethanol produced, depending on the fraction of coproducts used without drying, the proportion of coproduct used to feed beef cattle (Bos taurus) vs. dairy or swine (Sus scrofa), and the location of corn production. Regional variability in the GHG intensity of crop production and future livestock feeding trends will determine the magnitude of the coproduct GHG offset against GHG emissions elsewhere in the corn-ethanol life cycle. Expansion of annual U.S. corn-ethanol production to 57 billion liters by 2015, as mandated in current federal law, will require feeding of coproduct at inclusion levels near the biological limit to the entire U.S. feedlot cattle, dairy, and swine herds. Under this future scenario, the coproduct GHG offset will decrease by 8% from current levels due to expanded use by dairy and swine, which are less efficient in use of coproduct than beef feedlot cattle. Because the coproduct GHG credit represents 19 to 38% of total life cycle GHG emissions, accurate estimation of the coproduct credit is important for determining the net impact of corn-ethanol production on atmospheric warming and whether corn-ethanol producers meet state- and national-level GHG emissions regulations

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level