The use of Riccati equation in digital computer arithmetic /

Includes bibliographical references.

Handbuch der algebraischen Analysis.

Mode of access: Internet.

The Boston colloquium. Lectures on mathematics delivered from September 2 to 5, 1903, before members of the American Mathematical Society in connection with the summer meeting held at the Massachusetts Institute of Technology, Boston, Mass.,

"Bibliography of memoirs relating to algebraic continued fractions": p. 167-187.

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.

Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0

This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

Privileged Words and Sturmian Words

This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently. A word is privileged if it is a complete first return to a shorter privileged word, the shortest privileged words being letters and the empty word. Here we give and prove almost all results on privileged words known to date. On the other hand, the study of Sturmian words is a well-established topic in combinatorics on words. In this dissertation, we focus on questions concerning repetitions in Sturmian words, reproving old results and giving new ones, and on establishing completely new research directions. The study of privileged words presented in this dissertation aims to derive their basic properties and to answer basic questions regarding them. We explore a connection between privileged words and palindromes and seek out answers to questions on context-freeness, computability, and enumeration. It turns out that the language of privileged words is not context-free, but privileged words are recognizable by a linear-time algorithm. A lower bound on the number of binary privileged words of given length is proven. The main interest, however, lies in the privileged complexity functions of the Thue-Morse word and Sturmian words. We derive recurrences for computing the privileged complexity function of the Thue-Morse word, and we prove that Sturmian words are characterized by their privileged complexity function. As a slightly separate topic, we give an overview of a certain method of automated theorem-proving and show how it can be applied to study privileged factors of automatic words. The second part of this dissertation is devoted to Sturmian words. We extensively exploit the interpretation of Sturmian words as irrational rotation words. The essential tools are continued fractions and elementary, but powerful, results of Diophantine approximation theory. With these tools at our disposal, we reprove old results on powers occurring in Sturmian words with emphasis on the fractional index of a Sturmian word. Further, we consider abelian powers and abelian repetitions and characterize the maximum exponents of abelian powers with given period occurring in a Sturmian word in terms of the continued fraction expansion of its slope. We define the notion of abelian critical exponent for Sturmian words and explore its connection to the Lagrange spectrum of irrational numbers. The results obtained are often specialized for the Fibonacci word; for instance, we show that the minimum abelian period of a factor of the Fibonacci word is a Fibonacci number. In addition, we propose a completely new research topic: the square root map. We prove that the square root map preserves the language of any Sturmian word. Moreover, we construct a family of non-Sturmian optimal squareful words whose language the square root map also preserves.This construction yields examples of aperiodic infinite words whose square roots are periodic.

Sorghum Flour Fractions: Correlations Among Polysaccharides, Phenolic Compounds, Antioxidant Activity And Glycemic Index.

Nutrients composition, phenolic compounds, antioxidant activity and estimated glycemic index (EGI) were evaluated in sorghum bran (SB) and decorticated sorghum flour (DSF), obtained by a rice-polisher, as well as whole sorghum flour (WSF). Correlation between EGI and the studied parameters were determined. SB presented the highest protein, lipid, ash, β-glucan, total and insoluble dietary fiber contents; and the lowest non-resistant and total starch contents. The highest carbohydrate and resistant starch contents were in DSF and WSF, respectively. Phenolic compounds and antioxidant activities were concentrated in SB. The EGI values were: DSF 84.5±0.41; WSF 77.2±0.33; and SB 60.3±0.78. Phenolic compounds, specific flavonoids and antioxidant activities, as well as total, insoluble and soluble dietary fiber and β-glucans of sorghum flour samples were all negatively correlated to EGI. RS content was not correlated to EGI.

Chromatographic analysis of lipid fractions in healthy dogs and dogs with obesity or hyperadrenocorticism

Obesity and endogenous hyperadrenocorticism (HAC) are common clinical conditions in veterinary practice, and both conditions have clinical and laboratory similarities, Such as weight gain and dyslipidemia. The objective of the present study was to characterize and compare the lipid profiles and plasma lipoprotein fractions in healthy dogs (n = 10), in obese dogs (n = 10), and in dogs with HAC (n = 6). All of the dogs were client owned. The lipoproteins were separated by fast protein liquid chromatography, and the plasma concentrations of total cholesterol and total triacylglycerol (TAG) were determined by enzymatic methods. When compared with the healthy and obese groups, dogs with HAC had a significant increase (P < 0.01) in the total concentrations of TAGs and cholesterol (CHOL), with higher distribution in the very low-density lipoprotein (VLDL)-CHOL fractions. In addition, the distributions of the high-density lipoprotein (HDL)-CHOL and HDL-TAG fractions were significantly lower (P < 0.01) in dogs with HAC than in healthy dogs. Considering the animals in this study, it was determined that the dogs with HAC differed significantly from the healthy and obese dogs regarding the metabolism of CHOL and TAG, as well as their VLDL and HDL fractions. Similar laboratory findings could allow veterinarians to distinguish obese dogs from those with HAC. In addition, dogs with HAC may be at higher risk for developing metabolic and atherosclerotic complications.

Gastric anti-ulcer activity of leaf fractions obtained of polar extract from Wilbrandia ebracteata in mice

Leaf fractions of Wilbrandia ebracteata were investigated for anti-ulcerogenic effects in ethanol and indomethacin-induced gastric ulcer assays in mice. Protective anti-ulcer effects were detected only in the ethanol-induced ulcer assay effects after pre-treatment with MeOH extract, MeOH chlorophyll-free, chlorophyll residue, HEX, DCM, aqueous MeOH fraction, ethyl acetate (EtOAc) and aqueous fractions. A potent anti-ulcerogenic effect was determined after pre-treatment of animals with EtOAc fraction, which was fractionated for isolation of active constituents. Seven flavonoids, 3`,4`,5,6,7,8-hexahydroxyflavonol, orientin, isoorientin, vitexin, isovitexin, luteolin, 6-methoxi-luteolin were isolated from the leaves of W. ebracteata (Cucurbitaceae) by chromatographic methods and identified by their spectral data. The data suggest that flavonoids are active anti-ulcerogenic compounds from leaves of W. ebracteata. The ability of scavenging free radicals was evaluated by DPPH reduction assay by TLC of flavonoids isolated.

Cytotoxic activity of a dichloromethane extract and fractions obtained from Eudistoma vannamei (Tunicata: Ascidiacea)

This study consists of the bioassay-guided fractionation of the dichloromethane extract from Eudistoma vannamei and the pharmacological characterization of the active fractions. The dried hydromethanolic extract dissolved in aqueous methanol was partitioned with dichloromethane and chromatographed on a silica gel flash column. The anti-proliferative effect was monitored by the MTT assay. Four of the latest fractions, numbered 14 to 17, which held many chemical similarities amongst each other, were found to be the most active. The selected fractions were tested for viability, proliferation and death induction on cultures of HL-60 promycloblastic leukemia cells. The results suggested that the observed cytotoxicity is related to apoptosis induction. (C) 2007 Elsevier Inc. All rights reserved.

Neutralization of pharmacological and toxic activities of Bothrops snake venoms by Schizolobium parahyba (Fabaceae) aqueous extract and its fractions

The aqueous extract prepared from Schizolobium parahyba (Sp) leaves, a native plant from Atlantic Forest (Brazil), was tested to analyse its ability to inhibit some biological and enzymatic activities induced by Bothrops alternatus (BaltCV) and Bothrops moojeni (BmooCV) snake venoms. Sp inhibited 100% of lethality, blood incoagulability, haemorrhagic and indirect haemolytic activities at a 1:10 ratio (venom/extract, w/w), as well as coagulant activity at a 1:5 ratio (venom/extract, w/w) induced by both venoms. BaltCV fibrinogenolytic activity was also neutralized by Sp at a 1:10 ratio, resulting in total protection of fibrinogen B beta chain and partial protection of A alpha chain. Interaction tests have demonstrated that, at certain extract/proteins ratios, Sp precipitates proteins non-specifically suggesting the presence of tannins, which are very likely responsible for the excellent inhibiting effects of the analysed ophidian activities. Sp aqueous extract chromatography on Sephadex LH-20 was carried out aiming at the separation of these compounds that mask the obtained results. Thus, the fractionation of Sp resulted in three fractions: F1 (methanolic fraction); F2 (methanol:water fraction, 1:1 v/v); and F3 (aqueous fraction). These fractions were analysed for their ability to inhibit the BaltCV fibrinogenolytic activity. F1 inhibited 100% the venom fibrinogenolytic activity without presenting protein precipitation effect; F2 showed only partial inhibition of this venom activity. Finally, F3 did not inhibit fibrinogen proteolysis, but presented strong protein precipitating action. We conclude that Sp aqueous extract, together with tannins, also contains other compounds that can display specific inhibitory activity against snake venom toxins.

Hysterectomy fractions in New South Wales, 1971-2006

Hysterectomy fractions by age group for particular periods are of interest for: estimating proper population denominators for calculation of disease and procedure rates affecting the cervix and uterus; estimating the target population for Pap test programs, and response rates; and as a way of displaying the cumulative consequences of hysterectomies in a population. Hysterectomy fractions for populations can be determined by direct inquiry via a representative sample survey, or, as in this study, from prior hysterectomy rates of the cohorts of women which compose each age bracket. Hysterectomy data 1979-93 were obtained from the hospital In-patients Statistics Collection (ISC) which covers both public and private hospitals in NSW. Annual population denominators of women were obtained from Census data. Data were modelled by Poisson regression, using five.-year age group (15-greater than or equal to 85 years), annual period, and five-year birth cohort (APC model). Forward- and back-projection of the period effects were undertaken. The resultant NSW hysterectomy fractions by age and period are consistent with fractions obtained from modelled hysterectomy rates for Western Australia (1980-84), and fractions from national representative sample surveys (1989/90 and 1995) for younger women, but not for women aged greater than or equal to 70 years in 1995, which revealed higher hysterectomy fractions than modelled hysterectomy data would suggest. Hysterectomy fractions for NSW women by five-year age group for quinquennia centred on 1971 to 2006 are provided.

The binding of closantel to ovine serum albumin, and homogenate fractions of Haemonchus contortus

Closantel binds to the serum proteins of the host and affects blood sucking parasites when they ingest the brood of treated hosts. Closantel binds specifically to ovine serum albumin (K-a of 9.3 x 10(6)M(-1)) at site I, the warfarin/phenylbutazone binding site of albumin Closantel also binds to invertebrate haemocyanin and haemolymph. The strongest binding of closantel in homogenates of H. contortus is found in fractions containing soluble proteins. This binding is of low affinity and, because the site itself is not fully denaturable, it may not be proteinaceous. There is no detectable difference in binding affinity between homogenate fractions from closantel susceptible and resistant isolates of adult or larval worms suggesting that closantel resistance is not due to changes in the closantel receptor or carrier. (C) 2000 Australian Society for Parasitology Inc. Published by Elsevier Science Ltd. All rights reserved.