Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

The true position of Rev. Theodore Parker : being a review of Rev. R.C. Waterston's letter in the fourth quarterly report of the Benevolent Fraternity of Churches.

Attributed to Sargent in NUC pre-1956 imprints.

The fourth book of Moses, called Numbers;

Mode of access: Internet.

A comparison of dissected follicle numbers and follicle counts on the ovarian surface for the evaluation of ovarian follicular populations in Bos indicus cows

Ovaries (n = 140) from 70 mixed-age multiparous, lactating Brahman cross (3/4-7/8 Bos indicus) cows were used to examine the hypothesis that counts of follicles visible on the surface of the ovaries of Bos indicus cows and their classification into diameter size classes, are closely correlated with numbers of follicles in those size classes found by complete dissection of the ovary. immediately after ovariectomy, mean diameters (long and short axes averaged) of all follicles greater than or equal to 2 mm visible on the surface of each ovary were measured. All follicles greater than or equal to 2 mm were dissected from the ovaries, excess stroma removed and follicle diameters measured under a stereomicroscope using an ocular graticule. For each ovary, follicles were classified in either small (8 mm) categories based on either diameters of surface or dissected follicles. Data for numbers of surface and dissected follicles (mean +/- SE) in small, medium, large categories and total follicle numbers, respectively, were 24.4 +/- 1.6 vs. 28.0 +/- 1.9, 1.6 +/- + 0.2 vs. 11.6 +/- 1.0, 0.5 +/- 0.1 vs. 0.7 +/- 0.1 and 26.4 +/- 1.6 vs. 40.4 +/- 2.5. Correlation coefficients (r) for counts of surface and dissected follicles in small, medium, large and total follicle numbers were 0.76, 0.40, 0.69 and 0.79, respectively. Medium size follicles presented only a small translucent area on the surface of the ovary, leading to an underestimate of numbers when categorised by surface evaluation. Counts of follicles visible on the surface of the ovaries of Bos indicus cows and their classification into size classes based on estimated diameter, are closely correlated with numbers of follicles in those size classes found at dissection of the ovary for small (8 mm) and total follicles but not for medium sized (4-8 mm) follicles. (C) 1997 Elsevier Science B.V.

The influence of Flutter (R) VRP1 components on mucus transport of patients with bronchiectasis

Background: The Flutter (R) VRP1 combines high frequency oscillation and positive expiratory pressure (PEP). Objective: To separately evaluate the effect of the Flutter (R) VRP1 components (high frequency oscillation and PEP) on mucus transportability in patients with bronchiectasis. Methods: Eighteen patients with bronchiectasis received sessions with the Flutter (R) VRP1 or PEP for 30 min daily in a randomized, crossover study. The treatment duration was four weeks with one of the therapies, one week of a ""wash-out"" period and followed by four more weeks with the other treatment. Weekly secretion samples were collected and evaluated for mucociliary relative transport velocity (RTV), displacement in a simulated cough machine (SCM) and contact angle measurement (CAM). For the proposed comparisons, a linear regression model was used with mixed effects with a significance level of 5%. Results: The Flutter (R) VRP1 treatment resulted in greater displacement in SCM and lower CAM when comparing results from the first (9.6 +/- 3.4 cm and 29.4 +/- 5.7 degrees, respectively) and fourth weeks of treatment (12.44 +/- 10.5 cm and 23.28 +/- 6.2, respectively; p < 0.05). There was no significant difference in the RTV between the treatment weeks for either the Flutter (R) VRP1 or PEP. Conclusion: The use of the Flutter (R) VRP1 for four weeks is capable of altering the respiratory secretion transport properties, and this alteration is related to the high frequency oscillation component. (C) 2011 Elsevier Ltd. All rights reserved.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

Algebra of Classical Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type.

Oversight--Public Law 96-479--National Material and Minerals Policy, R. & D. Act of 1980 and consideration of H.R. 4281--Critical Materials Act of 1981 [microform] : hearings before the Subcommittee on Transportation, Aviation, and Materials and the Subcommittee on Science, Research, and Technology of the Committee on Science and Technology, U.S. House of Representatives, Ninety-seventh Congress, second session, April 20, 22, 1982.

"No. 117."

On a Class of Vertex Folkman Numbers

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).

The Inner Corona Algebra of a C0(X)-Algebra

Date of Acceptance: 15/07/2015

The Inner Corona Algebra of a C0(X)-Algebra

Date of Acceptance: 15/07/2015