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

MSC 2010: 30C10, 32A30, 30G35

New mathematical tables containing the factors, squares, cubes, square roots, cube roots, reciprocals, and hyperbolic logarithms, of all numbers from 1 to 10000; tables of powers and prime numbers; an extensive table of formulæ, or general synopsis of the most important particulars relating to the doctrines of equations, series, fluxions, fluents, &c. &c. &c.

Mode of access: Internet.

The root extractor, exhibiting new rules and processes, for the formation and the resolution of equations of all orders in algebra; and for the evolution of the roots of any power in numbers: serving likewise as a key to all the examples of the cubic and higher equations in Bonnycastle's introduction to algebra.

Mode of access: Internet.

GA-based Optimization of a Fourth-order Sigma-delta Modulator for WLAN

Over-sampling sigma-delta analogue-to-digital converters (ADCs) are one of the key building blocks of state of the art wireless transceivers. In the sigma-delta modulator design the scaling coefficients determine the overall signal-to-noise ratio. Therefore, selecting the optimum value of the coefficient is very important. To this end, this paper addresses the design of a fourthorder multi-bit sigma-delta modulator for Wireless Local Area Networks (WLAN) receiver with feed-forward path and the optimum coefficients are selected using genetic algorithm (GA)- based search method. In particular, the proposed converter makes use of low-distortion swing suppression SDM architecture which is highly suitable for low oversampling ratios to attain high linearity over a wide bandwidth. The focus of this paper is the identification of the best coefficients suitable for the proposed topology as well as the optimization of a set of system parameters in order to achieve the desired signal-to-noise ratio. GA-based search engine is a stochastic search method which can find the optimum solution within the given constraints.

Distances between critical points and midpoints of zeros of hyperbolic polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Approximation of hyperbolic tangent activation function using hybrid methods

Artificial Neural Networks are widely used in various applications in engineering, as such solutions of nonlinear problems. The implementation of this technique in reconfigurable devices is a great challenge to researchers by several factors, such as floating point precision, nonlinear activation function, performance and area used in FPGA. The contribution of this work is the approximation of a nonlinear function used in ANN, the popular hyperbolic tangent activation function. The system architecture is composed of several scenarios that provide a tradeoff of performance, precision and area used in FPGA. The results are compared in different scenarios and with current literature on error analysis, area and system performance. © 2013 IEEE.

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.

Methods to convert continuous outcomes into odds ratios of treatment response and numbers needed to treat: meta-epidemiological study

Clinicians find standardized mean differences (SMDs) calculated from continuous outcomes difficult to interpret. Our objective was to determine the performance of methods in converting SMDs or means to odds ratios of treatment response and numbers needed to treat (NNTs) as more intuitive measures of treatment effect.

Histomorphologic evaluation of extracorporeal shock wave therapy of the fourth metatarsal bone and the origin of the suspensory ligament in horses without lameness

OBJECTIVE: To determine via histologic examination and scintigraphy the effect of focused extracorporeal shock wave therapy (ESWT) on normal bone and the bone-ligament interface in horses. ANIMALS: 6 horses without lameness. PROCEDURE: Origins of the suspensory ligament at the metacarpus (35-mm probe depth) and fourth metatarsal bone (5-mm probe depth) were treated twice (days 0 and 16) with 2,000 shocks (energy flux density, 0.15 mJ/mm2). One forelimb and 1 hind limb were randomly treated, and the contralateral limbs served as nontreated controls. Bone scans were performed on days -1 (before ESWT), 3, 16, and 19. Histomorphologic studies of control and treated tissues were performed on day 30. RESULTS: ESWT significantly increased the number of osteoblasts but caused no damage to associated soft tissue structures and did not induce cortical microfractures. A significant correlation between osteoblast numbers and radiopharmaceutical uptake was noticed on lateral views of the hind limb on days 3 and 16 and on caudal views of the forelimb on day 3. CONCLUSIONS AND CLINICAL RELEVANCE: Results suggested that ESWT has the potential to increase osteoblast numbers in horses. The correlation between increased osteoblast numbers and radio-pharmaceutical uptake 3 days and 16 days after the first ESWT suggested that stimulation of osteogenesis occurred soon after ESWT. No damage to bone or the bone-ligament interface should occur at the settings used in this study, and ESWT can therefore be administered safely in horses.

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.

Comparing the performance of hyperbolic and circular rod quadrupole mass spectrometers with applied higher order auxiliary excitation

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

Cloning of a receptor for amphibian [Phe13]bombesin distinct from the receptor for gastrin-releasing peptide: identification of a fourth bombesin receptor subtype (BB4).

Bombesin is a tetradecapeptide originally isolated from frog skin and demonstrated to have a wide range of actions in mammals. Based on structural homology and similar biological activities, gastrin-releasing peptide (GRP) has been considered the mammalian equivalent of bombesin. We previously reported that frogs have both GRP and bombesin, which therefore are distinct peptides. We now report the cloning of a bombesin receptor subtype (BB4) that has higher affinity for bombesin than GRP. PCR was used to amplify cDNAs related to the known bombesin receptors from frog brain. Sequence analysis of the amplified cDNAs revealed 3 classes of receptor subtypes. Based on amino acid homology, two classes were clearly the amphibian homologs of the GRP and neuromedin B receptors. The third class was unusual and a full-length clone was isolated from a Bombina orientalis brain cDNA library. Expression of the receptor in Xenopus oocytes demonstrated that the receptor responded to picomolar concentrations of [Phe13]-bombesin, the form of bombesin most prevalent in frog brain. The relative rank potency of bombesin-like peptides for this receptor was [Phe13]bombesin > [Leu13]bombesin > GRP > neuromedin B. In contrast, the rank potency for the GRP receptor is GRP > [Leu13]bombesin > [Phe13]bombesin > neuromedin B. Transient expression in CHOP cells gave a Ki for [Phe13]bombesin of 0.2 nM versus a Ki of 2.1 nM for GRP. Distribution analysis showed that this receptor was expressed only in brain, consistent with the distribution of [Phe13]-bombesin. Thus, based on distribution and affinity, this bombesin receptor is the receptor for [Phe13]bombesin. Phylogenetic analysis suggests that this receptor separated prior to separation of the GRP and neuromedin B receptors; thus, BB4 receptors and their cognate ligands may also exist in mammals.