scholarly journals Pythagorean Triples before and after Pythagoras

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 62
Author(s):  
Ravi P. Agarwal

Following the corrected chronology of ancient Hindu scientists/mathematicians, in this article, a sincere effort is made to report the origin of Pythagorean triples. We shall account for the development of these triples from the period of their origin and list some known astonishing directions. Although for researchers in this field, there is not much that is new in this article, we genuinely hope students and teachers of mathematics will enjoy this article and search for new directions/patterns.

1986 ◽  
Vol 9 (4) ◽  
pp. 274-284 ◽  
Author(s):  
Virginia L. Fortner

This study examined whether intermediate-grade LD students could generalize creativity training to increase competency on a spontaneous writing task. The investigation used seven intact classrooms to analyze differences between groups on initial creative productive-thinking level, measured by Torrance Test of Creative Thinking (TTCT) subtest Tin Can: Unusual Uses. Mean difference scores were compared for number of (a) words, (b) thought units, (c) subordinate clauses, (d) vocabulary, and (e) thematic maturity on the story subtest of the Test of Written Language (TOWL) given before and after training in New Directions in Creativity (NDC). A nonequivalent control-group design was used. Teachers administered the TTCT and TOWL pre- and posttests to 49 subjects in self-contained LD classrooms. Teachers of a 25-member experimental (E) group also conducted NDC intervention, including nonjudgmental brainstorming activities, three times per week for nine weeks. Analysis of covariance results revealed that, after creative productive-thinking training, the E group significantly improved (p < .05) in number of thought units, subordinate clauses, and thematic maturity. The results of this initial probe should impact upon training of teachers of LD students.


2018 ◽  
Vol 14 (2) ◽  
pp. 20170743 ◽  
Author(s):  
Kevin D. Lafferty ◽  
John P. McLaughlin ◽  
Daniel S. Gruner ◽  
Taylor A. Bogar ◽  
An Bui ◽  
...  

The Asian tiger mosquito, Aedes albopictus, appears to have been extirpated from Palmyra Atoll following rat eradication. Anecdotal biting reports, collection records, and regular captures in black-light traps showed the species was present before rat eradication. Since then, there have been no biting reports and no captures over 2 years of extensive trapping (black-light and scent traps). By contrast, the southern house mosquito, Culex quinquefasciatus, was abundant before and after rat eradication. We hypothesize that mammals were a substantial and preferred blood meal for Aedes , whereas Culex feeds mostly on seabirds. Therefore, after rat eradication, humans and seabirds alone could not support positive population growth or maintenance of Aedes . This seems to be the first documented accidental secondary extinction of a mosquito. Furthermore, it suggests that preferred host abundance can limit mosquito populations, opening new directions for controlling important disease vectors that depend on introduced species like rats.


2020 ◽  
Vol 12 (3) ◽  
pp. 58
Author(s):  
Ahmad Hassan ◽  
Wade Cook

Project portfolio management (PPM) is an important area of interest in many organizations. There is a wide literature on each of many different aspects of PPM. The central purpose of the current paper is to focus on a specific sub-area of PPM, namely the project portfolio selection (PPS) problem. Specifically, we develop a new methodology that will aid management in choosing from a set of candidate project proposals, a subset of those project proposals that align with strategic objectives of the organization. Research methodology is based on the data envelopment analysis (DEA) construct to compare a set of decision making units (such as proposed projects) to arrive at an efficiency score for each member of this competing set, derive the best performers, generate an efficiency frontier and quantify inefficiency in the non-best performers. While DEA has been applied in numerous settings, the unique feature of the project portfolio application is the presence of two sets of data, namely pre-implementation “estimates”, and post-implementation “actuals”. Our methodology is unique in that it uses the idea of dual DEA frontiers based on such before and after data for a set of past projects. Dual frontier concept makes not only an important practical contribution to the PPS literature, but as well it opens new directions and provides an innovative advancement in the DEA literature. The requisite data is not publicly available. We believe, however, that the stand-alone methodology makes an important contribution to both the DEA and PPS literature.


2019 ◽  
Vol 42 ◽  
Author(s):  
Penny Van Bergen ◽  
John Sutton

Abstract Sociocultural developmental psychology can drive new directions in gadgetry science. We use autobiographical memory, a compound capacity incorporating episodic memory, as a case study. Autobiographical memory emerges late in development, supported by interactions with parents. Intervention research highlights the causal influence of these interactions, whereas cross-cultural research demonstrates culturally determined diversity. Different patterns of inheritance are discussed.


Author(s):  
J. Temple Black

Tool materials used in ultramicrotomy are glass, developed by Latta and Hartmann (1) and diamond, introduced by Fernandez-Moran (2). While diamonds produce more good sections per knife edge than glass, they are expensive; require careful mounting and handling; and are time consuming to clean before and after usage, purchase from vendors (3-6 months waiting time), and regrind. Glass offers an easily accessible, inexpensive material ($0.04 per knife) with very high compressive strength (3) that can be employed in microtomy of metals (4) as well as biological materials. When the orthogonal machining process is being studied, glass offers additional advantages. Sections of metal or plastic can be dried down on the rake face, coated with Au-Pd, and examined directly in the SEM with no additional handling (5). Figure 1 shows aluminum chips microtomed with a 75° glass knife at a cutting speed of 1 mm/sec with a depth of cut of 1000 Å lying on the rake face of the knife.


Author(s):  
R. F. Bils ◽  
W. F. Diller ◽  
F. Huth

Phosgene still plays an important role as a toxic substance in the chemical industry. Thiess (1968) recently reported observations on numerous cases of phosgene poisoning. A serious difficulty in the clinical handling of phosgene poisoning cases is a relatively long latent period, up to 12 hours, with no obvious signs of severity. At about 12 hours heavy lung edema appears suddenly, however changes can be seen in routine X-rays taken after only a few hours' exposure (Diller et al., 1969). This study was undertaken to correlate these early changes seen by the roengenologist with morphological alterations in the lungs seen in the'light and electron microscopes.Forty-two adult male and female Beagle dogs were selected for these exposure experiments. Treated animals were exposed to 94.5-107-5 ppm phosgene for 10 min. in a 15 m3 chamber. Roentgenograms were made of the thorax of each animal before and after exposure, up to 24 hrs.


Author(s):  
M. H. Wheeler ◽  
W. J. Tolmsoff ◽  
A. A. Bell

(+)-Scytalone [3,4-dihydro-3,6,8-trihydroxy-l-(2Hj-naphthalenone] and 1,8-di- hydroxynaphthalene (DHN) have been proposed as intermediates of melanin synthesis in the fungi Verticillium dahliae (1, 2, 3, 4) and Thielaviopsis basicola (4, 5). Scytalone is enzymatically dehydrated by V. dahliae to 1,3,8-trihydroxynaphthalene which is then reduced to (-)-vermelone [(-)-3,4- dihydro-3,8-dihydroxy-1(2H)-naphthalenone]. Vermelone is subsequently dehydrated to DHN which is enzymatically polymerized to melanin.Melanin formation in Curvularia sp., Alternaria sp., and Drechslera soro- kiniana was examined by light and electron-transmission microscopy. Wild-type isolates of each fungus were compared with albino mutants before and after treatment with 1 mM scytalone or 0.1 mM DHN in 50 mM potassium phosphate buffer, pH 7.0. Both chemicals were converted to dark pigments in the walls of hyphae and conidia of the albino mutants. The darkened cells were similar in appearance to corresponding cells of the wild types under the light microscope.


Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.


Author(s):  
R. M. Anderson

Aluminum-copper-silicon thin films have been considered as an interconnection metallurgy for integrated circuit applications. Various schemes have been proposed to incorporate small percent-ages of silicon into films that typically contain two to five percent copper. We undertook a study of the total effect of silicon on the aluminum copper film as revealed by transmission electron microscopy, scanning electron microscopy, x-ray diffraction and ion microprobe techniques as a function of the various deposition methods.X-ray investigations noted a change in solid solution concentration as a function of Si content before and after heat-treatment. The amount of solid solution in the Al increased with heat-treatment for films with ≥2% silicon and decreased for films <2% silicon.


Author(s):  
T. C. Tisone ◽  
S. Lau

In a study of the properties of a Ta-Au metallization system for thin film technology application, the interdiffusion between Ta(bcc)-Au, βTa-Au and Ta2M-Au films was studied. Considered here is a discussion of the use of the transmission electron microscope(TEM) in the identification of phases formed and characterization of the film microstructures before and after annealing.The films were deposited by sputtering onto silicon wafers with 5000 Å of thermally grown oxide. The film thicknesses were 2000 Å of Ta and 2000 Å of Au. Samples for TEM observation were prepared by ultrasonically cutting 3mm disks from the wafers. The disks were first chemically etched from the silicon side using a HNO3 :HF(19:5) solution followed by ion milling to perforation of the Au side.


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