A New Proof of Winquist's Identity

Integers ◽  
2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Zhu Cao
Keyword(s):  
Vital Role ◽  
Winquist’S Identity ◽  
Winquist's Identity

Abstract.Winquist's identity plays a vital role in the proof of Ramanujan's congruence

ON GENERAL SERIES-PRODUCT IDENTITIES

2009 ◽  
Vol 05 (06) ◽  
pp. 1129-1148 ◽  
Author(s):  
SIN-DA CHEN ◽  
SEN-SHAN HUANG
Keyword(s):  
Quintuple Product Identity ◽  
General Series ◽  
Product Identity ◽  
Winquist’S Identity ◽  
Series Product ◽  
Winquist's Identity

We derive the general series-product identities from which we deduce several applications, including an identity of Gauss, the generalization of Winquist's identity by Carlitz and Subbarao, an identity for [Formula: see text], the quintuple product identity, and the octuple product identity.

scholarly journals Hirschhorn's identities

1999 ◽  
Vol 60 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Paul Hammond ◽  
Richard Lewis ◽  
Zhi-Guo Liu
Keyword(s):  
Power Series ◽  
General Identity ◽  
Quintuple Product Identity ◽  
Product Identity ◽  
Winquist’S Identity ◽  
Winquist's Identity

We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identity.

scholarly journals Two Simple Proofs of Winquist's Identity

10.37236/388 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Chutchai Nupet ◽  
Sarachai Kongsiriwong
Keyword(s):  
Triple Product ◽  
Roots Of Unity ◽  
Basic Properties ◽  
Product Identity ◽  
Jacobi Triple Product Identity ◽  
Winquist’S Identity ◽  
Winquist's Identity

We give two new proofs of Winquist's identity. In the first proof, we use basic properties of cube roots of unity and the Jacobi triple product identity. The latter does not use the Jacobi triple product identity.

Ultrastructure of Lymphatic Capillaries in the Transport of Colloidal Particles

1967 ◽  
Vol 25 ◽  
pp. 186-187
Author(s):  
L. V. Leak ◽  
J. F. Burke
Keyword(s):  
Connective Tissue ◽  
Colloidal Particles ◽  
Ultrastructural Level ◽  
Vital Role ◽  
Time Intervals ◽  
Thorium Dioxide ◽  
Lymphatic Capillary ◽  
Tissue Area ◽  
Rapid Removal ◽  
Tissue Fluids

The vital role played by the lymphatic capillaries in the transfer of tissue fluids and particulate materials from the connective tissue area can be demonstrated by the rapid removal of injected vital dyes into the tissue areas. In order to ascertain the mechanisms involved in the transfer of substances from the connective tissue area at the ultrastructural level, we have injected colloidal particles of varying sizes which range from 80 A up to 900-mμ. These colloidal particles (colloidal ferritin 80-100A, thorium dioxide 100-200 A, biological carbon 200-300 and latex spheres 900-mμ) are injected directly into the interstitial spaces of the connective tissue with glass micro-needles mounted in a modified Chambers micromanipulator. The progress of the particles from the interstitial space into the lymphatic capillary lumen is followed by observing tissues from animals (skin of the guinea pig ear) that were injected at various time intervals ranging from 5 minutes up to 6 months.

Three-Dimensional reconstruction of isolated centrosomes by automated electron tomography

1994 ◽  
Vol 52 ◽  
pp. 310-311
Author(s):  
M.B. Braunfeld ◽  
M. Moritz ◽  
B.M. Alberts ◽  
J.W. Sedat ◽  
D.A. Agard
Keyword(s):  
Electron Tomography ◽  
Three Dimensional ◽  
Vital Role ◽  
Complex Nature ◽  
Animal Cells ◽  
Microtubule Organizing Center ◽  
Nucleation Sites ◽  
Dimensional Reconstruction ◽  
Organizing Center ◽  
Resolution Model

In animal cells, the centrosome functions as the primary microtubule organizing center (MTOC). As such the centrosome plays a vital role in determining a cell's shape, migration, and perhaps most importantly, its division. Despite the obvious importance of this organelle little is known about centrosomal regulation, duplication, or how it nucleates microtubules. Furthermore, no high resolution model for centrosomal structure exists.We have used automated electron tomography, and reconstruction techniques in an attempt to better understand the complex nature of the centrosome. Additionally we hope to identify nucleation sites for microtubule growth.Centrosomes were isolated from early Drosophila embryos. Briefly, after large organelles and debris from homogenized embryos were pelleted, the resulting supernatant was separated on a sucrose velocity gradient. Fractions were collected and assayed for centrosome-mediated microtubule -nucleating activity by incubating with fluorescently-labeled tubulin subunits. The resulting microtubule asters were then spun onto coverslips and viewed by fluorescence microscopy.

Asiana Airlines Flight 214

2014 ◽  
Vol 4 (2) ◽  
pp. 113-121 ◽  
Author(s):  
Stephanie Chow ◽  
Stephen Yortsos ◽  
Najmedin Meshkati
Keyword(s):  
Human Factors ◽  
Aviation Safety ◽  
Cultural Factors ◽  
Vital Role ◽  
Cultural Issues ◽  
Flight Crew ◽  
Pilot Performance ◽  
Engineering Designs ◽  
Flight Deck

This article focuses on a major human factors–related issue that includes the undeniable role of cultural factors and cockpit automation and their serious impact on flight crew performance, communication, and aviation safety. The report concentrates on the flight crew performance of the Boeing 777–Asiana Airlines Flight 214 accident, by exploring issues concerning mode confusion and autothrottle systems. It also further reviews the vital role of cultural factors in aviation safety and provides a brief overview of past, related accidents. Automation progressions have been created in an attempt to design an error-free flight deck. However, to do that, the pilot must still thoroughly understand every component of the flight deck – most importantly, the automation. Otherwise, if pilots are not completely competent in terms of their automation, the slightest errors can lead to fatal accidents. As seen in the case of Asiana Flight 214, even though engineering designs and pilot training have greatly evolved over the years, there are many cultural, design, and communication factors that affect pilot performance. It is concluded that aviation systems designers, in cooperation with pilots and regulatory bodies, should lead the strategic effort of systematically addressing the serious issues of cockpit automation, human factors, and cultural issues, including their interactions, which will certainly lead to better solutions for safer flights.

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