scholarly journals Analysis, Evaluation and Exact Tracking of the Finite Precision Error Generated in Arbitrary Number of Multiplications

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1199
Author(s):  
Constantin Papaodysseus ◽  
Dimitris Arabadjis ◽  
Fotios Giannopoulos ◽  
Athanasios Rafail Mamatsis ◽  
Constantinos Chalatsis
Keyword(s):  
Theoretical Analysis ◽  
Statistical Properties ◽  
General Applicability ◽  
Precision Error ◽  
Finite Precision ◽  
Novel Approach ◽  
Exact Evaluation ◽  
Error Accumulation ◽  
Accumulated Error

In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications. It is shown that, as a rule, this operation is very “toxic”, in the sense that it may force the finite precision error accumulation to grow arbitrarily large, under specific conditions that are fully described here. First, an ensemble of definitions of general applicability is given for the rigorous determination of the number of erroneous digits accumulated in any quantity of an arbitrary algorithm. Next, the exact number of erroneous digits produced in a single multiplication is given as a function of the involved operands, together with formulae offering the corresponding probabilities. In case the statistical properties of these operands are known, exact evaluation of the aforementioned probabilities takes place. Subsequently, the statistical properties of the accumulated finite precision error during any number of successive multiplications are explicitly analyzed. A method for exact tracking of this accumulated error is presented, together with associated theorems. Moreover, numerous dedicated experiments are developed and the corresponding results that fully support the theoretical analysis are given. Eventually, a number of important, probable and possible applications is proposed, where all of them are based on the methodology and the results introduced in the present work. The proposed methodology is expandable, so as to tackle the round-off error analysis in all arithmetic operations.

The Use of TMAH to Etch Silicon and Expose Metal Bridging Failures

2000 ◽  
Author(s):  
Mark Morris ◽  
James Mohr ◽  
Esteban Ortiz ◽  
Steven Englebretson
Keyword(s):  
Failure Mechanism ◽  
Schottky Diodes ◽  
Tetramethylammonium Hydroxide ◽  
Novel Approach ◽  
Failure Location ◽  
Metal Etching ◽  
Plastic Mold

Abstract Determination of metal bridging failures on plastic encapsulated devices is difficult due to the metal etching effects that occur while removing many of the plastic mold compounds. Typically, the acids used to remove the encapsulation are corrosive to the metals that are found within the device. Thus, decapsulation can result in removal of the failure mechanism. Mechanical techniques are often not successful due to damage that results in destruction of the die and failure mechanism. This paper discusses a novel approach to these types of failures using a silicon etch and a backside evaluation. The desirable characteristics of the technique would be to remove the silicon and leave typical device metals unaffected. It would also be preferable that the device passivation and oxides not be etched so that the failure location is not disturbed. The use of Tetramethylammonium Hydroxide (TMAH), was found to fit these prerequisites. The technique was tested on clip attached Schottky diodes that exhibited resistive shorting. The use of the TMAH technique was successful at exposing thin solder bridges that extruded over the edge of the die resulting in failure.

Toward Fast Determination of Protein Stability Maps: Experimental and Theoretical Analysis of Mutants of a Nocardiopsis prasina Serine Protease

Biochemistry ◽  
2012 ◽  
Vol 51 (26) ◽  
pp. 5339-5347 ◽  
Author(s):  
Damien Farrell ◽  
Helen Webb ◽  
Michael A. Johnston ◽  
Thomas A. Poulsen ◽  
Fergal O’Meara ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Protein Stability ◽  
Serine Protease ◽  
Fast Determination ◽  
Stability Maps

Preservation for diverse users: digital preservation and the “Designated Community” at the Ontario Jewish Archives

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nathan Moles
Keyword(s):  
Digital Preservation ◽  
Reference Points ◽  
Digital Information ◽  
User Group ◽  
Content Type ◽  
Open Archival Information System ◽  
Novel Approach ◽  
Core Components ◽  
Unique Approach

PurposeConventional approaches to digital preservation posit that archives should define a Designated Community, or future user group, for whom they preserve digital information. Archivists can then use their knowledge of these users as a reference to help them deliver digital information that is intelligible and usable. However, this approach is challenging for archives with mandates to serve wide and diverse audiences; these archives risk undermining their efforts by focusing on the interests of a narrow user group.Design/methodology/approachA unique approach to this challenge was developed in the context of a project to build a digital preservation program at the Ontario Jewish Archives (OJA). It draws from previous research on this topic and is based on a combination of practical and theoretical considerations.FindingsThe approach described here replaces the reference of a Designated Community with three core components: a re-articulation of the Open Archival Information System (OAIS) mandatory responsibilities; the identification of three distinct tiers of access for digital records; and the implementation of an access portal that allows digital records to be accessed and rendered online. Together with supplemental shifts in reference points, they provide an alternative to the concept of a Designated Community in the determination of preservation requirements, the identification of significant properties, the creation of Representation Information and in the evaluation of success.Originality/valueThis article contributes a novel approach to the ongoing conversation about the Designated Community in digital preservation, its application and its limitations in an archival context.

Experimental Determination of Statistical Properties of Two-Phase Turbulent Motion

1960 ◽  
Vol 82 (3) ◽  
pp. 609-621 ◽  
Author(s):  
S. L. Soo ◽  
H. K. Ihrig ◽  
A. F. El Kouh
Keyword(s):  
Gas Phase ◽  
Tracer Diffusion ◽  
Statistical Properties ◽  
Solid Particles ◽  
Turbulent Motion ◽  
Two Phase ◽  
Gaseous State ◽  
Diffusion Technique ◽  
And Diffusion

Experimental methods for the determination of certain statistical properties of turbulent conveyance and diffusion of solid particles in a gaseous state are presented. Methods include a tracer-diffusion technique for the determination of gas-phase turbulent motion and a photo-optical technique for the determination of motion of solid particles. Results are discussed and compared with previous analytical results.

scholarly journals Fabrication of Carbohydrate Chips Based on Polydopamine for Real-Time Determination of Carbohydrate–Lectin Interactions by QCM Biosensor

Polymers ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1275 ◽  
Author(s):  
Kun Shang ◽  
Siyu Song ◽  
Yaping Cheng ◽  
Lili Guo ◽  
Yuxin Pei ◽  
...  
Keyword(s):  
Real Time ◽  
Con A ◽  
Quartz Crystals ◽  
Ulex Europaeus ◽  
Novel Approach ◽  
Ulex Europaeus Agglutinin I ◽  
Flow Through ◽  
Time Determination ◽  
Kinetics Of

A novel approach for preparing carbohydrate chips based on polydopamine (PDA) surface to study carbohydrate–lectin interactions by quartz crystal microbalance (QCM) biosensor instrument has been developed. The amino-carbohydrates were immobilized on PDA-coated quartz crystals via Schiff base reaction and/or Michael addition reaction. The resulting carbohydrate-chips were applied to QCM biosensor instrument with flow-through system for real-time detection of lectin–carbohydrate interactions. A series of plant lectins, including wheat germ agglutinin (WGA), concanavalin A (Con A), Ulex europaeus agglutinin I (UEA-I), soybean agglutinin (SBA), and peanut agglutinin (PNA), were evaluated for the binding to different kinds of carbohydrate chips. Clearly, the results show that the predicted lectin selectively binds to the carbohydrates, which demonstrates the applicability of the approach. Furthermore, the kinetics of the interactions between Con A and mannose, WGA and N-Acetylglucosamine were studied, respectively. This study provides an efficient approach to preparing carbohydrate chips based on PDA for the lectin–carbohydrate interactions study.

The Sequence of the Phase Growth during Diffusion in Ti-Based Systems

2019 ◽  
Vol 38 (2019) ◽  
pp. 151-157 ◽  
Author(s):  
Bartek Wierzba ◽  
Wojciech J. Nowak ◽  
Daria Serafin
Keyword(s):  
Theoretical Analysis ◽  
Entropy Production ◽  
Diffusion Coefficients ◽  
Intermetallic Phase ◽  
Intermetallic Phases ◽  
Diffusion Couples ◽  
Intrinsic Diffusion ◽  
Phase Growth ◽  
Diffusion Paths

AbstractThe interdiffusion in Ti-based alloys was studied. It was shown that during diffusion at 1,123 K formation of four intermetallic phases occurs. The diffusion paths for six different diffusion couples were determined. Moreover, the entropy production was calculated – the approximation used for determination of the sequence of intermetallic phase formation. In theoretical analysis, the intrinsic diffusion coefficients were determined from the modified Wagner method.

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