scholarly journals Logical Principles in Ternary Mathematics

2021 ◽  
pp. 49-54
Author(s):  
Ruslan Pozinkevych
Keyword(s):  
Fundamental Principle ◽  
Functional Approach ◽  
Truth Table ◽  
Ternary Addition ◽  
Triangle Diagram ◽  
Logical Operators ◽  
Form And Function ◽  
Set Up ◽  
The Given ◽  
Truth Tables

Introduction/Background:Our new research called “Logical Principles in Ternary Mathematics“ is  an attempt to establish connection between logical and mathematical principles governing Ternary Mathematics and address issues that appeared earlier while making truth tables for “Ternary addition” and “Ternary Multiplication” presented by the same author in “Ternary Mathematics Principles Truth Tables and Logical Operators 3 D Placement of Logical Elements Extensions of Boolean Algebra” publication.The title “Logical Principles in Ternary Mathematics“ is not randomly chosen To be able to set up relations between elements in the given discipline one usually employs the basic principle of meaning-form and function In the same way we propose a logical triangle “Component”,”Vector”,”Decimal” to prove fundamental principle governing “Ternary Mathematics” presented in the given research. Aims/Objectives: The aim of the article is to set up connection between mathematical and logical rules governing Ternary Mathematics The main postulates of the Ternary Mathematics can be demonstrated by the abstract scheme or a triangle the vertices of which are “Component”,”Vector”,”Decimal” We use a triangle diagram to prove the functionality of the chosen principle. The three components are each connected with other two and transition is possible from one to another without changing the shape of a diagram and the principle applied. Methodology: The most difficult part is to “translate” Algebra and Numeric Analysis into Mathematical Logic and vice versa Traditional methods of logic fail to do this transition therefore a new functional approach is chosen. Results and Conclusion: As  a result of this functional approach a new Ternary addition Truth Table is made The new Ternary Truth Table consists of the 3 literals (Т, ₸,F) Truth Negative, False and the last column of the table is the logical sum of the two. For example: Т+T=T Unlike the old table it presents a sum of two numbers in a vector form and therefore makes it possible to use it in mathematics as well as in logic.

A New Approach for Simplification of Logical Propositions with Two Propositional Variables Using Truth Tables

2020 ◽  
Vol 13 ◽  
Author(s):  
Maher Nabulsi ◽  
Nesreen Hamad ◽  
Sokyna Alqatawneh
Keyword(s):  
Digital Circuits ◽  
Truth Table ◽  
New Method ◽  
Alternative Methods ◽  
Discrete Mathematics ◽  
New Approach ◽  
Logical Proposition ◽  
The Given ◽  
First Time ◽  
Truth Tables

Background: Propositions simplification is a classic topic in discrete mathematics that is applied in different areas of science such as programs development and digital circuits design. Investigating alternative methods would assist in presenting different approaches that can be used to obtain better results. This paper proposes a new method to simplify any logical proposition with two propositional variables without using the logical equivalences. Methods: This method is based on constructing a truth table for the given proposition, and applying one of the following two concepts: the sum of Minterms or the product of Maxterms which has not been used previously in discrete mathematics, along with five new rules that are introduced for the first time in this work. Results: The proposed approach was applied to some examples, where its correctness was verified by applying the logical equivalences method. Applying the two methods showed that the logical equivalences method cannot give the simplest form easily; especially if the proposition cannot be simplified, and it cannot assist in determining whether the obtained solution represent the simplest form of this proposition or not. Conclusion: In comparison with the logical equivalences method, the results of all the tested propositions show that our method is outperforming the current used method, as it provides the simplest form of logical propositions in fewer steps, and it overcomes the limitations of logical equivalences method. Originality/value: This paper fulfils an identified need to provide a new method to simplify any logical proposition with two propositional variables.

Prediction of root damaging during mechanical shaking of fruit trees

2014 ◽  
Vol 10 (1) ◽  
pp. 1-15
Author(s):  
Z. Láng
Keyword(s):  
Field Experiments ◽  
Calculated Data ◽  
Fruit Trees ◽  
List Type ◽  
Structure Model ◽  
Root Damage ◽  
Set Up ◽  
Simple Tree ◽  
The Given ◽  
Cherry Trees

The possible effect of shaker harvest on root damage of 10-year-old cherry trees was studied on a simple tree structure model. The model was composed of elastic trunk and rigid main roots, the ends of which were connected to the surrounding soil via springs and dumping elements. Equations were set up to be able to calculate the relation between shaking height on the trunk and strain in the roots. To get the data for root break and their elongation at different shaking heights on the trunk, laboratory and field experiments were carried out on cherry trees and on their roots. Having evaluated the measured and calculated data it could be concluded that root damage is to be expected even at 3.6% strain and the risk of it increases with increased trunk amplitudes, i.e.with the decrease of shaking heightat smaller stem diameters (i.e. in younger plantation), andif the unbalanced mass of the shaker machine is too large for the given tree size.

scholarly journals The impact of translation modality on user experience: an eye-tracking study of the Microsoft Word user interface

2021 ◽  
Author(s):  
Ana Guerberof Arenas ◽  
Joss Moorkens ◽  
Sharon O’Brien
Keyword(s):  
User Interface ◽  
Eye Tracking ◽  
Cognitive Load ◽  
Task Completion ◽  
Eye Tracker ◽  
Software Products ◽  
Microsoft Word ◽  
Set Up ◽  
The Impact ◽  
The Given

AbstractThis paper presents results of the effect of different translation modalities on users when working with the Microsoft Word user interface. An experimental study was set up with 84 Japanese, German, Spanish, and English native speakers working with Microsoft Word in three modalities: the published translated version, a machine translated (MT) version (with unedited MT strings incorporated into the MS Word interface) and the published English version. An eye-tracker measured the cognitive load and usability according to the ISO/TR 16982 guidelines: i.e., effectiveness, efficiency, and satisfaction followed by retrospective think-aloud protocol. The results show that the users’ effectiveness (number of tasks completed) does not significantly differ due to the translation modality. However, their efficiency (time for task completion) and self-reported satisfaction are significantly higher when working with the released product as opposed to the unedited MT version, especially when participants are less experienced. The eye-tracking results show that users experience a higher cognitive load when working with MT and with the human-translated versions as opposed to the English original. The results suggest that language and translation modality play a significant role in the usability of software products whether users complete the given tasks or not and even if they are unaware that MT was used to translate the interface.

scholarly journals Neutralization of Acidic Wastewater from a Steel Plant by Using CaO-Containing Waste Materials from Pulp and Paper Industries

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2653
Author(s):  
Tova Jarnerud ◽  
Andrey V. Karasev ◽  
Pär G. Jönsson
Keyword(s):  
Fly Ash ◽  
Pulp And Paper ◽  
Waste Materials ◽  
Paper Mills ◽  
Steel Mills ◽  
Lime Mud ◽  
Set Up ◽  
Pulp And Paper Industries ◽  
The Given ◽  
Acidic Wastewater

In this study, CaO-containing wastes from pulp and paper industries such as fly ash (FA) and calcined lime mud (LM) were utilized to neutralize and purify acidic wastewaters from the pickling processes in steel mills. The investigations were conducted by laboratory scale trials using four different batches of wastewaters and additions of two types of CaO-containing waste materials. Primary lime (PL), which is usually used for the neutralization, was also tested in the same experimental set up in the sake of comparison. The results show that these secondary lime sources can effectively increase the pH of the acidic wastewaters as good as the commonly used primary lime. Therefore, these secondary lime sources could be potential candidates for application in neutralization processes of industrial acidic wastewater treatment. Moreover, concentrations of metals (such as Cr, Fe, Ni, Mo and Zn) can decrease dramatically after neutralization by using secondary lime. The LM has a purification effect from the given metals, similar to the PL. Application of fly ash and calcined lime mud as neutralizing agents can reduce the amount of waste from pulp and paper mills sent to landfill and decrease the need for nature lime materials in the steel industry.

Feeder Bus Timetable Design and Vehicle Size Setting in Peak Hour Demand Conditions

2019 ◽  
Vol 2673 (10) ◽  
pp. 321-332 ◽  
Author(s):  
Xueping Dou ◽  
Qiang Meng
Keyword(s):  
Mixed Integer ◽  
Arrival Times ◽  
Non Linear Programming ◽  
Bee Colony ◽  
Proposed Model ◽  
Feeder Bus ◽  
Minlp Model ◽  
Failure Cost ◽  
Set Up ◽  
The Given

This study proposes a solution to the feeder bus timetabling problem, in which the terminal departure times and vehicle sizes are simultaneously determined based on the given transfer passengers and their arrival times at a bus terminal. The problem is formulated as a mixed integer non-linear programming (MINLP) model with the objective of minimizing the transfer waiting time of served passengers, the transfer failure cost of non-served passengers, and the operating costs of bus companies. In addition to train passengers who plan to transfer to buses, local passengers who intend to board buses are considered and treated as passengers from virtual trains in the proposed model. Passenger attitudes and behaviors toward the waiting queue caused by bus capacity constraints in peak hour demand conditions are explicitly embedded in the MINLP model. A hybrid artificial bee colony (ABC) algorithm is developed to solve the MINLP model. Various experiments are set up to account for the performance of the proposed model and solution algorithm.

scholarly journals A survey of short-term and long-term stability of tube parameters in a mammography unit

2014 ◽  
Vol 29 (4) ◽  
pp. 321-325
Author(s):  
Jovica Praskalo ◽  
Jasna Davidovic ◽  
Biljana Kocic ◽  
Monika Zivkovic ◽  
Svetlana Pejovic
Keyword(s):  
Screening Program ◽  
Short Term ◽  
X Ray ◽  
Term Stability ◽  
Long Term Stability ◽  
Mammography Screening Program ◽  
The Republic ◽  
Set Up ◽  
The Given

In order to set up a successful mammography screening program in the Republic of Srpska, a Siemens Mammomat 1000 X-ray machine was selected for analysis as the said mammography system is widely used in clinical practice. The variations in tube parameters (specific air kerma, high-voltage accuracy and reproducibility, linearity between exposure and dose exposure time) were monitored over a five-year period, from 2008 to 2012. In addition, due to observed daily fluctuations for chosen parameters, a series of measurements were performed three times a day within a single-month period (mainly October 2012). The goal of such an experimental set up is to assess short-term and long-term stability of tube parameters in the given mammography unit and to make a comparison between them. The present paper shows how an early detection of significant parameter fluctuations can help eliminate irregularities and optimize the performance of mammography systems.

Affect and letter-writing: Unconventional conventions in casual writing by young Japanese women

1997 ◽  
Vol 26 (1) ◽  
pp. 103-136 ◽  
Author(s):  
Kuniyoshi Kataoka
Keyword(s):  
Social Change ◽  
Japanese Women ◽  
Written Language ◽  
Letter Writing ◽  
Form And Function ◽  
Young Japanese Women ◽  
And Function ◽  
The Given

ABSTRACTWith special attention to the use of unconventional practices and pictorial signs in casual letter writing, this article shows how young Japanese women effectively exploit affect-laden shape, form, and function in order to establish intimate and solidary relationships. They rely on both conventional and unconventional aspects of Japanese orthography, encoding affect specific to the given context and merging spoken with written modes of self-representation. In so doing, they seem to draw on diverse “frames” of written language, and to manipulate symbolic means of association and integration for achieving reciprocity. These features not only provide the basis for reciprocity, but may also suggest a new mode of literacy caused by social change. (Writing, literacy, affect, Japanese, pictorial signs, letter-writing)

scholarly journals Admissible Hybrid Z-Contractions in b-Metric Spaces

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 2 ◽  
Author(s):  
Ioan Cristian Chifu ◽  
Erdal Karapınar
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Uniqueness Result ◽  
Point Problem ◽  
Well Posedness ◽  
Simulation Functions ◽  
Set Up ◽  
The Given

In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied.

scholarly journals Friction and Wear Performance of Various Polymer Coatings for Journal Bearings under Stop Start Sliding

Lubricants ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Florian Summer ◽  
Florian Grün ◽  
Emma R Ravenhill
Keyword(s):  
Friction And Wear ◽  
Combustion Engine ◽  
Polymer Coatings ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Wear Performance ◽  
Set Up ◽  
Many Core ◽  
The Given

Increasing environmental legislation and demands for improved fuel economy performance have resulted in the introduction of various measures to optimize the internal combustion engine. Many of these actions significantly change the operating conditions of the engines and bring with them new challenges that original engine manufacturers (OEMs) have to solve. One example is stop start technology, which changes the operation of many core parts of engines such as journal bearings. Hence, the current paper deals with this topic. In particular, different polymer coated bearings have been studied regarding their friction and wear performance under stop start sliding. Detailed material characterization of the materials was carried out using light microscopy and scanning electron microscopy. Furthermore, tribometric tests were conducted under controlled and similar conditions on a TE92 tribometer using a bearing segment test set up. The results show that the various polymer coated bearings tested provide enhanced friction and wear performance in comparison to other bearing types (e.g., lead-based electroplated) and that friction and wear performance differs also among them. In this regard, a higher amount of solid lubricant fillers and a dense filler structure appears to be beneficial under the given test conditions.

Graphing True-False Statements

1969 ◽  
Vol 62 (7) ◽  
pp. 553-556
Author(s):  
Margaret Wiscamb
Keyword(s):  
Truth Table ◽  
Graphic Representation ◽  
Truth Values ◽  
Truth Tables ◽  
True False ◽  
Tedious Process ◽  
Three Components

In elementary logic the construction of truth tables, while not difficult, can be a long and tedious process. In this article I would like to present a simple graphic representation of the truth values of compound statements involving two or three components. The graph gives all the information found in a truth table and pictures the statement as an easily recognizable pattern. By using this graphing procedure, the simplifying of statements is shortened considerably. In fact, for statements involving only two components, with a little practice it can usually be done by inspection. Proving that a statement is a tautology becomes almost trivial.

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