The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. ...Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years ...and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves.
The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
To date, researchers investigating nonsymbolic number processes devoted little attention to the visual properties of their stimuli. This is unexpected, as nonsymbolic number is defined by its visual ...characteristics. When number changes, its visual properties change accordingly. In this study, we investigated the influence of different visual properties on nonsymbolic number processes and show that the current assumptions about the relation between number and its visual characteristics are incorrect. Similar to previous studies, we controlled the visual cues: Each visual cue was not predictive of number. Nevertheless, participants showed congruency effects induced by the visual properties of the stimuli. These congruency effects scaled with the number of visual cues manipulated, implicating that people do not extract number from a visual scene independent of its visual cues. Instead, number judgments are based on the integration of information from multiple visual cues. Consequently, current ways to control the visual cues of the number stimuli are insufficient, as they control only a single variable at the time. And, more important, the existence of an approximate number system that can extract number independent of the visual cues appears unlikely. We therefore propose that number judgment is the result of the weighing of several distinct visual cues. (Contains 3 figures and 1 footnote.)
Prior studies indicate that children vary widely in their mathematical knowledge by the time they enter preschool and that this variation predicts levels of achievement in elementary school. In a ...longitudinal study of a diverse sample of 44 preschool children, we examined the extent to which their understanding of the cardinal meanings of the number words (e.g., knowing that the word "four" refers to sets with 4 items) is predicted by the "number talk" they hear from their primary caregiver in the early home environment. Results from 5 visits showed substantial variation in parents' number talk to children between the ages of 14 and 30 months. Moreover, this variation predicted children's knowledge of the cardinal meanings of number words at 46 months, even when socioeconomic status and other measures of parent and child talk were controlled. These findings suggest that encouraging parents to talk about number with their toddlers, and providing them with effective ways to do so, may positively impact children's school achievement.
•Excessive addition or improper use of SPAs can produce possible harms.•BHT can induce apoptosis and promote tumorigenesis.•BHA metabolites are involved in carcinogenicity process.•TBHQ ...carcinogenicity is related to induction of TQ and CYP1A1.
Synthetic phenolic antioxidants can interact with peroxides produced by food. This paper reviews correlation between BHA, BHT and TBHQ metabolism and harms they cause and provides a theoretical basis for rational use of BHA, BHT and TBHQ in food, and also put some attention on the transformation and metabolic products of PG. We introduce BHA, BHT, TBHQ, PG and their possible metabolic pathways, and discuss possible harms and their specific mechanisms responsible. Excessive addition or incorrect use of synthetic phenolic antioxidants results in carcinogenicity, cytotoxicity, oxidative stress induction and endocrine disrupting effects, which warrant attention. BHA carcinogenicity is related to production of metabolites TBHQ and TQ, and cytotoxic effect of BHA is the main cause of apoptosis induction. BHT carcinogenicity depends on DNA damage degree, and tumour promotion is mainly related to production of quinone methylation metabolites. TBHQ carcinogenicity is related to induction of metabolite TQ and enzyme CYP1A1.
Summing It Up Ash, Avner; Gross, Robert
2016, 2016., 20160517, 2016-05-17
eBook
We use addition on a daily basis-yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity?Summing It Upuses addition as a springboard to ...present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research.
Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series-long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms-the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.
Appropriate for numbers novices as well as college math majors,Summing It Updelves into mathematics that will enlighten anyone fascinated by numbers.
•A combined micropolar and nanofluid effects of thermal system has been investigated.•Energy conversion is application for thermal system.•Thermal energy enhancement are observed with various values ...of pertinent parameters.•The results are comparison with other studies have been examined.
An applied thermal system for heat and mass transfer and energy management problem of hydromagnetic flow with magnetic and viscous dissipation effects micropolar nanofluids towards a stretching sheet has been studied. A system of partial differential equations for micropolar and nanofluid has been analyzed by a combination of the similarity transformation and accurate finite-difference method. Those solutions are used to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. The related importance dimensionless parameters are Prandtl number Pr, magnetic parameter M, material parameter K, Eckert number Ec, Brownian motion number Nb, thermophoresis parameter Nt and the Schmidt number Sc, respectively. The numerical results are indicated that an increasing in the magnetic parameter is given a decreasing in the values of the velocities and Nusselt number, or an increasing in the values of the shear stress, couple stress at the surface, temperature and concentration. The material parameter K has the opposite effect of magnetic field parameter on the values of the velocities, temperature, concentration, shear stress, Nusselt number and Schmidt number. The temperature is decreased as the Prandtl number increasing, or is increased as the Eckert number increasing. The concentration is decreased as Schmidt number increasing. At last, the study has been presented one multimedia video to show its main contain, it will be appeared at Elsevier AudioSlides website.
Physical model experiments as well as numerical simulations are widely carried out to estimate flow phenomena of high-temperature liquid flow because it is difficult to observe or measure the ...high-temperature liquid flow directly. As for the physical modelling, similitude is an essential matter that has a great influence on the representation of real flow phenomena in the prototype. A commonsense of the physical modelling had been satisfying the similitude of one or two dimensionless numbers considering dominant forces influence on the objective flow phenomena. In this paper, physical modelling conditions required for the simultaneous similitude of multiple dimensionless numbers (SMDN) has been studied to enhance the accuracy of the flow phenomena representation. As a result, a simple relationship between physical properties of fluids and scale ratio of the physical model has become clear for the simultaneous similitude of the Froude, Reynolds, Galilei, capillary, Weber, Eötvös and Morton numbers. Then, rising velocity of bubbles has been investigated obtaining a result that the relative rising time of bubbles in the physical model corresponds well with that of the prototype under the SMDN condition. This result indicates physical models that satisfy the SMDN condition precisely represent flow phenomena of gas-liquid systems influenced by four forces; inertial force, gravitational force, viscous force and surface tension force, including bubble rising behavior as well as the bulk flow phenomena.
In real world, there exists determinate and/or indeterminate information. Hence, the indeterminate problems are inevitable and have to be taken into account in optimization problems. Then, a ...neutrosophic number (NN) is very suitable for expressing determinate and/or indeterminate information because a NN (
z
=
a
+
b
I
) consists of its determinate part
a
and its indeterminate part
bI
for
a
,
b
∈
R
, where the symbol “
I
” denotes indeterminacy and
R
is all real numbers. This paper firstly presents some basic operations of NNs and a neutrosophic function involving NNs, which is simply called a NN function and then develops a NN linear programming (NNLP) method to handle NN optimization problems. Moreover, a numerical example and an application of production planning are provided, respectively, to show the solving method and application of NNLP problems. In general, the NNLP method yields the basic NN solutions. Further, the possible ranges of the optimal solution are discussed when the indeterminacy
I
is specified as a possible interval ranges corresponding to actual requirements in real applications.
Keywords SNARC · Digit · Numerosity · Approximate number system · A theory of magnitude · Working memory Introduction Previous studies suggest that people represent numbers spatially resembling a ...mental number line (Restle, 1970; for a review, see Toomarian & Hubbard, 2018). ...while the ATOM model focuses on the magnitude properties of the stimuli, the working memory (WM) model (van Dijck & Fias, 2011) claims that all stimuli can be spatially organized in WM and can elicit SNARC-like effects. ...both models fundamentally suggest that numbers have no special relationship with space and that numerical and non-numerical stimuli should elicit comparable SNARC-like effects. In sum, symbolic numerals are deemed to be represented in a linear fashion, while non-symbolic numerals in a logarithmic fashion. ...psychophysical laws only apply to non-symbolic numerals, which are processed in the same way as all other perceptual continua (such as loudness or brightness), while symbolic numerals are processed in a unique and exact way. According to previous literature, both symbolic and non-symbolic numerals should elicit a SNARC effect.
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