ON THE REAL INTERSECTION POINTS OF THE GRAPHS OF AN EXPONENTIAL FUNCTION AND A POLYNOMIAL FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 175-206
Author(s):  
David E. Dobbs
Keyword(s):  
Exponential Function ◽  
Polynomial Function ◽  
The Real ◽  
Intersection Points

scholarly journals The Intensity-Curvature of Human Brain Vessels Detected with Magnetic Resonance Imaging

2017 ◽  
Vol 5 (3) ◽  
pp. 326-335
Author(s):  
Carlo Ciulla ◽  
Ustijana Rechkoska Shikoska ◽  
Dimitar Veljanovski ◽  
Filip A. Risteski
Keyword(s):  
Magnetic Resonance Imaging ◽  
Magnetic Resonance ◽  
Human Brain ◽  
Polynomial Function ◽  
Resonance Imaging ◽  
Signal Processing Technique ◽  
Brain Vessels ◽  
Pixel Intensity ◽  
The Real ◽  
Curvature Term

The intensity-curvature term is the concept at the root foundation of this paper. The concept entails the multiplication between the value of the image pixel intensity and the value of the classic-curvature (CC(x, y)). The CC(x, y) is the sum of all of the second order partial derivatives of the model polynomial function fitted to the image pixel. The intensity-curvature term (ICT) before interpolation E0(x, y) is defined as the antiderivative of the product between the pixel intensity and the classic-curvature calculated at the origin of the pixel coordinate system (CC(0, 0)). The intensity-curvature term (ICT) after interpolation EIN(x, y) is defined as the antiderivative of the product between the signal re-sampled by the model polynomial function at the intra-pixel location (x, y) and the classic-curvature. The intensity-curvature functional (ICF) is defined as the ratio between E0(x, y) and EIN(x, y). When the ICF is almost equal to the numerical value of one (‘1’), E0(x, y) and EIN(x, y) are two additional domains (images) where to study the image from which they are calculated. The ICTs presented in this paper are able to highlight the human brain vessels detected with Magnetic Resonance Imaging (MRI), through a signal processing technique called inverse Fourier transformation procedure. The real and imaginary parts of the k-space of the ICT are subtracted from the real and imaginary parts of the k-space of the MRI signal. The resulting k-space is inverse Fourier transformed, and the human brain vessels are highlighted.Int. J. Appl. Sci. Biotechnol. Vol 5(3): 326-335

scholarly journals The asymptotic values of a polynomial function on the real plane

1996 ◽  
Vol 106 (3) ◽  
pp. 263-273 ◽  
Author(s):  
J. Ferrera ◽  
M.J. de la Puente
Keyword(s):  
Polynomial Function ◽  
Real Plane ◽  
The Real ◽  
Asymptotic Values

The double cusp has five minima

1978 ◽  
Vol 84 (3) ◽  
pp. 537-538 ◽  
Author(s):  
J. Callahan
Keyword(s):  
Critical Points ◽  
Standard Form ◽  
Singularity Theory ◽  
The Other ◽  
Universal Unfolding ◽  
The Real ◽  
Level Curves ◽  
Intersection Points ◽  
The One ◽  
Image Position

The double cusp is the real, compact, unimodal singularitysee (2), (4). Functions in a universal unfolding of the double cusp can have nine non-degenerate critical points near the origin, but no more. Index considerations show that precisely four of the nine are saddles, and it has long been part of the folklore of singularity theory that one of the other five must be a maximum. Indeed, a standard form of the unfolded double cusp (1), (3) is a function having a pair of intersecting ellipses as one of its level curves; see Fig. 1(a). There are saddles at the four intersection points, a maximum inside the central quadrilateral, and a minimum inside each of the other four finite regions bounded by the ellipses. The rest of Fig. 1 suggests, however, that a deformation of this function (in which one of the saddles drops below the level of the other three) might turn the maximum into a fifth minimum. The following proposition shows that a function similar to the one in Fig. 1(d) can be realized in an unfolding of the double cusp.

scholarly journals Metaphysical unity of transcendental psychology and quantum mechanics. Article 2.

2021 ◽  
Vol 4 (121) ◽  
pp. 64-75
Author(s):  
Ruben M. Nagdyan ◽  
Keyword(s):  
Quantum Mechanics ◽  
Interpretation Of Quantum Mechanics ◽  
Equal Opportunities ◽  
Quantum Object ◽  
Principle Of Superposition ◽  
Classical Physics ◽  
The Real ◽  
Principle Of Relativity ◽  
Intersection Points ◽  
The Relationship

This article is a continuation of the previous one, published in this journal under the same title. The article continues the theoretical consideration of signs of the unity of transcendental psychology (TP) and quantum mechanics (QM) in the vision of Aristotle's metaphysics. In the context of the metaphysical triad necessary-possible-real, the «intersection points» of A. I. Mirakyan’s transcendental psychology and the interpretation of quantum mechanics by A. Yu. Sevalnikov. It is shown that in the both transcendental psychology and quantum mechanics epistemological problems are associated with the impossibility of using the language of their classical predecessors. In both sciences, it becomes necessary to use a new language, a new way of thinking and a new logic of understanding the phenomena under study. All this allows us to conclude that both in transcendental psychology and in quantum mechanics, researchers are dealing with a new ontology of reality that differs from that studied in classical physics and in the phenomenology of classical psychology. It became necessary to divide reality into observable and unobservable. This allows us to say that we are talking about polyontic (or modal) philosophy – different modalities or modes of being, within the framework of which it is necessary to consider the relationship between the necessary, the possible and the real things. Both sciences are the sciences of becoming. If QM is the science of the formation of the observed world, then TP is the science of the generation of phenomena of psychical reality. This is one of the reasons for the unity of their methodological foundations. There is a fairly close similarity in the understanding of the concept of «coexisting opportunities» (or «potential opportunities»). In TP, it coincides with the concept of the coexistence of functionally equal opportunities for reflecting various concomitant properties of objects, and in QM – with the principle of superposition of states of elementary particles. The relative nature of the formation of the phenomenon in the reality of the real follows it. In TP, this is expressed in the realization of one of the coexisting possibilities of reflecting any of the presented properties of the object, and in QM this is expressed as a result of the reduction of the wave function to one of the possible states of a quantum object. The relativity of the formation of a specific phenomenon, determined by the existence of «coexisting possibilities», is realized according to the principle of relativity to the means of observation.

scholarly journals Soil porosity modelling for immersive serious game based on vertical angle, depth, and speed of tillage

2018 ◽  
Vol 4 (2) ◽  
pp. 107 ◽  
Author(s):  
Anang Kukuh Adisusilo ◽  
Mochamad Hariadi ◽  
Eko Mulyanto Yuniarno ◽  
Bambang Purwantana ◽  
Radi Radi
Keyword(s):  
Serious Games ◽  
Polynomial Function ◽  
Real Data ◽  
Serious Game ◽  
Soil Porosity ◽  
Vertical Angle ◽  
The Real ◽  
Data Support ◽  
Soil Bin ◽  
Moldboard Plow

The real data support the “seriousness” of the serious game and give more authentic situations, which can make players feel immersed in scenarios, and gain a real experience. Therefore, the modeler must be able to recognize whether a model reflects reality to identify and deal with divergences between theory and data. In this paper, we present a model for design a basis of immersive in serious games. The studied case is the tillage using a moldboard plow, by taking real data through an experiment use a device called soil bin. It aims to determine the effect of angle, depth, and speed on the soil porosity; by comparing the value of the smallest error using the polynomial function of the use of different orders. The result of an average smallest error with the polynomial approach is 1.10E-07 in the 3rd order, closer to the experimental value. Therefore, the model can be used for designing immersive serious game.

scholarly journals Central limit theorems for the real eigenvalues of large Gaussian random matrices

2017 ◽  
Vol 06 (01) ◽  
pp. 1750002 ◽  
Author(s):  
N. J. Simm
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Polynomial Function ◽  
Random Variable ◽  
Real Matrix ◽  
Two Component System ◽  
The Real ◽  
Two Component ◽  
Standard Normal ◽  
Independent Identically Distributed

Let [Formula: see text] be an [Formula: see text] real matrix whose entries are independent identically distributed standard normal random variables [Formula: see text]. The eigenvalues of such matrices are known to form a two-component system consisting of purely real and complex conjugated points. The purpose of this paper is to show that by appropriately adapting the methods of [E. Kanzieper, M. Poplavskyi, C. Timm, R. Tribe and O. Zaboronski, Annals of Applied Probability 26(5) (2016) 2733–2753], we can prove a central limit theorem of the following form: if [Formula: see text] are the real eigenvalues of [Formula: see text], then for any even polynomial function [Formula: see text] and even [Formula: see text], we have the convergence in distribution to a normal random variable [Formula: see text] as [Formula: see text], where [Formula: see text].

scholarly journals Geometric and arithmetic postulation of the exponential function

1993 ◽  
Vol 54 (1) ◽  
pp. 111-127 ◽  
Author(s):  
J. Pila
Keyword(s):  
Exponential Function ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Real Variable ◽  
Mean Value ◽  
The Real ◽  
Mean Value Theorems ◽  
Auxiliary Functions

AbstractThis paper presents new proofs of some classical transcendence theorems. We use real variable methods, and hence obtain only the real variable versions of the theorems we consider: the Hermite-Lindemann theorem, the Gelfond-Schneider theorem, and the Six Exponentials theorem. We do not appeal to the Siegel lemma to build auxiliary functions. Instead, the proof employs certain natural determinants formed by evaluating n functions at n points (alternants), and two mean value theorems for alternants. The first, due to Pólya, gives sufficient conditions for an alternant to be non-vanishing. The second, due to H. A. Schwarz, provides an upper bound.

scholarly journals Pappus’s Hexagon Theorem in Real Projective PlaneThis work has been supported by the “Centre autonome de formation et de recherche en mathématiques et sciences avec assistants de preuve” ASBL (non-profit organization). Enterprise number: 0777.779.751. Belgium.

2021 ◽  
Vol 29 (2) ◽  
pp. 69-76
Author(s):  
Roland Coghetto
Keyword(s):  
Projective Plane ◽  
Metric Space ◽  
Real Projective Plane ◽  
Non Profit ◽  
The Real ◽  
Link Type ◽  
Cayley Algebra ◽  
Intersection Points ◽  
Grassmann Cayley Algebra

Summary. In this article we prove, using Mizar [2], [1], the Pappus’s hexagon theorem in the real projective plane: “Given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear” https://en.wikipedia.org/wiki/Pappus’s_hexagon_theorem . More precisely, we prove that the structure ProjectiveSpace TOP-REAL3 [10] (where TOP-REAL3 is a metric space defined in [5]) satisfies the Pappus’s axiom defined in [11] by Wojciech Leończuk and Krzysztof Prażmowski. Eugeniusz Kusak and Wojciech Leończuk formalized the Hessenberg theorem early in the MML [9]. With this result, the real projective plane is Desarguesian. For proving the Pappus’s theorem, two different proofs are given. First, we use the techniques developed in the section “Projective Proofs of Pappus’s Theorem” in the chapter “Pappos’s Theorem: Nine proofs and three variations” [12]. Secondly, Pascal’s theorem [4] is used. In both cases, to prove some lemmas, we use Prover9 https://www.cs.unm.edu/~mccune/prover9/ , the successor of the Otter prover and ott2miz by Josef Urban See its homepage https://github.com/JUrban/ott2miz [13], [8], [7]. In Coq, the Pappus’s theorem is proved as the application of Grassmann-Cayley algebra [6] and more recently in Tarski’s geometry [3].

Cardinal Interpolation and Generalized Exponential Euler Splines

1976 ◽  
Vol 28 (2) ◽  
pp. 291-300 ◽  
Author(s):  
A. Sharma ◽  
J. Tzimbalario
Keyword(s):  
Real Axis ◽  
Exponential Function ◽  
Cardinal Interpolation ◽  
The Real ◽  
Integer Points ◽  
Cardinal Splines ◽  
Image Position

Let denote the class of cardinal splines S(x) of degree n (n ≧ 1) having their knots at the integer points of the real axis. We assume that the knots are simple so that . Recently Schoenberg [3] has studied cardinal splines such that S(x) interpolates the exponential function tx at the integers and

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