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On hyper Z-algebras
Full text linkThis study introduces the concept of hyperZ-algebra and investigates its features. In addition, we establish and prove a number of theorems about the relation between (Ṟ-ḧZ , Ḉ-ḧZ , Ḓ-ḧZ , Ṱ-ḧZ , Ṿ-ḧZ ). Moreover, we explain the hyper subalgebra ,a weakhyper Z-ideal and a stronghyper Z-ideal, as well as their relationship. Finally, the hyperhomomorphism Z-algebra is constructed and the isomorphism theorems are examined
W-Power N-Binormal Operator on Hilbert Space
Full text linkIn this paper we present a new class of operators on Hilbert space called w-power n-binormal operator. We study this operator and give some properties of it
On the solvability of a functional Volterra integral equation
Full text linkIn this article, we will investigate the existence of a unique bounded variation solution for a functional integral equation of Volterra type in the space L1(R+) of Lebesgue integrable functions
A Unifying Theory for Quantum Physics, Part 1:: How to Motivate Students to Want to Study Quantum Technologies
Full text linkIs the quantum world as strange as they say? If this were an unsolved mathematics question, we might try a new angle of attack. We know quantum mechanics (QM) is the most accurate and productive science humans ever had, meaning its probability predictions are accurate. Every probability has two square roots. The Born rule says either would produce the same probability. Assume nature uses the negative of QM’s equations. What could that mean? We’d need to revise Feynman’s path-integrals and Schrödinger’s equation. If waves travel in the opposite direction as what QM believes, that could produce the negative equations. No wave-particle duality. Free particles would follow backwards zero-energy waves coming from detectors. This, surprisingly, gets rid of quantum weirdness. Our proposal is that nature uses the negative of QM’s equations because particles follow zero-energy waves backwards. Considerable evidence fits this model, including a neutron-interferometer and the Davisson-Germer experiments, a quantum-eraser experiment, Wheeler-gedanken and double-slit experiments, Bell-test experiments, Stern-Gerlach, and high-energy scattering experiments. Finally, we propose a plan for how to motivate students to want to study quantum technologies, thereby addressing the most prominent problem in QM today: the shortage of an educated workforce, the scarcity of aspiring students
Some properties of meromrphic univalent functions with negative coefficients defined by Dziok-Srivastava operator
Full text linkThe main aim of the present investigation is to introduce a new class of meromorphic univalent functions with negative coefficients defined by Dziok-Srivastava operator. Some geometric properties are introduced, like coefficient estimate, integral operator, Feket-Szegӧ bounds for this class of meromorphic functions
Golden Ratio
Full text linkThis paper introduces the unique geometric features of 1:2: right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2: triangle, with all its peculiar geometric attributes described herein, turns out to be the real ‘Golden Ratio Triangle’ in every sense of the term. This special right triangle also reveals the fundamental Pi:Phi (π:φ) correlation, in terms of precise geometric ratios, with an extreme level of precision. Further, this 1:2: triangle is found to have a classical geometric relationship with 3-4-5 Pythagorean triple. The perfect complementary relationship between1:2: triangle and 3-4-5 triangle not only unveils several new aspects of Golden Ratio, but it also imparts the most accurate π:φ correlation, which is firmly premised upon the classical geometric principles. Moreover, this paper introduces the concept of special right triangles; those provide the generalised geometric substantiation of all Metallic Means
Metallic Ratios, Pythagorean Triples & p≡1(mod 4) Primes : Metallic Means, Right Triangles and the Pythagoras Theorem
Full text linkThis paper synergizes the newly discovered geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper illustrates the concept of the “Triads of Metallic Means”, and aslo the close correspondence between Metallic Ratios and the Pythagorean Triples as well as Pythagorean Primes
Visualization In Mathematics Teaching
Full text linkIn recent years, there has been an increased use of information and communication technologies and mathematical software in mathematics teaching. Numerous studies of the effectiveness of mathematical learning have shown the justification and usefulness of the implementation of new teaching aids. They also showed that learning with educational software has a great impact on students' achievement in the overall acquisition of mathematical knowledge during the school year as well as in the final exam at the end of primary education. Teaching realized by using computers and software packages is interesting for students, increases their interest and active participation. It is indisputable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by many researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is to develop constructive thinking of students. Visualization and representation of mathematical laws are of great importance in the realization of mathematics teaching. They should be applied everywhere and whenever possible
For the Fourier transform of the convolution in and D' and Z'
No full textIn this paper, we give another proof of the known lemma considering the Fourier transform of the convolution of a distribution and a function. Also, we give its application in the mentioned spaces
New Iterative Method with Application
Full text linkIn this paper, we consider iterative methods to find a simple root of a nonlinear equation
f(x) = 0, where f : D∈R→R for an open interval D is a scalar function