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2023
Featured Articles
If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.
Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.
by
Z. M. Saleh, A. O. Mostafa, S. M. Madian
Math. Syst. Sci.
2023
,
1(1);
708 Views
Received: 30 June 2023; Accepted: 3 August 2023; Available online: 22 August 2023;
Issue release: 15 November 2023
Issue release: 15 November 2023
Abstract
In this paper, we define a new subclass of bi-univalent functions of complex order ∑q(τ,ζ;φ) which is defined by subordination in the open unit disc D by using ∇qF(ϑ) operator. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of function belonging to this class. It is known that the calculus without the notion of limits is called q-calculus which has influenced many scientific fields due to its important applications. The generalization of derivative in q-calculus that is q-derivative was defined and studied by Jackson. A function 𝐹 ∈ 𝐴 is said to be bi-univalent in D if both F and F -1 are univalent in D. The class consisting of bi-univalent functions is denoted by σ. The Faber polynomials play an important role in various areas of mathematical sciences, especially in geometric function theory. The purpose of our study is to obtain bounds for the general coefficients |an|(n≥3)by using Faber polynomial expansion under certain conditions for analytic bi-univalent functions in subclass ∑q(τ,ζ;ϕ) and also, we obtain improvements on the bounds for the first two coefficients |a2|and|a3| of functions in this subclass. In certain cases, our estimates improve some of those existing coefficient bounds. Keywords: analytic functions; bi-univalent functions; coefficient bounds; subordination; q-derivative; Faber polynomials 2010 Mathematical Subject Classification: 30C45
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by
Joab Onyango Odhiambo
Math. Syst. Sci.
2023
,
1(1);
974 Views
Received: 21 June 2023; Accepted: 7 August 2023; Available online: 26 August 2023;
Issue release: 15 November 2023
Issue release: 15 November 2023
Abstract
This study explores a multiple-security, high-risk pricing model where the implied volatility has been portrayed through Generalized Wishart affine processes. The presence of dual dependency matrices distinctively characterizes this multifaceted model. These matrices encapsulate the relationship between the generalized Wishart processes and the evolving dynamics of several securities. The adaptability of the proposed model makes it a perfect fit for high-frequency market data, whether dealing with either long or short-term maturities of calls. The main objective paper is on its derivation and addressing the call option pricing problem within the context of the volatility mode using generalized Wishart stochastic. A combination of Fourier transforms techniques and perturbation methods are utilized, mainly focusing on pricing European call options. The model proposed in this study is theoretical and practical, showcasing the strong potential for real-world applications within the financial derivative market.
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by
Alexander Dmitrievich Bruno, Alexander Borisovich Batkhin
Math. Syst. Sci.
2023
,
1(1);
749 Views
Received: 3 August 2023; Accepted: 21 October 2023; Available online: 3 November 2023;
Issue release: 15 November 2023
Issue release: 15 November 2023
Abstract
We consider conditions of three types of stability: Lyapunov, formal and weak of a stationary solution, and of a periodic solution in a Hamiltonian system with a finite number of degrees of freedom. The conditions contain restrictions on the order of resonances and some inequalities for initial coefficients of the normal forms of the Hamiltonian functions. We show that the number-theoretical analysis of frequencies can help in proof of stability. We also estimate the orders of solutions’ divergence from the stationary or the periodic ones under lack of formal stability.
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by
Yehu Lv
Math. Syst. Sci.
2023
,
1(1);
1211 Views
Received: 25 August 2023; Accepted: 26 October 2023; Available online: 12 November 2023;
Issue release: 15 November 2023
Issue release: 15 November 2023
Abstract
In this paper, by introducing predator-taxis into the diffusive predator-prey system with spatial memory, then we study the inhomogeneous spatial patterns of this system. Since in this system, the memory delay appears in the diffusion term, and the diffusion term is nonlinear, the classical normal form of Hopf bifurcation for the reaction-diffusion system with delay can’t be applied to this system. Thus, in this paper, we first derive an algorithm for calculating the normal form of Hopf bifurcation for this system. Then in order to illustrate the effectiveness of our newly developed algorithm, we consider the diffusive Holling-Tanner model with spatial memory and predator-taxis. The stability and Hopf bifurcation analysis of this model are investigated, and the direction and stability of Hopf bifurcation periodic solution are also studied by using our newly developed algorithm for calculating the normal form of Hopf bifurcation. At last, we carry out some numerical simulations to verify our theoretical analysis results, and two stable spatially inhomogeneous periodic solutions corresponding to the mode-1 and mode-2 Hopf bifurcations are found.
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by
Yingqiu Gu
Math. Syst. Sci.
2023
,
1(1);
721 Views
Received: 2 August 2023; Accepted: 14 September 2023; Available online: 25 September 2023;
Issue release: 15 November 2023
Issue release: 15 November 2023
Abstract
The development of the number system has been a long and difficult process, and many landmark concepts and theorems have been put forward. By briefly reviewing the development of hypercomplex systems, the rules for constructing the unit elements are discussed. As a vector space defining multiplication, division, and norm of vectors, hypercomplex numbers synthesize the advantages of mathematical tools such as algebra, geometry, and analysis, faithfully describe the intrinsic properties of space-time and physical systems, and provide a unified language and a powerful tool for basic theories and engineering technology. In the application of hypercomplex numbers, the group-like properties of the basis vectors are the most important, and the zero factor has little influence on the algebraic operation. The multiplication table of the basis vectors fully describes the intrinsic properties of the hypercomplex system, and the matrix A constructed from the multiplication table satisfies the structure equation A 2 = n A and thus obtains a set of faithful matrix representations of the basic elements. This paper also uses typical examples to show the simple and clear concepts and wide application of hypercomplex numbers. Therefore, hypercomplex numbers are worth learning in basic education and applying in scientific research and engineering technology.
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Editor-in-Chief
Prof. Youssri Hassan Youssri
Cairo University, Egypt
Processing Speed (2023)
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- <7 days: submission to screening review decision
- 53 days: received to accepted
- 68 days: received to online
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News & Announcements
2024-09-20
Highly Read Article Recommendation
Since the journal launch in 2023, we have been proud to publish a plethora of insightful findings in the realms of mathematics and systems science....
2024-07-10
Meeting our Editor-in-Chief and Associate Editor
It is with great pride that we introduce Prof. Youssri Hassan Youssri and Prof. Ali Akgül, who are the Editor-in-Chief and Associate Editor of our esteemed journal.
2024-01-05
Articles in the First Issue of Volume 1 - Now Available Online
We are delighted to announce that the articles in the first issue of Volume 1 of Mathematics and Systems Science is now live and accessible online.
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