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Ptolemy Scientific Research Press (PSR Press) is a highly regarded publisher of scientific literature dedicated to bringing the latest research and findings to a broader audience. With a focus on cutting-edge research and technology, Ptolemy Scientific Research Press offers a range of publications catering to professionals, researchers, and student’s needs. Whether looking for information on the latest breakthroughs in physics, biology, engineering, or computer science, you can trust Ptolemy Scientific Research Press to deliver insightful, accurate, and engaging content. With its commitment to quality, accessibility, and innovation, Ptolemy Scientific Research Press is an essential resource for anyone interested in science and technology.

Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Our Journals

Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Latest in Press

Author(s): Rasul Rasuli1
1Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.
Abstract:

The purpose of this paper is introduce the notion of intuitionistic fuzzy subgroups with respect to norms (\(t\)-norm \(T\) and \(s\)-norm \(S\)). Also we introduce intersection and normality of them and investigate some properties of them. Finally, we provide some results of them under group homomorphisms

Author(s): Saad Ihsan Butt1, Mehroz Nadeem2, Ghulam Farid3
1Department of Mathematics, COMSATS University of Islamabad, Lahore Campus, Pakistan.
2Department of Mathematics, COMSATS University of Islamabad, Lahore Campus, Pakistan.;
3Department of Mathematics COMSATS University of Islamabad, Attock Campus, Pakistan.
Abstract:

In this paper, we establish several integral inequalities including Caputo fractional derivatives for exponential \((s,m)\)-convex functions. By using convexity for exponential \((s,m)\)-convex functions of any positive integer order differentiable function some novel results are obtained.

Author(s): Anders S. G. Andrae1
1Huawei Technologies Sweden AB, Kista, Sweden.
Abstract:

The main problems with several existing Information and Communication Technology (ICT) power footprint investigations are: too limited (geographical and temporal) system boundary, overestimation of power saving potential in the next decade, assume that historical power use can predict future global power use in the next decade despite unprecedented data traffic growth, assume that Moore´s law relation to digital circuitry can continue “forever” and that no problems with extra cooling power will occur for several decades. The highly variable outlooks for the future power consumptions depend on “starting values”, disruptions, regional differences and perceptual estimations of electricity intensity reductions and data traffic increase. A hugely optimistic scenario – which takes into account 20% annual improvement of the J/bit in data centers and networks until 2030 is presented. However, the electric power consumption of the present ICT scope will be significant unless great efforts are put into power saving features enabling such improvements of J/bit. Despite evident risks, it seems though that planned power saving measures and innovation will be able to keep the electricity consumption of ICT and the World under some kind of control. The major conclusion is based on several simulations in the present study – that future consumer ICT infrastructure cannot slow its overall electricity use until 2030 and it will use more than today. Data traffic may not be the best proxy metric for estimating computing electricity. Operations and J/operation seem more promising for forecasting and scaling of bottom-up models.

Author(s): Abdelhakam Hassan Mohammed1, Shengmao Fu2
1Faculty of Petroleum and Hydrology Engineering, Peace University, Almugled, West Kordofan, Sudan.
2College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P.R. China.
Abstract:

In this paper, we investigate the nonlinear dynamics for an attraction-repulsion chemotaxis Keller-Segel model with logistic source term
\(u_{1t}=d_{1}\Delta{u_{1}}-\chi \nabla (u_{1}\nabla{u_{2}})+ \xi{ \nabla (u_{1}\nabla{u_{3}})}+\mathbf g(u),{\mathbf x}\in\mathbb{T}^{d}, t>0,\)
\( u_{2t}=d_{2}\Delta{u_{2}}+\alpha u_{1}-\beta u_{2},{\mathbf x}\in\mathbb{T}^{d}, t>0,\)
\(u_{3t}=d_{3}\Delta{u_{3}}+\gamma u_{1}- \eta u_{3},{\mathbf x}\in\mathbb{T}^{d}, t>0,\)
\( \frac{\partial{u_{1}}}{\partial{x_{i}}}=\frac{\partial{u_{2}}}{\partial{x_{i}}}=\frac{\partial{u_{3}}}{\partial{x_{i}}}=0,x_{i}=0,\pi, 1\leq i\leq d,\)
\( u_{1}(x,0)=u_{10}(x), u_{2}(x,0)=u_{20}(x), u_{3}(x,0)=u_{30}(x), {\mathbf x}\in\mathbb{T}^{d} (d=1,2,3).\)
Under the assumptions of the unequal diffusion coefficients, the conditions of chemotaxis-driven instability are given in a \(d\)-dimensional box \(\mathbb{T}^{d}=(0,\pi)^{d} (d=1,2,3)\). It is proved that in the condition of the unique positive constant equilibrium point \({\mathbf w_{c}}=(u_{1c},u_{2c},u_{3c})\) of above model is nonlinearly unstable. Moreover, our results provide a quantitative characterization for the early-stage pattern formation in the model.

Author(s): Zirhumanana Balike1, Arne Ring2, Meseyeki Saiguran3
1Department of Mathematics and Physics, Institut Supérieur Pédagogique de Bukavu, Democratic Republic of the Congo.
2Department of Mathematics, University of the Free State, South Africa.
3Department of Mathematical Sciences, St. Johns University of Tanzania, Tanzania.
Abstract:

This paper studies the movement of a molecule in two types of cell complexes: the square tiling and the hexagonal one. This movement from a cell \(i\) to a cell \(j\) is referred to as an homogeneous Markov chain. States with the same stochastic behavior are grouped together using symmetries of states deduced from groups acting on the cellular complexes. This technique of lumpability is effective in forming new chains from the old ones without losing the primitive properties and simplifying tedious calculations. Numerical simulations are performed using R software to determine the impact of the shape of the tiling and other parameters on the achievement of the equilibrium. We start from small square tiling to small hexagonal tiling before comparing the results obtained for each of them. In this paper, only continuous Markov chains are considered. In each tiling, the molecule is supposed to leave the central cell and move into the surrounding cells.

Author(s): Abdelbaki Choucha1, Djamel Ouchenane2, Khaled Zennir3
1Department of Mathematics, Faculty of Exact Sciences, University of El Oued, B.P. 789, El Oued 39000, Algeria.
2Laboratory of pure and applied Mathematics, Amar Teledji Laghouat University, Algeria.
3Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia.
Abstract:

In this work, we are concerned with a problem for a viscoelastic wave equation with strong damping, nonlinear source and distributed delay terms. We show the exponential growth of solution with \(L_{p}\)-norm, i.e., \(\lim\limits_{t\rightarrow \infty}\Vert u\Vert_p^p \rightarrow \infty\).

Author(s): Helmut Prodinger1
1Department of Mathematical Sciences, Stellenbosch University, 7602 Stellenbosch, South Africa
Abstract:

A new recursion in only one variable allows very simple verifications of Bressoud’s polynomial identities, which lead to the Rogers-Ramanujan identities. This approach might be compared with an earlier approach due to Chapman. Applying the \(q\)-Chu-Vandermonde convolution, as suggested by Cigler, makes the computations particularly simple and elementary. The same treatment is also applied to the Santos polynomials and perhaps more polynomials from a list of Rogers-Ramanujan like polynomials [1].

Author(s): Italo Jose Dejter1
1Department of Mathematics, University of Puerto Rico, San Juan, Puerto Rico.
Abstract:

Let \(0<k\in\mathbb{Z}\). A reinterpretation of the proof of existence of Hamilton cycles in the middle-levels graph \(M_k\) induced by the vertices of the \((2k+1)\)-cube representing the \(k\)- and \((k+1)\)-subsets of \(\{0,\ldots,2k\}\) is given via an associated dihedral quotient graph of \(M_k\) whose vertices represent the ordered (rooted) trees of order \(k+1\) and size \(k\).

Author(s): Saeid Alikhani1, Nima Ghanbari1
1Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
Abstract:

Let \(G\) be a simple graph. A total dominator coloring of \(G\) is a proper coloring of the vertices of \(G\) in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number \(\chi_d^t(G)\) of \(G\) is the minimum number of colors among all total dominator coloring of \(G\). In this paper, we study the total dominator chromatic number of some graphs with specific construction. Also we compare \(\chi_d^t(G)\) with \(\chi_d^t(G-e)\), where \(e\in E(G)\).

Author(s): Daniel A. Romano1
1 International Mathematical Virtual Institute 6, Kordunav ska Street, 78000 Banja Luka, Bosnia and Herzegovina.
Abstract:

As a generalization of KU-algebras, the notion of pseudo-KU algebras is introduced in 2020 by the author (D. A. Romano. Pseudo-UP algebras, An introduction. Bull. Int. Math. Virtual Inst., 10(2)(2020), 349-355). Some characterizations of pseudo-KU algebras are established in that article. In addition, it is shown that each pseudo-KU algebra is a pseudo-UP algebra. In this paper it is a concept developed of pseudo-KU algebras in more detail and it has identified some of the main features of this type of universal algebras such as the notions of pseudo-subalgebras, pseudo-ideals, pseudo-filters and pseudo homomorphisms. Also, it has been shown that every pseudo-KU algebra is a pseudo-BE algebra. In addition, a congruence was constructed on a pseudo-KU algebra generated by a pseudo-ideal and shown that the corresponding factor-structure is and pseudo-KU algebra as well.

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