In this paper we consider X() anisotropic symmetric space 2π of periodic functions of m variables, in particular, the generalized Lorentz space L_,^*(𝕋^m) and Nikol'skii–Besov's class S_X(),^r̅B. The article proves an embedding theorem for the Nikol'skii - Besov class in the generalized Lorentz space and establishes an upper bound for the best approximations by trigonometric polynomials with harmonic numbers from the hyperbolic cross of functions from the class S_X(),^r̅B.
It is a great pleasure to congratulate Professor Mehmed Nurkanović, Managing Editor of Sarajevo Journal of Mathematics, on the occasion of his 65th birthday. We dedicate this issue to him in recognition of his significant scientific contributions to mathematics - particularly in the fields of difference equations and discrete dynamical systems - as well as for his devoted service to our journal.
In sustainable portfolio management, categorizing assets as “brown“ or “green“ based solely on ESG ratings can be misleading. A positive ESG score does not inherently indicate environmental responsibility unless it is evaluated relative to a meaningful benchmark. We propose a rescaled ESG rating system that measures each asset’s environmental standing relative to a threshold set by policymakers, reflecting the urgency of the current climate crisis. In this system, assets are assigned positive scores if they exceed the threshold (green) and negative scores if they fall below it (brown), enhancing the interpretability of sustainability metrics in portfolio construction. However, a challenge arises when aggregating these scores into an overall portfolio rating. Under sustainable portfolio optimization developed in [11], short positions in brown assets, otherwise effectively betting against polluting companies, can paradoxically improve the portfolio’s sustainability score. This creates a misleading incentive structure. To address this, we introduce a constraint that prohibits short positions in brown assets, ensuring that such investments do not positively impact the portfolio’s sustainability rating. While this restriction better aligns with environmental objectives, it also introduces complexity into the optimization process. To resolve this, we present an intuitive algorithm inspired by the active set method, which we refer to as Green Portfolio Optimization, capable of handling these constraints efficiently even in high-dimensional settings.
We consider a Cartesian coordinate system. A point in a plane whose both coordinates are integers is called a lattice point. A polygon that has lattice points for all its vertices is called a convex lattice polygon. A quadrilateral whose vertices are four consecutive vertices of a convex integer polygon is called a boundary quadrilateral of that polygon. It is interesting to investigate convex lattice polygons whose all boundary quadrilaterals are trapezoids.
In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model. The existence and local stability of the equilibrium points of the model are analyzed algebraically. It is shown that the model can undergo a transcritical bifurcation at equilibrium point on the $x$-axis and a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium point. Some numerical simulations are presented to illustrate our theoretical results.
This study examines the stability in variable-order fractional discrete neural networks modeled via the generalized proportional Caputo fractional difference operator. By employing the Krasnoselskii fixed-point theorem, we establish solution existence under Lipschitz continuity, and we prove Ulam–Hyers stability. Numerical simulations validate that balancing network parameters and fractional orders ensure robustness.
On November 3, 2025, at the Academy of Sciences and Arts of Bosnia and Herzegovina, a major jubilee was celebrated - forty years since the publication of the first Bosnian and Herzegovinian mathematical scientific journal, Radovi matematički, which today is published under the title Sarajevo Journal of Mathematics.
In the paper Global Dynamics of Anti-Competitive Systems in the Plane [4], the authors proved two major theorems that can be used to determine the global dynamics of anti-competitive systems of difference equations. These theorems require three hypotheses to be satisfied: (1) the corresponding map must be strongly anti-competitive, (2) the determinant of the Jacobian matrix of the map, evaluated at an interior fixed-point, does not equal zero, and (3) the only point mapped onto a fixed-point is the fixed-point itself.In this paper, we prove theorems that obtain the same results as in [4], but do not require any of these hypotheses; furthermore, the new theorems use weaker hypotheses that extend the scope of the theorems to apply to many more cases. Finally, we demonstrate how to use the modified theorems to determine the global dynamics of a weakly anti-competitive system where hypothesis (1) is false in every region of parameter space.
In this paper, we investigate the stability and Neimark-Sacker bifurcation of Ginzburg-Taneyhill model under the assumption of minimal maternal quality. The analysis begins with an examination of the existence and classification of equilibrium points, followed by a detailed study of their local stability. We show that the system undergoes a Neimark-Sacker bifurcation under certain parameter conditions, leading to the emergence of an invariant closed curve. Numerical simulations are presented to illustrate and confirm the theoretical results.
In this paper, we conduct a comprehensive exploration of the dynamical characteristics of a higher-order non-symmetric system of difference equations. Our investigation covers various fundamental aspects, including the existence of equilibria, persistence, periodic points, boundedness, local behavior at equilibria, convergence rate, and global dynamics. Our results significantly extend and improve upon existing findings in the literature. Finally, theoretical findings are illustrative numerically.
In this paper, we investigate an open-access fishery model which is used to examine the dynamics of the resource and industry and to explain the current economic status of the anchovy fishery. We consider the local character of the interior and boundary equilibrium points. Also, we show that the considered system of difference equations exhibits Neimark-Sacker bifurcation under certain conditions. The existence of the repelling curve and invariant curve is demonstrated. We show that in a certain parameter region the corresponding map of the considered system is an area-preserving map, so the positive equilibrium point in that case is stable. Also, we produce numerical simulations to support our findings.
In this paper, we observe cubic eigenvalue problems, which belong to a special class of nonlinear eigenvalue problems. Degree of a cubic eigenvalue problem is relatively small, which allows us to determine some important properties of these problems. We present an algorithm to determine whether a cubic pencil is hyperbolic or not. Also, a definite cubic pencils will be considered. We use a variational characterization as a tool for solving cubic eigenvalue problems and compare the results with the application of the linearization method.
This study is devoted to dynamical analysis of following higher order difference equation \begin{eqnarray*}x_{n+1}=px_{n}+\frac{q}{rx_{n-k}^{2}},k\in \{1,2,...\}, \end{eqnarray*} where $p, q, r$ and the initial conditions are positive real numbers. In particular, we discuss the existence of periodic solutions of the difference equation. We also handle the boundedness, local and global stability of solutions of the difference equation. Moreover, we study the existence of Neimark-Sacker bifurcation of solutions of the difference equation for $k=1$ and also give an invariant curve of the difference equation. Finally, we provide some numerical examples to support our results and present some open problems for future works.
A well-known characterization of Jordan vectors of a matrix polynomial L(z) is generalized to a characterization of Jordan vectors of the operator-valued function Q(z) at an eigenvalue α∈ℂ. The results are then applied to solve a system of nonlinear ordinary differential equations.
In this paper, we investigate Finsler space with a cubic modification of the Matsumoto metric, given by $F=\frac{\gamma^{2}}{\gamma-\beta}$, where $\gamma$ is a cubic metric and $\beta$ is one form metric. We identify the fundamental characteristics of this modified metric. The reducibility of the Cartan torsion tensor is a key factor, as it measures how closely a Finsler metric approximates a Riemannian metric. Specifically, if $C_{ijk}$ vanishes, the Finsler metric becomes Riemannian. Accordingly, we analyze various forms of the Cartan torsion tensor's reducibility within the context of this cubic-changed Matsumoto metric. We also establish conditions for determining whether the Finsler space is quasi C-reducible, semi C-reducible, C-reducible and C2-like.
The integer translation of a function $f(z)$ is denoted by $f\left(z+n\right) $ for each $n\in%TCIMACRO{\U{2124} }%%BeginExpansion\mathbb{Z}%EndExpansion.$ It is possible to obtain a function with certain characteristics for each$n\in%TCIMACRO{\U{2124} }%%BeginExpansion\mathbb{Z}%EndExpansion.$ This study examines the impact of integer translations on the growth and behavior of a meromorphic function $f(z)$. Specifically, we consider the family of meromorphic functions generated by integer shifts of $f(z)$, denoted as,%\[f_{n}\left( z\right) =\left\{ f\left( z+n\right) :n\in%TCIMACRO{\U{2124} }%%BeginExpansion\mathbb{Z}%EndExpansion\right\} .\]The primary focus is on understanding how these integer translations affect the Nevanlinna characteristic function $T(r,f),$ which is a key tool for assessing the growth of meromorphic functions. Our study also includes a comparative growth analysis between integer-translated versions of both entire and meromorphic functions. By examining a range of conditions, we provide insights into how translation influences the growth and value distribution of the functions. This investigation contributes to a deeper understanding of translation-invariant properties in complex analysis and offers new perspectives on the dynamic growth behavior of meromorphic and entire functions.
For two graphs $G_1$ and $G_2$, graph obtained with two disjoint copies of join structure $G_1 \vee G_2$ by joining the corresponding vertices in $G_2$'s, is the Indu--Bala product $G_1 \blacktriangledown G_2$. Present work focuses on the study of complementary distance ($\mathcal{CD}$) and reciprocal complementary distance ($\mathcal{RCD}$) spectrum for Indu--Bala product of regular graphs via the concept of equitable partition. Hence note $\mathcal{CD}$ and $\mathcal{RCD}$ spectrum of dumbbell graph as a particular case of the Indu--Bala product.
Close-to-convex functions have a great importance in the field of Geometric function theory. Many researchers of this field have extensively established various subclasses of close-to-convex univalent functions and studied certain important properties of these subclasses. In this paper, we introduce a generalized subclass of multivalent close-to-convex functions in the open unit disc. We investigate several properties such as coefficient estimates, inclusion relation, distortion theorem,argument theorem and an important result for the defined class. Many known results follow as consequences of the results derived in this paper.
Small functions were defined in complex analysis and next in ultrametric analysis. Order of growth and type of growth were also defined in complex analysis and have a similar definition in ultrametric analysis. Here we compare these two notions in the same way, on a complete ultrametric algebraically closed field $\K$ of characteristic $0$ such as $\C_p$. Small functions with respect to an entire function $f$ were studied in several articles. Inside an ''open'' disk, small functions also exist. After a general study, here we examine how two analytic functions inside an open disk can share three small functions, ignoring multiplicity and we give sufficient conditions proving that these two functions are equal.
In this paper, we present extensions of dynamic Lyapunov's inequalities and their reverse versions on time scales by using Specht's and Kantorovich's ratios. Our approach unifies and extends some continuous inequalities and their corresponding discrete and quantum analogues.
