In this paper, we consider the boundedness and compactness of operator $M_uC_\psi$ between $(\alpha,p)$-Besov-Zygmund spaces in terms of Carleson-type measures. Also we obtain some equivalent statements for the boundedness and compactness of a generalized product type operator $T_{u_1,u_2,\psi}$ which is well-known as Stevi'c-Sharma operator between $(\alpha,p)$-Besov-Zygmund spaces.
Let $G$ be a finite group. The undirected power graph on the conjugacy classes of $G$ is the simple graph $\mathcal{P_C}(G)$ whose vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent if one is a subset of a power of the other. In this paper, we show that the graph $\mathcal{P_C}(G)$ is $2$-connected whenever either $|\pi(G)|>1$ or ${\rm Z}(G)$ is cyclic. Moreover, we classify finite groups $G$ whose associated graph $\mathcal{P_C}(G)-\{e\}$ are bipartite.
In this paper, we critically evaluate the Capital Asset Pricing Model (CAPM) and its limitations in predicting future returns using Linear Regression (LR) models. We propose an alternative approach, Bayesian Regression, which offers a more informative and accurate prediction framework. Our study compares the performance of LR and Bayesian Regression models in forecasting the returns of popular cryptocurrencies, Doge (for asset) and Bitcoin (for market). Through the use of Mean Squared Error (MSE), we demonstrate that the Bayesian Regression model outperforms the LR model in terms of prediction accuracy. The findings highlight the advantages of Bayesian methods in capturing the complex relationships and uncertainties inherent in financial markets. Our research contributes to the ongoing discourse on investment decision-making, providing valuable insights into the effectiveness of Bayesian Regression in the context of cryptocurrency investments.
This paper discusses stochastic comparisons on the finite $\alpha$-mixture of additive hazard models. Sufficient conditions on the underlying distribution parameters and the mixing probabilities are established for the comparisons of different $\alpha$-mixtures of survival or distribution functions of these models with respect to the usual stochastic order and the hazard rate order, respectively. Several examples are also presented to illustrate the theoretical findings.
Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset $S$ of the vertices of a graph $G$ is an adjacency resolving set for $G$ if for each pair of distinct vertices $x, y \in V(G)\setminus S$, there exists $s \in S$ which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of $G$. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.
In this paper, the problem of multiple watchman routes in staircase polygons is studied. The watchman route problem (WRP) is a variation of the art gallery problem (AGP) in computational geometry, where each point in the given polygon must be visible from at least one point along the route taken by one of the watchmen. A greedy algorithm is presented for the min-max criterion, where we minimize the maximum route length. We assume some starting points of the watchmen may dominate the others. This algorithm finds an optimal solution in $O(n^2 \cdot k^2 \cdot \log{n})$ time, where $n$ represents the number of vertices of the give polygon, and $k$ represents the number of watchmen.
In this paper, we introduce a novel simplicial complex named Game Complex for finite non-cooperative games in the strategic form. We prove that the number of Nash equilibrium in non-cooperative games with more than two players is the rank of the first homology group of the game complex. Furthermore, we give a decomposition of the game complex.
This paper introduces a novel method for solving the matrix equation $X^2 - A = 0$ by computing matrix square roots. Inspired by George Pólya's structured problem-solving strategies and leveraging Wolfram Mathematica, the approach offers a systematic, efficient, and clear solution to the problem. The method extends the computation of matrix square roots to large matrices and those with complex eigenvalues, significantly broadening its applicability in diverse fields, including control theory, quantum physics, and signal processing. The approach is demonstrated through comprehensive examples and original Mathematica code, providing a practical toolkit for solving similar mathematical challenges. The method is designed to be both intuitive and versatile, making it a valuable resource for educators, students, and researchers engaged in advanced mathematical problem-solving.
Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset $S$ of the vertices of a graph $G$ is an adjacency resolving set for $G$ if for each pair of distinct vertices $x, y \in V(G)\setminus S$, there exists $s \in S$ which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of $G$. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.
The Lyapunov matrix equations occur in many branches of control theory, such as stability analysis and optimal control. In this work, we introduce a novel iterative approach to address the generalized Lyapunov matrix equation within the framework of complex matrices. At each iteration, the procedure involves solving two conventional Lyapunov equations with real-valued coefficient matrices. The scheme incorporates two positive parameters, for which we establish sufficient conditions to guarantee the convergence of the method under certain assumptions. Then we solve the Lyapunov equation arising by applying a finite difference procedure to Helmholtz equation by proposed method.
The work employs a numerical method for the solution of Fractional Fokker-Planck Equation (FFPE) using the Homotopy Perturbation and Aboodh Transform Method (HPATM). Fractional derivatives issues are successfully solved using the hybrid approach, which yields rapidly convergent solutions. By resolving two cases and contrasting estimated outcomes with exact solutions for various fractional orders, the correctness of the technique was proven. The accuracy of the technique is demonstrated by the good match between the precise and approximation solutions at $\alpha=1$. The findings indicate that fractional differential equations may be solved with a strong and dependable approach using HPATM, which can also be used to describe anomalous diffusion and other intricate physical phenomena.
In this paper, we investigate the conditions under which a lifted almost complex structure $J$ on the tangent bundle $TM$ of a manifold $M$ exhibits various Kählerian properties. We establish several characterizations relating the geometry of $(TM, J)$ to the cosymplectic structure on $M$. Specifically, we show that $(TM, J)$ is Kählerian if and only if $(M, \eta, \xi, \varphi)$ is cosymplectic and $R = 0$. Similarly, we prove that $(TM, J)$ is nearly Kählerian under the same conditions on $M$. Furthermore, we present an alternative criterion for $(TM, J)$ to be Kählerian, involving a nearly cosymplectic condition on $M$ alongside a specific curvature relation. Finally, we demonstrate that $(TM, J)$ is semi-Kählerian if and only if $(M, \eta, \xi, \varphi)$ is semi-cosymplectic with $R(X, Y) \varphi Z = 0$. These results reveal intricate connections between cosymplectic structures on $M$ and Kählerian-type structures on $TM$, contributing to the broader understanding of almost complex geometry on tangent bundles.
In this paper, we introduce new general location model for mixed responses including correlated nominal, ordinal and continuous outcomes by using latent variable approach. We discuss regression methods for jointly analysis of continuous and categorical (nominal and ordinal) responses. After presenting the Leon and Carrière general location model [7], new general location model is introduced. A full likelihood-based approach is used to obtain maximum likelihood estimations of the models parameters. The proposed model is applied to BMI, Steatosis and Osteoporosis data.
In this brief note, we present a proof for a general form of the Serre-Swan theorem.
This review paper focuses on the numerical solution of the time-fractional diffusion equation using various discretization techniques. For the time-fractional derivative, we consider methods such as L-type approximations and Grünwald-Letnikov-based formulas, while for the spatial diffusion term, we utilize the compact finite difference method, finite element method, spectral element method, meshless method, Chebyshev spectral method, and finite block method. In addition, stability and convergence theorems are presented, accompanied by numerical examples that confirm the theoretical results.
We show that every quasi-multiplier $\phi:L^1(G)\times L^1(G)\longrightarrow L^1(G)$, where $G$ is a locally compact group, is of the form $$\phi(f,g)=f\star \mu\star g,\ \ \ \ \ f,g\in L^1(G),$$ for a unique measure $\mu\in M(G)$. As a consequence, we obtain a well-known result due to Wendel. We also prove the analogues result for $C^*$-algebras. Moreover, we introduce the notion of quasi Jordan multipliers and prove that each such map on a $C^*$-algebra, as well as group algebra $L^1(G)$, is a quasi-multiplier.
This article presents the interpolative fixed point theorem with reference to complete partial metric spaces, by taking the multi-valued contraction into account. In particular, the idea of multivalued interpolative Reich–Rus–Ćirić type contractions is introduced and criteria for the existence of fixed points of such operators are established. A nontrivial example is provided to support the validity of the obtained results.
Loop closure detection (LCD) and trajectory generation are critical components of visual simultaneous localization and mapping (vSLAM). In this paper, we aim to solve the LCD and trajectory generation problem in vSLAM using a newly devised vector quantization (VQ) algorithm. The proposed new VQ algorithm is constructed based on a selfsupervised deep convolutional autoencoder (AE). The new VQ step is then incorporated into the two famous SLAM algorithms fast appearance-based mapping (FABMAP) and ORB-SLAM, which we now call AE-FABMAP and AE-ORB-SLAM, respectively. Experiments show that using self-supervised autoencoders in the VQ step is far more efficient in terms of speed and memory consumption with respect to other methods such as graph convolutional neural networks. Furthermore, the newly presented algorithms, AE-ORB-SLAM and AE-FABMAP outperform the standard FABMAP2 and ORB SLAM, and in large-scale SLAM, the new approaches improve the accuracy and recall of the LCD.
In this paper, the ordinary character table of a finite extension of structure $\overline{G}=2^7{:}G_2(2)$ is computed via the Fischer-Clifford matrices technique. The group $\overline{G}$ sits maximally in the affine subgroup $2^7{:}Sp_6(2)$ of the symplectic group $Sp_8(2)$.
A subset $D$ of vertices of a simple graph $G$ is an exact double dominating set if each vertex $v$ of $G$ is dominated by exactly two vertices of $D$, i.e. $|N_G[v]\cap D|=2$, in which $N_G[v]$ is the closed neighborhood of $v$ in $G$. The generalized Sierpiński graph $S(G,t)$ is a fractal-like graph that uses $G$ as a building block and can be constructed recursively in $t$ steps from the base graph $G$. In this paper we study and determine the existence of exact double dominating sets in generalized Sierpiński graphs $S(P_n,t),$ $S(C_n,t),$ $S(K_{1,n},t)$ and $S(K_n,t)$.
