Current Issue : October-December Volume : 2024 Issue Number : 4 Articles : 5 Articles
In this paper, we delve into the intricate connections between the numerical ranges of specific operators and their transformations using a convex function. Furthermore, we derive inequalities related to the numerical radius. These relationships and inequalities are built upon well-established principles of convexity, which are applicable to non-negative real numbers and operator inequalities. To be more precise, our investigation yields the following outcome: consider the operators A and B, both of which are positive and have spectra within the interval [m,M], denoted as σ(A) and σ(B). In addition, let us introduce two monotone continuous functions, namely, g and h, defined on the interval [m,M]. Let f be a positive, increasing, convex function possessing a supermultiplicative property, which means that for all real numbers t and s, we have f(ts) ≤ f(t)f(s). Under these specified conditions, we establish the following inequality: for all 0 ≤ ] ≤ 1, this outcome highlights the intricate relationship between the numerical range of the expression g](A)Xh1−] when transformed by the convex function f and the norm of X. Importantly, this inequality holds true for a broad range of values of ]. Furthermore, we provide supportive examples to validate these results....
The focus of this study is to classify flag-transitive 2-designs. We have come to the conclusion that if D is a nontrivial 2-design having block size 5 and G is a two-dimensional projective special linear group which acts flag-transitively onDwith q ≢ 1 (mod 4), then D is a 2-(11, 5, 2) design, a 2-(11, 5, 12) design, a 2-(q + 1, 5, 2(q − 1)) design with q ≡ 3 (mod 4) or a 2-(q + 1, 5, (q − 1)/3) design with q 2f (where f > 2 is an even)....
We consider a regularized periodic three-dimensional Boussinesq system. For a mean free initial temperature, we use the coupling between the velocity and temperature to close the energy estimates independently of time. This allows proving the existence of a global in time unique weak solution. Also, we establish that this solution depends continuously on the initial data. Moreover, we prove that this solution converges to a Leray-Hopf weak solution of the three-dimensional Boussinesq system as the regularizing parameter vanishes....
Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space Hs(R). We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results....
In this research, the modified subgradient extragradient method and K-mapping generated by a finite family of finite Lipschitzian demicontractions are introduced. Then, a strong convergence theorem for finding a common element of the common fixed point set of finite Lipschitzian demicontraction mappings and the common solution set of variational inequality problems is established. Furthermore, numerical examples are given to support the main theorem....
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