Let (Kge 1). We prove Zygmund theorem for (K-)quasiregular harmonic mappings in the unit disk (mathbb {D}) in the complex plane by providing a constant C(K) in the inequality
provided that (textrm{Im},f(0)=0). Moreover for a quasiregular harmonic mapping (f=(f_1,dots , f_n)) defined in the unit ball (mathbb {B}subset mathbb {R}^n), we prove the asymptotically sharp inequality
when (Krightarrow 1), provided that (f_1) is positive.
We study an averaging procedure for completely bounded multipliers on a locally compact quantum group with respect to a compact quantum subgroup. As a consequence we show that central approximation properties of discrete quantum groups are equivalent to the corresponding approximation properties of their Drinfeld doubles. This is complemented by a discussion of the averaging of Fourier algebra elements. We compare the biinvariant Fourier algebra of the Drinfeld double of a discrete quantum group with the central Fourier algebra. In the unimodular case these are naturally identified, but we show by exhibiting a family of counter-examples that they differ in general.
Desktop cloud technology has revolutionized modern computing by enabling remote desktop functionality through cloud computing and virtualization. However, traditional fuzzy set theories struggle with the uncertainties inherent in these environments. This study addresses this gap by introducing the probabilistic p, q-rung orthopair fuzzy model, a novel extension that integrates probabilistic elements to improve precision and robustness in decision-making. Key contributions include the development of advanced aggregation operators, such as probabilistic weighted averaging and geometric operators, and their application in a multi-attribute decision-making algorithm. The model is validated through a case study on cloud service provider selection, demonstrating its effectiveness in supporting sustainable development and planning. The results show that the proposed model outperforms existing approaches, offering enhanced accuracy and reliability. This contribution advances decision-making frameworks in desktop cloud environments, fostering sustainability and improving the efficiency of daily office tasks.
This paper focuses on the study of triple-twisted generalized Reed–Solomon (TTGRS) codes over a finite field ({mathbb {F}}_q), having twists (varvec{t} = (1, 2, 3)) and hooks (varvec{h} = (0, 1, 2)). We have obtained the necessary and sufficient conditions for such TTGRS codes to be MDS, AMDS, and AAMDS via algebraic techniques. We have also enumerated these codes for some particular values of the parameters. Moreover, we have presented some non-trivial examples for MDS, AMDS, and AAMDS TTGRS codes with various parameters. Further, we have studied the hulls of these codes, and under various conditions, obtained necessary and sufficient conditions for these codes to have a hull with dimensions varying from 0 to 5.
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