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In this article, we propose some subspace methods such as the conjugate residual, generalized conjugate residual, biconjugate gradient, conjugate gradient squared and biconjugate gradient stabilized methods based on the tensor forms for solving the tensor equation involving the Einstein product. These proposed algorithms keep the tensor structure. The convergence analysis shows that the proposed methods converge to the solution of the tensor equation for any initial value. Some numerical results confirm the feasibility and applicability of the proposed algorithms in practice. [ABSTRACT FROM AUTHOR]

Summary: The rhamnosyl group of naringin dihydrochalcone, neohesperidin dihydrochalcone, naringin and hesperidin was selectively removed by enzymatic hydrolysis using an immobilised α‐L‐rhamnosidase. Monoglycosylated products, including trilobatin, hesperetin dihydrochalcone‐7‐O‐glucoside, prunin and hesperetin‐7‐O‐glucoside, were isolated and characterised by 1H and 13C NMR and ESI‐MS. To optimise the enzymatic reaction conditions and its process costs, the hydrolysis of neohesperidin dihydrochalcone to produce trilobatin was selected as a model reaction. Using a ratio of neohesperidin dihydrochalcone: immobilised α‐L‐rhamnosidase equal to 1:0.6, the trilobatin yields was over 98%. The recycle of enzyme was also investigated, obtaining trilobatin with a yields of 80% even when the twentieth reaction cycle was conducted. Moreover, antiradical and antimicrobial activities of the obtained flavonoid monoglucosides were examined by DPPH, FRAP and ORAC methods, and compared with the efficacy of parental flavonoid glycosides and their aglycone. The results highlight that some of the obtained flavonoid monoglucosides show significant improvement in the antioxidant activity. [ABSTRACT FROM AUTHOR]

Summary: An efficient and cost‐effective enzymatic production method for preparation of a high‐valued natural sweetener (dihydrochalcone glucoside trilobatin) was developed by the combination of hydrogenation and enzymatic hydrolysis reactions with α‐ l‐rhamnosidase as the catalyst in aqueous medium. This technology is adopting the cheap and largely available citrus flavanone naringin as the starting material for trilobatin synthesis, and the present enzymatic technology is possibly utilised by commercial for scale‐up production. The production is a straightforward two‐step process, in which naringin was hydrogenated into naringin dihydrochalcone and followed by removal of the rhamnosyl group of naringin dihydrochalcone by enzymatic hydrolysis using immobilised α‐ l‐rhamnosidase as the catalyst. Under optimised conditions, an overall yield of 96% was achieved with a very low loading of α‐ l‐rhamnosidase catalyst at 60 °C in a neutral aqueous buffer solution within 2 h. The immobilised α‐ l‐rhamnosidase catalyst can be recycled for 10 reactions (90% yield retained). [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with some of the well‐known iterative methods in their tensor forms to solve a class of tensor equations via the Einstein product. More precisely, the tensor forms of the Arnoldi and Lanczos processes are derived and the tensor form of the global GMRES method is presented. Meanwhile, the tensor forms of the MINIRES and SYMMLQ methods are also established. The proposed methods use tensor computations with no matricizations involved. Numerical examples are provided to illustrate the efficiency of the proposed methods and testify the conclusions suggested in this paper. [ABSTRACT FROM AUTHOR]

BACKGROUND: The pericarp of citrus in rutaceae is rich in flavonoids that may possess diverse biological activities. Some citrus flavonoids have been used as natural bitterness inhibitors; however, many citrus flavonoid analogues that possess merit taste amelioration functions have not been reported with respect to utilization in food industry. RESULTS: The effects of 12 citrus flavonoids on the inhibition of the bitter taste of naringin, quinine hydrochloride and stevioside were evaluated both by a sensory panel and electronic tongue analysis. Among the flavonoid compounds evaluated, both neohesperidin dihydrochalcone (NHDC) and neodiosmin were identified to show an excellent bitterness inhibition effect on all three bitterness vehicles tested. The results of the electronic tongue evaluation also showed that the addition of neodiosmin, NHDC or hesperidin dihydrochalcone‐7‐o‐glucoside (HDC‐7‐G) was able to reduce significantly the bitterness response value of quinine hydrochloride, which is consistent with the sensory panel evaluation. Structure–activity relationship analysis found that the 7‐linked neohesperidosyloxy group in the A‐ring of the citrus flavonoid skeleton has the best bitterness inhibition effect. In addition, a ternary mixture of NHDC, neodiosmin and naringin, and neodiosmin/β‐cyclodextrin was formulated and it demonstrated, for the first time in the flavor improvement of citrus fruit wine, an enhancement of sweetness and a reduction of bitter taste. CONCLUSION: Twelve citrus flavonoids were found to inhibit the bitter taste of naringin, quinine hydrochloride and stevioside. With respect to the structure–activity relationship analysis, it was found that the 7‐linked neohesperidosyloxy group in the A‐ring of the citrus flavonoid skeleton possessed the best bitterness inhibition effect. © 2021 Society of Chemical Industry [ABSTRACT FROM AUTHOR]