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In this study, the fractional variational iteration method using He’s polynomials is employed for constructing semi-analytical solutions of the fractional-in-time generalized nonlinear Schrödinger equation involving Jumarie’s modified Riemann–Liouville derivative. As a result, we obtain the solutions of the original problems in the forms of convergent series that are calculated easily. Our calculation results indicate that the method is quite efficient and convenient for these problems.

C14H22N2O5, orthorhombic, P212121 (no. 19), a = 8.0704(12) Å, b = 9.0136(13) Å, c = 20.596(3) Å, V = 1498.2(4) Å3, Z = 4, Rgt(F) = 0.0429, wRref(F2) = 0.1112, T = 296 K.

C16H16FN3O, orthorhombic, Pbca (no. 61), a = 12.5936(10) Å, b = 7.7308(9) Å, c = 29.568(3) Å, V = 2878.7(5) Å3, Z = 8, Rgt(F) = 0.0872, wRref(F2) = 0.1893, T = 293 K.

C17H14Cl2N2O2, monoclinic, P21/n (no. 14), a = 8.4863(17) Å, b = 12.654(2) Å, c = 15.088(3) Å, β = 103.612(5)°, V = 1574.8(5) Å3, Z = 4, Rgt(F) = 0.0423, wRref(F2) = 0.1472, T = 205 K.

Background: Breast cancer is the prevailing malignancy among women, exhibiting a discernible escalation in incidence within our nation; hormone receptor‐positive (HR+) human epidermal growth factor receptor 2‐negative (HER2−) breast cancer is the most common subtype. In this study, we aimed to search for a non‐invasive, specific, blood‐based biomarker for the early detection of luminal A breast cancer through proteomic studies. Methods: To explore new potential plasma biomarkers, we applied data‐independent acquisition (DIA), a technique combining liquid chromatography and tandem mass spectrometry, to quantify breast cancer‐associated plasma protein abundance from a small number of plasma samples in 10 patients with luminal A breast cancer, 10 patients with benign breast tumors, and 10 healthy controls. Results: The proteomes of 30 participants in all cohorts were analyzed using the DIA method, and a total of 517 proteins and 3584 peptides were quantified. We found that there were significant differences in plasma protein expression profiles between breast cancer patients and non‐breast cancer patients, and breast cancer was mainly related to lipid metabolism pathways. Finally, the optimal protein combinations for the diagnosis of breast cancer were PON3, IGLV3‐10, and IGHV3‐73 through multi‐model analysis, which had a high prediction accuracy for breast cancer (AUC = 0.92), and the model could also distinguish breast cancer from HC (AUC = 0.92) and breast cancer from benign breast tumor (AUC = 0.91). Conclusions: The study revealed proteomic signatures of patients with luminal A breast cancer, identified multiple differential proteins, and identified three plasma proteins as potential diagnostic biomarkers for breast cancer. It provides a reference for the screening of biomarkers for breast cancer. [ABSTRACT FROM AUTHOR]

Using asymmetric topology cryptography to encrypt networks on the basis of topology coding is a new topic of cryptography, which consists of two major elements, i.e., topological structures and mathematical constraints. The topological signature of asymmetric topology cryptography is stored in the computer by matrices that can produce number-based strings for application. By means of algebra, we introduce every-zero mixed graphic groups, graphic lattices, and various graph-type homomorphisms and graphic lattices based on mixed graphic groups into cloud computing technology. The whole network encryption will be realized by various graphic groups. [ABSTRACT FROM AUTHOR]

Safety of plain text passwords has been questioned in current researching information passwords. Graphical passwords are another way for alternative text-based passwords and to improve the user account security. As we are constructing Topsnut-graphical passwords that can be traced to an idea of “Graph structure plus the number theory” proposed first by Hongyu Wang with her colleagues, we find that some of Topsnut-graphical passwords can be composed of algebraic groups under the principle of Abelian additive finite group. We apply the odd-elegant labelling of graph theory to produce Topsnut-graphical passwords, and verify our Topsnut-graphical passwords can form algebraic groups, called labelling graphical groups. Our results can provide those users who have business in two or more banks, and our methods are easily transformed into algorithms with polynomial times.