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In this note, we introduce the concept of semi-*-IFP, the involutive version of semi-IFP, which is a generalization of quasi-*-IFP and *-reducedness of *-rings. We study the basic structure and properties of *-rings having semi-*-IFP and give results for IFPs in rings with involution. Several results and counterexamples are stated to connect the involutive versions of IFP. We discuss the conditions for the involutive IFPs to be extended into *-subrings of the ring of upper triangular matrices. In *-rings with quasi-*-IFP, it is shown that Köthe’s conjecture has a strong affirmative solution. We investigate its related properties and the relationship between *-rings with quasi-*-IFP and *-Armendariz properties.

With the rising use of Internet technologies around the world, the number of network intruders and attackers has skyrocketed. For this reason, introducing systems for detecting attacks within the network security measures stops hackers from gaining access to data. In order to detect various forms of assaults, the development of intrusion detection systems is quite crucial. The election of features and elimination of the unrelated information can improve the classifier's accuracy execution because the network traffic dataset contains many useful and unhelpful features. Along these lines, in this work, three hybrid strategies for selecting the feature were implemented, which include the constant feature by standard deviation, the Quasi constant by variance threshold, and the information gain. These approaches were used to order and rank features, after which the best higher ranking was selected for classification and intrusion detection. These features were tested on three classifiers long shortـterm memory, convolutional neural network, and CNN-LSTM. From the acquired results, a high level of attacks was detected, and classification accuracy was achieved by cross-breeding the selection of the different best features. Furthermore, the convolutional neural network classifier achieved the highest accuracy rate, which exceeded the value of 99.5%.

The consistent way of investigating rings with involution, briefly *-rings, is to study them in the category of *-rings with morphisms preserving also involution. In this paper we continue the study of *-rings and the notion of *-reduced *-rings is introduced and their properties are studied. We introduce also the class of *-Baer *-rings. This class is defined in terms of *-annihilators and principal *-biideals, and it naturally extends the class of Baer *-rings. The use of *-biideals makes this concept more consistent with the involution than the use of right ideals in the notion of Baer *-rings. We prove that each *-Baer *-ring is semiprime. Moreover, we show that the property of *-Baer extends to both the *-corner and the center of the *-ring. Finally, we discuss the relation between *-Baer and quasi-Baer *-rings; the generalization of Baer *-ring.

Objectives To evaluate the cost-effectiveness of sofosbuvir (SOF) + ribavirin (RBV), SOF + daclatasvir (DCV), and SOF + ledipasvir (LDV) + RBV compared with SOF + pegylated interferon alfa (pegIFN) + RBV in the treatment of patients infected with hepatitis C virus in Egypt. Methods Two Markov models were developed on the basis of the Egyptian clinical data and practice and were derived from published sources. The clinical parameters were derived from two sources: the Egypt multicenter national treatment program and previously published randomized clinical trials. The utility of the health states was derived using the available published data. Direct medical costs were obtained from the National Liver Institute database. Results In noncirrhotic patients, incremental cost-effectiveness ratios of US $2330 per quality-adjusted life-year (QALY) gained for the SOF + LDV + RBV, −US $9043/QALY for the SOF + DCV, and −US $1332/QALY for the SOF + RBV regimens were yielded. In cirrhotic patients, incremental cost-effectiveness ratios of −US $4170/QALY gained for the SOF + LDV + RBV, −US $9515/QALY for the SOF + DCV, and –US $2289/QALY for the SOF + RBV regimens were yielded. The SOF + DCV regimen was the most cost-saving option for cirrhotic and noncirrhotic patients. Deterministic sensitivity analyses remain robust. Conclusions The present study concludes that the SOF + DCV regimen among other currently available regimens is the most cost-saving option that yields the most favorable future health economic outcomes compared with the SOF + pegIFN + RBV regimen across a broad spectrum of patients, including those with cirrhosis.

If a radical class is closed under involution in every ring with involution then the radical theoretic conditions involving *-bi-ideals are equivalent to the corresponding conditions concerning bi-ideals without involution.