AUT Journal of Mathematics and Computing
Volume:4 Issue: 2, Mar 2023

In this paper, we derive a formula for the (mean) Cartan torsion of a class of general (α,β)-metrics. Also, we study weak Landsberg general (α,β)-metrics under a certain condition.

This work is intended to compute the µ-symmetry and µ-conservation laws for the Cammasa-Holm (CH) equation and the Hunter-Saxton (HS) equation. In other words, µ-symmetry, µ-symmetry reduction, variational problem, and µ-conservation laws for the CH equation and the HS equation are provided. Since the CH equation and the HS equation are of odd order, they do not admit a variational problem. First we obtain µ-conservation laws for both of them in potential form because they admit a variational problem and then using them, we obtain µ-conservation laws for the CH equation and the HS equation.

The Ricci curvature is introduced by spray on Mn. Sprays are deformed to projective sprays with a volume form dV on Mn. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays. With this paper, we use the new notion that is called weakly isotropic projective Ricci curvature. We have introduced the idea of weakly isotropic projective Ricci curvature in [3]. Then we study and characterize m-th root metrics of weakly isotropic projective Ricci curvature. We obtain that every m-th root metric of weakly isotropic projective Ricci curvature is projectively Ricci-flat.

In this paper, we introduce the concept of biamenability of Banach algebras and we show that despite the apparent similarities between amenability and biamenability of Banach algebras, they lead to very different, and somewhat opposed, theories. In this regard, we show that commutative Banach algebras and the group algebra L1(G) for each locally compact group G, tend to lack biamenability, while they may be amenable and highly non-commutative Banach algebras such as B(H) for an infinite-dimensional Hilbert space H tend to be biamenable, while they are not amenable. Also, we show that although the unconditional unitization of an amenable Banach algebra is amenable but in general unconditional unitization of a Banach algebra is not biamenable. This concept may be applied for studying the character space of some Banach algebras and also for studying some spansion or density problems.

In this paper, we use the Plackett-Luce model for detecting some referees judge arbitrariness with inaccuracy or without paying enough attention which is called semi-referees. We will investigate our method by simulation and sample of real data.

Along with the advent of social networks such as Twitter; Politicians, social media, and ordinary citizens regularly turn to them to share their thoughts and feelings, such as political views. This article analyzes the political ideology of Iranian Twitter users using deep learning and combining the deep layers of LSTM and CNN with BERT, enabling us to target groups of sympathizers and opponents of the Islamic Republic of Iran that are also of particular interest to political scientists. We trained a model for predicting whether a tweet is a sympathizer or opponent, using a novel dataset from Twitter, including tweets from sympathizers and opponent people. Then, using the trained model, the people's ideology can be identified. The results show that using the proposed model, tweets can be categorized with a 75.68\% F1-Score, and the classification of individuals based on political orientation to a 93.18\% F1-Score can be done correctly

Let Bn be the open unit ball in Cn and Bn×Bn. The symmetric lifting operator which lifts analytic functions from H(Bn) to H(Bn2) is defined as follow‎‎                                                                         L(f)(z,w) = f(z)-f(w)/z-w.‎‎In this paper we investigate the action of symmetric lifting operator on the Bergman space in the unit ball‎. ‎Also‎, ‎we state a characterization for Dirichlet space and consider symmetric lifting operator on the Dirichlet space in the unit ball‎.

We give several inequalities involving numerical radii $\omega \left( \cdot \right)$ and the usual operator norm $\left\| \cdot \right\|$ of Hilbert space operators. These inequalities lead to a considerable improvement in the well-known inequalities                                                                        ½||T||≤ω(T)≤||T||

In this study, we present a bi-level formulation for a sequential stochastic attacker-defender game with multiple targets. In this game, the vulnerability of targets is a stochastic parameter, and the attacker has only one attack type. Thedefender’s aim is to find the optimal allocation of the budget to minimize the conditional value at risk of damage. In response to the defender’s decisions, the attacker seeks an optimal allocation of its budget to maximize the expected damage. By using Karush-Kuhn-Tucker transformations, we reduce the proposed bi-level formulation to a single-level one. We also explore some important relationships between the solutions of the single-level and bi-level problems. Finally, by means of numerical experiments, we apply our formulation to several stochastic attacker-defender games to show the efficiency of our formulation in practice.

In this paper, we define the warped generalized Lagrangian (WGL) spaces and then examine some of their properties. In the following, we generalize the Tavakol-van den Bergh" condition in the theory of relativity (see [9]) in this space, which is an example of the application of the warped generalized Lagrangian spaces in relativity (Theorem 4.6). We show that condition EPS in these spaces holds provided that the warped function f satisfies the condition (e^2f)^i=0.

‎In this paper‎, ‎by applying the non-classical symmetry method‎, ‎non-classical symmetries of the Kodryashov-Sinleschikov (K-S) and‎ ‎modified Korteweg-de Vries-Zaharov-Kuznetsov (mKdV-ZK) equations are‎ ‎obtained‎. ‎Apart from classical symmetries‎, ‎this theory can be‎ ‎effective in finding a few other solutions for a system of PDEs and‎ ‎ODEs‎. ‎Also‎, ‎non-classical symmetries of a system of PDEs can be‎ ‎applied to reduce the number of independent variables‎. ‎By adding the‎‎invariance surface condition to the assumed equations and applying‎ ‎the classical symmetry method for them‎, ‎non-classical symmetries are‎ ‎calculated‎. ‎Finally‎, ‎some of the group invariant solutions and the‎ ‎similarity reduced equations associated to non-classical symmetry‎ ‎are obtained‎.

Simultaneous optimization of vehicle routing and loading decisions in three-dimensional case is one of the important problems in logistics and has received great attention from researchers. To the best of our knowledge, optimization models presented in the literature for this problem either are too complicated or do not include important loading assumptions such as item fragility, last-in-first-out arrangement, and the possibility of rotation. To overcome the shortcoming of the existing models, in this paper, we present a novel mixed-integer linear programming (MILP) model which not only involves important loading assumptions, but also does not have the complexity of previous models. Moreover, we provide valid inequalities to strengthen the LP relaxation bound and accelerate the solution process. Further, we show that how a restricted version of our model can be incorporated in loading procedures of meta-heuristic algorithms to improve their efficiency. Computational results over instances, taken from the literature, show the performance of the proposed approach.