Optimization of first-passage times is required in applications ranging from nanobots navigation to market trading. In such settings, one often encounters unevenly distributed noise levels across the environment. We extensively study how a learning agent fares 1- and 2- dimensional heated gridworlds with an uneven temperature distribution. The results show certain bias effects agents trained vi...

This work establishes some new inequalities to find error bounds for Maclaurin’s formulas in the framework of q-calculus. For this, we first prove an integral identity involving q-integral and q-derivative. Then, use this q-differentiable convex functions. The proved here are very important literature because, with their help, can formula both q classical calculus.

We construct a family of (q−1) 2 -ovoids of Q(4, q), the parabolic quadric of PG(4, q), for q ≡ 3 (mod 4). The existence of (q−1) 2 -ovoids of Q(4, q) was only known for q = 3, 7, or 11. Our construction provides the first infinite family of (q−1) 2 -ovoids of Q(4, q). Along the way, we also give a construction of (q+1) 2 -ovoids in Q(4, q) for q ≡ 1 (mod 4).

1. Examples Example 1.1. The field extension Q(√ 2, √ 3)/Q is Galois of degree 4, so its Galois group has order 4. The elements of the Galois group are determined by their values on √ 2 and √ 3. The Q-conjugates of √ 2 and √ 3 are ± √ 2 and ± √ 3, so we get at most four possible automorphisms in the Galois group. See Table 1. Since the Galois group has order 4, these 4 possible assignments of v...

This paper presents a novel approach for evaluating impacts of price-sensitive loads on electricity price and market power. To accomplish this aim an analytical method along with agent-based computational economics are used. At first, Nash equilibrium is achieved by computational approach of Q-learning then based on the optimal bidding strategies of GenCos, which are figured out by Q-learning, ...