Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigen...

This work is motivated by the sign problem in a logarithmic parameter of black hole entropy and existing more massive white dwarfs than Chandrasekhar mass limit. We examine quadratic, linear, linear–quadratic generalized uncertainty principle (GUP) models within virtue recent masses radii dwarfs. consider modification generated introducing minimal length on degenerate Fermi gas equation state (...

Funding information U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program, DE-SC-0011077, Defense Advanced Research Projects Agency’s Enabling Quantification of Uncertainty in Physical Systems, U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, DE-SC0006402, NSF, CMMI-1454601, Renewa...

calculate some thermodynamic properties of molten polymers including specific volume and isothermal compressibility (S.M. Hoseini, Physical Chemistry & Electrochemistry, 2 (2014) 56-65). This work extended that EOS to predict the volumetric properties of some molten ethylene copolymers including ethylene/1-octene, ethylene/1-butene (xethylene equal to 0.8543 and 0.563), ethylene/propene. The ab...

In this study, a temperature-dependent of the dispersion coefficients is calculated from equation state.The Lennard-Jones LJ (12-6-3) effective pair potential function and simple thermodynamic argumentwith the input PVT data of liquid metals are used to calculate the dispersion coefficients. The dispersioncoefficients ( , , ) 3 6 12 C C C are found to be a linear function of 1/T1+α , where T is...

There is a question attributed to Irving Kaplansky concerning the solvability of the quadratic equation x2 − py2 = a in the case that the prime p = a2 + (2b)2. This question was answered in the affirmative by Mollin [1], although according to [3], this result is implicit in the work of Gauss and Legendre. The proof appearing in [1] was later simplified in [4], and it was also shown therein that...

Hall, K.R., Iglesias-Silva, G.A. and Mansoori, G.A., 1993. Quadratic mixing rules for equations of state. Origins and relationships to the virial expansion. Fluid Phase Equilibria, 91: 67-76. Quadratic mixing rules, originally proposed by van der Waals, are used extensively in mixture calculations involving equations of state. Several ways exist to derive such mixing rules from the principles o...

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = accele...

We use Palm calculus to derive a simple, intuitive system of two linear-quadratic equations and two unknowns, whose algebraic solution yields Harel’s (1988) upper bound to the Erlang loss probability. We then derive a sequence of progressively stronger systems of equations, which eventually become exact. We provide two example applications.