Bayesian model comparison involves the evaluation of the marginal likelihood, the expectation of the likelihood under the prior distribution. Typically, this high-dimensional integral over all model parameters is approximated using Markov chain Monte Carlo methods. Thermodynamic integration is a popular method to estimate the marginal likelihood by using samples from annealed posteriors. Here w...

the thermodynamic of the known and very effective catalytic system, hydrogen peroxide (h2o2) and methyltrioxorhenium (mto) is studied in different solvents using uv-visible spectroscopic method. the thermodynamic parameters (δg, δh and δs) for two equilibrium reactions, mto + h2o2 ⇌ a + h2o and a + h2o2 ⇌ b.h2o (a, [mere(o)2(o2)]; b.h2o, [mere(oh2)(o)(o2)2]), are determined. the obtained free e...

The major issue with active pharmaceutical ingredients (APIs) is their slow dissolution rate and solubility. This makes them less likely to get into the body bioavailable. About 40 % of drugs already on market 90 being made have APIs that do not dissolve well in water. To deal this problem, authors designed eutectic mixture (EMs) different (danazol, griseofulvin, mefenamic acid, tolfenamic acid...

We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological phase transitions in spin-$\frac{1}{2}$ toric code model on a square lattice with external fields. show QFI density of ground state be written terms expectation values gauge-invariant Wilson loops for different sizes regions and identify $\mathbb{Z}_2$ order its scaling...

2 Thermodynamics 4 2.1 The Foundations of Thermodynamics . . . . . . . . . . . . . . . 4 2.2 Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . 5 2.3 The Conditions for Equilibrium . . . . . . . . . . . . . . . . . . . 7 2.4 The Equations of State . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 Thermodynamic Processes . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Ther...

A new method of successive construction of a solution is developed for problems of strongly nonequilibrium Boltzmann kinetics beyond normal solutions. Firstly, the method provides dynamic equations for any manifold of distributions where one looks for an approximate solution. Secondly, it gives a successive procedure of obtaining corrections to these approximations. The method requires neither ...

The geometric study of thermodynamics began with Gibbs’s reformulation of the theory in terms of equilibrium states rather than processes [1]. The surface of the set of equilibrium states was Gibbs’s primary object of study and foreshadowed much of the modern differential geometric theory manifolds. Gibbs surfaces is where the geometric theory stood when I became a graduate student. The story t...

in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

The Witt construction describes a functor from the category of Rings to the category of characteristic 0 rings. It is uniquely determined by a few associativity constraints which do not depend on the types of the variables considered, in other words, by integer polynomials. This universality allowed Alain Connes and Caterina Consani to devise an analogue of the Witt ring for characteristic one,...

Restoring and non-restoring divider has become widely applicability in the era of digital computing application due to its computation speed. In this paper, we have proposed the design of divider of different architecture for the computation of Vedic sutra based. The design of divider in the Vedic mode results in high computation throughput due to its replica architecture, where latency is mini...