In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...

We put constraints on the degenerate higher-order scalar-tensor (DHOST) theories using Planck 2018 likelihoods. In our previous paper, we developed a Boltzmann solver incorporating effective field theory parameterised by six time-dependent functions, $\alpha_i$ $(i={\rm B},{\rm K},{\rm T},{\rm M},{\rm H})$ and $\beta_1$, which can describe DHOST theories. Using Markov-Chain Monte-Carlo method w...

It is well-known that the construction of Zariski spectra (commutative) rings yields a dual adjunction between category and locally ringed spaces. There are many constructions algebras in various contexts giving such adjunctions. Michel Coste unified them language categorical logic by showing that, for an appropriate triple $ (T_0,T,\Lambda) (which we call spatial context), each T_0 $-model can...

We study the statistical mechanics of supercooled liquids when system evolves at a temperature $T$ with field $\epsilon$ linearly coupled to its overlap reference configuration same liquid sampled $T_0$. use mean-field theory fully characterize influence $T_0$, and we mainly case fixed, low-$T_0$ value in computer simulations. numerically investigate extended phase diagram $(\epsilon,T)$ plane ...

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

Graph theory, which is used effectively in many fields from science to liberal arts, has very important place our lives. As a result of this, the topological structure graphs studied by researchers. In this paper, we investigate spaces generated graphs. The states being an accumulation point and interior these are examined. It defined that relative topology on subgraph graph. shown different su...