Emergent unitarity in de Sitter from matrix integrals

We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and an infinite-time evolution operator between the far past and far future. This evolution is not unitary, although we find that it acts unitarily on a subspace up to non-perturbative corrections. These corrections come from processes which involve changes in the spatial topology, including the nucleation of baby universes. There is significant evidence that this 1+1 dimensional model is dual to a 0+0 dimensional matrix integral in the double-scaled limit. So the bulk quantum mechanics, including the Hilbert space and approximately unitary evolution, emerge from a classical integral. We find that this emergence is a robust consequence of the level repulsion of eigenvalues along with the double scaling limit, and so is rather universal in random matrix theory.

Estimates of the topological degree of a class of piecewise linear maps with applications

We provide some new estimates for the topological degree of a class of continuous and piecewise linear maps based on a classical integral computation formula. We provide applications to some nonlinear problems that exhibit a local [Formula: see text] structure.

Some New Simpson’s and Newton’s Formulas Type Inequalities for Convex Functions in Quantum Calculus

In this paper, using the notions of qκ2-quantum integral and qκ2-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.

Combined Effects of Heat and Mass Transfer on MHD Free Convective Flow of Maxwell Fluid with Variable Temperature and Concentration

Heat and mass transfer combined effects on MHD natural convection for a viscoelastic fluid flow are investigated. The dynamics of the fluid are controlled by the motion of the plate with arbitrary velocity along with varying temperature and mass diffusion. The non-dimensional forms of the governing equations of the model are developed along with generalized boundary conditions and the resulting forms are solved by the classical integral (Laplace) transform technique/method and closed-form solutions are developed. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences; few of them are highlighted here as limiting cases. Moreover, parametric analysis of system parameters P r , S , K c , G T , G c , M , S c , λ is done via graphical simulations.

Fredholm and Volterra nonlinear possibilistic integral equations

Fredholm and Volterra nonlinear possibilistic integral equations In this paper we study the nonlinear functional equations obtained from the classical integral equations of Fredholm and of Volterra of second kind, by replacing there the linear Lebesgue integral with the nonlinear possibilistic integral.

Generalizations of Hardy’s Type Inequalities via Conformable Calculus

In this paper, we derive some new fractional extensions of Hardy’s type inequalities. The corresponding reverse relations are also obtained by using the conformable fractional calculus from which the classical integral inequalities are deduced as special cases at α=1.

Exploring algebraic structures of nonlocal classical integral systems

Mathematics underpins so many aspects of nature and society, from the mathematical array of natural structures to the use of statistics, fractions and mathematical models in everyday life. The application of mathematics to real life problems is vital, yet there are many examples of failed attempts to apply mathematics to solve everyday issues that have arisen as a result of an underinvestment in and underdevelopment of the field of mathematics. One prominent example of this lack is non-linearity. Dr Yohei Tutiya, an Associate Professor from the Center for Basic Education and Integrated Learning at Kanagawa Institute of Technology in Japan, has been exploring the classical integrable system in relation to the possibility of developing further non-local differential equations.

Certain Generalized Quantum Simpson's and Quantum Newton's type Inequalities for Convex Functions in Quantum Calculus

In this paper first we present some new identities by using the notions of quantum integrals and derivatives which allows us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for differentiable convex functions by using the q_{x}-quantum integral and q^{y}-quantum integral. In particular, this paper generalises and extends previous results obtained by the various authors in the field of quantum and classical integral inequalities.