Related papers: ge_gravity2: a command for solving universal gravi…
In this short note, we have generalized and constructed gravity solutions with two "exponents" {\it a la} Kachru, Liu and Mulligan. The coordinate system that is used to construct the gravity solution is useful when $b$ vanishes. It means…
We present a general two-side market model with divisible commodities and price functions of participants. A general existence result on unbounded sets is obtained from its variational inequality re-formulation. We describe an extension of…
Within the framework of a manifestly gauge invariant exact renormalization group for SU(N) Yang-Mills, we derive a simple expression for the expectation value of an arbitrary gauge invariant operator. We illustrate the use of this formula…
The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
We obtain some "universal" estimates for $L_2$-norm of the solution of a parabolic equation via a weighted version of $H^{-1}$-norm of the free term. More precisely, we found the limit upper estimate that can be achieved by transformation…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These…
This paper defines an equation for causality. This equation is then combined with the postulates of quantum mechanics and mass-energy equivalence to produce a quantum mechanical telegrapher's equation and to reproduce the Schrodinger and…
The bigravity models coupled with two scalar fields are constructed. We show that a wide class of the expansion history of the universe, especially corresponding to dark energy and/or inflation, can be described by a solution of the…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group…
We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…
The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe…
We investigate contributions of giant gravitons to the superconformal index. We concentrate on coincident giant gravitons wrapped around a single cycle, and each contribution is obtained by a certain variable change for fugacities from the…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We present three types of non-conformal symmetries for a wide class of 2D dilaton-gravity models. For the particular CGHS, or string-inspired model, a linear combination of these symmetries is conformal and turns out to be the well-known…
We give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in…