Related papers: On a generalization of the Dvoretzky-Wald-Wolfowit…
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
In this note we introduce a Waldschmidt decomposition of divisors which might be viewed as a generalization of Zariski decomposition based on the effectivity rather than the nefness of divisors. As an immediate application we prove a…
We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.
We investigate a McKean-Vlasov stochastic differential equation with an additive common noise and in which the interaction is through the conditional expectation. We show that, in the presence of an additive individual noise, existence and…
One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert…
The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl…
We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…
Given multiple source domains, domain generalization aims at learning a universal model that performs well on any unseen but related target domain. In this work, we focus on the domain generalization scenario where domain shifts occur among…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
In this paper, we generalize the classical Freidlin-Wentzell's theorem for random perturbations of Hamiltonian systems. In stead of the two-dimensional standard Brownian motion, the coefficient for the noise term is no longer the identity…
The new global version of the Cauchy-Kovalevskaia theorem presented here is a strengthening and extension of the regularity of similar global solutions obtained earlier by the author. Recently the space-time foam differential algebras of…
In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces.
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
Explicit realizations of quantum field theory (QFT) are admitted by a revision to the Wightman axioms for the vacuum expectation values (VEV) of fields. The technical development of QFT is expanded beyond positive functionals on *-algebras…
Quantization of gravity is discussed in the context of field quantization based on an analogue of canonical formalism (the De Donder-Weyl canonical theory) which does not require the space+time decomposition. Using Horava's (1991) De…
A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.
This paper proposes a theoretical framework of the grey wolf optimizer (GWO) based on several interesting theoretical findings, involving sampling distribution, order-1 and order-2 stability, and global convergence analysis. In the part II…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons…