Related papers: On the Nakano vanishing theorem
The following two papers form a natural development of a previous series of three articles on the foundations of quantum mechanics; they are intended to take the theory there developed to its utmost logical and epistemological consequences.…
The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.
This paper has been withdrawn by the author due to inconsistency of the considered working hypothesis. The consistent treatment is presented in the last publications of the author.
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem…
Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the…
In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the…
We investigate the possibility of negative mass particles and whether physics as we know it today allows or excludes their existence and what properties they might have in the light these laws. We show that nothing prohibit their existence,…
In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
We generalize the construction of Raynaud of smooth projective surfaces of general type in positive characteristic that violate the Kodaira vanishing theorem. This corrects an earlier paper of the same purpose. These examples are smooth…
The weak value approximation has been in use for thirty-five years, but it has not as of yet received a truly complete derivation, leaving its mathematical validity in a state of limbo. Herein, I fill this gap, deriving the weak value…
We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.
The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…
Some aspects of weak sufficiency of quantum statistics are investigated. In particular, we give necessary and sufficient conditions for the existence of a weakly sufficient statistic for a given family of vector states, investigate the…
In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…
We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different…
We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in…