Related papers: Comment on "Hara's theorem in the constituent quar…
We expose here a short proof of Cramer's theorem in R based on convex duality.
We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of $SU(3)_{L}\times SU(3)_{R}$ external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the…
We construct a quasi-local formalism for conserved charges in a theory of gravity in the presence of matter fields which may have slow falloff behaviors at the asymptotic infinity. This construction depends only on equations of motion and…
The regularized theories are non-local at the scale of the cutoff, leading so to the usual difficulties of non-local theories. In this work the conservation laws and causality are investigated for classical field theories with multi-cluster…
Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved…
We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active…
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
We provide a type theoretic treatment of the paper "On Tarski's fixed point theorem" by Giovanni Curi. There are benefits to having a type theoretic formulation apart from routine implementation in a proof assistant. By taking advantage of…
When deriving a formula for the Hall conductivity of interacting electrons in Phys. Rev. B 86, 165133, we have relied on an unjustified implicit assumption that a certain gauge choice could be made. Only under this condition would the…
In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its non-linear completion through the identically conserved current. Our formulation for conserved charges is…
According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of local…
F(R) theory of gravity is claimed to admit a host of conserved currents under the imposition of Noether symmetry following various techniques. However, for a constrained system such as gravity, Noether symmetry is not on-shell. As a result,…
It will be shown that the comment [1] contains numerous errors, misconceptions, inaccuracies, false assumptions, misunderstandings and unjustified claims. The analysis of the comment is built on a false assumption that the terminal current…
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. That current includes, apart from the well-established delta-function term which is sufficient for its…
We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.