Proof of the universal density of charged states in QFT

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

On The Solvability of an Inverse Fractional Abstract Cauchy Problems with Conformable Derivative

In this paper, we discuss the solvability of fractional inverse problem for the conformable derivative in Banach space. We establish an equivalent statement of the existence and uniqueness of solution using fractional semigroup. Some special cases of the inverse problem are studied. An application is given to study an inverse problem in a suitable Sobolev space for fractional parabolic partial differential equations with unknown source functions.

Onpairwise Compactness in Fuzzy Finebi-Topological Spaces

In this paper the concepts of Pairwise ( , ) Tif Tjf fuzzy fine dually open cover, Pairwise ( , ) Tif Tjf fuzzy fine dually compact spacesand Pairwise ( , ) Tif Tjf fuzzy fine connected spaces are introduced and also an equivalent statement on Pairwise ( , ) Tif Tjf fuzzy fine dually compact spaces is established.

Decidability of affine solution problems

We present formula equations—first-order formulas with unknowns standing for predicates—as a general formalism for treating certain questions in logic and computer science, like the Auflösungsproblem and loop invariant generation. In the case of the language of affine terms over $\mathbb{Q}$, we translate a quantifier-free formula equation into an equivalent statement about affine spaces over $\mathbb{Q}$, which can then be decided by an iteration procedure.

Limit Sets and Cartan D – space

The main goal of this work is to create a general type of D – space , namely, Cartan D – space and a new type of limit sets , namely, limit sets , and, give some properties and some equivalent statement of these concept also we explain the relationship among the definitions Cartan D – space and ,

A Solution of Riemann Hypothesis

In 1898, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\sigma+it$ of the zeta function, defined by: $$\zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$have real part $\sigma= \ds \frac{1}{2}$. We give a proof that $\sigma= \ds \frac{1}{2}$ using an equivalent statement of Riemann Hypothesis.

An effective study of polynomial maps

In this paper, using an effective algorithm, we obtain an equivalent statement to the Jacobian Conjecture. For a polynomial map [Formula: see text] on an affine space of dimension [Formula: see text] over a field of characteristic [Formula: see text], we define recursively a finite sequence of polynomial maps. We give an equivalent condition to the invertibility of [Formula: see text] as well as a formula for [Formula: see text] in terms of this finite sequence of polynomial maps. Some examples illustrate the effective aspects of our approach.

On Negabent Functions and Nega-Hadamard Transform

The Boolean function which has equal absolute spectral values under the nega-Hadamard transform is called negabent function. In this paper, the special Boolean functions by concatenation are presented. We investigate their nega-Hadamard transforms, nega-autocorrelation coefficients, sum-of-squares indicators, and so on. We establish a new equivalent statement onf1∥f2which is negabent function. Based on them, the construction for generating the negabent functions by concatenation is given. Finally, the function expressed asf(Ax⊕a)⊕b·x⊕cis discussed. The nega-Hadamard transform and nega-autocorrelation coefficient of this function are derived. By applying these results, some properties are obtained.

DISCRETE VECTOR LATTICES AND THE RANGE OF ORTHOMORPHISMS

We give a counterexample to Theorem 3.2 in Toumi and Toumi [The range of an orthomorphism, J. Algebra Appl.8 (2009) 863–868]. In the process we add a new equivalent statement to those in Theorem 7.48 of Aliprantis and Burkinshaw [Locally Solid Riesz Spaces with Applications to Economics, Mathematical Surveys and Monographs, Vol. 105 (American Mathematical Society, 2003)].

Structure of Taylor coefficients by equivalence of Tauberian conditions

From the equivalent statement of a sequence (