Related papers: Unambiguous discrimination among oracle operators
First-order logic fragments mixing quantifiers, arithmetic, and uninterpreted predicates are often undecidable, as is, for instance, Presburger arithmetic extended with a single uninterpreted unary predicate. In the SMT world, difference…
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
We give an oracle separation between QMA and QCMA for quantum algorithms that have bounded adaptivity in their oracle queries; that is, the number of rounds of oracle calls is small, though each round may involve polynomially many queries…
We define and discuss properties of the class of unbounded operators which attain minimum modulus. We establish a relationship between this class and the class of norm attaining bounded operators and compare the properties of both. Also we…
Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$…
Operator-valued concentration inequalities are foundational to the analysis of modern high-dimensional statistics and randomized algorithms. However, standard oracle bounds are frequently limited in practice: they require explicit a priori…
We provide new query complexity separations against sensitivity for total Boolean functions: a power $3$ separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power $2.22$ separation…
We study a class of pseudo-differential operators with oscillating symbols or osc illating amplitudes appearing in the long-range scattering theory. We develop the basic calc ulus for operators from such classes and solve some concrete…
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…
We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of (P(N), U), its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame (P(N),…
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…
A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
In this paper our aim is to extend and improve the sufficient conditions for integral operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
To construct more homogeneous operators, B. Bagchi and G. Misra in \cite{d} introduced the operator $\left(\begin{smallmatrix} T_0 & T_0-T_1 \\ 0 & T_1\\ \end{smallmatrix}\right)$ and proved that when $T_0$ and $T_1$ are homogeneous…
We are interested in testing properties of distributions with systematically mislabeled samples. Our goal is to make decisions about unknown probability distributions, using a sample that has been collected by a confused collector, such as…