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We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse H\"older constants associated to the weight. The method of proof uses a decoupling of the…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
We show how sub-Planck phase-space structures in the Wigner function can be used to achieve Heisenberg-limited sensitivity in weak force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent…
In this note we show that the usual notion of fuzzy norm defined on a linear space is equivalent to that of quasiconcave function, in the sense that every fuzzy norm $N:X\times\mathbb{R}[0,1]$ defined on a (real or complex) linear space X…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
The correlation function in quantum systems plays a vital role in decoding their properties and gaining insights into physical phenomena. Its interpretation corresponds to the propagation of particle excitations between space-time, similar…
We introduce and study a new concept called doubly-weighted pseudo-almost periodicity, which generalizes the notion of weighted pseudo-almost periodicity due to Diagana. Properties of such a new concept such as the stability of the…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
In this paper, we make another step in the study of weak error of the stochastic heat equation by considering norms as functional.
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and…
We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1], we give a streamlined proof of the Quillen…
We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…
The aim of this paper is to introduce and investigate a new class of functions called weakly almost contra-$T^*$-continuity which is defined as a function from an operator topological space $(X, \tau, T)$ into an arbitrary topological space…
The aim of this paper is to understand the influence of a dissipative term which is small in the sense that it is asymptotically below scaling on the asymptotic properties of solutions. A diagonalization procedure is applied in order to…
Weak measurements can provide a complete characterization of post-selected ensembles, including the uncertainties of observables. Interestingly, the average uncertainties for pure initial and final states are always zero, suggesting the…
The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions---it is not a scientific question. Good questions, when comparing theories, are operational---they deal with the…
In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions. We give also some inclusions.
We study the notions of weak partial $b$-metric space and weak partial Hausdorff $b$-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial $b$-metric space by using weak partial Hausdorff $b$-metric spaces. A…
We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.