Some useful topological properties of the moment space of the family of distributions with increasing failure rates are established. These results are exploited to obtain tight inequalities for moments of such distributions and also to derive some interesting facts concerning weak convergence within this family.

In this paper we study a sixth order Cahn-Hilliard type equation that arises as a model for the faceting of a growing surface. We show global in time existence of weak solutions and uniform in time a priori estimates in the H3 norm. These bounds enable us to show the uniqueness of weak solutions.

I propose a scheme for reconstructing the weak value of an observable without the need for weak measurements. The post-selection in weak measurements is replaced by an initial projector measurement. The observable can be measured using any form of interaction, including projective measurements. The reconstruction is effected by measuring the change in the expectation value of the observable due...

An analysis of errors in measurement yields new insight into classically forbidden quantum processes. In addition to " physical " values, a realistic measurement can yield " unphysical " values; we show that in sequences of measurements , the " unphysical " values can form a consistent pattern. An experiment to isolate a particle in a classically forbidden region obtains a negative value for it...

Precise definitions of “weak [quantum] measurements” and “weak value” [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional examples are given showing that weak values are not unique. They therefore cannot correspond to any physical attribute of the system being “weakly” measured, c...

In this article we present an analytical calculation of the probability distribution of the magnification of distant sources due to weak gravitational lensing from non-linear scales. We use a realistic description of the nonlinear density field, which has already been compared with some numerical simulations of structure formation within hierarchical scenarios. Then, we can directly express the...

1. Morley, Marsh, Baldwin/Lachlan, Zilber; and Macintyre 2 2. The Borovik Program: CFSG and tameness 3 2.1. The setting: tame or not 3 2.2. The basic framework: even, odd, mixed, degenerate 4 3. Mixed type 5 3.1. Strong and weak embedding 5 3.2. Toward weak embedding: U(G) 6 3.3. The subgroups B(G) and D(G) 6 3.4. The strategy 7 3.5. The curious incident of the dog in the night 8 3.6. Weak embe...

The design and verification of an asynchronous communicating system can be very complex. In this paper we focus on weak termination: in each reachable state, the system has the option to eventually terminate. We present a component framework and construction method that guarantees weak termination. In the framework, communication between components is modeled by portnets, a special class of wor...

We describe how the notion of optical beam shifts (including the spatial and angular Goos–Hänchen shift and Imbert–Federov shift) can be understood as a classical analogue of a quantum measurement of the polarization state of a paraxial beam by its transverse amplitude distribution. Under this scheme, complex quantum weak values are interpreted as spatial and angular shifts of polarized scalar ...