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...

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical log...

-Macerations of fragmented plant compressions of Silurian (Llandoverian) age yield sheets of organic material bearing ridges and depressions (interpreted as corresponding to surficial dimensions of cells), fragments of smooth walled tubular elements, and fragments of tubular elements with differentially thickened walls ("banded tubes"). A fragment of tissue (1.2 mOl long), consisting of smooth ...

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we intr...

We show that the extent of a Tychonoff space of countable weak extent can be arbitrary big. The extent of X is e(X) = sup{|F | : F ⊂ X is closed and discrete} while we(X) = min{τ : for every open cover U of X there is A ⊂ X such that |A| ≤ τ and St(A,U) = X} is the weak extent of X (also called the star-Lindelöf number of X). Also we show that the extent of a normal space with countable weak ex...

Weak gravitational lensing of distant galaxies by foreground structures has proven to be a powerful tool to study the mass distribution in the universe. Nowadays, attention has shifted from clusters of galaxies to the statistical properties of the large scale structures and the halos of (field) galaxies. These applications have become feasible with the advent of panoramic cameras on 4m class te...

We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs. In [1,2], Babai and Frankl provided strong constraints on which finite groups could be CI-groups with respect to graphs. As a tool in this program, they proved [1, Lemma 3.5] that a quotient group G/N of a CI-group G with respect to graphs is a CI-group with respect to graphs provide...

where 1 sp < co. This definition is far from being intrinsic. For an intrinsic definition of WrTp(Mm, N”) see [ 11. In this space, beside the standard topology induced by the norm (1. ]ll,p, we also have weak topology and weak convergence. Let fk, f E W’~p(Mm), where 1 < p < co. We say that fk converges to f in weak topology iff fk + f in Lp and the set (lIVfk[lp)k is bounded. Weak convergence ...

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods a...

We propose a method for image set-based hand shape recognition that uses the multi-class AdaBoost framework. The recognition of hand shape is a difficult problem, as a hand’s appearance depends greatly on view point and individual characteristics. Using multiple images from a video camera or a multiple-camera system is known to be an effective solution to this problem. In our proposed method, a...