We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments positive-operator-valued measures. The emphasis of this work are optimality properties measurements, namely, extremality, informational completeness, rank-1 property which contrast complementary class (rank-1) projection-valued first half concentrates solely on finite-outcom...

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. by consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully ...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

To avoid both the inconsistency of the Kalman filter and the performance conservation of the covariance intersection (CI) in the case of unknown correlations, an internal ellipsoidal approximation (IEA) method is proposed to fuse the local estimations. A numerical example of three-state radar tracking system is presented to illustrate the implementation and effectiveness of the proposed algorit...

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of ...

We consider two Gaussian measures μ,μ˜ on a separable Hilbert space, with fractional-order covariance operators A−2β and A˜−2β˜, respectively, derive necessary sufficient conditions A,A˜ β,β˜>0 for I. equivalence of the μ μ˜, II. uniform asymptotic optimality linear predictions based misspecified measure μ˜. These results hold, e.g., processes compact metric spaces. As an important special case...

We show how standard parameter estimation methods can be applied to Geometric Algebra in order to fit geometric entities and operators to uncertain data. These methods are applied to three selected problems. One of which is the perspective pose estimation problem. We show experiments with synthetic data and compare the results of our algorithm with standard approaches. In general, our aim is to...

Hybridization in context to Evolutionary Computation (EC) aims at combining the operators and methodologies from different EC paradigms to form a single algorithm that may enjoy a statistically superior performance on a wide variety of optimization problems. In this article we propose an efficient hybrid evolutionary algorithm that embeds the difference vector-based mutation scheme, the crossov...

In this work we are concerned with the study of strong order convergence in averaging principle for slow-fast systems stochastic evolution equations Hilbert spaces additive noise. particular perturbations general Wiener processes, i.e their covariance operators allowed to be not trace class. We prove that slow component converges strongly averaged one $1/2$ which is known optimal. Moreover appl...