Hubble's law and faster than light expansion speeds

Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.Comment: 5 pages, 2 figures, to appear in Am. J. Phy

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

Corporate Dividend Policies during the COVID-19 Pandemic

: In this paper, we examine the changes in corporate dividend policies during the COVID-19 shock. For empirical analysis, we employ annual data of 360 companies from the Pakistan Stock Exchange over the period 2015–2020. Using descriptive analysis and Logit regression models, we find that firms were more likely to either omit or reduce dividend payments during the pandemic year of 2020 as compared to the trends in pre-COVID-19 years of 2015–2019. Further, firms with higher profitability, asset turnover and size were less likely to opt for dividend omissions. On the contrary, dividend omissions were more likely among firms with higher debt ratios. The findings of this study helps to understand firm dividend policies during crisis periods

Performance of Prefabricated Vertical Drains in Improvement of Malaysian Soft Marine Clay

In Malaysia, an increasing need has developed for various types of construction on sites underlain by soft cohesive soil. The use of vertical drains in conjunction with preloading is one of widely used methods to improve the geotechnical properties of the soft soil. This is due to its relatively cheap cost and availability of drains as well as the practical ease of application. This paper presents a number of high quality case studies which had been carried out to study the effectiveness of the vertical drains. The results of the studies are presented and discussed. The performance as well as the effectiveness of the soil improvement method are evaluated

Final state rescattering as a contribution to B→ργB \to \rho \gamma

We provide a new estimate of the long-distance component to the radiative transition $B \to \rho \gamma$. Our mechanism involves the soft-scattering of on-shell hadronic products of nonleptonic $B$ decay, as in the chain $B \to \rho\rho \to \rho\gamma$. We employ a phenomenological fit to scattering data to estimate the effect. The specific intermediate states considered here modify the $B \to \rho \gamma$ decay rate at roughly the $5 \to 8$ level, although the underlying effect has the potential to be larger. Contrary to other mechanisms of long distance physics which have been discussed in the literature, this yields a non-negligible modification of the $B^0 \to \rho^0 \gamma$ channel and hence will provide an uncertainty in the extraction of $V_{td}$. This mechanism also affects the isospin relation between the rates for $B^- \to \rho^-\gamma$ and $B^0 \to \rho^0 \gamma$ and may generate CP asymmetries at experimentally observable levels.Comment: 15 pages, RevTex, 3 figure

Active Sampling-based Binary Verification of Dynamical Systems

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While analytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system's response at different operating conditions, they often produce conservative approximations due to restrictive assumptions and are difficult to construct in many applications. In contrast, popular statistical verification techniques relax the restrictions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into "safe" and "unsafe" subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction error. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.Comment: 23 page

Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory

Supersymmetric Effects on Isospin Symmetry Breaking and Direct CP Violation in B→ργB \to \rho \gamma

We argue that one can search for physics beyond the standard model through measurements of the isospin-violating quantity $\Delta^{-0} \equiv \Gamma(B^- \to \rho^- \gamma)/2\Gamma(B^0 \to \rho^0 \gamma)-1$, its charge conjugate $\Delta^{+0}$, and direct CP violation in the partial decay rates of $B^\pm \to \rho^\pm \gamma$. We illustrate this by working out theoretical profiles of the charge-conjugate averaged ratio $\Delta \equiv {1 \over 2}(\Delta^{+0} +\Delta^{-0})$ and the CP asymmetry $A_{CP}(B^\pm \to \rho^\pm \gamma)$ in the standard model and in some variants of the minimal supersymmetric standard model. We find that chargino contributions in the large $\tan \beta$ region may modify the magnitudes and flip the signs of $\Delta$ and $A_{CP}(B^\pm \to \rho^\pm \gamma)$ compared to their standard-model values, providing an unmistakeable signature of supersymmetry.Comment: 10 pages, 7 figures (requires graphicx