Injectivity of sections of convex harmonic mappings and convolution theorems

In the article the authors consider the class ${\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\mathcal{P}_H^0(\alpha)$ and $\mathcal{G}_H^0(\beta)$ of functions from ${\mathcal H}_0$ and show that if $f\in \mathcal{P}_H^0(\alpha)$ and $F\in\mathcal{G}_H^0(\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $\alpha$ and $\beta$ are satisfied. In the second part we study the harmonic sections (partial sums) $$s_{n, n}(f)(z)=s_n(h)(z)+\overline{s_n(g)(z)},$$ where $f=h+\overline{g}\in {\mathcal H}_0$, $s_n(h)$ and $s_n(g)$ denote the $n$-th partial sums of $h$ and $g$, respectively. We prove, among others, that if $f=h+\overline{g}\in{\mathcal H}_0$ is a univalent harmonic convex mapping, then $s_{n, n}(f)$ is univalent and close-to-convex in the disk $|z|< 1/4$ for $n\geq 2$, and $s_{n, n}(f)$ is also convex in the disk $|z|< 1/4$ for $n\geq2$ and $n\neq 3$. Moreover, we show that the section $s_{3,3}(f)$ of $f\in {\mathcal C}_H^0$ is not convex in the disk $|z|<1/4$ but is shown to be convex in a smaller disk.Comment: 16 pages, 3 figures; To appear in Czechoslovak Mathematical Journa

Two years of satellite-based carbon dioxide emission quantification at the world's largest coal-fired power plants

Carbon dioxide (CO2) emissions from combustion sources are uncertain in many places across the globe. Satellites have the ability to detect and quantify emissions from large CO2 point sources, including coal-fired power plants. In this study, we routinely made observations with the PRecursore IperSpettrale della Missione Applicativa (PRISMA) satellite imaging spectrometer and the Orbiting Carbon Observatory-3 (OCO-3) instrument aboard the International Space Station at over 30 coal-fired power plants between 2021 and 2022. CO2 plumes were detected in 50 % of the acquired PRISMA scenes, which is consistent with the combined influence of viewing parameters on detection (solar illumination and surface reflectance) and unknown factors (e.g., daily operational status). We compare satellite-derived emission rates to in situ stack emission observations and find average agreement to within 27 % for PRISMA and 30 % for OCO-3, although more observations are needed to robustly characterize the error. We highlight two examples of fusing PRISMA with OCO-2 and OCO-3 observations in South Africa and India. For India, we acquired PRISMA and OCO-3 observations on the same day and used the high-spatial-resolution capability of PRISMA (30 m spatial/pixel resolution) to partition relative contributions of two distinct emitting power plants to the net emission. Although an encouraging start, 2 years of observations from these satellites did not produce sufficient observations to estimate annual average emission rates within low (&lt;15 %) uncertainties. However, as the constellation of CO2-observing satellites is poised to significantly improve in the coming decade, this study offers an approach to leverage multiple observation platforms to better quantify and characterize uncertainty for large anthropogenic emission sources.</p

On the inconsistency of the Bohm-Gadella theory with quantum mechanics

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page

Glory Oscillations in the Index of Refraction for Matter-Waves

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and nitrogen over a wide range of sodium velocities. We observe glory oscillations -- a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Boundedness, compactness and Schatten-class membership of weighted composition operators

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces $\mathcal{A}^2 \alpha(\mathbb{D})$ are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.Comment: 12 page

Large and seasonally varying biospheric CO₂ fluxes in the Los Angeles megacity revealed by atmospheric radiocarbon

Measurements of Δ¹⁴C and CO₂ can cleanly separate biogenic and fossil contributions to CO₂ enhancements above background. Our measurements of these tracers in air around Los Angeles in 2015 reveal high values of fossil CO₂ and a significant and seasonally varying contribution of CO₂ from the urban biosphere. The biogenic CO₂ is composed of sources such as biofuel combustion and human metabolism and an urban biospheric component likely originating from urban vegetation, including turf and trees. The urban biospheric component is a source in winter and a sink in summer, with an estimated amplitude of 4.3 parts per million (ppm), equivalent to 33% of the observed annual mean fossil fuel contribution of 13 ppm. While the timing of the net carbon sink is out of phase with wintertime rainfall and the sink seasonality of Southern California Mediterranean ecosystems (which show maximum uptake in spring), it is in phase with the seasonal cycle of urban water usage, suggesting that irrigated urban vegetation drives the biospheric signal we observe. Although 2015 was very dry, the biospheric seasonality we observe is similar to the 2006–2015 mean derived from an independent Δ¹⁴C record in the Los Angeles area, indicating that 2015 biospheric exchange was not highly anomalous. The presence of a large and seasonally varying biospheric signal even in the relatively dry climate of Los Angeles implies that atmospheric estimates of fossil fuel–CO₂ emissions in other, potentially wetter, urban areas will be biased in the absence of reliable methods to separate fossil and biogenic CO₂