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"The relational complexity of urban and rural landscapes in space and in time. The development of historical geographical information systems (HGIS) and other methods from the digital humanities have revolutionised historical research on cultural landscapes. Additionally, the opening up of increasingly diverse collections of source material, often incomplete and difficult to interpret, has led to methodologically innovative experiments. One of today’s major challenges, however, concerns the concepts and tools to be deployed for mapping processes of transformation—that is, interpreting and imagining the relational complexity of urban and rural landscapes, both in space and in time, at micro- and macro-scale. Mapping Landscapes in Transformation gathers experts from different disciplines, active in the fields of historical geography, urban and landscape history, archaeology and heritage conservation. They are specialised in a wide variety of space-time contexts, including regions within Europe, Asia, and the Americas, and periods from antiquity to the 21st century."

"The relational complexity of urban and rural landscapes in space and in time. The development of historical geographical information systems (HGIS) and other methods from the digital humanities have revolutionised historical research on cultural landscapes. Additionally, the opening up of increasingly diverse collections of source material, often incomplete and difficult to interpret, has led to methodologically innovative experiments. One of today’s major challenges, however, concerns the concepts and tools to be deployed for mapping processes of transformation—that is, interpreting and imagining the relational complexity of urban and rural landscapes, both in space and in time, at micro- and macro-scale. Mapping Landscapes in Transformation gathers experts from different disciplines, active in the fields of historical geography, urban and landscape history, archaeology and heritage conservation. They are specialised in a wide variety of space-time contexts, including regions within Europe, Asia, and the Americas, and periods from antiquity to the 21st century."

In this paper, considering the time scale concept on Smarandache space  we introduce the tangent vector and some properties according to directional derivative, the delta differentiable vector fields on regular curve parameterized by time scales and the Jacobian matrix of completely delta differentiable two variables function.

"The relational complexity of urban and rural landscapes in space and in time. The development of historical geographical information systems (HGIS) and other methods from the digital humanities have revolutionised historical research on cultural landscapes. Additionally, the opening up of increasingly diverse collections of source material, often incomplete and difficult to interpret, has led to methodologically innovative experiments. One of today’s major challenges, however, concerns the concepts and tools to be deployed for mapping processes of transformation—that is, interpreting and imagining the relational complexity of urban and rural landscapes, both in space and in time, at micro- and macro-scale. Mapping Landscapes in Transformation gathers experts from different disciplines, active in the fields of historical geography, urban and landscape history, archaeology and heritage conservation. They are specialised in a wide variety of space-time contexts, including regions within Europe, Asia, and the Americas, and periods from antiquity to the 21st century."

We present ground-based optical photometric monitoring data for NGC 5548, part of an extended multi-wavelength reverberation mapping campaign. The light curves have nearly daily cadence from 2014 January to July in nine filters (\emph{BVRI} and \emph{ugriz}). Combined with ultraviolet data from the \emph{Hubble Space Telescope} and \emph{Swift}, we confirm significant time delays between the continuum bands as a function of wavelength, extending the wavelength coverage from 1158\,\AA\ to the $z$ band ($\sim\!9160$\,\AA). We find that the lags at wavelengths longer than the {\it V} band are equal to or greater than the lags of high-ionization-state emission lines (such as He\,{\sc ii}\,$\lambda 1640$ and $\lambda 4686$), suggesting that the continuum-emitting source is of a physical size comparable to the inner broad-line region (BLR). The trend of lag with wavelength is broadly consistent with the prediction for continuum reprocessing by an accretion disk with $\tau \propto \lambda^{4/3}$. However, the lags also imply a disk radius that is 3 times larger than the prediction from standard thin-disk theory, assuming that the bolometric luminosity is 10\% of the Eddington luminosity ($L = 0.1L_{\rm Edd}$). Using optical spectra from the Large Binocular Telescope, we estimate the bias of the interband continuum lags due to BLR emission observed in the filters. We find that the bias for filters with high levels of BLR contamination ($\sim\! 20\%$) can be important for the shortest continuum lags, and likely has a significant impact on the {\it u} and {\it U} bands owing to Balmer continuum emission.

Causality creates an asymmetry between space and time, even though the wave equation treats them on equal footing. In this work, we leverage this asymmetry to construct a cross-mapping between space and time. This cross-mapping is applied to simplify scattering in space-varying media, by eliminating the infinite reflections between interfaces. The method is shown to transform the implicit transfer matrix method into an explicit method for the analysis of electromagnetic field scattering by a stratified medium.