Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces

We investigate the logarithmic convexity of the length of the level curves for harmonic functions on surfaces and related isoperimetric type inequalities. The results deal with smooth surfaces, as well as with singular Alexandrov surfaces (also called surfaces with bounded integral curvature), a class which includes for instance surfaces with conical singularities and surfaces of CAT(0) type. Moreover, we study the geodesic curvature of the level curves and of the steepest descent for harmonic functions on surfaces with non-necessarily constant Gaussian curvature K. Such geodesic curvature functions turn out to satisfy certain Laplace-type equations and inequalities, from which we infer various maximum and minimum principles. The results are complemented by a number of growth estimates for the derivatives $$L'$$ L ′ and $$L''$$ L ′ ′ of the length of the level curve function L, as well as by examples illustrating the presentation. Our work generalizes some results due to Alessandrini, Longinetti, Talenti, Ma–Zhang and Wang–Wang.

Sound Enhancement of Orthotropic Sound Radiation Plates Using Line Loads and Considering Resonance Characteristics

A new vibro-acoustic method is presented to analyze the sound radiation behavior of orthotropic panel-form sound radiators using strip-type exciters to exert line loads to the panels for sound radiation. The simple first-order shear deformation theory together with the Ritz method is used to formulate the proposed method that makes the vibro-acoustic analysis of elastically restrained stiffened orthotropic plates more computationally efficient than the methods formulated on the basis of the other shear deformation theories. An elastically restrained orthotropic plate consisting of two parallel strip-type exciters was tested to measure the experimental sound pressure level curve for validating the effectiveness and accuracy of the proposed method. The resonance characteristics (natural frequency and mode shape) detrimental to sound radiation are identified in the vibro-acoustic analysis of the orthotropic plate. For any orthotropic sound radiation plate, based on the detrimental mode shapes, a practical procedure is presented to design the line load locations on the plate to suppress the major sound pressure level dips for enhancing the smoothness of the plate sound pressure level curve. For illustration, the sound radiation enhancement of orthotropic plates with different fiber orientations for aspect ratios equal to 3, 2, and 1 subjected to one or two line loads is conducted using the proposed procedure. The results for the cases with two line loads perpendicular to the fiber direction and located at the nodal lines of the major detrimental mode shape may find applications in designing orthotropic panel-form speakers with relatively smooth sound pressure level curves.

LSTM-Enabled Level Curve Tracking in Scalar Fields Using Multiple Mobile Robots

In this work, we investigate the problem of level curve tracking in unknown scalar fields using a limited number of mobile robots. We design and implement a long short term memory (LSTM) enabled control strategy for a mobile sensor network to detect and track desired level curves. Based on the existing work of cooperative Kalman filter, we design an LSTM-enhanced Kalman filter that utilizes the sensor measurements and a sequence of past fields and gradients to estimate the current field value and gradient. We also design an LSTM model to estimate the Hessian of the field. The LSTM enabled strategy has some benefits such as it can be trained offline on a collection of level curves in known fields prior to deployment, where the trained model will enable the mobile sensor network to track level curves in unknown fields for various applications. Another benefit is that we can train using larger resources to get more accurate models, while utilizing a limited number of resources when the mobile sensor network is deployed in production. Simulation results show that this LSTM enabled control strategy successfully tracks the level curve using a mobile multi-robot sensor network.

Metode Clustering K-Medoids untuk Aplikasi Pembelajaran di Masa Pandemi COVID-19

The central government took a policy to carry out social distancing with this social distancing having an impact on all activities such as having an impact on the learning process that usually takes place in the classroom turning into online learning using several supporting applications in the learning process during the Covid 19 pandemic. Such as using WhatsApp, Moodle , and Zoom for the learning process. Of the three applications commonly used by students and lecturers for the learning process, it can be grouped using the K-Medoids method which will get a cluster of preferred and disliked applications. The researcher took data from a questionnaire made with Google Form which was distributed to 100 students who often did the learning process with the three applications. Can produce a grouping of applications that students like and dislike in the learning process. By looking at the level curve in Figure 7. There are two clusters of red and blue. If the curved line to the right increases, there are many things that are not liked in the application used. Conversely, if the line from the curve to the right decreases, then online applications are less favorable. The results of this study can be seen from the curve picture that learning is most prioritized in the learning process during the Covid 19 pandemic using the Moodle and WhatsApp applications, and the use of zoom is not prioritized in the learning process. if the line from the curve to the right decreases, then online applications are less favored. The results of this study can be seen from the curve image that learning is most prioritized in the learning process during the Covid 19 pandemic using the Moodle and WhatsApp applications, and zooming is not prioritized in the learning process. if the line from the curve to the right decreases, then online applications are less favored. The results of this study can be seen from the curve picture that learning is most prioritized in the learning process during the Covid 19 pandemic using the Moodle and WhatsApp applications, and the use of zoom is not prioritized in the learning process.

Bio-Sequence Stratigraphy of Asmari Formation in the Southeast of Norabad (Zagros Basin, SW Iran)

Asmari Formation is the thick sequence of carbonate sediment in the range of Oligocene-Miocene which is deposited in the foreland basins of the Zagros and is considered as the original and most famous reservoir rock of Zagros basin. To study of lithostratigraphic units and sequence stratigraphy of this Formation, the section in the southeast of Norabad was selected. Field study indicated that Asmari Formation possessed the thickness of 401.5m and included 9 lithostratigraphic units. According to the study of microfacies, Stacking pattern and identification of main sequence level, three depositional sequences including two-second order and one-third order sequence were recognized. The sea-level curve in the studied section indicated that it was correspondence to the global sea level curve. These facies deposited in five environmental sedimentations as follow Open Sea Shelf (Fore Barrier), Bar, Lagoon, Back bar shelf, and Shoal. The environment is part of a carbonate platform that has been formed on an open shelf. In addition, according to the Study of foraminifer dispersion pattern the range of Asmari Formation in Norabad was suggested to be Oligocene (Rupelian- Chattian) to lower Miocene (Aquitanian- Burdigalian).

Late Pleistocene paleo-hydrological reconstruction based on a new lake-level curve of the Dead Sea

<p><span><span>The Dead Sea depression features exceptionally well preserved lacustrine sedimentary sequences and fossil lake-level markers that attest to a much more extensive lake with a maximum highstand water level of more than 200 m above the modern Dead Sea. Lake-level reconstructions based on sedimentary sequences places this highstand phase within the interval of 15-29 ka. Regional paleoclimatic records, however, indicate arid conditions during this time. This apparent contradiction has been explained by spatially heterogeneous moisture delivery resulting from a southward shift of the Westerly wind system and a change in the path and intensity of winter storms. A newly established lake level-chronology based on </span><sup><span>14</span></sup><span>C- and U/Th-dating of fossil stromatolites has provided contrasting results with respect to previous investigations. Accordingly, the paleolake-highstand was of much shorter duration and occurred at least 10 ka earlier than previously suggested</span><span>. The new lake-level curve agrees with evidence of arid glacial and humid interglacial periods in the Levant.  </span><span>In this study we compared these different lake-level reconstructions quantitatively, using a distributed hydrological balance model. This model computes evaporation based on an aerodynamic- /mass-transfer approach. Calibration and validation of this model is achieved by using ~30 years of pre-anthropogenic lake-level observations combined with interpolated climate surfaces based on weather-station records. In the paleo-hydrological reconstruction we account for parameter uncertainties using Monte-Carlo simulations. Our preliminary results show a pronounced sensitivity of the lake-level to precipitation, wind speed, and surface roughness.</span></span></p>

Novel geometric classification of 3D seismic and its application to the Habshan clinoforms of Western Oman

The principles and benefits of seismic sequence stratigraphy have withstood the test of time, but the application of seismic sequence stratigraphy is still carried out mostly manually. Several tool kits have been developed to semiautomatically extract dense stacks of horizons from seismic data, but they stop short of exploiting the full potential of seismo-stratigraphic models. We introduce novel geometric seismic attributes that associate relative geologic age models with seismic geomorphological models. We propose that a relative sea level curve can be derived from the models. The approach is demonstrated on a case study from the Lower Cretaceous Kahmah Group in the northwestern part of Oman where it helps in sweet-spotting and derisking elusive stratigraphic traps.

Holocene relative sea-level data for the East Frisian barrier coast, NW Germany, southern North Sea

Collecting sea-level data from restricted coastal areas is essential for understanding local effects on relative sea level. Here, a revised relative mean sea-level curve for the area of the East Frisian island Langeoog, northwestern Germany, for the time period from 7200 cal BP until Recent is presented. The revision is based on the reinterpretation of previously published and unpublished data following the HOLSEA standardisation of data handling. Altogether 68 sea-level data taken from 32 cores and outcrops from Langeoog, its back-barrier and the adjacent mainland, which have been collected since the 1950s for mapping and landscape reconstruction purposes, are presented. The age constraints, derived from radiocarbon ages of basal peat, intercalated peat and molluscs and optical dating of tidal deposits, were evaluated in terms of the HOLSEA sea-level protocol and their stratigraphic context. For 7200 cal BP until modern times, 30 sea-level index points with different uncertainty ranges were defined. Additionally, a factor of decompaction was estimated for the remaining basal peat samples as well as for the underlying sediments of intercalated peat samples. The comparison of the Langeoog relative sea-level curve with the relative sea-level curve from the western Netherlands shows that the Langeoog curve lies up to 0.80 m lower than the Dutch curve and diverges for the time before 6000 cal BP. Though the offset coincides with the overall predicted trend of glacial-isostatic adjustment, it is less than predicted. Our study provides a useful assessment of legacy data and contributes to an improved sea-level index dataset for the southern North Sea coast.