The Existence of Entire Positive Solutions to Monge-Amp`ere Type Equations

Aims/ Objectives: In this paper, we study the Monge-Amp`ere type equation det D2u + α∆u = p(|x|)f(u)(x ∈ Rn). In the previous articles, the equation with Monge-Amp`ere operator or Laplace operator has been studied extensively. However, the research about the combination of two kinds of operator is scarce. We would like do some research on this topic. We obtain a sufficient condition of the existence of entire positive solutions for the equation. Study Design: Study on the existence of solutions. Place and Duration of Study: Department of Mathematics and Physics, North China Electric Power University, September 2019 to present. Methodology: We prove the existence of the solution by constructing Euler’s break line, combining the idea of transformation and the method of mathematical analysis. Results: We obtain a sufficient condition of the existence of entire positive solutions for the equation. Conclusion: We prove the existence of entire positive solutions to Monge-Amp`ere type equation det D2u + α∆u = p(|x|)f(u)(x ∈ Rn) and obtain the sufficient condition for the existence of solutions.

Die Runeninschrift auf dem Rinderknochen von Břeclav, Flur Lány (Südmähren, Tschechische Republik)

During recent excavations at Břeclav-Lány (southern Moravia, Czech Republic), archaeologists have found a fragmented bovine rib with runes. The rib was unearthed in an early Slavic pit-house and is radiocarbon- dated to ca. 600. The inscription begins at the break line and reads xbemdo (probably tbemdo), representing six of the last eight runes of the older fuþark – it seems that the lost piece of the rib exhibited the preceding part of the rune row. There is reason to believe that the carver was a Langobard who did not join the migration into northern Italy in 568 (or, alternatively, a Slav who learned and used the Germanic script?).

Determining the optimum thickness of the lining of a heating furnace

The problem of choosing the optimal thicknesses of the layers of refractory and heat-insulating materials that provide the minimum total cost of the lining and fuel used to compensate for heat losses is considered. The proposed technique (when specifying the required temperature at the boundary of the lining layers as an additional condition) reduces the problem of conditional two-dimensional optimization of the objective function, which does not have an unconditional minimum and has a break line, to the problem of finding the minimum of a unimodal one-dimensional objective function. The relevance of this work is due to the fact that during the overhaul of the furnace it is possible to replace its lining using new materials and optimize costs taking into account the updated state of the range of materials and their prices.

A method for estimating the socioeconomic impact of Earth observations in wildland fire suppression decisions

A method for estimating the socioeconomic impact of Earth observations is proposed and deployed. The core of the method is the analysis of outcomes of hypothetical fire suppression scenarios generated using a coupled atmosphere–fire behaviour model, based on decisions made by an experienced wildfire incident management team with and without the benefits of MODIS (Moderate Resolution Imaging Spectroradiometer) satellite observations and the WRF-SFIRE wildfire behaviour simulation system. The scenarios were based on New Mexico’s 2011 Las Conchas fire. For each scenario, fire break line location decisions served as inputs to the model, generating fire progression outcomes. Fire model output was integrated with a property database containing thousands of coordinates and property values and other asset values to estimate the total losses associated with each scenario. An attempt to estimate the socioeconomic impact of satellite and modelling data used during the decision-making process was made. We analysed the impact of Earth observations and include considerations for estimating other socioeconomic impacts.

Incorporation of Spirulina (Athrospira platensis) in Traditional Egyptian Cookies as a Source of Natural Bioactive Molecules and Functional Ingredients: Preparation and Sensory Evaluation of Nutrition Snack for School Children

Spirulina (Athrospira platensis) is very rich in protein, amino acids, fatty acids, vitamins and minerals and its incorporation into foods will enrich their nutritional values. The objectives of this study were to incorporate spirulina into traditional Egyptian cookies as a source of natural bioactive molecules and to evaluate the effect of the amount of added spirulina on their sensory properties (texture, shred, color, odor and taste) and acceptability using a panel of 10 members. The results indicated that addition of spirulina to the cookies affected the texture, the mouth feel, the easiness with which breaking a cookie was made, the fragmentation and the appearance of the break line. The cookies that received no spirulina had smoother texture and moist-smooth mouth feel whereas those received spirulina had more sandy-course texture and heavy-chewy mouth feel. Increasing spirulina content from 5 to 15% made the cookies more firm and harder to break. Irregular large parts and continuous break lines were observed with the cookies that received no spirulina while more granules and smaller parts with irregular line were observed with all the cookies that received spirulina. The results showed that adding spirulina to cookies may help maintain their integrity and reduce breakage during packaging and distributions. The color of the cookies that received no spirulina was yellow to yellow-orange and that of the cookies that received 5 and 10% spirulina was yellow- green to green-yellow-green while that of the cookies received 15% spirulina was green-yellow-green to green-blue-green. All the baked cookies had a noticeable smell and the odor intensity ranged from faint to strong. Increasing the spirulina content from 5 to 15% (3-fold) increased the odor intensity by 19.6%. The nature of the smell of the cookies that received 0 and 5% spirulina was pleasant while that of the cookies that revived 10 and 15% spirulina was musty-seawater and fishy-seawater, respectively. The addition of spirulina affected both the taste and the degree of acceptance. The taste of the cookies that received no spirulina was sweet-delicious with a high degree of acceptance while the taste of the cookies that received spirulina varied from sweet-sour to bitter-fishy with lower degree of acceptance. Adding 5% spirulina did not affect the smell or the taste. However, addition of a flavoring agent to cookies having higher spirulina contents (10-15%) may be required to musk the smell and taste of spirulina. The results showed that addition of spirulina enhanced the nutritional value of the cookies by increasing the protein content of the cookies and enriching them with vitamins, mineral, omega fatty acids and amino acids, all of which have significant health benefits to school children. Therefore, a further work should be directed towards improving the smell and the taste of spirulina cookies.

Continued Hydrothermal and Radiative Pressure on Changed Cropland in China

Both cropland and climate change over time, but the potential effects of climate change on cropland is currently not well understood. Here, we combined temporally and spatially explicit dynamics of cropland with air temperature, precipitation, and solar radiation datasets. China’s cropland showed a clear northward-shifting trend from 1990 to 2015. The cropland decreased south of the break line at 38° N, whereas it increased from the break line to northern regions. Correspondingly, the temperature showed a significant warming trend in the early part of the study period, which slowed down in later years. During the whole study period, both precipitation and solar radiation decreased over time, showed no significant linear characteristics, and the annual fluctuations were very large. The cropland areas in China showed a displacement characteristic with the increasing temperature, precipitation, and radiation. Overall, the cropland was shifting towards the high-temperature, low-precipitation, and low-radiation areas. The cropland dynamics indicate that they are likely to face severe drought and radiation pressure. Our findings imply that more resources such as irrigation may be needed for cropland, which will undoubtedly aggravate the agricultural water use in most northern regions, and the potential impacts on food security will further emerge in the future.

Remedying the Legacy of State Collapse

This chapter discusses why the campaign of clan cleansing of 1991–1992 was a key shift in the Somali civil war and remains the major break-line underlying Somali national politics today. It then lays out three principles that might help avoid simply redrawing the lines along which the civil war was fought, and concludes with recommendations for three tangible steps towards peace and reconciliation. At the heart of the mistrust and mutual rejection in Somalia today lie the actions of former leaders of the United Somali Congress and Somali National Movement, who resorted to clan-based killings and expulsions in order to cover up their past complicity with the military regime; spun false clan histories to rebrand themselves as heroic leaders of their clans; and then tried to establish authority over parts of the state and country in the name of clan.

Augmented Reality-Assisted Percutaneous Dilatational Tracheostomy in Critically Ill Patients With Chronic Respiratory Disease

Percutaneous dilatational tracheostomy is a minimally invasive procedure performed for those who require prolonged mechanical ventilation. It is a procedure that is performed routinely at the bedside in the intensive care unit. Complications nonetheless still occur, and as a result, several technique modifications have been employed. At Loma Linda University Medical Center, we have implemented a novel technique using augmented reality during percutaneous dilatational tracheostomy placement in an attempt to minimize such complications. Using Brother’s AiRScouter WD-200B head mounted display, the tracheostomy operator is able to focus on the surgical field without having to significantly break line of sight to view the traditional bronchoscopy monitor. Six cases have been treated with this procedure to date with good success and excellent user feedback. We aim to assess augmented reality-assisted percutaneous dilatational tracheostomy and determine its overall efficacy when compared to traditional percutaneous dilatational tracheostomy.

High-Quality Contour Line Generation from LiDAR Point Clouds for the Area of Forests

A methodology for both accurate and smooth contour line generation from Light Detection and Ranging (LiDAR) point clouds is proposed in this paper. In order to improve the accuracy of contour lines in the area of forests, constrained triangulation networks with break lines are then constructed to generate contour lines. In break line extraction, a bi-threshold method for edge line detection is used to extract both complete and reliable break lines. A point clouds elevation adjustment with constrain of break lines and an interpolator considering a contour interval is proposed to improve the smoothness of contour lines. The proposed interpotator is also can avoid contour line intersection when contour lines are interpolated. Statistical parameters and shape index are then used to evaluate quantitatively the accuracy and smoothness of the resultant contour lines, which fill in the blank of contour lines evaluation in theory. The experiments show that high-quality contours in terms of smoothness and accuracy can be generated from LiDAR point clouds.