Straight Line Route Research Articles

Examining quantum gravity's effects on gravitational rainbows

This paper delves into the fundamental implications of quantum gravity on gravitational rainbows, an intriguing phenomenon resulting from the interaction between quantum mechanics and gravity. We explore the theoretical underpinnings of quantum gravity and how they affect light bending around enormous objects, providing insight into the phenomenon known as gravitational rainbows. We investigate the complex interplay between quantum gravity and gravitational events by thoroughly analyzing theoretical models, experimental findings, and computer simulations, providing insights into the essence of the cosmos. The results show that according to the basic theories of light propagation, light moves along the x-axis at a constant speed based on observing a straight-line route between the affine parameters and the x-coordinate. The analysis of shifting gravitational potentials reveals significant influences on the routes taken by light beams traveling through gravitational fields. The impact of quantum gravitational effects is emphasized by the gravitational potential spreading outward, reaching magnitudes of 10 × 1011 and decreasing towards zero outward. Moreover, the gravitational disturbance distribution is closest to the coordinate system center, with minor perturbations in the z-direction, especially in ℎxx and ℎyy. This distribution highlights how gravitational influences vary throughout space. Finally, the analysis shows that, due to a decrease in the impact parameter, the deflection angle of light increases as the angle of incidence lowers. Additionally, the deflection angle is directly influenced by the mass of the deflecting objects, suggesting a proportionate link between mass and deflection. These findings advance our knowledge of gravitational events in astrophysical and cosmological contexts and offer insight into how light behaves in gravitational fields.

Six-minute walk test in healthy British service personnel

IntroductionThe 6 min walk test (6MWT) is a widely used, safe and effective submaximal exercise test. The primary outcome is the distance walked, but additional physiological and patient-reported metrics can...

Влияние вихревого спутного следа на взаимную безопасность крылатых летательных аппаратов, следующих по одному маршруту

The wake vortex consists mainly of two vortices, which are formed when the stream flows around the wings of an aircraft. A semi-empirical model of a stable vortex wake is proposed and analyzed. The model allows describing the velocity field in a vortex, depending on the characteristics of the aircraft generator, as well as assessing the effect of the vortex on the subsequent aircraft. Statistical modeling was carried out to determine the safe interval between the aircrafts for the characteristic sections of the trajectory. When moving over the sea, a straight-line route, a trajectory with turns and an ascent to an altitude for flying around the island were chosen; on the land section of the movement, a flight over the relief was simulated. A significant influence of the ruggedness of the relief on the probability of an aircraft falling when it enters a wake vortex is shown. The effect of the displacement of the aircraft trajectories in the vertical and horizontal planes and the increase in the average flight speed on the safe interval between the aircrafts is investigated.

IOT based Land Mine Detection Robot

Such equipment is usually automatically blasted through pressure when a target steps on it or drives on it. Demining or mine clearance is the process of removing land mines from an area, while minesweeping describes the task of locating mines. Landmines are generally easy to lay and difficult and dangerous. They are harmful due to their unknown positions and are often difficult to detect. Although dimming has been given the highest priority, currently my clearing operation is a labor-intensive, slow, very dangerous, expensive and low technology operation. The current rate of human quarry is about 100 thousand per year. The idea is to build and develop an automated robot capable of detecting buried landmines and taking them from their locations, enabling the operator to control the robot from afar. The buried quarry is detected using metal detectors as most land mines have metal components. The robot will travel in a straight line route. The system allows the operator to stay at a safe distance by enabling the robot to safely control. Wireless control is for the safety of the operator, designed robots must be able to operate remotely, and is equipped with wireless data transmission capabilities.

A lifestyle medicine model for family medical practices based on 9-years of clinical data including food, weight, glucose, carbs/sugar, and walking using linear elastic glucose theory and GH-Method: math-physical medicine, Part 14 (No. 367)

This article is aimed at assisting family medical practices for obesity and type 2 diabetes (T2D) control using the lifestyle medicine model, which is also the Part 14 of his recently developed linear elastic glucose theory (LEGT). More than 33 million Americans, about 1 in 10, have diabetes, and approximately 90% to 95% of them have type 2 diabetes (T2D), where 86% also have problems with being overweight or obese. In other words, 7.7% to 8.2 % of the US population or 25 to 27 million Americans have issues with weight, T2D conditions and multiple complications. The author is a patient who suffered with being overweight/obesity and T2D for over 25 years. He faced many complications from 2002 to 2010. Over the past 11 years, he dedicated himself to research diabetes and its complications. In this article, he describes the simple and straightforward yet highly precise method to control his chronic disease conditions, including weight and glucose. The results of his research provide proof through a big data analytics of his collected input data through the continuous research and implementation efforts during the past 9 years. His findings have finally achieved satisfactory health results with high mathematical precision on his various biomarker predictions. He named this the “lifestyle medicine” approach. The purpose of writing this article is to offer a simple but practical approach to patients with chronic diseases like him self. In summary, the author describes his straightforward implementation model in the following four steps: By reducing his weight from 189 lb. to 170 lb. (-19 lb. or -10% in total weight), cutting off about 50% of his original over-eating food portion size (from 130% in 2012 down to 66% in 2020, which is -7% of his annual food portion reduction from original amount, or -6% averaged annual reduction continuously). This food portion reduction will automatically reduce the intake amount of fat and carbohydrates. Although he strictly controls his sugar, and sodium amounts, he maintains a sufficient intake amount of high-quality protein. When his weight dropped from 189 lbs. to 170 lbs. (-10% or -1.1% per year), his FPG then decreased from 140 mg/dL to 102 mg/dL (-38 mg/dL or -27%, or -3% per year) accordingly. Weight and FPG are highly correlated (93%). When his FPG dropped, his PPG also reduced from 128 mg/dL to 108 mg/dL (-20 mg/dL or -16%, or -1.7% per year), providing he limits his carb/sugar intake amount below 15 grams per meal and walking at least 30 minutes after each meal. He also increased his post-meal walking from 500 steps to 4,400 steps (+433 post-meal steps per year or +87% per year in comparison with his walking steps in 2012). He wants to re-emphasize the importance of diet and exercise. Normally, reduction on food and meal portion will automatically assist on limiting the carbs/sugar intake amount. However, patients should always watch out for the overall nutritional balance. For the author, his carbs/sugar intake amount has been cut down from 20 grams to 12.5 grams per meal (-7.5 grams or -38%, or -4% per year) as a result of his food portion reduction from 130% to 66% (-64% of food portion or -7% per year). This article merely provides a clinical proof using a quantitative and precision approach. These mathematical and biomedical accomplishments are based on careful physical phenomena observations and related biomedical interpretation and proof process. This particular research project of food nutrition and biomedicine has utilized his developed GH-Method: math-physical medicine in which 366 medical papers have been published. The above four statements are simple to understand; therefore, there is no need to learn fancy theories, complex formulas or equations. No need to take special seminars or attend college courses, take high dosages of medications or supplements, or go through any unnecessary surgeries. There are straight-line relationships existing among food, exercise, weight, and glucose that follow a simple and straight-line route from food portion control to weight reduction and arrive at glucose stability for both FPG and PPG.

A Lifestyle Medicine Model for Family Medical Practices based on 9-Years of Clinical Data Including Food, Weight, Glucose, Carbs/Sugar, and Walking Using Linear Elastic Glucose Theory along with GH-Method: Math-Physical Medicine, Part 14 (No. 367)

This article is aimed at assisting family medical practices for obesity and type 2 diabetes (T2D) control using the lifestyle medicine model, which is Part 14 of his recently developed linear elastic glucose theory (LEGT). More than 33 million Americans, about 1 in 10, have diabetes, and approximately 90% to 95% of them have T2D, where 86% also have problems with being overweight or obese. In other words, 7.7% to 8.2 % of the US population or 25 to 27 million Americans have issues with weight, T2D conditions, and multiple complications. The author is a patient who suffered with being overweight/obese and T2D for over 25 years. He faced many complications from 2002 to 2010. Over the past 11 years, he dedicated himself to research diabetes and its complications. In this study, he describes the simple and straightforward yet highly precise method to control his chronic disease conditions, including weight and glucose. The results of his research provide proof through a big data analytics of his collected input data through the continuous research and implementation efforts over the past 9 years. His findings have finally achieved satisfactory health results with high mathematical precision on his various biomarker predictions. He named this the “lifestyle medicine” approach. The purpose of writing this article is to offer a simple but practical approach to patients with chronic diseases like himself. In summary, the author describes his straightforward implementation model in the following four steps: 1. By reducing his weight from 189 lb. to 170 lb. (-19 lb. or -10% in total weight), cutting off about 50% of his original over-eating food portion size (from 130% in 2012 down to 66% in 2020, which is -7% of his annual food portion reduction from original amount, or -6% average annual reduction continuously). This food portion reduction will automatically reduce the intake amount of fat and carbohydrates along with strictly controlling his sugar and sodium amounts, while maintaining a sufficient intake amount of high-quality protein. 2. 2. When his weight dropped from 189 lbs. to 170 lbs. (-10% or -1.1% per year), his FPG then decreased from 140 mg/dL to 102 mg/dL (-38 mg/dL or -27%, or -3% per year) accordingly. Weight and FPG are highly correlated (93%). 3. When his FPG decreased, his PPG also reduced from 128 mg/dL to 108 mg/dL (-20 mg/dL or -16%, or -1.7% per year), providing he limits his carb/sugar intake amount below 15 grams per meal along with walking at least 30 minutes after each meal. He also increased his post-meal walking from 500 steps to 4,400 steps (+433 post-meal steps per year or +87% per year in comparison with his walking steps in 2012). 4. He wants to re-emphasize the importance of diet and exercise. Normally, reduction on food and meal portion will automatically assist in limiting the carbs/sugar intake amount. However, patients should always watch for the overall nutritional balance. For the author, his carbs/sugar intake amount has been cut down from 20 grams to 12.5 grams per meal (-7.5 grams or -38%, or -4% per year) because of his food portion reduction from 130% to 66% (-64% of food portion or -7% per year). This article merely provides a clinical proof using a quantitative and precision approach. These mathematical and biomedical accomplishments are based on careful physical phenomena observations, related biomedical interpretation, and proof process. This particular research project of food nutrition and biomedicine has utilized his developed GH-Method: math-physical medicine in which 366 medical papers have been published. The above four statements are simple to understand. Therefore, there is no need to learn fancy theories, complex formulas or equations. No need to take special seminars or attend college courses, take high dosages of medications or supplements, or go through any unnecessary surgeries. There are straight-line relationships existing among food, exercise, weight, and glucose that follow a simple and straight-line route of from food portion control to weight reduction and arrive at glucose stability for both FPG and PPG.

Chimpanzees Use Least-Cost Routes to Out-of-Sight Goals

While the ability of naturally ranging animals to recall the location of food resources and use straight-line routes between them has been demonstrated in several studies [1, 2], it is not known whether animals can use knowledge of their landscape to walk least-cost routes [3]. This ability is likely to be particularly important for animals living in highly variable energy landscapes, where movement costs are exacerbated [4, 5]. Here, we used least-cost modeling, which determines the most efficient route assuming full knowledge of the environment, to investigate whether chimpanzees (Pan troglodytes) living in a rugged, montane environment walk least-cost routes to out-of-sight goals. We compared the "costs" and geometry of observed movements with predicted least-cost routes and local knowledge (agent-based) and straight-line null models. The least-cost model performed better than the local knowledge and straight-line models across all parameters, and linear mixed modeling showed a strong relationship between the cost of observed chimpanzee travel and least-cost routes. Our study provides the first example of the ability to take least-cost routes to out-of-sight goals by chimpanzees and suggests they have spatial memory of their home range landscape. This ability may be a key trait that has enabled chimpanzees to maintain their energy balance in a low-resource environment. Our findings provide a further example of how the advanced cognitive complexity of hominins may have facilitated their adaptation to a variety of environmental conditions and lead us to hypothesize that landscape complexity may play a role in shaping cognition.

NUMBER OF CONFLICTS AT THE ROUTE INTERSECTION – MINIMUM DISTANCE MODEL

A conflict is an infringement of minimum separation between at least two aircraft. The model is based on these assumptions: aircraft fly on level straight line routes, only an infringement of the lateral separation is considered, deviations are excluded, aircraft at the same flight level fly the same average speed, and aircraft fly towards an intersection and may change direction after intersection. Hence, conflicts mainly occur owing to a loss of minimum separation between aircraft flying at the same flight level. Calculation of average number of potential conflicts is designated for long time interval; hence, aircraft velocity deviations are negligible. The mathematical model in this paper is intended to compare different alternatives of intersection configuration of air traffic services routes. The comparison is based on the results: an average number of potential conflicts per hour on intersection of routes, index of conflicts intensity, and intersection capacity.

Proposta de implantação do sistema de veículo leve sobre trilhos na região central de Caxias do Sul/RS

A ideia do transporte público fortemente baseado no ônibus se tornou ultrapassada e pode trazer uma imagem negativa para o sistema. Paralelamente a isso, os cenários atuais nas médias e grandes cidades revelam que a infraestrutura pública para os transportes necessita explorar novas alternativas, além das já consolidadas, inclusive para a promoção de mais sustentabilidade na vida das pessoas. O Veículo Leve sobre Trilhos, além de eficiente e atraente, pode oferecer os atributos necessários para que as regiões onde é inserido se tornem mais sustentáveis, devido a redução do consumo de recursos naturais e das poluições atmosférica e sonora. A intenção do presente estudo é realçar a importância desta tecnologia, por meio de um estudo de caso na região central de Caxias do Sul/RS. Ao longo do texto são mencionadas algumas vantagens da implantação desse sistema, como a de reurbanização/revitalização de zonas históricas. Foram analisados dois cenários de implantação do VLT: 1) traçado em linha reta, na Avenida Júlio de Castilhos; 2) traçado circular, nas Avenidas Júlio de Castilhos e Itália e Rua Sinimbu. Ambas as alternativas se apresentaram viáveis, cada uma com suas peculiaridades. O primeiro cenário resultou em um veículo trafegando com velocidade de 21km/h passando por cada ponto de embarque/desembarque a cada 10 minutos, em média. Já a velocidade dos veículos no segundo cenário é de 26km/h e a frequência média é de 1 veículo a cada 8 minutos. Salienta-se que no Cenário II há a possibilidade de inserção de mais veículos na via conforme o aumento da demanda, por ser circular.

Minimization of Energy Consumption in WSN using Hybrid WECRA Approach

In wireless sensor network, the energy efficiency protocols are utilized to improve the energy conservation of the system and enhance the lifetime. The transmission is done by the deployment of nodes instead of any physical medium for communication in WSN. The deployed nodes transmit the data to sink or to the destination node. The nodes are gathered for better communication and this is known as clustering. In clustering, the nearby nodes are situated in compatible cluster and send the information to the cluster head which aggregates the information from various nodes and send it further to the sink. Different clustering algorithms and techniques have been developed for the enhancement of WSN. In traditional approach, the central node in the network preferred as cluster head and this node constrained for network transmission. This single node consumes more energy rather than other nodes leads to dead node. On the other hand, it follows the straight line route therefore the route is overloaded which consumes more energy with the reduction in lifetime of the network. We proposed an energy efficient genetic algorithm based approach with the concept of Virtual Grid based Dynamic Routes Adjustment (VGDRA) which enhances the overall performance of wireless sensor networks. The proposed approach has better energy efficiency as compare to LEACH because it is dynamic approach not static, balanced the load and optimization creates more chance of better result in less number of loops that are not possible in other techniques. The simulation result of the proposed approach is carried out in MATLAB.

The Effectiveness of Straight Line Walk Application Used on Straight-Walking Skills for Blind Students

Some studies explore the needs and problems in navigating on the blind person, the ability to walk in a straight line and avoid the tendency to veer. Difficulties that often occur from the tendency to turn is that when traveling straight on the road or open area where environmental information is not good enough to be considered a clue for the visually impaired to help them in maintaining a straight line route. The development of aids for the visually impaired in this era is growing rapidly, both tools to help navigate using global internet-based positioning system and tools to train straight walking using a compass-based system like straight line walks. The purpose of this research is to see the effectiveness of the straight line walk application for visually impaired students walking skills. This research is based on the absence of special attention from the school with the veering phenomenon that occurs in blind students, and its effect which endangers students (such as tripping, crashing into trees, and even walking towards the middle of the highway). This research used the experimental approach with SSR A-B design method. The results showed a decrease in turning distance on the three subjects after being given intervention by using the straight line walk application. Based on the results of this study, it can be concluded that the training program using the straight line walk application can improve the skills of walking straight on blind students.

A Number of Conflicts at Route Intersections - Rectangular Model

A conflict is an infringement of minimum separation between at least two aircraft. Air traffic controllers build a protected area in front of an aircraft; its shapes and dimensions depend on the speed of an aircraft and on the minimum separation. The protected zone in this mathematical model is the horizontal rectangular zone. If an aircraft is inside this protected zone, a conflict occurs. The model is based on these assumptions: aircraft fly in level straight line routes; only an infringement of the lateral separation is considered; deviations are excluded; aircraft at the same flight level fly at the same average speed; aircraft fly towards an intersection and change direction after the intersection. Hence, conflicts mainly occur owing to the loss of minimum separation between aircraft flying at the same flight level. The calculation of average number of potential conflicts is designed for a long time interval; hence, aircraft velocity deviations are negligible. The mathematical model in this paper is intended to compare different alternative intersection configurations of air traffic service routes. The comparison is based on the following results: an average number of potential conflicts per hour at route intersections, index of conflict intensity, and intersection capacity.

Honey buzzards don't always make a beeline.

(a) European honey buzzards breeding in Western Europe primarily use soaring flight to make annual long-range migrations via the Strait of Gibraltar to winter in West Africa; this adult male was photographed on migration near Gibraltar. Photo: Javier Elloriaga. (b) Autumn migration routes of 12 satellite tagged adult European honey buzzards (colour-coded lines); compared with the shortest possible straight-line routes (dashed lines), most routes involved substantial westerly detours in Africa. Adapted from Vansteelant etal. (2016). (c) In contrast, Montagu's harriers predominantly use flapping flight during their migrations; this adult male is carrying a satellite transmitter. Photo: Theo van Kooten. (d) Autumn migration routes of 34 satellite tagged adult Montagu's harriers; migratory tracks more closely approached straight-line routes, and typically involved longer sea crossings, than seen in European honey buzzards. Adapted from Trierweiler etal. (). In Focus: Vansteelant, W.M.G., Shamoun-Baranes, J., van Manen, W., van Diermen, J. & Bouten, W. (2017) Seasonal detours by soaring migrants shaped by wind regimes along the East Atlantic Flyway. Journal of Animal Ecology, 86, 179-191. Migratory birds often make substantial detours from the shortest possible route during their annual migrations, which may potentially increase the duration and energetic cost of their journeys. Vansteelant etal. () investigate repeated migrations of adult European honey buzzards between the Netherlands and sub-Saharan Africa, and find that they make large westerly detours in Africa on both the spring and autumn routes. These detours allow migrants to capitalise on more favourable winds further along the route, thus reducing energy expenditure. Lifelong tracking studies will allow researchers to identify how migration routes have evolved to exploit predictable atmospheric and oceanic circulation patterns.

Analysis of Geometric Disaster Evaluation Model for Physical Networks

A geometric model of a physical network affected by a disaster is proposed and analyzed using integral geometry (geometric probability). This analysis provides a theoretical method of evaluating performance metrics, such as the probability of maintaining connectivity, and a network design rule that can make the network robust against disasters. The proposed model is of when the disaster area is much larger than the part of the network in which we are interested. Performance metrics, such as the probability of maintaining connectivity, are explicitly given by linear functions of the perimeter length of convex hulls determined by physical routes. The derived network design rule includes the following. (1) Reducing the convex hull of the physical route reduces the expected number of nodes that cannot connect to the destination. (2) The probability of maintaining the connectivity of two nodes on a loop cannot be changed by changing the physical route of that loop. (3) The effect of introducing a loop is identical to that of a single physical route implemented by the straight-line route.

Western Veeries use an eastern shortest-distance pathway: New insights to migration routes and phenology using light-level geolocators

ABSTRACT We investigated movements of a western population of Veeries (Catharus fuscescens) breeding in the Okanagan region of British Columbia, Canada, in 2013–2014 using light-level geolocators. We tracked 9 individuals and incorporated a state-space Kalman filter model approach to estimate movement parameters. During migration, Veeries traversed the Rocky Mountains, Great Plains, Gulf of Mexico, and Caribbean Sea with stopovers generally closer to the shorter orthodromic (great circle) route than a loxodromic (straight line) route between breeding and first wintering grounds, particularly on fall migration. Birds initially settled in the south-central portion of the Amazon basin in Brazil at sites that were 666 ± 299 km apart, suggesting low migratory connectivity. Intra-tropical movements were observed for 8 of 9 (88.9%) birds, with second wintering sites an average of 1,447 ± 472 km to the northwest (initial bearing x = 316 ± 16°). Veeries typically followed a pattern of loop migration at the Gulf o...

Short-term public transport solutions in Auckland, New Zealand

This paper investigates policy approaches which will improve the existing public transport system in Auckland, New Zealand. The four principles of public transport network planning: line structure, frequency, transfers and fare systems, are applied to the Auckland Northern Express (the only Bus Rapid Transit (BRT) in New Zealand). The data concerning the Northern Express and its associated network was collected from policy and planning documents, timetables and websites. The data was further verified by conducting detailed fieldwork on the selected network. The results show that the Northern Express exhibits some network planning principles such as a simple straight-line route, high frequency and transferrable fares. However, the Northern Express is poorly coordinated with the surrounding bus network; this coordination could be improved to gain higher patronage levels. The analysis indicates that the poor performance of public transport in Auckland can be addressed in the short-term by improving public transport services at relatively little cost.

Evaluating inputs to models of hominin raw material selection: map resolution and path choices

Selection of an appropriate scale is an important decision in study design in many branches of science, since perceived patterns often change with the scales of spatial extent or resolution of an analysis. In previously published work, we created a resource selection model to determine the importance of several independent variables for the selection of lithic materials by hominins at a Middle Palaeolithic site in southern France. Two of these independent variables (calories exerted and difficulty of the terrain covered in travel from source to site) were calculated using elevation data extracted from maps. In the present paper, we examine the differences in model performance when the variables ‘Calories’ and ‘Difficulty’ are calculated using 1) three base maps for elevation that differed in map resolution (from finest to coarsest: a 1:25,000 topographic base map, SPOT DEM, and SRTM DEM), and 2) two different methods for determining the route from source to site (straight-line route and least-cost route; both methods exclude areas with slopes >60% from travel). Our best model was the one that used data calculated using the topographic base map; however, the SRTM DEM-based data produced models of essentially equal quality. Regardless of map scale, models that used data calculated using a straight-line route always outperformed models that used data calculated using a least-cost route. This supports our previous finding that a straight-line route is a more appropriate measure for the path from lithic source to site than a least-cost route. We conclude that the map resolution of each of the base maps used here is appropriate for analyses involving spatial data pertaining to Neandertal activity because this type of data is essentially always coarse-grained.

Route Choice in Hilly Terrain

The orienteering route choice problem involves finding the fastest route between two given points, with running speed determined by various properties of the terrain. In this study, I consider only the effect of climbing or descending on running speed. If a runner's pace p (the reciprocal of speed) varies linearly with gradient m, the straight‐line route always is fastest. However, a nonlinear formulation for p(m), with d2p/dm2 > 0, will more accurately model runners’ capabilities. As a result, critical gradients may exist for ascent and/or descent, such that optimal routes will never ascend or descend more steeply than the critical gradient. I review and propose several formulations for the pace function p(m) and calculate their critical gradients. In principle, the Euler–Lagrange equation can be used to find optimal routes between arbitrary points on any topography where the height can be expressed as a smooth function of horizontal coordinates. I obtain first integrals of this equation for idealized landforms: hillsides with straight contours and axisymmetric hills. Next, optimal routes are computed for various combinations of start‐ and endpoints on these landforms based on various pace functions. These routes are classified as either subcritical or maximal steepness: The former ascends or descends less steeply than the critical gradient; the latter takes the line of steepest ascent where it is not steeper than the critical gradient, but follows a curve at the critical gradient where the slope is steeper. In some cases, the optimal route zigzags up or down a hill along sections of a critical‐gradient curve.El problema de trazo y selección de ruta en terrenos accidentados (orienteering route choice problem) consiste en encontrar la ruta más rápida entre dos puntos dados, cuando la velocidad de desplazamiento está en función a varias propiedades del terreno. En este estudio, el autor sólo considera el efecto de subir o bajar sobre la velocidad de desplazamiento. Si el paso p de un individuo (la inversa de la velocidad) varía linealmente con la pendiente m, la ruta en línea recta siempre es la más rápida. Sin embargo, una formulación no lineal de p (m), con D2P / dm 2> 0, resulta en un modelo más preciso de las capacidades de los individuos que se desplazan por el terreno. Como resultado, es posible que existan gradientes críticos tanto para el movimiento de ascenso como el de descenso. En dicho caso, las rutas óptimas nunca ascenderán o descenderán por gradientes más pronunciados que las identificadas comode gradiente crítico. El autor revisa y propone varias fórmulas para una función de paso p (m) y calcula los gradientes críticos respectivos. En principio, la ecuación de Euler‐Lagrange puede ser utilizada para trazar las rutas óptimas entre puntos arbitrarios en cualquier topografía en donde la altura pueda ser expresada como una función suavizada de las coordenadas horizontales. El autor calcula las integrales de esta ecuación para dos formas terrestres idealizadas: laderas con contornos rectos, y colinas con simetría axial. A continuación, las rutas óptimas son calculadas para diversas combinaciones de puntos de inicio y destino de estos accidentes geográficos basados en varias funciones de paso. Una vez identificadas, estas rutas se clasifican ya sea como subcríticas o como de máxima‐pendiente. Las primeras ascienden o descienden gradientes menos pronunciadas que el gradiente crítico. Las segundas ascienden por la línea del gradiente más pronunciado que es menor que el gradiente crítico, pero siguen una curva en la gradiente crítica donde la pendiente es más pronunciada. En algunos casos, la ruta óptima se desplaza en zigzags hacia arriba o abajo de una colina a lo largo algunas secciones de una curva de gradiente crítica.移动速度受制于地表形态的诸多属性，定向路线选择问题涉及给定两点之间最快路线查找。本研究仅考虑爬升或下降对移动速度的影响。如果奔跑者的步速p（速度的倒数）与坡度m呈线性相关，那么直线路线始终是最快的。然而，当d2p∕ dm2 > 0时，非线性方程p(m)具有更好的行进模拟性能。试验表明，在上坡或下坡的过程中存在一个临界的坡度值，相应地上坡或下坡的最佳路线坡度将一定不超过较陡的临界坡度值。本文总结并提出了函数p(m)的几个公式，并对其临界坡度值进行了估计。欧拉‐拉格朗日方程原则上可用于寻找任何地形中任意两点之间的最优路径，高度可表示为横坐标的光滑函数。首先，通过方程的一次积分得到理想化地形，即具有直等高线的山坡和对称的山地；然后在这些地形面上，基于起点和终点的多种组合和不同的步速方程计算最佳路线。计算路径被分类为次临界或最大坡度的路线：前者上坡或下坡的坡度大于临界坡度值；后者则在不超过临界坡度值时采用最陡上坡路径，但在坡度陡峭的地区遵循临界坡度曲线。在某些情况下，最优到达路径沿临界坡度曲线截面呈“之”字型曲折上下变化。

The other cold war: the United States and Greenland’s ice sheet environment, 1948–1966

During the early Cold War, no part of the Arctic was as important to the United States’ strategic interests as Greenland: situated on the shortest straight-line route between the industrial centers of the two superpowers, Greenland was integral to North American continental security. The US desire to control Greenland, however, was complicated by the island’s isolated geography, harsh climate and barren landscape. Between 1948 and 1966, US forces in Greenland were entrenched in the ‘other cold war’: the struggle with the ice sheet environment which threatened to impede American capabilities in the region. This paper explores the ‘other cold war’ through two case studies: US scientific efforts to understand and cope with polar whiteouts and the plastic deformation of ice. These case studies illuminate a struggle between two philosophical approaches to nature: a brash, aggressive approach which aimed to conquer the Greenland environment, and a more nuanced approach which aimed to collaborate with that environment. I show that the second approach won out as Greenland’s exceptional geography and environment forced the US military to reassess its relationship with nature: rather than striving for control over the island space, US military personnel ultimately chose strategic cooperation with that space.

Resource selection of lithic raw materials in the Middle Palaeolithic in southern France

The work reported here uses several approaches to examine the costs and benefits associated with exploiting potential sources of lithic raw material in the Vaucluse, southern France, and then tests the results against the proportions of raw materials from various sources found in the lithic assemblage of a Middle Palaeolithic site, the Bau de l’Aubesier. A previously published equation designed to quantify the attractiveness of each source proves to be significantly correlated with source use, but the results show that it can be improved. We then individually test the components of the attractiveness equation (raw material quality, source extent, terrain difficulty, and the size and abundance of raw material pieces at the source) and additional variables (Calories expended to get from the source to the site using a straight-line route, Calories expended using a least-cost path, surface distance of the source from the site, and distance to the closest used source) using generalized linear models. Since very similar raw materials can be found at more than one source, we combine such similar sources into source areas, and test the area of the source area (AOSA) and the total area of sources within the source area (AOSISA), as two additional independent variables. The best model shows that raw material quality, source extent, abundance of large and very large rocks, and AOSISA, are positively correlated with use of sources, while terrain difficulty, abundance of small and medium rocks, Calories, and AOSA, are negatively correlated with source use. This shows that the hominins at the Bau de l’Aubesier optimized their raw material procurement to get the most good quality material that they could, while minimizing the time and energy spent getting and using it.