In this paper we study the properties of a complete quadrangle in the Euclidean plane. Similarly, as it was done in our previous work the proofs are based on using rectangular coordinates symmetrically on four vertices and four parameters a,b,c,d. Here, we gather many properties of the complete quadrangle known from earlier but proved by the same method together with some new results given.

This study delves into the foundational aspects of electrocardiographic (ECG) lead systems, specifically focusing on Einthoven’s Triangle and Wilson’s Central Terminal. We introduce the innovative concept of a Precordial Central Terminal, a strategic arrangement of thoracic electrodes that establishes two Einthoven’s triangles within the horizontal plane, in accordance with physical-mathematical principles. Furthermore, we meticulously scrutinize Goldberger’s contributions to the field of ECG, particularly augmented leads, which shed light on the development of our theory. Additionally, we propose the implementation of a novel standardized electrocardiograph, characterized by its use of exclusively “precordial” electrodes, yet capable of providing a comprehensive three-dimensional perspective of cardiac electrical activity. By amalgamating theoretical underpinnings with empirical experimentation, our study lays the groundwork for future investigations, including the experimental validation of our innovative Precordial Terminal. This validation holds the promise of yielding substantial advancements in the realm of clinical electrocardiography.

Abstract: The objective of Peter Chew Triangle Diagram is to clearly illustrate the topic solution of triangle and provide a complete design for the knowledge of AI age. Peter Chew's triangle diagram will suggest a better single rule that allows us to solve any problem of topic solution of triangle simple , directly and more accurately. There are two important rules for solving the topic solution of triangle today [1,2], namely the sine rule and the cosine rule. The sine rule is used to find a non-included angle when are given two sides and a non-included angle or the opposite side angle given when are given two angles and one side. The cosine rule normally is used to find the included angle when are given three sides or the third side when are given two sides and the included angle. Peter Chew Method[3] allow us to find the third side simple and directly when given two sides and a non-included angle. Peter Chew rule [4] allow us to find a non included angle simple, directly and more accurately when given 2 sides and an included angle. Aply Peter Chew Triangle Diagram to Education 4.0 Calculator , Peter Chew Triangle Diagram Calculator allows the Calculator to solve any problems in the topic solution of triangle simple, directly and more accurate. This can be effective in increasing students' interest in using technology while learning mathematics and will help in the learning of mathematics, especially when similar covid-19 issues arise in the future.

In this work we study the following problem, from a computational point of view: If three points are selected in the unit square at random, what is the probability that the triangle obtained is obtuse, acute or right? We provide two convergent strategies: the frst derived from the ideas introduced in [2] and the second built on the combinatorics theory. The combined use of these two methods allows us to address the random triangle theory from a new perspective and, we hope, to work out a general method of dealing with some classes of computational problems.

Let $\mathcal{N}$ be an arbitrary class of matroids, closed under isomorphism. For $k$ a positive integer, we say that $M \in \mathcal{N}$ is \emph{$k$-minor-irreducible} if $M$ has no minor $N \in \mathcal{N}$ such that $1\leq\left|E\left(M\right)\right|-\left|E\left(N\right)\right|\leq k $. Tutte's Wheels and Whirls Theorem establish that, up to isomorphism, there are only two families of 1-minor-irreducible matroids in the class of 3-connected matroids. More recently, Lemos classified the 3-minor-irreducibles with at least 14 elements in the class of triangle-free 3-connected matroids. Here we prove a local characterization for the 2-minor-irreducible matroids with at least 11 elements in the class of triangle-free 3-connected matroids. This local characterization is used to establish two new families of 2-minor-irreducible matroids in this class.

There are abundant coal, oil and natural gas resources in "Golden Triangle" energy region. Energy resources development, coal chemical industry, coal power and other industries play an important role in promoting regional economic growth, but facing the insufficient water supply. Under the condition of marginal equilibrium of water resources, the paper firstly analyzes the water utilization, and calculates the potential water-saving amount. Then, the paper constructs a cooperative game model and allocates the newly increased GDP by using the weight distribution method. Finally, the paper puts forward some policy suggestions to reduce the efficiency gap of water utilization among regions.

The worldwide number of migrants has had a rapid increase during the last fifteen years. Despite the extensive research studies that elucidate the increase in migrants' recipient countries, we know little about the relationship between the climate factors and human mobility in the countries of origin. Hence, this study focuses on the effects of weather and the propensity of individuals to leave a territory by measuring the importance of rain precipitation or the lack of it in one of the critical food corridors of Central America, formed by El Salvador, Honduras, and Guatemala. To study the mobility process, we develop a stochastic frontier model; the main result shows a greater propensity to migrate when there is a significant drought event in the place of origin. Some other factors that motivate people to leave their homeland are the effect of other climate events measured through the control system (ENSO), homicide levels, economic performance, and exchange rate. The findings allow differentiating between drought and excess precipitation on a population and mobility to other territories. In addition, these results permit us to derive observable implications of the different effects of flooding and drought and create public policies of prevention, mitigation, and resilience.

In this short paper we study some properties of the lines associated with van Aubel’s theorem in the special case when squares are replaced with equilateral triangles constructed on the sides of an arbitrary quadrilateral.

This article deals with special curves similar to those known in mathematics as Lamé curves. Their equations have a certain similarity with the equations of Lamé curves. But these curves are more like ellipses in appearance. Like ellipses, they have major and minor axes. These are such curves that their major and minor semi-axis coincide with an ellipse but are different than an ellipse. The main feature of these curves is that for any triangle whose base coincides with the axis of a given curve and the vertex is on a given curve, the condition aⁿ+bⁿ=cⁿ is obtained. The number “n” is called the degree or rank of this curve. To distinguish this group of curves, we called them Elbe curves. The equations of these lines are also provided in the paper.

Triangular resonators re-shaped with the Sierpinski geometry and U-shaped resonators have been designed, linking them with single-pole-double-through (SPDT) RF MEMS switches to provide frequency tuning for potential applications in the K-Band. Prototypes of band-stop narrowband filters working around 20 GHz and 26 GHz, interesting for RADAR and satellite communications, have been studied in coplanar waveguide (CPW) configuration, and the tuning was obtained by switching between two paths of the devices loaded with different resonators. As a result, dual-band operation or fine-tuning can be obtained depending on the choice of the resonator, acting as a building block. The studied filters belong to the more general group of devices inspired by the metamaterial design.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

The brain, rather than being homogeneous, displays an almost infinite topological genus, because is punctured with a very high number of topological vortexes, i.e., .e., nesting, non-concentric brain signal cycles resulting from inhibitory neurons devoid of excitatory oscillations. Starting from this observation, we show that the occurrence of topological vortexes is constrained by random walks taking place during self-organized brain activity. We introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, that describes three-dimensional random walks of excitatory spike activity propagating throughout the brain tissue. In case of nonlinear 3D paths, the trajectories in brains crossed by spiking oscillations can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to excitatory neuronal assemblies, spaced out by empty area of inhibitory neuronal assemblies. These procedures allow us to describe the topology of a brain of infinite genus, to assess inhibitory neurons in terms of Betti numbers, and to highlight how non-linear random walks cause spike diffusion in neural tissues when tiny groups of excitatory neurons start to fire.

The paper primarily demonstrates that the three internal triangles formed by connecting any point on a midsegment with the vertices of a generic triangle satisfy the geometric Proof of the Pythagorean theorem in Euclidean geometry. Moreover, this study elucidates the Pythagorean relationships inherent within three-dimensional geometric constructs resulting from the arrangement of three-dimensional spatial triangles. This geometric relationship, akin to a generalized extension of the Pythagorean theorem, unveils a unique spatial region characterized by this harmonious area interrelation among triangles.

The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.

This article concerns the adoption of small-scale irrigation farming as a climate-smart agriculture practice and its influence on household income in the Chinyanja Triangle. Chinyanja Triangle is a region that experiences mid-season dry spells and an increase in occurrences of drought due to low and erratic rainfall patterns which is attributed largely to climate variability and change. This poses high agricultural production risks, which aggravate poverty and food insecurity. For this region, adoption of small-scale irrigation farming as a climate-smart agriculture practice is very important. Through a binary logistic and ordinary least squares regression, the article determines factors that influence the adoption of small-scale irrigation farming as a climate-smart agriculture practice and its influence on income among smallholder farmers. The results show that off-farm employment, access to irrigation equipment, access to reliable water sources and awareness of water conservation practices, such as rainwater harvesting have a significant influence on the adoption of small-scale irrigation farming. On the other hand, the farmer’s age, distance travelled to the nearest market and nature of employment negatively influenced the adoption of small-scale irrigation farming decisions. Ordinary least squares regression results showed that the adoption of small-scale irrigation farming as a climate-smart agriculture practice has a significant positive influence on agricultural income. We therefore conclude that to empower smallholder farmers to quickly respond to climate variability and change, practices that will enhance adoption of small-scale irrigation farming in the Chinyanja Triangle are critical as this will significantly impact on agricultural income.

Vector-borne disease (VBD) accounts for more than 17% of the global infectious disease burden, disproportionately affecting developing nations within tropical and subtropical areas. As Aedes aegypti mosquitoes are the principal vector for the transmission of many Public Health pathogens, our study examined their population dynamics within the seasonal context of tropical dry biomes in El Salvador as incidence of VBD in this region has increased in recent years. Species that rely on sexual reproduction must maintain a balanced sex ratio (1:1) to support their population dynamics, however, our phenological analysis of field-collected A. aegypti specimens revealed significant sex ratio variations during dry and wet seasons. Interestingly, we detected a seasonal shift that favored female mosquitoes during the dry season, highlighting the dynamic nature of mosquito populations in highly urbanized environments like El Salvador. By linking sex ratio distortions to anthropogenic factors, our study underscores the importance of comprehensively characterizing the urban ecology of vectors for the development of effective biocontrol strategies. As such, we advocate for more nuanced vector control approaches that consider ecological factors as well as the human behaviors that influence mosquito breeding habitats to effectively combat the rise of VBDs amid global climate changes.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle.

The proliferation of the Internet of Things (IoT) has revolutionized traditional services, giving rise to emerging smart infrastructures by connecting the physical and digital worlds. Sensory data is essential in IoT-based systems for providing context-aware and location-based services. Hence, the accurate localization of IoT devices is paramount. Anchor misplacement can significantly affect location information and coverage services in IoT. We study the effect of anchor misplacement in typical IoT settings where sensors are randomly deployed, can be mobile and may belong to multiple providers. We identify sensing coverage holes formed by anchor misplacement and analyze their presence and impact. To mitigate the impact of anchor misplacement on network reliability, we propose a framework to identify the affected sensor nodes and then identify and remove misplaced anchor nodes. The validity of our approach is verified, and its effectiveness is demonstrated by several experiments with different network topologies and parameters. Our results are promising and can be utilized in multiple coverage applications, such as smart agriculture systems and habitat monitoring, regardless of the sensors or deployment types. It also sheds light on best practices and methods for a reliable design of IoT-based systems.