The Aufbau principle is a fundamental concept in quantum chemistry and atomic physics that describes the process by which electrons populate atomic orbitals in a particular order. According to this principle, electrons fill atomic orbitals starting from the lowest energy level and move to higher energy levels only after the lower ones are filled. The general guideline for this filling order is summarized by the "n + l" rule, where "n" is the principal quantum number and "l" is the azimuthal quantum number.

In the context of aircraft navigation and aerodynamics, the term "F-plane" refers to a specific type of reference plane used in flight dynamics and control theory. It is typically part of the formulation of aircraft equations of motion. The F-plane is aligned with the flight path of the aircraft and is used to analyze how the aircraft responds to various forces and moments during flight.

"Flow conditions" can refer to different contexts depending on the field of study or application, such as fluid dynamics, project management, or even psychology. Below are explanations of flow conditions in a few relevant areas: 1. **Fluid Dynamics**: In this context, flow conditions refer to the characteristics of a fluid in motion. This can include factors such as velocity, pressure, density, temperature, and viscosity.

Flow meter error refers to the discrepancy between the measured flow rate as indicated by a flow meter and the actual flow rate of a fluid passing through the meter. This error can arise from various factors, including: 1. **Calibration Error**: If the flow meter is not properly calibrated, it may provide inaccurate readings. Regular calibration is necessary to ensure accuracy. 2. **Installation Effects**: Poor installation can lead to errors.

Flux-Corrected Transport (FCT) is a numerical method used in computational fluid dynamics and other fields for the transport of scalar quantities, such as mass, energy, or chemical concentration, in a spatial domain. The method is particularly useful when dealing with convection-dominated problems, where the transport process can exhibit steep gradients or sharp fronts, such as in the advection of a pollutant in a fluid or the evolution of a shock wave.

Force density is a physical concept often used in fields like physics and engineering, particularly in the context of continuum mechanics and material science. It is defined as the force per unit volume applied to a material or system. In mathematical terms, force density \(\mathbf{f}\) is expressed as: \[ \mathbf{f} = \frac{\mathbf{F}}{V} \] where \(\mathbf{F}\) is the total force acting on the volume \(V\).

Free molecular flow refers to a regime of gas flow where the mean free path of gas molecules is much larger than the characteristic dimensions of the system through which the gas is flowing. In this condition, gas molecules travel between collisions without interacting with other molecules, often behaving as if they are in a vacuum. ### Key Characteristics of Free Molecular Flow: 1. **Mean Free Path**: This is the average distance a molecule travels between successive collisions.

The term "freestream" can refer to different concepts depending on the context in which it is used, but it is most commonly associated with fluid dynamics and aerodynamics. 1. **Fluid Dynamics/Aerodynamics**: In these fields, "freestream" refers to the region of fluid (such as air, water, or another substance) that is undisturbed or unaffected by the presence of an object moving through it.

Gravity feed is a method of transporting liquids, typically utilized in systems where fluid movement relies on the force of gravity. In gravity feed systems, liquids are stored at a higher elevation than the point of use, allowing the liquid to flow downward through pipes or hoses due to gravitational pull.

The term "gun tunnel" can refer to a few different contexts, depending on the field or area of discussion. Here are a couple of interpretations: 1. **Military/Defense Context:** In military terms, a "gun tunnel" can refer to a fortified passage or tunnel system that houses artillery or firearms. These tunnels might be used to protect weapons from enemy attacks, facilitate movement, or serve as a strategic advantage.

The Haynes similitude principle, often referred to simply as "similitude," is a concept used primarily in fluid dynamics and related fields. It is a method that allows engineers and scientists to predict the behavior of one fluid system based on the behavior of another fluid system that is similar in certain respects. The principle is based on the idea that certain dimensionless parameters can be used to create relationships between different systems.

Helmholtz flow is a type of fluid flow that is governed by a specific mathematical description of velocity fields. Named after the German physicist Hermann von Helmholtz, this flow often refers to the analysis of potential flow, especially in the context of inviscid, incompressible flows.

Homentropic flow refers to a type of fluid flow in which the temperature, pressure, and other properties of the fluid remain uniform throughout the flow field. In this context, "homentropic" typically implies that the flow characteristics do not vary significantly with location within the flow path. This is in contrast to other flow types where properties may change due to variations in temperature, pressure, or composition.

Hydrometeor loading refers to the accumulation of water (in the form of rain, snow, or ice) and the resulting stress it exerts on structures, natural landscapes, or the atmosphere. This concept is relevant in meteorology, civil engineering, and environmental science. The loading can have various impacts, including: 1. **Structural Load**: In engineering, hydrometeor loading is critical for assessing the structural integrity of buildings, bridges, and other constructions.

The hyporheic zone is a region located beneath and alongside a river or streambed, where there is a mixing of surface water and groundwater. This zone plays a critical role in river ecosystems as it supports various biogeochemical processes and provides habitat for diverse organisms. Key features of the hyporheic zone include: 1. **Water Exchange**: The hyporheic zone is characterized by the interaction between river water and groundwater, with water moving in and out of this zone.

"Inspirator" can refer to different things depending on the context, but it generally involves concepts related to inspiration, creativity, or motivation. There might be products, services, organizations, or even software named "Inspirator." 1. **Brand/Company**: Some companies may use the name "Inspirator" to convey a sense of creativity and motivation in their offerings.

The International Journal of Multiphase Flow is a scholarly publication that focuses on the study and research of multiphase flow phenomena, which involve the simultaneous flow of multiple phases, such as gas, liquid, and solid. This journal covers a wide range of topics related to the theoretical, experimental, and computational aspects of multiphase flow, including fluid mechanics, transport phenomena, and the interactions between different phases.

Hélène Bellosta is a French academic known for her work in the fields of culture, media, and technology. She has contributed to various studies related to the impact of digital technologies on society and has been involved in research concerning cultural practices in the context of globalization.

This construction takes as input:and it produces an elliptic curve over a finite field of order $p$ as output.

The constructions is used in the Birch and Swinnerton-Dyer conjecture.

To do it, we just convert the coefficients $a$ and $b$ from the Equation "Definition of the elliptic curves" from rational numbers to elements of the finite field.

For example, suppose we have $a=3/4$ and we are using $p=11$.

For the denominator $4$, we just use the multiplicative inverse, e.g. supposing we havewhere $4^{-1}=3\mathrm{mod}11$ because $4\times 3=1\mathrm{mod}11$, related: math.stackexchange.com/questions/1204034/elliptic-curve-reduction-modulo-p