Since the gradient coils are within the bore of the scanner, there are large forces between them and the main field coils, producing most of the noise that is heard during operation.

Since the pheromone is carried by the wind, males tend to travel up the concentration gradient, i. e., toward the source.

: Since 2008, there has been discussion among professional users of SVG that either gradient meshes or preferably diffusion curves could usefully be added to the SVG specification.

Since the pressure gradient normal to the flow within a boundary layer is approximately zero for low to moderate hypersonic Mach numbers, the increase of temperature through the boundary layer coincides with a decrease in density.

Since it does not ordinarily pass through cell membranes, protein pores in cell membranes are used to provide a channel through which it can be ' pumped ' -- an activity which requires energy if done against a concentration gradient.

Since high pressure areas usually migrate east, changing the pressure gradient in southern California to the northeast, it is common for " sundowner " wind events to precede Santa Ana events by a day or two.

Since this carrier enzyme ( Na < sup >+</ sup >- Ca < sup > 2 +</ sup > translocator ) uses the Na gradient generated by the Na < sup >+</ sup >- K < sup >+</ sup > pump to remove Ca < sup > 2 +</ sup > from the intracellular space, slowing down the Na < sup >+</ sup >- K < sup >+</ sup > pump results in a permanently elevated Ca < sup > 2 +</ sup > level in the muscle, which may be the mechanism of the long-term inotropic effect of cardiac glycosides such as digoxin.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero.

Since the fluid in the inner part of the boundary layer is relatively slower, it is more greatly affected by the increasing pressure gradient.

Since diffusion moves materials from an area of higher concentration to the lower, it is described as moving solutes " down the concentration gradient " ( compared with active transport, which often moves material from area of low concentration to area of higher concentration, and therefore referred to as moving the material " against the concentration gradient ").

Since the curl of v is zero, it follows that v can be expressed as the gradient of a scalar potential ( see irrotational field ) φ:

Since the gradient varies along the route, the floor of each car is never quite level, and slopes slightly " uphill " or " downhill " depending on the location.

Since the normal left ventricular diastolic pressures is about 5 mmHg, a pressure gradient across the mitral valve of 20 mmHg due to severe mitral stenosis will cause a left atrial pressure of about 25 mmHg.

Since the field is the gradient of the electrostatic potential, another way of saying this is that in electrostatics, the potential ( voltage ) throughout a conductive object is constant.

Since the force fields are related to their potentials by the gradient:

Since the direction of the force is dependent on field gradient rather than field direction, DEP will occur in AC as well as DC electric fields ; polarization ( and hence the direction of the force ) will depend on the relative polarizabilities of particle and medium.

Since the head drops are uniform by construction, the gradient is inversely proportional to the size of the blocks.

Since a liquid with a high surface tension pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a gradient in surface tension will naturally cause the liquid to flow away from regions of low surface tension.

Since the source is located at the end of the solenoid which generates the main LaPD background field, there is a gradient in the magnetic field within the cavity.

Since in the open air, as many engines as needed can be added to a train to overcome a steep gradient, a better solution would have been to have a level tunnel from " New Tye " ( West ) to Cascade Tunnel Station ( West ), with a 2. 6 mile stretch of say 4 % gradient ( 1 in 25 ) on the western approaches from say Windy Point Tunnel.

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since the removal force is a function of coating thickness, a differential transformer pickup has been incorporated into the instrument to accurately measure film thickness.

Since the 12th century, courts have had parallel and co-equal authority to make law -- " legislating from the bench " is a traditional and essential function of courts, which was carried over into the U. S. system as an essential component of the " judicial power " specified by Article III of the U. S. constitution.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

: Since the result is a function of, this function can be defined as.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Since such life utilised strong nuclear forces instead of electromagnetic interactions, it was posited that life might function millions of times faster than typical on Earth.

Since these devices are used to run countless different types of programs, these CPU designs are not specifically targeted at one type of application or one function.

Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

Since μ is a function of x, we cannot simplify any further directly.

Since all structural levels of the protein determines its function, the protein can no longer perform its function once it has been denatured.

Since the latter is valid over the entire cycle, this gave Clausius the hint that at each stage of the cycle, work and heat would not be equal, but rather their difference would be a state function that would vanish upon completion of the cycle.

Since 2001, 40 non-natural amino acids have been added into protein by creating a unique codon ( recoding ) and a corresponding transfer-RNA: aminoacyl – tRNA-synthetase pair to encode it with diverse physicochemical and biological properties in order to be used as a tool to exploring protein structure and function or to create novel or enhanced proteins.

Since its inception it has broadened to find applications in many other areas, including statistical inference, natural language processing, cryptography, neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, plagiarism detection and other forms of data analysis.

Since the identity element of a monoid is unique, one can alternately define the identity function on M to be this identity element.

Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.

Since the names of functions are largely a convenience, the lambda calculus has no means of naming a function.

Since any fluorescence image is made up of a large number of such small fluorescent light sources, the image is said to be " convolved by the point spread function ".

Since the energy of the photoelectrons emitted is exactly the energy of the incident photon minus the material's work function or binding energy, the work function of a sample can be determined by bombarding it with a monochromatic X-ray source or UV source, and measuring the kinetic energy distribution of the electrons emitted.

Since each sample is a random variable, the sample mean is a function of random variables and hence a random variable itself, whose distribution can be computed and properties determined.

Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.

Since this variable is not passed as a parameter but can be altered, the results of subsequent calls to the function can differ even if the parameters are identical.