The Problems of Random Flight and Conduction of Heat

1924 ◽  
Vol 22 (2) ◽  
pp. 167-168
Author(s):  
W. Burnside
Keyword(s):  
Constant Velocity ◽  
Time Interval ◽  
Straight Line ◽  
Random Flight ◽  
Image Position

In a paper on random flight Lord Rayleigh proved the following result: A number is formed by adding together n numbers each of which is equally likely to have any value from − a to + a. Then, if f (n, s) ds is the probability that the number so formed lies between s and s + ds, and if n is sufficiently great,This result may be stated as follows: A point moves discontinuously in a straight line. For a time τ it has a constant velocity. During the next time-interval τ it again has a constant velocity, and so on. Then if each of these velocities is equally likely to have any value from − v to + v, the probability that in the time nτ, the point moves a distance lying between s and s + ds is f (n, s) ds, with vτ written for a.

Coarse-To-Fine 3D Randomized Hough Transform for Dim Target Detection

2014 ◽  
Vol 519-520 ◽  
pp. 1040-1045
Author(s):  
Ling Fan
Keyword(s):  
Target Detection ◽  
Hough Transform ◽  
Constant Velocity ◽  
Three Dimensional ◽  
Randomized Hough Transform ◽  
Straight Line ◽  
Memory Complexity ◽  
Coarse To Fine

This paper makes some improvements on Roberts representation for straight line in space and proposes a coarse-to-fine three-dimensional (3D) Randomized Hough Transform (RHT) for the detection of dim targets. Using range, bearing and elevation information of the received echoes, 3D RHT can detect constant velocity target in space. In addition, this paper applies a coarse-to-fine strategy to the 3D RHT, which aims to solve both the computational and memory complexity problems. The validity of the coarse-to-fine 3D RHT is verified by simulations. In comparison with the 2D case, which only uses the range-bearing information, the coarse-to-fine 3D RHT has a better practical value in dim target detection.

XVIII.—The Invariant Theory of Forms in Six Variables relating to the Line Complex

1927 ◽  
Vol 46 ◽  
pp. 210-222 ◽  
Author(s):  
H. W. Turnbull
Keyword(s):  
Invariant Theory ◽  
Line Geometry ◽  
Five Dimensions ◽  
Ordinary Space ◽  
Homogeneous Coordinates ◽  
Plücker Coordinates ◽  
Algebraic Theories ◽  
Straight Line ◽  
Image Position ◽  
Theory Of Forms

It is well known that the Plücker coordinates of a straight line in ordinary space satisfy a quadratic identitywhich may also be considered as the equation of a point-quadric in five dimensions, if the six coordinates Pij are treated as six homogeneous coordinates of a point. Projective properties of line geometry may therefore be treated as projective properties of point geometry in five dimensions. This suggests that certain algebraic theories of quaternary forms (corresponding to the geometry of ordinary space) can best be treated as algebraic theories of senary forms: that is, forms in six homogeneous variables.

Mechanical properties of cat soleus muscle elicited by sequential ramp stretches: implications for control of muscle

1993 ◽  
Vol 70 (3) ◽  
pp. 997-1008 ◽  
Author(s):  
D. C. Lin ◽  
W. Z. Rymer
Keyword(s):  
Soleus Muscle ◽  
Constant Velocity ◽  
Short Range ◽  
Single Pulse ◽  
Fold Increase ◽  
Elastic Behavior ◽  
Time Interval ◽  
Mechanical Stiffness ◽  
Initial Portion ◽  
High Stiffness

1. Force changes in areflexive cat soleus muscle in decerebrate cats were recorded in response to two sequential constant velocity (ramp) stretches, separated by a variable time interval during which the length was held constant. Initial (i.e., prestretch) background force was generated by activating the crossed-extension reflex, and stretch reflexes were eliminated by section of ipsilateral dorsal roots. 2. For the initial 400-900 microns of the first stretch, the muscle exhibited high stiffness, classically termed "short-range stiffness." This high stiffness region was followed by an abrupt reduction in stiffness, called muscle "yield," after which force remained at a relatively constant level, achieving a plateau in force. This plateau force level depended largely on stretch velocity, but this dependence was much less than proportional to the increase in stretch velocity, in that a 10-fold increase in velocity produced < 2-fold increase in plateau force. 3. In experiments where the velocities of the two sequential ramp stretches were identical, the force plateau level was the same for each stretch, regardless of the time elapsed before the second stretch (varied from 0 to 500 ms). In contrast, measures of stiffness during the initial portion of the second stretch showed time-dependent magnitude reductions. However, stiffness recovered quickly after the first stretch was completed, returning to control values within 30-40 ms. 4. In one preparation, in which the velocities of the two sequential ramp stretches were different, the force plateau elicited during the second stretch exhibited velocity dependence comparable with that recorded in the earlier single velocity studies. Furthermore, muscle yield was still evident in the case where the force change was due solely to the change in velocity and where short-range stiffness had not yet recovered fully from the initial stretch. On the basis of these findings, we argue that the classical descriptions of short-range stiffness and yield are inadequate and that the change in force that has typically been called the muscle yield reflects a transition between short-range, transient elastic behavior to steady-state, essentially viscous behavior. 5. To examine changes in the muscle's mechanical stiffness during single ramp stretches, a single pulse perturbation was superimposed at various times before, during, and subsequent to the constant velocity stretch. The force increment elicited in response to each pulse decreased relative to the initial isometric value, remained essentially constant until the end of the ramp, and then returned to its prestretch magnitude shortly (30-40 ms) after stretch termination.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Extended Kalman Filter for Bearings-Only Tracking

2019 ◽  
Vol 8 (6) ◽  
pp. 637-640 ◽  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Constant Velocity ◽  
Target Motion ◽  
Passive Mode ◽  
Crucial Issue ◽  
Straight Line ◽  
Optimal Linear ◽  
Target Motion Analysis ◽  
Line Path

Target tracking using bearings-only measurements in passive mode operation of sonar is a crucial issue of underwater tracking. Target motion in underwater scenario is analyzed using bearings-only measurements and calculating parameters like range, course and speed of the target. This is called Target Motion Analysis (TMA). TMA process is highly non-linear as the measurements chosen are nonlinearly related to the selected target state vector and the traditional, optimal linear Kalman filter will not be appropriate to use. It is presumed that the target is moving in straight line path with constant velocity, so Extended Kalman Filter (EKF) is proposed in this paper. The algorithm is simulated for several scenarios using MATLAB. Monte-Carlo runs are performed to evaluate the capability of the algorithm.

A Thin Aerofoil of Small Camber in a Non-Uniform Flow

1967 ◽  
Vol 71 (675) ◽  
pp. 214-216
Author(s):  
L. N. Nigam
Keyword(s):  
Pressure Distribution ◽  
Stream Function ◽  
Constant Velocity ◽  
Direct Problem ◽  
Lift Coefficient ◽  
Aerodynamic Characteristics ◽  
Angle Of Incidence ◽  
Pitching Moment ◽  
Image Position ◽  
General Profile

The direct problem of aerodynamics (profile of the aerofoil is given—calculate the aerodynamic characteristics) has been studied for thin aerofoils with small camber. Given the undisturbed stream functionV, ω, α being the constant velocity, vorticity and angle of incidence respectively, the pressure distribution, lift coefficient and pitching moment have been calculated for a general profile.

Some results on a traffic model of Rényi

1969 ◽  
Vol 6 (02) ◽  
pp. 293-300
Author(s):  
Mark Brown
Keyword(s):  
Poisson Process ◽  
Constant Velocity ◽  
Random Variables ◽  
Traffic Model ◽  
Homogeneous Poisson Process ◽  
Image Position

In [5] Renyi considers the following traffic model: Vehicles enter a highway at times 〈Ti , i = 1, 2, … 〉, forming a homogeneous Poisson process of intensity λ. The vehicle entering at time Ti will choose a velocity Vi and will travel at that constant velocity. The random variables 〈Vi , i = 1, 2, …〉 are independently and identically distributed (i.i.d.) and independent of 〈Ti 〉 with c.d.f. F satisfying All vehicles travel in the same direction.

scholarly journals On the stationary eccentricity of a system of four-tangent conics

1909 ◽  
Vol 28 ◽  
pp. 2-5
Author(s):  
F. E. Edwards
Keyword(s):  
Variable Parameter ◽  
Convex Quadrilateral ◽  
Straight Line ◽  
Image Position

Let the convex quadrilateral formed by the four given tangents be ABA′B′, and O the intersection of the diagonals. Let OA and OB be taken as axes of x and y. Denote OA, OA′, OB and OB′ by a, a′, b and b′, a and b being positive, and a′ and b′ negative. The tangential equation of the system is thenwhere k is a variable parameter; for the equation is satisfied when the straight line lx + my + 1 = 0 passes through any two adjacent angular points of the quadrilateral.

Velocity estimates derived from three‐dimensional seismic data

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1486-1497 ◽  
Author(s):  
Kwame Owusu ◽  
G. H. F. Gardner ◽  
Wulf F. Massell
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Three Dimensional ◽  
Logarithmic Scale ◽  
Model Data ◽  
Reconstruction Process ◽  
Input Field ◽  
Scattering Center ◽  
Straight Line ◽  
The Matrix

A new computer algorithm is described by which velocity estimates can be derived from three‐dimensional (3-D) multifold seismic data. The velocity estimate, referred to as “imaging velocity,” is that which best describes the diffraction hyperboloid due to a scatterer. The scattering center is best imaged when this velocity is used in the reconstruction process. The method is based on the 3-D Kirchhoff summation migration before stack. The implementation consists of two basic phases: (1) differentiating the input field traces and resampling them to a logarithmic time scale, and (2) shifting, weighting, and summing each resampled trace to a range of depth levels also chosen on a logarithmic scale. Peak amplitudes in the resulting image matrix give a time T and depth Z from which velocity is obtained using the relation [Formula: see text] The locus of constant velocity is a slanted straight line in the coordinate system of the matrix. In the usual application of migration for velocity analysis, each input trace of N samples is migrated for each of M constant velocity functions requiring [Formula: see text] moveout shift calculations. In the new method presented here, a constant shift is calculated for a given resampled trace, for each depth into which it is summed. This reduces the number of calculations per trace to about N, resulting in a significant improvement in computing efficiency. The operation of the algorithm is illustrated using synthetic and physical model data.

On the Synthesis of Straight Line, Constant Velocity Scanning Mechanisms

1991 ◽  
Vol 113 (4) ◽  
pp. 464-472 ◽  
Author(s):  
P. H. Hodges ◽  
A. P. Pisano
Keyword(s):  
Constant Velocity ◽  
Transverse Velocity ◽  
Grid Search ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Velocity Error ◽  
Straight Line ◽  
Transmission Angle ◽  
Point Motion ◽  
Input Motion

This paper presents a kinematic synthesis of constant-velocity, straight-line coupler-point motion of two planar mechanisms. After the derivation of synthesis equations, the numerical results of a grid search to determine the linkage dimensions for maximum constant velocity, with minimal straight line error, are presented. Plots of acceleration magnitude, transmission angles, and transverse velocity are presented as a function of the percentage of the constant velocity portion of a cycle of input motion. For a 5R2P Stephenson 6-bar linkage, normalized velocity errors as small as 2 percent can be maintained over 40 percent, or more, of the input cycle. A 7R Watt 6-bar linkage, while not achieving quite as high values as the 5R2P linkage, nevertheless can maintain normalized velocity errors as low as 2.5 percent over as much as 39 percent of the input cycle. These levels of performance must be weighed against unfavorable transmission angles, and in many cases, other undesirable effects, such as large accelerations and large transverse travel. The results show that, in order to maintain minimally acceptable transmission angle requirements, the velocity error and scan fraction requirements may be as little as 2.0 percent and as much as 35 percent, respectively.

scholarly journals XIII.—The General Form of the Involutive 1-1 Quadric Transformation in a Plane

1905 ◽  
Vol 40 (2) ◽  
pp. 253-262
Author(s):  
Charles Tweedie
Keyword(s):  
Special Property ◽  
Cremona Transformation ◽  
Straight Line ◽  
Image Position

§ 1. In a communication read before the Society, 3rd December 1900, Dr Muir discusses the generalisation, for more than two pairs of variables, of the proposition that: IfthenIf we interpret (x, y) and (ξ, η) iis points in a plane, it is manifest that the transformation thereby obtained is a Cremona transformation. It has the special property of being reciprocal or involutive in character; i.e., if the point P is transformed into Q, then the repetition of the same transformation on Q transforms Q into P. Symbolically, if the transformation is denoted by T. T(P) = Q, and T(Q) = T2(P) = P; so that T2 = 1, and T = T−1. Moreover, if the locus of P (x, y) is a straight line, the locus of Q (ξ, η) is in general a conic.

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