Multiple gene identities

1975 ◽  
Vol 7 (1) ◽  
pp. 26-27
Author(s):  
E. A. Thompson
Keyword(s):  
General Solution ◽  
General Problem ◽  
Conditional Distribution ◽  
Common Ancestor ◽  
Algebraic Method ◽  
Multiple Gene ◽  
Identical By Descent ◽  
Number Of Individuals ◽  
Special Case ◽  
Combining Information

The relationships between individuals may be specified by the genes which they have in common, where two genes are considered to be the same only if they are identical by descent from some common ancestor. Relationships between two individuals have been extensively studied by, amongst many others, Cotterman (1940), Malécot (1948) and Li and Sacks (1954). Less progress has been made with the more general problem of relationships between an arbitrary number of individuals. Elandt-Johnson (1971) has considered the special case of joint genotype distributions in a sibship, and Hilden (1970) has constructed an algebraic method of combining information on several individuals to give the conditional distribution of a single unborn relative, but neither of these approaches provides a general solution to the problem.

Multiple gene identities

1975 ◽  
Vol 7 (01) ◽  
pp. 26-27
Author(s):  
E. A. Thompson
Keyword(s):  
General Solution ◽  
General Problem ◽  
Conditional Distribution ◽  
Common Ancestor ◽  
Algebraic Method ◽  
Multiple Gene ◽  
Identical By Descent ◽  
Number Of Individuals ◽  
Special Case ◽  
Combining Information

The relationships between individuals may be specified by the genes which they have in common, where two genes are considered to be the same only if they are identical by descent from some common ancestor. Relationships between two individuals have been extensively studied by, amongst many others, Cotterman (1940), Malécot (1948) and Li and Sacks (1954). Less progress has been made with the more general problem of relationships between an arbitrary number of individuals. Elandt-Johnson (1971) has considered the special case of joint genotype distributions in a sibship, and Hilden (1970) has constructed an algebraic method of combining information on several individuals to give the conditional distribution of a single unborn relative, but neither of these approaches provides a general solution to the problem.

Optimal Order Picking in Carousels Storage System

2012 ◽  
Vol 601 ◽  
pp. 347-353
Author(s):  
Xiong Zhi Wang ◽  
Guo Qing Wang
Keyword(s):  
Approximation Algorithm ◽  
General Problem ◽  
Storage System ◽  
Order Picking ◽  
Total Order ◽  
Experimental Results ◽  
Optimal Order ◽  
Np Hard ◽  
Special Case

We study the order picking problem in carousels system with a single picker. The objective is to find a picking scheduling to minimizing the total order picking time. After showing the problem being strongly in NP-Hard and finding two characteristics, we construct an approximation algorithm for a special case (two carousels) and a heuristics for the general problem. Experimental results verify that the solutions are quickly and steadily achieved and show its better performance.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

Note on Best Approximation of |x|

1979 ◽  
Vol 22 (3) ◽  
pp. 363-366
Author(s):  
Colin Bennett ◽  
Karl Rudnick ◽  
Jeffrey D. Vaaler
Keyword(s):  
General Problem ◽  
Uniform Approximation ◽  
Best Approximation ◽  
Best Uniform Approximation ◽  
Linear Fractional Transformations ◽  
Symmetric Complex ◽  
Image Position ◽  
Complex Valued ◽  
Special Case

In this note the best uniform approximation on [—1,1] to the function |x| by symmetric complex valued linear fractional transformations is determined. This is a special case of the more general problem studied in [1]. Namely, for any even, real valued function f(x) on [-1,1] satsifying 0 = f ( 0 ) ≤ f (x) ≤ f (1) = 1, determine the degree of symmetric approximationand the extremal transformations U whenever they exist.

A differential equation for undamped forced non-linear oscillations. III

1965 ◽  
Vol 61 (1) ◽  
pp. 133-155 ◽  
Author(s):  
G. R. Morris
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Periodic Solutions ◽  
Special Interest ◽  
Bounded Solutions ◽  
General Differential Equation ◽  
Dynamical Description ◽  
Image Position ◽  
Essential Problem ◽  
Special Case

The most general differential equation to which the dynamical description of the title applies iswhere dots denote differentiation with respect to t. The essential problem for this equation is to determine the behaviour of solutions as t → ∞. When we attack this problem, the most obvious question is whether, under reasonable conditions on p(t), every solution is bounded as t → ∞ this question is open except when g(x) is linear. In the special case when p(t) is periodic, (1·1) may have periodic solutions; it is clear that any such solution is bounded, and it is worth mentioning that finding periodic solutions is the easiest way of finding particular bounded ones. So long as the bounded-ness problem is unsolved, there is a special interest in finding a large class of particular bounded solutions: if we know such a class then, although we cannot say whether the general solution is bounded or not, we can make the imprecise comment that either the general solution is in fact bounded or the structure of the whole set of solutions is quite complicated.

scholarly journals Coalescent lineage distributions

2006 ◽  
Vol 38 (02) ◽  
pp. 405-429 ◽  
Author(s):  
Robert C. Griffiths
Keyword(s):  
Brownian Motion ◽  
Hypergeometric Functions ◽  
Common Ancestor ◽  
Recent Common Ancestor ◽  
Series Expansions ◽  
Standard Brownian Motion ◽  
Most Recent Common Ancestor ◽  
Coalescent Tree ◽  
Expected Values ◽  
Special Case

We study identities for the distribution of the number of edges at time t back (i.e. measured backwards) in a coalescent tree whose subtrees have no mutations. This distribution is important in the infinitely-many-alleles model of mutation, where every mutation is unique. The model includes, as a special case, the number of edges in a coalescent tree at time t back when mutation is ignored. The identities take the form of expected values of functions of Z t =eiX t , where X t is distributed as standard Brownian motion. Associated identities are also found for the distributions of the time to the most recent common ancestor, the time until loss of ancestral lines by coalescence or mutation, and the age of a mutation. Hypergeometric functions play an important role in the identities. The identities are of mathematical interest, as well as potentially being formulae to use for numerical integration or simulation to compute distributions that are usually expressed as alternating-sign series expansions, which are difficult to compute.

scholarly journals Symmetric Four-mass Schubart-like Systems

2014 ◽  
Vol 9 (S310) ◽  
pp. 106-107 ◽  
Author(s):  
Winston L. Sweatman
Keyword(s):  
General Problem ◽  
Body Problem ◽  
Four Body Problem ◽  
Special Case ◽  
Simple Models

AbstractThe general four-body problem can be simplified by considering the special case where the system contains two pairs of identical masses and is symmetrical. The simple models that occur may aid our understanding of the general problem. Systems that arise from Schubart-like interplay orbits are an important feature of the dynamics.

scholarly journals Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Riccati Equation ◽  
Newton Method ◽  
Continuous Time ◽  
Iterative Algorithms ◽  
Algebraic Method ◽  
Matrix Inversion ◽  
Square Root ◽  
Special Case ◽  
New Algorithms

New algorithms are presented about the principal square root of ann×nmatrixA. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.

ON THE BEHAVIOR OF A SELF-EXCITING FARADAY DISK HOMOPOLAR DYNAMO WITH A VARIABLE NONLINEAR SERIES MOTOR

2002 ◽  
Vol 12 (10) ◽  
pp. 2123-2135 ◽  
Author(s):  
IRENE M. MOROZ
Keyword(s):  
General Problem ◽  
Eddy Currents ◽  
Steady States ◽  
Equilibrium States ◽  
Hopf Bifurcations ◽  
Multiple Steady States ◽  
Double Zero ◽  
Oscillatory Solutions ◽  
Codimension Two ◽  
Special Case

In this paper we seek to bridge the gap between the study of a self-exciting Faraday disk homopolar dynamo with a linear series motor [Hide et al., 1996] and the case when the torque acting on the armature of the motor is proportional to the square of the current flowing through the dynamo [Hide, 1998]. We also focus on the issue of when the nonlinear quenching of oscillatory solutions can occur. The present study is a special case of the more general problem when azimuthal eddy currents are permitted to flow [Moroz & Hide, 2000] and shares with that problem the existence of multiple steady states and Hopf bifurcations. This results in distinct double-zero bifurcations for the trivial and the nontrivial equilibrium states as well as other codimension-two bifurcations, which leads to the suppression of oscillatory solutions.

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