Finite-Degree Utility Independence

1982 ◽  
Vol 7 (3) ◽  
pp. 348-353 ◽  
Author(s):  
Peter C. Fishburn ◽  
Peter H. Farquhar
Keyword(s):  
Finite Degree ◽  
Utility Independence

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

scholarly journals On finite degree partial representations of groups

2004 ◽  
Vol 274 (1) ◽  
pp. 309-334 ◽  
Author(s):  
M. Dokuchaev ◽  
N. Zhukavets
Keyword(s):  
Finite Degree ◽  
Representations Of Groups

scholarly journals Finite degree clones are undecidable

2019 ◽  
Vol 796 ◽  
pp. 237-271
Author(s):  
Matthew Moore
Keyword(s):  
Finite Degree

Trace Forms on Lie Algebras

1962 ◽  
Vol 14 ◽  
pp. 553-564 ◽  
Author(s):  
Richard Block
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Bilinear Form ◽  
Symmetric Bilinear Form ◽  
Trace Form ◽  
Finite Degree ◽  
Trace Forms ◽  
Matrix Products ◽  
The Matrix ◽  
Image Position

If L is a Lie algebra with a representation Δ a→aΔ (a in L) (of finite degree), then by the trace form f = fΔ of Δ is meant the symmetric bilinear form on L obtained by taking the trace of the matrix products:Then f is invariant, that is, f is symmetric and f(ab, c) — f(a, bc) for all a, b, c in L. By the Δ-radical L⊥ = L⊥ of L is meant the set of a in L such that f(a, b) = 0 for all b in L. Then L⊥ is an ideal and f induces a bilinear form , called a quotient trace form, on L/L⊥. Thus an algebra has a quotient trace form if and only if there exists a Lie algebra L with a representation Δ such that

scholarly journals A diagrammatic approach to link invariants of finite degree

2004 ◽  
Vol 94 (2) ◽  
pp. 295 ◽  
Author(s):  
Olof-Petter Östlund
Keyword(s):  
Finite Degree ◽  
Explicit Formulas ◽  
Connected Sum ◽  
Knot Invariants ◽  
Graphical Calculus ◽  
Link Invariants ◽  
Low Degree ◽  
Coalgebra Structure ◽  
Arrow Diagrams

In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev link invariants, and presented several explicit formulas for low degree invariants. M. Goussarov [2] proved that this arrow diagram calculus provides formulas for all Vassiliev knot invariants. The original note [5] contained no proofs, and it also contained some minor inaccuracies. This paper fills the gap in literature by presenting the material of [5] with all proofs and details, in a self-contained form. Furthermore, a compatible coalgebra structure, related to the connected sum of knots, is introduced on the algebra of based arrow diagrams with one circle.

CHOQUET INTEGRAL MODELS AND INDEPENDENCE CONCEPTS IN MULTIATTRIBUTE UTILITY THEORY

2000 ◽  
Vol 08 (04) ◽  
pp. 385-415 ◽  
Author(s):  
T. MUROFUSHI ◽  
M. SUGENO
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Multiattribute Utility ◽  
Preference Relations ◽  
Multiattribute Utility Theory ◽  
A Value ◽  
Utility Independence

This paper discusses multiattribute preference relations compatible with a value/utility function represented by the Choquet integral with respect to a fuzzy measure, and shows that the additivity of the fuzzy measure is equivalent to each of mutual preferential independence, mutual weak difference independence, mutual difference independence, mutual utility independence, and additive independence.

Congruence Relations Between the Traces of Matrix Powers

1949 ◽  
Vol 1 (3) ◽  
pp. 303-304 ◽  
Author(s):  
J. S Frame
Keyword(s):  
Finite Order ◽  
Rational Integer ◽  
Roots Of Unity ◽  
Finite Degree ◽  
Characteristic Roots ◽  
Congruence Relations ◽  
Image Position

Let A be a matrix of finite order n and finite degree d, whose characteristic roots are certain nth roots of unity a1, a2…, ad. We wish to prove a congruence (6) between the traces (tr) of certain powers of A, which is suggested by two somewhat simpler congruences (1) and (3). First, if tr (A) is a rational integer, it is easy to establish the familiar congruenceeven though tr(Ap) may not itself be rational.

scholarly journals p-Torsion points on elliptic curves defined over quadratic fields

1984 ◽  
Vol 96 ◽  
pp. 139-165 ◽  
Author(s):  
Fumiyuki Momose
Keyword(s):  
Elliptic Curves ◽  
Prime Number ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Quadratic Fields ◽  
Finite Degree ◽  
Torsion Points

Let p be a prime number and k an algebraic number field of finite degree d. Manin [14] showed that there exists an integer n = n(k,p) (≧0) which satisfies the condition

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