scholarly journals Reduced Canonical Forms of Stoppers

10.37236/1083 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Aaron N. Siegel
Keyword(s):  
Canonical Form ◽  
Canonical Forms ◽  
Alternate Proof

The reduced canonical form of a loopfree game $G$ is the simplest game infinitesimally close to $G$. Reduced canonical forms were introduced by Calistrate, and Grossman and Siegel provided an alternate proof of their existence. In this paper, we show that the Grossman–Siegel construction generalizes to find reduced canonical forms of certain loopy games.

Canonical forms for definable subsets of algebraically closed and real closed valued fields

1995 ◽  
Vol 60 (3) ◽  
pp. 843-860 ◽  
Author(s):  
Jan E. Holly
Keyword(s):  
Canonical Form ◽  
Simple Form ◽  
Finite Union ◽  
Canonical Forms ◽  
Boolean Combination ◽  
Valued Fields ◽  
The Real

AbstractWe present a canonical form for definable subsets of algebraically closed valued fields by means of decompositions into sets of a simple form, and do the same for definable subsets of real closed valued fields. Both cases involve discs, forming “Swiss cheeses” in the algebraically closed case, and cuts in the real closed case. As a step in the development, we give a proof for the fact that in “most” valued fields F, if f(x), g(x) ∈ F[x] and v is the valuation map, then the set {x: v(f(x)) ≤ v(g(x))} is a Boolean combination of discs; in fact, it is a finite union of Swiss cheeses. The development also depends on the introduction of “valued trees”, which we define formally.

VI.—On Singular Pencils of Zehfuss, Compound, and Schläflian Matrices

1937 ◽  
Vol 56 ◽  
pp. 50-89 ◽  
Author(s):  
W. Ledermann
Keyword(s):  
Canonical Form ◽  
Direct Product ◽  
Canonical Forms ◽  
Singular Case ◽  
Elementary Divisors ◽  
Compound Matrices ◽  
Matrix Pencils ◽  
The Subject

In this paper the canonical form of matrix pencils will be discussed which are based on a pair of direct product matrices (Zehfuss matrices), compound matrices, or Schläflian matrices derived from given pencils whose canonical forms are known.When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.

scholarly journals Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 766-779
Author(s):  
Taha Aziz ◽  
Aeeman Fatima ◽  
Chaudry Masood Khalique
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Equation ◽  
Canonical Form ◽  
Mathematical Finance ◽  
Fundamental Solutions ◽  
Bond Pricing ◽  
Canonical Forms ◽  
Pricing Model ◽  
Invariant Approach

AbstractThe invariant approach is employed to solve the Cauchy problem for the bond-pricing partial differential equation (PDE) of mathematical finance. We first briefly review the invariant criteria for a scalar second-order parabolic PDE in two independent variables and then utilize it to reduce the bond-pricing equation to different Lie canonical forms. We show that the invariant approach aids in transforming the bond-pricing equation to the second Lie canonical form and that with a proper parametric selection, the bond-pricing PDE can be converted to the first Lie canonical form which is the classical heat equation. Different cases are deduced for which the original equation reduces to the first and second Lie canonical forms. For each of the cases, we work out the transformations which map the bond-pricing equation into the heat equation and also to the second Lie canonical form. We construct the fundamental solutions for the bond-pricing model via these transformations by utilizing the fundamental solutions of the classical heat equation as well as solution to the second Lie canonical form. Finally, the closed-form analytical solutions of the Cauchy initial value problems for the bond-pricing model with proper choice of terminal conditions are obtained.

CANONICAL FORM AND SEPARABILITY OF PPT STATES IN ${\mathcal C}^2\otimes {\mathcal C}^M\otimes {\mathcal C}^N$ COMPOSITE QUANTUM SYSTEMS

2003 ◽  
Vol 01 (03) ◽  
pp. 337-347
Author(s):  
XIAO-HONG WANG ◽  
SHAO-MING FEI ◽  
ZHI-XI WANG ◽  
KE WU
Keyword(s):  
Canonical Form ◽  
General Expression ◽  
Quantum Systems ◽  
Canonical Forms ◽  
Density Matrices ◽  
Partial Transposition ◽  
Separability Condition ◽  
Ppt States

We investigate the canonical forms of positive partial transposition (PPT) density matrices in [Formula: see text] composite quantum systems with rank N. A general expression for these PPT states are explicitly obtained. From this canonical form a sufficient separability condition is presented.

scholarly journals Using probability distributions to account for recognition of canonical and reduced word forms

2010 ◽  
Vol 1 ◽  
pp. 49
Author(s):  
Meghan Clayards
Keyword(s):  
Canonical Form ◽  
Probability Distributions ◽  
Reduced Form ◽  
Canonical Forms ◽  
Word Form ◽  
Reduced Word ◽  
Word Forms ◽  
Lexical Items ◽  
Reduced Forms

The frequency of a word form influences how efficiently it is processed, but canonical forms often show an advantage over reduced forms even when the reduced form is more frequent. This paper addresses this paradox by considering a model in which representations of lexical items consist of a distribution over forms. Optimal inference given these distributions accounts for item based differences in recognition of phonological variants and canonical form advantage.

scholarly journals 6-Methyluracil: a redetermination of polymorph (II)

IUCrData ◽  
2019 ◽  
Vol 4 (6) ◽  
Author(s):  
Gustavo Portalone
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Canonical Form ◽  
Crystal Packing ◽  
Geometric Parameters ◽  
Monoclinic Space Group ◽  
Canonical Forms ◽  
Acta Cryst ◽  
Space Group ◽  
Hydrogen Bonding Interactions

6-Methyluracil, C5H6N2O2, exists in two crystalline phases: form (I), monoclinic, space group P21/c [Reck et al. (1988). Acta Cryst. A44, 417–421] and form (II), monoclinic, space group C2/c [Leonidov et al. (1993). Russ. J. Phys. Chem. 67, 2220–2223]. The structure of polymorph (II) has been redetermined providing a significant increase in the precision of the derived geometric parameters. In the crystal, molecules form ribbons approximately running parallel to the c-axis direction through N—H...O hydrogen bonds. The radical differences observed between the crystal packing of the two polymorphs may be responsible in form (II) for an increase in the contribution of the polar canonical forms C—(O−)=N—H+ relative to the neutral canonical form C(=O)—N—H induced by hydrogen-bonding interactions.

Generalized Bernoulli Polynomials Revisited and Some Other Appell Sequences

2005 ◽  
Vol 12 (4) ◽  
pp. 697-716
Author(s):  
Pascal Maroni ◽  
Manoubi Mejri
Keyword(s):  
Functional Equation ◽  
Canonical Form ◽  
Bernoulli Polynomials ◽  
Positive Definite ◽  
Canonical Forms ◽  
Appell Sequences ◽  
Bernoulli Sequence ◽  
Generalized Bernoulli Polynomials ◽  
Dual Sequences

Abstract We study the problem posed by Nörlund in terms of dual sequences. We determine the functional equation fulfilled by the canonical form of any generalized Bernoulli sequence. Surprisingly these canonical forms are positive definite. Some results are given for an Euler sequence.

Single premise Post canonical forms defined over one-letter alphabets

1974 ◽  
Vol 39 (3) ◽  
pp. 489-495 ◽  
Author(s):  
Charles E. Hughes
Keyword(s):  
Word Problem ◽  
Canonical Form ◽  
Decision Problem ◽  
Decision Problems ◽  
Canonical Forms ◽  
Restricted Class ◽  
Constructive Proofs

AbstractIn this paper we investigate some families of decision problems associated with a restricted class of Post canonical forms, specifically, those defined over one-letter alphabets whose productions have single premises and contain only one variable. For brevity sake, we call any such form an RPCF (Restricted Post Canonical Form). Constructive proofs are given which show, for any prescribed nonrecursive r.e. many-one degree of unsolvability D, the existence of an RPCF whose word problem is of degree D and an RPCF with axiom whose-decision problem is also of degree D. Finally, we show that both of these results are best possible in that they do not hold for one-one degrees.

Direct and Inverse Transformations Between Phase Variable and Canonical Forms

1972 ◽  
Vol 94 (4) ◽  
pp. 315-318 ◽  
Author(s):  
R. R. Beck ◽  
G. M. Lance
Keyword(s):  
Canonical Form ◽  
General Treatment ◽  
Phase Variable ◽  
Canonical Forms ◽  
System Matrix ◽  
Jordan Canonical Form ◽  
Variable Form ◽  
Repeated Eigenvalues ◽  
Analytical Expressions ◽  
Real Complex

A complete, general treatment of the transformations, direct and inverse, between the phase variable form and the canonical or Jordan canonical form of the system matrix is presented. Analytical expressions are obtained for the matrices and all combinations of real, complex, distinct, and repeated eigenvalues are covered.

scholarly journals Closure theories of powerset theories

2015 ◽  
Vol 64 (1) ◽  
pp. 101-126 ◽  
Author(s):  
Jiří Močkǒ
Keyword(s):  
Fuzzy Sets ◽  
Canonical Form ◽  
Closure Operator ◽  
Canonical Forms ◽  
Similarity Relations ◽  
Coreflective Subcategory ◽  
Fuzzy Objects ◽  
Topological Constructs ◽  
Closure Theory

Abstract A notion of a closure theory of a powerset theory in a ground category is introduced as a generalization of a topology theory of a powerset theory. Using examples of powerset theories in the category Set of sets and in the category of sets with similarity relations, it is proved that these theories can be used as ground theories for closure theories of powerset theories in these two categories. Moreover, it is proved that all these closure theories of powerset theories are topological constructs. A notion of a closure operator which preserves a canonical form of fuzzy objects in these categories is introduced, and it is proved that a closure theory of a powerset theory in the ground category Set is a coreflective subcategory of the closure theory of (Zadeh’s) powerset theory, which preserves canonical forms of fuzzy sets.

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