Substitution Theorem Research Articles

A rigorous model study of the adaptive dynamics of Mendelian diploids

Adaptive dynamics (AD) so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's in Proc Natl Acad Sci USA 54: 731-736, 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the 'long' time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod M 1 topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as 'canonical equation'.

Term Substitution Theorem in First-Order Fuzzy Predicate System

It has given out term substitution theorem in the system K *. R0-algebra is introduced firstly, and then the fuzzy interpretation of the first-order language. It discusses term substitution theorem in the first-order fuzzy predicate system K *.

ON THE IRREDUCIBLE COMPONENTS OF A SEMIALGEBRAIC SET

In this work we define a semialgebraic set S ⊂ ℝn to be irreducible if the noetherian ring [Formula: see text] of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring [Formula: see text]: Substitution Theorem, Positivstellensätze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we give full characterizations of the families of semialgebraic sets for which these classical results are true.

Possibilistic intermediate logic

We define what we call 'possibilistic intermediate logic (PIL)'; we present results analogous to those of the well-known intermediate logic, such as a deduction theorem, a generalised version of the deduction theorem, a cut rule, a weak version of a refutation theorem, a substitution theorem and Glivenko's theorem. Also, we present a definition for 'possibilistic safe beliefs'. This definition allows us to establish a relation between safe beliefs, as presented on 'applications of intuitionistic logic in answer set programming' by Osorio et al., and our version for possibilistic intermediate logic (PILX). We also present a characterisation of possibilistic safe beliefs for possibilistic normal logic programs.

Verification of Substitution Theorem Using HOL

Verification of Substitution Theorem Using HOL

Verification of Substitution Theorem Using HOL

Verification of Substitution Theorem Using HOL

Miller Equivalents and Their Applications

Miller’s theorems are utilized for approximate as well as exact analysis of both passive and active networks in conjunction with other theorems on a single element or different elements in succession. In this paper, all the four possible Miller equivalents are fully exploited for the exact analysis by applying on different elements simultaneously. This has never been attempted before and may be viewed as an alternate approach for analyzing the networks. The four Miller equivalents are derived using the substitution theorem followed by typical illustrative examples.

Generalizations of Blakesley's Source Shift Theorem

Abstract. It is shown that the well-known Voltage Source Shift Theorem due to Blakesley and its dual version, the Current Source Shift Theorem as well as the rules for the transformation of networks with loops of capacitors or cut sets of inductors into networks without such loops or cutsets, resp., and the relationships between capacitance coefficients and partial capacitors are special cases of general theorems on the terminal behavior of networks. The proof of these theorems is based on the theory of terminal behavior of networks. For these proofs we do not need the substitution theorem with its strong uniqueness assumptions. This fact is an essential advantage in comparison to the original proof given by Chua and Green.

A new simple unifying approach of finding the state equation model and its practical application

In the control signal process theory, the state equation is an important approach for modelling, analyzing and designing a wide range of systems. Furthermore, the state equation is often the most efficient form from the standpoint of computer simulation for highly complex systems. The existing researches exploit the fact that for networks containing dependent sources, bridging elements and coupling elements, the derivation of the closed-form state equation becomes rather complicated. On the other hand, a simple and valuable unifying approach of finding the state equations for complicated physical systems is successfully presented in the paper. The new unifying approach needs only the substitution theorem and the author’s invented simple matrix operations. The main fascinating peculiarity of this approach is exposed in its systematic, graphic and human structure that improves the shortcomings of those traditional approaches. One comparative example is proposed to show the distinguished advantages our method offers over existing methods. In order to demonstrate the practical applicability, the paper has investigated an electronic operational-amplifier circuit that can be easily stabilized by our approach.

Anticipating stochastic differential systems with memory

This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations (sfdes) and fully nonlinear sfdes with a sublinear drift term. For the semilinear case, we use Malliavin calculus techniques, existence of the stochastic semiflow and an infinite-dimensional substitution theorem. For the fully nonlinear case, we employ an anticipating version of the Itô–Ventzell formula due to Ocone and Pardoux [D. Ocone, E. Pardoux, A generalized Itô–Ventzell formula. Application to a class of anticipating stochastic differential equations, Annales de l’Institut Henri Poincaré. Probabilité s et Statistiques 25 (1) (1989) 39–71]. In both cases, the use of Malliavin calculus techniques is necessitated by the infinite dimensionality of the initial condition.

A substitution theorem for graceful trees and its applications

A graceful labeling of a graph G = ( V , E ) assigns | V | distinct integers from the set { 0 , … , | E | } to the vertices of G so that the absolute values of their differences on the | E | edges of G constitute the set { 1 , … , | E | } . A graph is graceful if it admits a graceful labeling. The forty-year old Graceful Tree Conjecture, due to Ringel and Kotzig, states that every tree is graceful. We prove a Substitution Theorem for graceful trees, which enables the construction of a larger graceful tree through combining smaller and not necessarily identical graceful trees. We present applications of the Substitution Theorem, which generalize earlier constructions combining smaller trees.

The substitution theorem for semilinear stochastic partial differential equations

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinite-dimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating initial conditions.

Shipping the Good Apples Out: A New Perspective

An alternative explanation is provided for the Alchian and Allen substitution theorem, which posits that a per unit tax or shipping fee applied to similar goods will increase the relative consumption of the higher‐quality good. The usual explanation is that consumers substitute out of “bad apples” and into “good apples.” This article generalizes the Alchian and Allen result in an n‐good world, providing an alternative explanation that is more cogent in situations where the two goods (for example $500 and $5 wines) are not close substitutes.

Propositional calculus under adjointness

We develop a formal system for the class of all implications A and conjunctions K, on partially ordered sets ( L,⩽) with top elements 1, such that A and K are related by adjointness and they satisfy the neutrality principle (that is, 1 is their left identity element). We call the resulting logic propositional calculus under adjointness, abbreviated AdjPC. Most algebraic theorems on those (L,⩽), A and K are inequalities in the posets ( L,⩽) of truth values. In consequence, we have to find means for abstracting inequalities within syntax; which must be free from partial truth values. This is achieved by employing a further, implication-like adjoint H of A and K, whereby the partial order of ( L,⩽) coincides with the binary relation H(•,•)=1. Accordingly, the semantical domain for AdjPC should become the class of all such quintuples ( L,⩽, A, K, H), which we call adjointness algebras. Our axiom scheme for AdjPC features seven axioms. However, it may be the case that no finite set of axioms can complete AdjPC if inference is carried out by means of modus ponens (MP) alone. This is because AdjPC is too general; it lacks some basic theorems of the more restricted logics (such as residuated logic and intuitionistic logic). As a result, we have to adopt four inference rules for AdjPC; namely, MP and three bits of the substitution theorem. We deduce enough theorems and inferences in AdjPC to delineate its basic structure. This enables us to establish the completeness of AdjPC for the semantical domain of adjointness algebras; by means of a quotient-algebra structure (a Lindenbaum type of algebra). We also show how certain models can help disprove some incorrect inferences in AdjPC. We end by developing complete syntax (with fewer axioms and inference rules) for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle.

On a specific substitution theorem: further results

International Journal of Circuit Theory and ApplicationsVolume 27, Issue 2 p. 277-281 Letter to the Editor On a specific substitution theorem: further results Antonino M. Sommariva, Corresponding Author Antonino M. Sommariva Sommariv@bsing.unibs.it Dipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItalyDipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItalySearch for more papers by this author Antonino M. Sommariva, Corresponding Author Antonino M. Sommariva Sommariv@bsing.unibs.it Dipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItalyDipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItalySearch for more papers by this author First published: 11 March 1999 https://doi.org/10.1002/(SICI)1097-007X(199903/04)27:2<277::AID-CTA55>3.0.CO;2-MCitations: 4AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume27, Issue2March/April 1999Pages 277-281 RelatedInformation

On a specific substitution theorem

International Journal of Circuit Theory and ApplicationsVolume 26, Issue 5 p. 509-512 Correspondence On a specific substitution theorem Professor Antonino M. Sommariva, Corresponding Author Professor Antonino M. Sommariva [email protected] Dipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItaliaDipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItaliaSearch for more papers by this author Professor Antonino M. Sommariva, Corresponding Author Professor Antonino M. Sommariva [email protected] Dipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItaliaDipartimento di Elettronica per l'Automazione, Via Branze 38, 25123 Brescia, ItaliaSearch for more papers by this author First published: 21 December 1998 https://doi.org/10.1002/(SICI)1097-007X(199809/10)26:5<509::AID-CTA22>3.0.CO;2-HCitations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume26, Issue5September/October 1998Pages 509-512 RelatedInformation

Adding up constraints and gross substitution in portfolio models

We consider a static portfolio system that satisfies adding-up constraints and Tobin's gross substitution theorem. We show the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables us to investigate effects of arbitrary simultaneous changes in interest rates on the asset demands. Finally, we show that all asset demands are invariant under a certain nonnegative, but nonzero, change of the interest rates.

The Augmentation Principle of nonlinear circuits and its application to continuation methods

The Augmentation Principle, which is a generalization of the well-known Substitution Theorem, is presented. This principle establishes that a circuit's DC operating point remains constant over all values of resistors placed in series with a set of properly chosen voltage sources or placed in parallel with a set of properly chosen current sources. A useful application of the Augmentation Principle to circuit simulation using continuation methods is also given.

Emphasizing some little-used theorems in introductory network analysis

This paper promotes the use of some little-used but most valuable theorems that are available to students in introductory network analysis: the voltage and current shifting theorems; the voltage and current source theorems; the reduction theorem; and the substitution theorem. Examples illustrate how these theorems can be used to solve for one or more variables in the many networks that contain dependent as well as independent sources. Network simplification techniques are maximized and the use of equations is minimized. A more extensive use of the duality concept is also recommended.

The Substitution Theorem

The substitution theorem states that an economy with many commodities but only one factor input (say labor) will not substitute inputs (commodities or labor) when final demand changes. This Note drops the assumption that all activities require some labor input and constructs the dominant technology. Journal of Economic Literature Classification Numbers: C67, D20.