scholarly journals Representations of solutions of a special class of first order systems

1977 ◽  
Vol 25 (3) ◽  
pp. 410-424 ◽  
Author(s):  
Gerald N Hile
Keyword(s):  
Special Class ◽  
First Order

scholarly journals Asymptotic Behavior of Solutions of Delayed Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
J. Diblík ◽  
I. Hlavičková
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Special Class ◽  
General Theorem ◽  
Asymptotic Behavior Of Solutions ◽  
Order Difference ◽  
First Order ◽  
Discrete Equations

This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations.

scholarly journals Completely integrable holonomic systems of first-order differential equations

1995 ◽  
Vol 125 (3) ◽  
pp. 567-586 ◽  
Author(s):  
Shyuichi Izumiya
Keyword(s):  
Differential Equations ◽  
Special Class ◽  
Normal Forms ◽  
First Order ◽  
Completely Integrable ◽  
Holonomic Systems ◽  
Point Transformations ◽  
First Order Differential Equations

We classify completely integrable holonomic systems of first-order differential equations for one real-valued function by equivalence under the group of point transformations in the sense of Sophus Lie. In order to pursue the classification, we use the notion of one parameter Legendrian unfoldings which induces a special class of divergent diagrams of map germs which are called integral diagrams. Our normal forms are represented by integral diagrams.

scholarly journals SOLOVAY-TYPE THEOREMS FOR CIRCULAR DEFINITIONS

2015 ◽  
Vol 8 (3) ◽  
pp. 467-487 ◽  
Author(s):  
SHAWN STANDEFER
Keyword(s):  
Modal Logic ◽  
Special Class ◽  
Completeness Theorem ◽  
Proof System ◽  
Revision Theory ◽  
First Order ◽  
Circular Definitions ◽  
Order Case ◽  
Unary Operator

AbstractWe present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to a special class of circular definitions as well as to the first-order case.

scholarly journals First-order swap structures semantics for some logics of formal inconsistency

2020 ◽  
Vol 30 (6) ◽  
pp. 1257-1290
Author(s):  
Marcelo E Coniglio ◽  
Aldo Figallo-Orellano ◽  
Ana C Golzio
Keyword(s):  
Classical Logic ◽  
Special Class ◽  
Paraconsistent Logics ◽  
First Order ◽  
Axiomatic Extension

Abstract The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called $\textbf{QLFI1}_\circ $ is also studied, which is equivalent to the quantified version of da Costa and D’Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and $\textbf{QLFI1}_\circ $ with a standard equality predicate is also considered.

scholarly journals Properties of solutions of optimization problems for set functions

2001 ◽  
Vol 26 (7) ◽  
pp. 399-408
Author(s):  
Slawomir Dorosiewicz
Keyword(s):  
Mathematical Programming ◽  
Euclidean Space ◽  
Special Class ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
First Order ◽  
Mixed Problems ◽  
Set Functions ◽  
Definition Of

A definition of a special class of optimization problems with set functions is given. The existence of optimal solutions and first-order optimality conditions are proved. This case of optimal problems can be transformed to standard mixed problems of mathematical programming in Euclidean space. It makes possible the applications of various algorithms for these optimization problems for finding conditional extrema of set functions.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

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