scholarly journals Concise Representations of Reversible Automata

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1157-1175
Author(s):  
Giovanna J. Lavado ◽  
Luca Prigioniero
Keyword(s):  
Deterministic Automaton ◽  
Explicit Representations

In this paper, we present two concise representations of reversible automata. Both representations have a size comparable to the size of the minimum equivalent deterministic automaton and can be exponentially smaller than the size of the explicit representations of corresponding reversible automata. Using these representations it is possible to simulate the computations of reversible automata without explicitly writing down their complete descriptions.

scholarly journals Least-thickness symmetric circular masonry arch of maximum horizontal thrust

2021 ◽  
Author(s):  
Giuseppe Cocchetti ◽  
Egidio Rizzi
Keyword(s):  
Optimization Problem ◽  
Research Work ◽  
Complementary Information ◽  
Masonry Arch ◽  
Collapse Mode ◽  
Hinge Position ◽  
Explicit Representations ◽  
Horizontal Thrust ◽  
Structural Optimization Problem ◽  
Typical Solution

AbstractThis analytical note shall provide a contribution to the understanding of general principles in the Mechanics of (symmetric circular) masonry arches. Within a mainstream of previous research work by the authors (and competent framing in the dedicated literature), devoted to investigate the classical structural optimization problem leading to the least-thickness condition under self-weight (“Couplet-Heyman problem”), and the relevant characteristics of the purely rotational five-hinge collapse mode, new and complementary information is here analytically derived. Peculiar extremal conditions are explicitly inspected, as those leading to the maximum intrinsic non-dimensional horizontal thrust and to the foremost wide angular inner-hinge position from the crown, both occurring for specific instances of over-complete (horseshoe) arches. The whole is obtained, and confronted, for three typical solution cases, i.e., Heyman, “CCR” and Milankovitch instances, all together, by full closed-form explicit representations, and elucidated by relevant illustrations.

scholarly journals Degenerate poly-Bell polynomials and numbers

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Hye Kyung Kim
Keyword(s):  
Combinatorial Identities ◽  
Bell Polynomials ◽  
Genocchi Polynomials ◽  
Special Polynomials ◽  
Explicit Representations

AbstractNumerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation to this, in this paper, we introduce the degenerate poly-Bell polynomials emanating from the degenerate polyexponential functions which are called the poly-Bell polynomials when $\lambda \rightarrow 0$ λ → 0 . Specifically, we demonstrate that they are reduced to the degenerate Bell polynomials if $k = 1$ k = 1 . We also provide explicit representations and combinatorial identities for these polynomials, including Dobinski-like formulas, recurrence relationships, etc.

scholarly journals Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
G. E. Tupholme
Keyword(s):  
Electric Displacement ◽  
Polar Angle ◽  
Antiplane Shear ◽  
Shear Cracks ◽  
Intensity Factors ◽  
One Dimensional ◽  
Isotropic Solid ◽  
Special Cases ◽  
Field Intensity Factors ◽  
Explicit Representations

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

Mathematical Existence

2005 ◽  
Vol 11 (3) ◽  
pp. 351-376 ◽  
Author(s):  
Penelope Maddy
Keyword(s):  
Set Theory ◽  
Elliptic Functions ◽  
Mathematical Truth ◽  
Mathematical Methods ◽  
Explicit Representations ◽  
Mathematical Existence ◽  
Synthetic Approaches ◽  
Areas Of Interest ◽  
Compare And Contrast ◽  
Excluded Middle

Despite some discomfort with this grandly philosophical topic, I do in fact hope to address a venerable pair of philosophical chestnuts: mathematical truth and existence. My plan is to set out three possible stands on these issues, for an exercise in compare and contrast. A word of warning, though, to philosophical purists (and perhaps of comfort to more mathematical readers): I will explore these philosophical positions with an eye to their interconnections with some concrete issues of set theoretic method.Let me begin with a brief look at what to count as ‘philosophy’. To some extent, this is a matter of usage, and mathematicians sometimes classify as ‘philosophical’ any considerations other than outright proofs. So, for example, discussions of the propriety of particular mathematical methods would fall under this heading: should we prefer analytic or synthetic approaches in geometry? Should elliptic functions be treated in terms of explicit representations (as in Weierstrass) or geometrically (as in Riemann)? Should we allow impredicative definitions? Should we restrict ourselves to a logic without bivalence or the law of the excluded middle? Also included in this category would be the trains of thought that shaped our central concepts: should a function always be defined by a formula? Should a group be required to have an inverse for every element? Should ideal divisors be defined contextually or explicitly, treated computationally or abstractly? In addition, there are more general questions concerning mathematical values, aims and goals: Should we strive for powerful theories or low-risk theories? How much stress should be placed on the fact or promise of physical applications? How important are interconnections between the various branches of mathematics? These philosophical questions of method naturally include several peculiar to set theory: should set theorists focus their efforts on drawing consequences for areas of interest to mathematicians outside mathematical logic? Should exploration of the standard axioms of ZFC be preferred to the exploration and exploitation of new axioms? How should axioms for set theory be chosen? What would a solution to the Continuum Problem look like?

Explicit representations in hypothetical thinking

1999 ◽  
Vol 22 (5) ◽  
pp. 763-764 ◽  
Author(s):  
Jonathan St. B. T. Evans ◽  
David E. Over
Keyword(s):  
Mental Models ◽  
Propositional Attitudes ◽  
Possible World ◽  
Processing Resources ◽  
Explicit Representations ◽  
Implicit Systems ◽  
Explicit Processing

Dienes' & Perner's proposals are discussed in relation to the distinction between explicit and implicit systems of thinking. Evans and Over (1996) propose that explicit processing resources are required for hypothetical thinking, in which mental models of possible world states are constructed. Such thinking requires representations in which the individuals' propositional attitudes including relevant beliefs and goals are made fully explicit.

scholarly journals The relaxation normal form of braids is regular

2017 ◽  
Vol 27 (01) ◽  
pp. 61-105
Author(s):  
Vincent Jugé
Keyword(s):  
Normal Form ◽  
Geometric Complexity ◽  
Deterministic Automaton ◽  
Relaxation Algorithm

Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form.

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