Search results for " Algebra"
showing 10 items of 2082 documents
A critical assessment of methods for the determination of the shear stress amplitude in multiaxial fatigue criteria belonging to critical plane class
2015
Abstract Multiaxial high cycle fatigue criteria based on the critical plane approach necessitate unambiguous definitions of the amplitude and mean value of the shear stress (τa and τm) acting on the material planes. Four of the existing definitions relate the values of τa and τm to a geometrical element of the curve described by the tip of the shear stress vector (curve Ψ), respectively, the radius of the Minimum Circumscribed Circle, the Longest Chord, the Longest Projection, the diagonal of the Maximum Rectangular Hull (MRH). In this paper a critical assessment of the above definitions is proposed, focusing on that based on the concept of MRH, which is the most recently developed. The mai…
La realtà multiculturale della scuola: comparazione di processi cognitivi tra studenti italiani e cinesi
2013
Obiettivo primario della ricerca è quello di riflettere sulle questioni riguardanti le Matematiche Elementari in una visione quanto più ampia possibile, alla luce di una scuola sempre più “diversificata”, multiculturale e globalizzata, trattando in maniera diretta non soltanto le problematiche strettamente riferite ai contenuti disciplinari relativi specificatamente al pensiero algebrico e geometrico per la scuola Primaria e Secondaria, ma anche quelli che in molti casi possono definirsi come gli aspetti storico-epistemologici della disciplina discussa in aula con gli allievi. Quale didattica disciplinare nella classe del terzo millennio? Quale formazione matematica? Quali saperi? E quindi.…
Musical pitch quantization as an eigenvalue problem
2020
How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz.
DenseYOLO: Yet Faster, Lighter and More Accurate YOLO
2020
As much as an object detector should be accurate, it should be light and fast as well. However, current object detectors tend to be either inaccurate when lightweight or very slow and heavy when accurate. Accordingly, determining tolerable tradeoff between speed and accuracy of an object detector is not a simple task. One of the object detectors that have commendable balance of speed and accuracy is YOLOv2. YOLOv2 performs detection by dividing an input image into grids and training each grid cell to predict certain number of objects. In this paper we propose a new approach to even make YOLOv2 more fast and accurate. We re-purpose YOLOv2 into a dense object detector by using fine-grained gr…
Permutability of injectors with a central socle in a finite solvable group
2017
In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (where π is a set of prime numbers), then the Zπ-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4].
Pseudocomplements in sum-ordered partial semirings
2007
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings – those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
Complex powers and non-compact manifolds
2002
We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, ``extended Weyl algebras,'' whose definition was inspired by Guillemin's paper on the subject. An extended Weyl algebra can be thought of as an algebra of ``abstract pseudodifferential operators.'' Many algebras of pseudodifferential operators are extended Weyl algebras. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between apropriate Sobolev spaces, >...) generalize to…
Evaluative linguistic expressions vs. fuzzy categories
2015
In this paper, we discuss the distinction between categories characterized by verbal labels taken from a fuzzy rating scale and special class of linguistic expressions, called evaluative. The latter form a general class of expressions that includes gradable and evaluative adjectives and their hedges. First, we will provide a brief linguistic analysis of them. Then we outline basic principles for construction of the mathematical model of semantics of evaluative expressions. In Section 3 we will analyze the concepts of rating scale with verbal labels (fuzzy rating scale), their semantics and demonstrate that the latter cannot be identified with the semantics of evaluative expressions. Finally…
Noise-tolerant efficient inductive synthesis of regular expressions from good examples
1997
We present an almost linear time method of inductive synthesis restoring simple regular expressions from one representative (good) example. In particular, we consider synthesis of expressions of star-height one, where we allow one union operation under each iteration, and synthesis of expressions without union operations from examples that may contain mistakes. In both cases we provide sufficient conditions defining precisely the class of target expressions and the notion of good examples under which the synthesis algorithm works correctly, and present the proof of correctness. In the case of expressions with unions the proof is based on novel results in the combinatorics of words. A genera…
Are locally finite MV-algebras a variety?
2021
We answer Mundici's problem number 3 (D. Mundici. Advanced {\L}ukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: (i) The category of locally finite MV-algebras is not equivalent to any finitary variety. (ii) More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. (iii) The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. (iv) The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon th…