Relevant bibliographies by topics / Polynomial functions : equivalence relations : symmetries

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Academic literature on the topic 'Polynomial functions : equivalence relations : symmetries'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Polynomial functions : equivalence relations : symmetries"

1

BALACHANDRAN, A. P., G. MARMO, A. SIMONI, and G. SPARANO. "QUANTUM BUNDLES AND THEIR SYMMETRIES." International Journal of Modern Physics A 07, no. 08 (1992): 1641–67. http://dx.doi.org/10.1142/s0217751x92000715.

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Wave functions in the domain of observables such as the Hamiltonian are not always smooth functions on the classical configuration space Q. Rather, they are often best regarded as functions on a G bundle EG over Q or as sections of an associated bundle. If H is a classical group which acts on Q, its quantum version HG, which acts on EG, is not always H, but an extension of H by G. A powerful and physically transparent construction of EG and HG, where G= U(1) and H1(Q, Z)=0, has been developed using the path space [Formula: see text]. ([Formula: see text] consists of paths on Q from a fixed poi
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2

IANOVSKI, EGOR, RUSSELL MILLER, KENG MENG NG, and ANDRÉ NIES. "COMPLEXITY OF EQUIVALENCE RELATIONS AND PREORDERS FROM COMPUTABILITY THEORY." Journal of Symbolic Logic 79, no. 3 (2014): 859–81. http://dx.doi.org/10.1017/jsl.2013.33.

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AbstractWe study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relationsR,S, a componentwise reducibility is defined byR≤S⇔ ∃f∀x, y[x R y↔f(x)S f(y)].Here,fis taken from a suitable class of effective functions. For us the relations will be on natural numbers, andfmust be computable. We show that there is a${\rm{\Pi }}_1^0$-complete equivalence relation, but no${\rm{\Pi }}_k^0$-complete fork≥ 2. We show that${\rm{\Sigma }}_k^0$preorders arising naturally in the above-mentioned areas are${\rm{\Sigma }}_k^0$-complete.
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3

Lambek, J. "Least fixpoints of endofunctors of cartesian closed categories." Mathematical Structures in Computer Science 3, no. 2 (1993): 229–57. http://dx.doi.org/10.1017/s0960129500000190.

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Least fixpoints are constructed for finite coproducts of definable endofunctors of Cartesian closed categories that have weak polynomial products and joint equalizers of arbitrary families of pairs of parallel arrows. Both conditions hold in PER, the category whose objects are partial equivalence relations on N, and whose arrows are partial recursive functions. Weak polynomial products exist in any cartesian closed category with a finite number of objects as well as in any model of second order polymorphic lambda calculus: that is, in the proof theory of any second order positive intuitionisti
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4

Bologna, E., M. Di Paola, K. Dayal, L. Deseri, and M. Zingales. "Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (2020): 20190294. http://dx.doi.org/10.1098/rsta.2019.0294.

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In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation func
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5

Rubel, Lee A. "On the ring of differentially-algebraic entire functions." Journal of Symbolic Logic 57, no. 2 (1992): 449–51. http://dx.doi.org/10.2307/2275279.

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Let be the ring of all entire functions of one complex variable, and let DA be the subring of those entire functions that are differentially algebraic (DA); that is, they satisfy a nontrivial algebraic differential equation.where P is a non-identically-zero polynomial in its n + 2 variables. It seems not to be known whether DA is elementarily equivalent to . This would mean that DA and have exactly the same true statements about them, in the first-order language of rings. (Roughly speaking, a sentence about a ring R is first-order if it has finite length and quantifies only over elements (i.e.
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6

Vasylyshyn, T. V. "Topology on the spectrum of the algebra of entire symmetric functions of bounded type on the complex $L_\infty$." Carpathian Mathematical Publications 9, no. 1 (2017): 22–27. http://dx.doi.org/10.15330/cmp.9.1.22-27.

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It is known that the so-called elementary symmetric polynomials $R_n(x) = \int_{[0,1]}(x(t))^n\,dt$ form an algebraic basis in the algebra of all symmetric continuous polynomials on the complex Banach space $L_\infty,$ which is dense in the Fr\'{e}chet algebra $H_{bs}(L_\infty)$ of all entire symmetric functions of bounded type on $L_\infty.$ Consequently, every continuous homomorphism $\varphi: H_{bs}(L_\infty) \to \mathbb{C}$ is uniquely determined by the sequence $\{\varphi(R_n)\}_{n=1}^\infty.$ By the continuity of the homomorphism $\varphi,$ the sequence $\{\sqrt[n]{|\varphi(R_n)|}\}_{n=1
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7

Nevskii, Mikhail V. "Geometric Estimates in Interpolation on an n-Dimensional Ball." Modeling and Analysis of Information Systems 26, no. 3 (2019): 441–49. http://dx.doi.org/10.18255/1818-1015-2019-3-441-449.

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Suppose \(n\in {\mathbb N}\). Let \(B_n\) be a Euclidean unit ball in \({\mathbb R}^n\) given by the inequality \(\|x\|\leq 1\), \(\|x\|:=\left(\sum\limits_{i=1}^n x_i^2\right)^{\frac{1}{2}}\). By \(C(B_n)\) we mean a set of continuous functions \(f:B_n\to{\mathbb R}\) with the norm \(\|f\|_{C(B_n)}:=\max\limits_{x\in B_n}|f(x)|\). The symbol \(\Pi_1\left({\mathbb R}^n\right)\) denotes a set of polynomials in \(n\) variables of degree \(\leq 1\), i.e. linear functions upon \({\mathbb R}^n\). Assume that \(x^{(1)}, \ldots, x^{(n+1)}\) are vertices of an \(n\)-dimensional nondegenerate simplex \
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8

Chakraborty, Nilanjan, Alexander Herbert, Umair Ahmed, Hong G. Im, and Markus Klein. "Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames." Flow, Turbulence and Combustion, August 10, 2021. http://dx.doi.org/10.1007/s10494-021-00283-w.

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AbstractA three-dimensional Direct Numerical Simulation (DNS) database of statistically planar $$H_{2} -$$ H 2 - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed $$S_{d}^{*}$$ S d ∗ . It has been found that the correlation between $$S_{d}^{*}$$ S d ∗ and curvature remains negative and a significantly non-linear interrelation between $$S_{d}^{*}$$ S d ∗ and stretch
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