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Journal articles on the topic 'Varsimax'

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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Afshari, H., and E. Karapinar. "A solution of the fractional differential equations in the setting of $b$-metric space." Carpathian Mathematical Publications 13, no. 3 (December 29, 2021): 764–74. http://dx.doi.org/10.15330/cmp.13.3.764-774.

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In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems \[ \begin{cases} D^{\mu}_{c}w(\varsigma)\pm D^{\nu}_{c}w(\varsigma)=h(\varsigma,w(\varsigma)),& \varsigma\in J,\ \ 0<\nu<\mu<1,\\ w(0)=w_0,& \ \end{cases} \] where $D^{\mu}$, $D^{\nu}$ is the Caputo derivative of order $\mu$, $\nu$, respectively and $h:J\times \mathbb{R}\rightarrow \mathbb{R}$ is continuous. The results are well demonstrated with the aid of exciting examples.

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2

Bearden, Clifford A. "Hilbert $C^*$-modules over $\varSigma ^*$-algebras II: $\varSigma ^*$-Morita equivalence." Studia Mathematica 243, no. 2 (2018): 139–69. http://dx.doi.org/10.4064/sm8806-9-2017.

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3

Kudlinska, Monika. "Algorithm for filling curves on surfaces." Geometriae Dedicata 208, no. 1 (January 10, 2020): 49–59. http://dx.doi.org/10.1007/s10711-019-00509-2.

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AbstractLet $$\varSigma $$ Σ be a compact, orientable surface of negative Euler characteristic, and let h be a complete hyperbolic metric on $$\varSigma $$ Σ . A geodesic curve $$\gamma $$ γ in $$\varSigma $$ Σ is filling if it cuts the surface into topological disks and annuli. We propose an efficient algorithm for deciding whether a geodesic curve, represented as a word in some generators of $$\pi _1(\varSigma )$$ π 1 ( Σ ) , is filling. In the process, we find an explicit bound for the combinatorial length of a curve given by its Dehn–Thurston coordinate, in terms of the hyperbolic length. This gives us an efficient method for producing a collection which is guaranteed to contain all words corresponding to simple geodesics of bounded hyperbolic length.

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Hauser, Raphael, Jüri Lember, Heinrich Matzinger, and Raul Kangro. "Quantifying the estimation error of principal component vectors." Information and Inference: A Journal of the IMA 9, no. 3 (July 11, 2019): 657–75. http://dx.doi.org/10.1093/imaiai/iaz014.

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Abstract Principal component analysis (PCA) is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\varSigma }$ that approximates a population covariance $\varSigma$, and these eigenvectors are often used to extract structural information about the variables (or attributes) of the studied population. Since PCA is based on the eigendecomposition of the proxy covariance $\widehat{\varSigma }$ rather than the ground-truth $\varSigma$, it is important to understand the approximation error in each individual eigenvector as a function of the number of available samples. The combination of recent results of Koltchinskii & Lounici (2017, Bernoulli, 23, 110–133) and Yu et al. (2015, Biometrika, 102, 315–323) yields such bounds. In the present paper we sharpen these bounds and show that eigenvectors can often be reconstructed to a required accuracy from a sample of strictly smaller size order.

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Bearden, Clifford A. "Hilbert $C^*$-modules over $\varSigma ^*$-algebras." Studia Mathematica 235, no. 3 (2016): 269–304. http://dx.doi.org/10.4064/sm8616-9-2016.

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6

Borges, Nerio, and Edwin Pin. "Universal first-order logic is superfluous in the second level of the polynomial-time hierarchy." Logic Journal of the IGPL 27, no. 6 (May 1, 2019): 895–909. http://dx.doi.org/10.1093/jigpal/jzz009.

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Abstract In this paper we prove that $\forall \textrm{FO}$, the universal fragment of first-order logic, is superfluous in $\varSigma _2^p$ and $\varPi _2^p$. As an example, we show that this yields a syntactic proof of the $\varSigma _2^p$-completeness of value-cost satisfiability. The superfluity method is interesting since it gives a way to prove completeness of problems involving numerical data such as lengths, weights and costs and it also adds to the programme started by Immerman and Medina about the syntactic approach in the study of completeness.

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Nicolopoulos, Anouk, Martin Campos Pinto, Bruno Després, and Patrick Ciarlet. "Degenerate elliptic equations for resonant wave problems." IMA Journal of Applied Mathematics 85, no. 1 (February 2020): 132–59. http://dx.doi.org/10.1093/imamat/hxaa001.

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Abstract The modelling of resonant waves in 2D plasma leads to the coupling of two degenerate elliptic equations with a smooth coefficient $\alpha $ and compact terms. The coefficient $\alpha $ changes sign. The region where $\{\alpha>0\}$ is propagative, and the region where $\{\alpha <0\}$ is non propagative and elliptic. The two models are coupled through the line $\varSigma =\{\alpha =0\}$. Generically, it is an ill-posed problem and additional information must be introduced to get a satisfactory treatment at $\varSigma $. In this work, we define the solution by relying on the limiting absorption principle ($\alpha $ is replaced by $\alpha +i0^+$) in an adapted functional setting. This setting lies on the decomposition of the solution in a regular and a singular part, which originates at $\varSigma $, and on quasi-solutions. It leads to a new well-posed mixed variational formulation with coupling. As we design explicit quasi-solutions, numerical experiments can be carried out, which illustrate the good properties of this new tool for numerical computation.

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8

Muturi, E. N., G. Pokhariyal, and J. Khalaghai. "Continuity of functions on function spaces defined on bitopological spaces." Journal of Advanced Studies in Topology 8, no. 2 (November 7, 2017): 130. http://dx.doi.org/10.20454/jast.2017.1270.

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In this paper, relationships between continuous functions defined on the spaces \((Y,\tau_{1},\tau_{2})\), \((Y,\tau_{1}\vee\tau_{2})\), \((Y,\tau_{1}\wedge\tau_{2})\) and \((Y,\tau_{i})\) for \(i=1,2\) are examined. Function spaces \(s-C_{\tau}(Y,Z)\), \(p-C_{\omega}(Y,Z)\), \(1-C_{\varsigma}(Y,Z)\), \(2-C_{\zeta}(Y,Z)\), \((1,2)-C_{\varphi}(Y,Z)\) and \((2,1)-C_{\xi}(Y,Z)\) are defined and continuous functions between them explored. A homeomorphism is also established between the spaces \(1-C_{\varsigma}(Y,Z)\) and \((2,1)-C_{\xi}(Y,Z)\).

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9

Fabre, Jean, and Bernardo Figueroa-Espinoza. "Taylor bubble rising in a vertical pipe against laminar or turbulent downward flow: symmetric to asymmetric shape transition." Journal of Fluid Mechanics 755 (August 20, 2014): 485–502. http://dx.doi.org/10.1017/jfm.2014.429.

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AbstractThe symmetry of Taylor bubbles moving in a vertical pipe is likely to break when the liquid flows downward at a velocity greater than some critical value. The present experiments performed in the inertial regime for Reynolds numbers in the range $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}100<\mathit{Re} < 10\, 000$ show that bifurcation to an eccentric motion occurs, with a noticeable increase of the bubble velocity. The influence of the surface tension parameter (an inverse Eötvös number), $\varSigma $, has been investigated for $0.0045<\varSigma <0.067$. It appears that the motion of an asymmetric bubble is much more sensitive to surface tension than that of a symmetric bubble. For any given $\varSigma $, the symmetry-breaking bifurcation occurs in both laminar and turbulent flow at the same vorticity-to-radius ratio ${(\omega /r)}_0$ on the axis of the carrier fluid. This conclusion also applies to results obtained previously from numerical experiments in plane flows.

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10

Zhang, Ch, and A. N. Skiba. "On $$ {\varSigma}_t^{\sigma } $$ -Closed Classes of Finite Groups." Ukrainian Mathematical Journal 70, no. 12 (May 2019): 1966–77. http://dx.doi.org/10.1007/s11253-019-01619-6.

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11

Chen, Jianlong, and Yiqiang Zhou. "STRONGLY CLEAN POWER SERIES RINGS." Proceedings of the Edinburgh Mathematical Society 50, no. 1 (February 2007): 73–85. http://dx.doi.org/10.1017/s0013091505000404.

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AbstractAn element $a$ in a ring $R$ with identity is called strongly clean if it is the sum of an idempotent and a unit that commute. And $a\in R$ is called strongly $\pi$-regular if both chains $aR\supseteq a^2R\supseteq\cdots$ and $Ra\supseteq Ra^2\supseteq\cdots$ terminate. A ring $R$ is called strongly clean (respectively, strongly $\pi$-regular) if every element of $R$ is strongly clean (respectively, strongly $\pi$-regular). Strongly $\pi$-regular elements of a ring are all strongly clean. Let $\sigma$ be an endomorphism of $R$. It is proved that for $\varSigma r_ix^i\in R[[x,\sigma]]$, if $r_0$ or $1-r_0$ is strongly $\pi$-regular in $R$, then $\varSigma r_ix^i$ is strongly clean in $R[[x,\sigma]]$. In particular, if $R$ is strongly $\pi$-regular, then $R[[x,\sigma]]$ is strongly clean. It is also proved that if $R$ is a strongly $\pi$-regular ring, then $R[x,\sigma]/(x^n)$ is strongly clean for all $n\ge1$ and that the group ring of a locally finite group over a strongly regular or commutative strongly $\pi$-regular ring is strongly clean.

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12

Nithin Kumar, Yernad Balachandra, Edoardo Bonizzoni, Amit Patra, and Franco Maloberti. "Interference rejection in quadrature band-pass $$\varSigma \varDelta $$ Σ Δ modulators." Analog Integrated Circuits and Signal Processing 83, no. 1 (February 28, 2015): 95–101. http://dx.doi.org/10.1007/s10470-015-0511-5.

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13

Estaremi, Y., and S. Shamsigamchi. "Unbounded Hyperexpansive Weighted Composition Operators on $$L^{2} (\varSigma )$$ L 2 ( Σ )." Iranian Journal of Science and Technology, Transactions A: Science 41, no. 3 (September 2017): 671–76. http://dx.doi.org/10.1007/s40995-017-0279-9.

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14

Turda, Marius. "Haralambos Oikonomou and Manos Spyridakis (eds), $A\nu \theta \rho \omega \pi o\lambda o\gamma \iota \kappa \acute {\varepsilon } \varsigma ~\kappa \alpha \iota ~\kappa o\iota \nu \omega \nu \iota o\lambda o\gamma \iota \kappa \acute {\varepsilon } \varsigma ~\pi \rho o\sigma \varepsilon \gamma \gamma i\sigma \varepsilon \iota \varsigma ~\tau \eta \varsigma ~\upsilon \gamma \varepsilon i\alpha \varsigma $ [Anthropological and Sociological Perspectives on Health] (Athens: I. Sideris, 2012), pp. 536, €37.28, hardback, ISBN: 978-960-08-0588-8." Medical History 57, no. 1 (January 2013): 149–51. http://dx.doi.org/10.1017/mdh.2012.96.

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15

Rashid, Maliha, Amna Kalsoom, Maria Sager, Mustafa Inc, Dumitru Baleanu, and Ali S. Alshomrani. "Mellin transform for fractional integrals with general analytic kernel." AIMS Mathematics 7, no. 5 (2022): 9443–62. http://dx.doi.org/10.3934/math.2022524.

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<abstract><p>Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order $ \varsigma\ge0 $ and $ \varrho $ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.</p></abstract>

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16

Lybrand, Eric, and Rayan Saab. "Quantization for low-rank matrix recovery." Information and Inference: A Journal of the IMA 8, no. 1 (May 25, 2018): 161–80. http://dx.doi.org/10.1093/imaiai/iay007.

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Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit rate. As an added benefit, our schemes are robust both to noise and to deviations from the low-rank assumption. In short, we provide a full generalization of analogous results, obtained in the classical setup of band-limited function acquisition, and more recently, in the finite frame and compressed sensing setups to the case of low-rank matrices sampled with sub-Gaussian linear operators. Finally, we believe our techniques for generalizing results from the compressed sensing setup to the analogous low-rank matrix setup is applicable to other quantization schemes.

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Rybakov, Mikhail, and Dmitry Shkatov. "Algorithmic properties of first-order modal logics of linear Kripke frames in restricted languages." Journal of Logic and Computation 31, no. 5 (May 14, 2021): 1266–88. http://dx.doi.org/10.1093/logcom/exab030.

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Abstract We study the algorithmic properties of first-order monomodal logics of frames $\langle {\textrm{I}\!\textrm{N}}, \leqslant \rangle $, $\langle {\textrm{I}\!\textrm{N}}, < \rangle $, $\langle \mathbb {Q}, \leqslant \rangle $, $\langle \mathbb {Q}, < \rangle $, $\langle {\textrm{I}\!\textrm{R}}, \leqslant \rangle $, $\langle {\textrm{I}\!\textrm{R}}, < \rangle $, as well as some related logics, in languages with restrictions on the number of individual variables as well as the number and arity of predicate letters. We show that the logics of frames based on $ {\textrm{I}\!\textrm{N}}$ are $\varPi ^1_1$-hard—thus, not recursively enumerable—in languages with two individual variables, one monadic predicate letter and one proposition letter. We also show that the logics of frames based on $\mathbb {Q}$ and ${\textrm{I}\!\textrm{R}}$ are $\varSigma ^0_1$-hard in languages with the same restrictions. Similar results are obtained for a number of related logics.

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Wang, Yingying, Jifu Liang, Leonid Belostotski, Arjuna Madanayake, and Soumyajit Mandal. "$$\varvec{\varDelta }$$–$$\varvec{\varSigma }$$ noise-shaping in 3-D space–time for 2-D wideband antenna array receivers." Multidimensional Systems and Signal Processing 30, no. 3 (October 19, 2018): 1609–31. http://dx.doi.org/10.1007/s11045-018-0620-2.

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Jabbour, Chadi, Hussein Fakhoury, Patrick Loumeau, and Van Tam Nguyen. "A reconfigurable low-pass/high-pass $$\varDelta \varSigma$$ Δ Σ ADC suited for a zero-IF/low-IF receiver." Analog Integrated Circuits and Signal Processing 79, no. 3 (March 27, 2014): 479–91. http://dx.doi.org/10.1007/s10470-014-0289-x.

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20

Mu, John C., Marghoob Mohiyuddin, Jian Li, Narges Bani Asadi, Mark B. Gerstein, Alexej Abyzov, Wing H. Wong, and Hugo Y. K. Lam. "VarSim: a high-fidelity simulation and validation framework for high-throughput genome sequencing with cancer applications." Bioinformatics 31, no. 9 (December 17, 2014): 1469–71. http://dx.doi.org/10.1093/bioinformatics/btu828.

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NÜRNBERG, ROBERT, and EDWARD J. W. TUCKER. "Stable finite element approximation of a Cahn–Hilliard–Stokes system coupled to an electric field." European Journal of Applied Mathematics 28, no. 3 (September 9, 2016): 470–98. http://dx.doi.org/10.1017/s0956792516000395.

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We consider a fully practical finite element approximation of the Cahn–Hilliard–Stokes system: $$\begin{align*} \gamma \tfrac{\partial u}{\partial t} + \beta v \cdot \nabla u - \nabla \cdot \left( \nabla w \right) & = 0 \,, \quad w= -\gamma \Delta u + \gamma ^{-1} \Psi ' (u) - \tfrac12 \alpha c'(\cdot,u) | \nabla \phi |^2\,, \\ \nabla \cdot (c(\cdot,u) \nabla \phi) & = 0\,,\quad \begin{cases} -\Delta v + \nabla p = \varsigma w \nabla u, \\ \nabla \cdot v = 0, \end{cases} \end{align*}$$ subject to an initial condition u0(.) ∈ [−1, 1] on the conserved order parameter u ∈ [−1, 1], and mixed boundary conditions. Here, γ ∈ $\mathbb{R}_{>0}$ is the interfacial parameter, α ∈ $\mathbb{R}_{\geq0}$ is the field strength parameter, Ψ is the obstacle potential, c(⋅, u) is the diffusion coefficient, and c′(⋅, u) denotes differentiation with respect to the second argument. Furthermore, w is the chemical potential, φ is the electro-static potential, and (v, p) are the velocity and pressure. The system has been proposed to model the manipulation of morphologies in organic solar cells with the help of an applied electric field and kinetics.

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Abdullah, Abdullah. "Tanggapan Siswa Terhadap Pembinaan Disiplin Belajar di Rumah dengan Prestasi Belajar pada Mata Pelajaran PAI." Matriks : Jurnal Sosial Sains 1, no. 2 (April 7, 2021): 36–50. http://dx.doi.org/10.36418/matriks.v1i2.51.

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Penelitian ini bertolak dari asumsi teoritik yang menyatakan bahwa prestasi belajar siswa pada mata pelajaran PAI ditentukan oleh tanggapan siswa terhadap pembinaan disiplin belajar anak di rumah. Dari asumsi teori ini diajukan hipotesis, semakin tinggi tanggapan siswa terhadap pembinaan disiplin belajar anak di rumah, semakin tinggi pula prestasi belajar mereka pada mata pelajaran PAI, sebaliknya semakin rendah tanggapan siswa terhadap pembinaan disiplin belajar anak di rumah, semakin rendah pula prestasi belajar mereka pada mata pelajaran PAI. Untuk membuktikan hipotesis tersebut diadakan penelitian dengan menggunakan metode deskriptif. Populasi penelitian ini 60 siswa SMP 2 Solokanjeruk Kab. Bandung. Sedangkan teknik pengumpulan datanya dilakukan observasi, wawancara, angket, tes dan studi kepustakaan. Kemudian untuk menganalisis datanya digunakan dua pendekatan yaitu analisis varsial dan analisis korelasi dan menghasilkan dua variabel X dan variabel Y berdistribusi tidak normal, karena berdistribusi tidak normal maka tidak perlu dianalisis linieritas regresinya dan digunakan korelasi spearman. Berdasarkan hasil perhitungan variabel X (tanggapan siswa terhadap pembinaan disiplin belajar anak di rumah) termasuk kategori cukup. Hasil perhitungan variabel Y (prestasi belajar mereka di sekolah) termasuk kategori cukup.

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Haghighitalab, Delaram, Diomadson Belfort, Alp Kiliç, Aziz Benlarbi-Delaï, and Hassan Aboushady. "A 2.4 GHz ISM-band highly digitized receiver based on a variable gain LNA and a subsampled $$\varSigma \varDelta$$ Σ Δ ADC." Analog Integrated Circuits and Signal Processing 95, no. 2 (March 3, 2018): 259–70. http://dx.doi.org/10.1007/s10470-018-1136-2.

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Howard, A. D. P., A. P. Whitworth, K. A. Marsh, S. D. Clarke, M. J. Griffin, M. W. L. Smith, and O. D. Lomax. "L1495 revisited: a ppmap view of a star-forming filament." Monthly Notices of the Royal Astronomical Society 489, no. 1 (August 12, 2019): 962–76. http://dx.doi.org/10.1093/mnras/stz2234.

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ABSTRACT We have analysed the Herschel and SCUBA-2 dust continuum observations of the main filament in the Taurus L1495 star-forming region, using the Bayesian fitting procedure ppmap. (i) If we construct an average profile along the whole length of the filament, it has FWHM $\simeq 0.087\pm 0.003\, {\rm pc};\,\,$ but the closeness to previous estimates is coincidental. (ii) If we analyse small local sections of the filament, the column-density profile approximates well to the form predicted for hydrostatic equilibrium of an isothermal cylinder. (iii) The ability of ppmap to distinguish dust emitting at different temperatures, and thereby to discriminate between the warm outer layers of the filament and the cold inner layers near the spine, leads to a significant reduction in the surface-density, $\varSigma$, and hence in the line-density, μ. If we adopt the canonical value for the critical line-density at a gas-kinetic temperature of $10\, {\rm K}$, $\mu _{{\rm CRIT}}\simeq 16\, {\rm M_{\odot }\, pc^{-1}}$, the filament is on average trans-critical, with ${\bar{\mu }}\sim \mu _{{\rm CRIT}};\,\,$ local sections where μ > μCRIT tend to lie close to prestellar cores. (iv) The ability of ppmap to distinguish different types of dust, i.e. dust characterized by different values of the emissivity index, β, reveals that the dust in the filament has a lower emissivity index, β ≲ 1.5, than the dust outside the filament, β ≳ 1.7, implying that the physical conditions in the filament have effected a change in the properties of the dust.

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Bisiaux, Pierre, Caroline Lelandais-Perrault, Anthony Kolar, Filipe Vinci dos Santos, and Philippe Benabes. "A 14-bit 250 kS/s two-step inverter-based incremental $$\varSigma \varDelta$$ Σ Δ ADC for CMOS image sensor in $$0.18\,\upmu \hbox {m}$$ 0.18 μ m technology." Analog Integrated Circuits and Signal Processing 97, no. 3 (July 4, 2018): 427–35. http://dx.doi.org/10.1007/s10470-018-1238-x.

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Carter, Campbell D., Stephen Hammack, and Tonghun Lee. "High-speed planar laser-induced fluorescence of the CH radical using the $$C^{ 2} \varSigma ^{ + } {-}X^{ 2} \varPi \left( {0,0} \right)$$ C 2 Σ + - X 2 Π 0 , 0 band." Applied Physics B 116, no. 3 (July 29, 2014): 515–19. http://dx.doi.org/10.1007/s00340-014-5899-6.

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Ivić, A. "Some remarks on the moments of % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaacq % aHcpGvdaqadaqaamaaleaaleaacaaIXaaabaGaaGOmaaaakiabgUca % RmXvP5wqonvsaeHbfv3ySLgzaGqbciab-LgaPjab-rha0bGaayjkai % aawMcaaaGaay5bSlaawIa7aaaa!4648! $$ \left| {\varsigma \left( {\tfrac{1} {2} + it} \right)} \right| $$ in short intervals." Acta Mathematica Hungarica 119, no. 1-2 (September 19, 2007): 15–24. http://dx.doi.org/10.1007/s10474-007-6233-0.

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He, Jun, and Dian-Yong Chen. "Molecular states from $$\varSigma ^{(*)}_c{\bar{D}}^{(*)}-\varLambda _c{\bar{D}}^{(*)}$$ interaction." European Physical Journal C 79, no. 11 (November 2019). http://dx.doi.org/10.1140/epjc/s10052-019-7419-7.

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Abstract In this work, we systemically investigate the molecular states from the $$\varSigma ^{(*)}_c{\bar{D}}^{(*)}-\varLambda _c{\bar{D}}^{(*)}$$Σc(∗)D¯(∗)-ΛcD¯(∗) interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe–Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) $$\varSigma _c{\bar{D}}$$ΣcD¯ interaction with spin parity $$J^P=1/2^-$$JP=1/2- and $$\varSigma _c{\bar{D}}^*$$ΣcD¯∗ interaction with $$1/2^-$$1/2- and $$ 3/2^-$$3/2-. Their masses and widths are consistent with the $$P_c(4312)$$Pc(4312), $$P_c(4440)$$Pc(4440) and $$P_c(4457)$$Pc(4457) observed at LHCb. The states, $$\varSigma _c^*{\bar{D}}^*(1/2^-)$$Σc∗D¯∗(1/2-), $$\varSigma _c^*{\bar{D}}^*(3/2^-)$$Σc∗D¯∗(3/2-) and $$\varSigma ^*_c{\bar{D}}(3/2^-)$$Σc∗D¯(3/2-), are also produced with the same parameters. The isodoublet $$\varSigma _c^*{\bar{D}}^*$$Σc∗D¯∗ interaction with $$5/2^-$$5/2-, as well as the isoquartet (I=3/2) $$\varSigma _c{\bar{D}}^*$$ΣcD¯∗ interactions with $$1/2^-$$1/2- and $$3/2^-$$3/2-, $$\varSigma _c^*{\bar{D}}^*$$Σc∗D¯∗ interaction with $$3/2^-$$3/2- and $$5/2^-$$5/2-, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The $$\varLambda {\bar{D}}^*$$ΛD¯∗ channel is dominant in the decays of the states, $$\varSigma _c{\bar{D}}^*(1/2^-)$$ΣcD¯∗(1/2-), $$\varSigma _c{\bar{D}}^*(3/2^-)$$ΣcD¯∗(3/2-), $$\varSigma _c^*{\bar{D}}(3/2^-)$$Σc∗D¯(3/2-), and $$\varSigma _c{\bar{D}}(1/2^-)$$ΣcD¯(1/2-). The $$\varSigma ^*_c{\bar{D}}^*(1/2^-)$$Σc∗D¯∗(1/2-) state has large coupling to $$\varSigma _c{\bar{D}}$$ΣcD¯ channel while the $$\varSigma _c{\bar{D}}^*$$ΣcD¯∗, $$\varSigma ^*_c{\bar{D}}$$Σc∗D¯ and $$\varLambda _c{\bar{D}}^*$$ΛcD¯∗ channels provide similar contributions to the width of the $$\varSigma ^*_c{\bar{D}}^*(3/2^-)$$Σc∗D¯∗(3/2-) state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.

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Butler, D., A. Lochbihler, D. Aspinall, and A. Gascón. "Formalising $$\varSigma $$-Protocols and Commitment Schemes Using CryptHOL." Journal of Automated Reasoning, September 9, 2020. http://dx.doi.org/10.1007/s10817-020-09581-w.

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Abstract Machine-checked proofs of security are important to increase the rigour of provable security. In this work we present a formalised theory of two fundamental two party cryptographic primitives: $$\varSigma $$ Σ -protocols and Commitment Schemes. $$\varSigma $$ Σ -protocols allow a prover to convince a verifier that they possess some knowledge without leaking information about the knowledge. Commitment schemes allow a committer to commit to a message and keep it secret until revealing it at a later time. We use CryptHOL (Lochbihler in Archive of formal proofs, 2017) to formalise both primitives and prove secure multiple examples namely; the Schnorr, Chaum-Pedersen and Okamoto $$\varSigma $$ Σ -protocols as well as a construction that allows for compound (AND and OR) $$\varSigma $$ Σ -protocols and the Pedersen and Rivest commitment schemes. A highlight of the work is a formalisation of the construction of commitment schemes from $$\varSigma $$ Σ -protocols (Damgard in Lecture notes, 2002). We formalise this proof at an abstract level using the modularity available in Isabelle/HOL and CryptHOL. This way, the proofs of the instantiations come for free.

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30

Celiberto, Roberto, and Annarita Laricchiuta. "Cross sections for the two-step radiative decay process $$X(v)\rightarrow A(v^{\prime \prime })\rightarrow X(v^\prime )$$ in e-LiH collisions." European Physical Journal D 75, no. 5 (May 2021). http://dx.doi.org/10.1140/epjd/s10053-021-00164-x.

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Abstract The cross sections for the two-step process, represented by the electron-impact vibro-electronic excitation $$X^1\varSigma ^+(v) \rightarrow A^1\varSigma ^+(v'')$$ X 1 Σ + ( v ) → A 1 Σ + ( v ′ ′ ) of the LiH molecule, followed by radiative decay back on the vibrational manifold of the ground state, $$A^1\varSigma ^+(v'')\rightarrow X^1\varSigma ^+(v')$$ A 1 Σ + ( v ′ ′ ) → X 1 Σ + ( v ′ ) , are calculated as a function of the incident electron energy from the threshold to 1000 eV. The final cross sections for the two-step process, which results in an overall vibrational excitation of the molecule, known also as E-v process, are provided for all the possible $$v,v'$$ v , v ′ transitions among the vibrational levels, including the continuum, of the electronic ground state. Graphic abstract

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31

Zhu, Jun-Tao, Shu-Yi Kong, Yi Liu, and Jun He. "Hidden-bottom molecular states from $$\varSigma ^{(*)}_bB^{(*)}-\varLambda _bB^{(*)}$$ interaction." European Physical Journal C 80, no. 11 (November 2020). http://dx.doi.org/10.1140/epjc/s10052-020-8410-z.

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AbstractIn this work, we study possible hidden-bottom molecular pentaquarks $$P_b$$ P b from coupled-channel $$\varSigma ^{(*)}_bB^{(*)}-\varLambda _bB^{(*)}$$ Σ b ( ∗ ) B ( ∗ ) - Λ b B ( ∗ ) interaction in the quasipotential Bethe-Salpeter equation approach. In isodoublet sector with $$I=1/2$$ I = 1 / 2 , with the same reasonable parameters the interaction produces seven molecular states, a state near $$ \varSigma _bB$$ Σ b B threshold with spin parity $$J^P=1/2^-$$ J P = 1 / 2 - , a state near $$\varSigma ^*_bB$$ Σ b ∗ B threshold with $$3/2^-$$ 3 / 2 - , two states near $$\varSigma _bB^*$$ Σ b B ∗ threshold with $$1/2^-$$ 1 / 2 - and $$3/2^-$$ 3 / 2 - , and three states near $$\varSigma _b^*B^*$$ Σ b ∗ B ∗ threshold with $$1/2^-$$ 1 / 2 - , $$3/2^-$$ 3 / 2 - , and $$5/2^-$$ 5 / 2 - . The results suggest that three states near $$\varSigma _b^* B^*$$ Σ b ∗ B ∗ threshold and two states near $$\varSigma _b B^*$$ Σ b B ∗ threshold are very close, respectively, which may be difficult to distinguish in experiment without partial wave analysis. Compared with the hidden-charm pentaquark, the $$P_b$$ P b states are relatively narrow with widths at an order of magnitude of 1 MeV or smaller. The importance of each channel considered is also discussed, and it is found that the $$\varLambda _b B^*$$ Λ b B ∗ channel provides important contribution for the widths of those states. In isoquartet sector with $$I=3/2$$ I = 3 / 2 , cutoff should be considerably enlarged to achieve bound states from the interaction, which makes the existence of such states unreliable. The results in the current work are helpful for searching for hidden-bottom molecular pentaquarks in future experiments, such as the COMPASS, J-PARC, and the Electron Ion Collider in China (EicC).

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32

Gong, Kui, Hao-Yang Jing, and Ailin Zhang. "Possible assignments of highly excited $$\varLambda _c(2860)^+$$, $$\varLambda _c(2880)^+$$ and $$\varLambda _c(2940)^+$$." European Physical Journal C 81, no. 5 (May 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09255-w.

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AbstractPossible assignments of highly excited $$\varLambda _c(2860)^+$$ Λ c ( 2860 ) + , $$\varLambda _c(2880)^+$$ Λ c ( 2880 ) + and $$\varLambda _c(2940)^+$$ Λ c ( 2940 ) + are explored in a $$^3P_0$$ 3 P 0 strong decay model. Decay widths, branching fraction ratios $$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}$$ R = Γ ( Σ c ( 2520 ) π ) Γ ( Σ c ( 2455 ) π ) and the branching fractions of DN channels of theses assignments are computed. $$D^0p$$ D 0 p channel is a very important channel to provide information on the inner excitation and structure of these highly excited $$\varLambda _c$$ Λ c . In our analysis, $$\varLambda _c(2860)^+$$ Λ c ( 2860 ) + may be a 1D-wave excited $$\varLambda _c$$ Λ c with $$J^P={3\over 2}^+$$ J P = 3 2 + , which has dominant DN decay channels with a branching fraction $${\mathcal {B}}(\varLambda _c(2860)^+\rightarrow DN)=75\%$$ B ( Λ c ( 2860 ) + → D N ) = 75 % and a branching ratio $$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.12$$ R = Γ ( Σ c ( 2520 ) π ) Γ ( Σ c ( 2455 ) π ) = 0.12 . $$\varLambda _c(2880)^+$$ Λ c ( 2880 ) + is very possibly a 1F-wave excited $$\varLambda _c$$ Λ c with $$J^P=\frac{5}{2}^-$$ J P = 5 2 - ; In this assignment, the predicted total decay width ($$\varGamma \approx 4.49$$ Γ ≈ 4.49 MeV) is comparable to the measured $$\varGamma =5.6^{+0.8}_{-0.6}$$ Γ = 5 . 6 - 0.6 + 0.8 MeV, and the predicted $$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.12$$ R = Γ ( Σ c ( 2520 ) π ) Γ ( Σ c ( 2455 ) π ) = 0.12 is consistent with the measured $$R=0.225\pm 0.062\pm 0.025$$ R = 0.225 ± 0.062 ± 0.025 ; The DN channels are its dominant strong decay channels with a branching fraction $${\mathcal {B}}(\varLambda _c(2880)^+\rightarrow DN)=94\%$$ B ( Λ c ( 2880 ) + → D N ) = 94 % . $$\varLambda _c(2880)^+$$ Λ c ( 2880 ) + seems impossibly a 1D-wave excited $$\varLambda _c$$ Λ c with $$J^P=\frac{5}{2}^+$$ J P = 5 2 + once the presently measured $$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}$$ R = Γ ( Σ c ( 2520 ) π ) Γ ( Σ c ( 2455 ) π ) is confirmed. $$\varLambda _c(2940)^+$$ Λ c ( 2940 ) + may be a 2P-wave excited $$\varLambda ^{1,0}_{c1,1}(\frac{3}{2}^-,2P)$$ Λ c 1 , 1 1 , 0 ( 3 2 - , 2 P ) . In this case, $$\varLambda _c(2940)^+$$ Λ c ( 2940 ) + has a total decay width $$\varGamma =17.56$$ Γ = 17.56 MeV, a branching ratio $$R={\varGamma (\varSigma _c(2520)\pi )\over \varGamma (\varSigma _c(2455)\pi )}=0.89$$ R = Γ ( Σ c ( 2520 ) π ) Γ ( Σ c ( 2455 ) π ) = 0.89 and the DN decay channels with a branching fraction $${\mathcal {B}}(\varLambda _c(2940)^+\rightarrow DN)=43\%$$ B ( Λ c ( 2940 ) + → D N ) = 43 % . In order to understand the inner excitation and structure of these highly excited $$\varLambda _c$$ Λ c , measurements of those predicted quantities are required in the future.

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33

Chen, Hua-Xing. "Decay properties of $$P_c$$ states through the Fierz rearrangement." European Physical Journal C 80, no. 10 (October 2020). http://dx.doi.org/10.1140/epjc/s10052-020-08519-1.

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AbstractWe systematically study hidden-charm pentaquark currents with the quark configurations $$[\bar{c} u][u d c]$$ [ c ¯ u ] [ u d c ] , $$[\bar{c} d][u u c]$$ [ c ¯ d ] [ u u c ] , and $$[\bar{c} c][u u d]$$ [ c ¯ c ] [ u u d ] . Some of their relations are derived using the Fierz rearrangement of the Dirac and color indices, and the obtained results are used to study strong decay properties of $$P_c$$ P c states as $$\bar{D}^{(*)} \varSigma _c$$ D ¯ ( ∗ ) Σ c hadronic molecules. We calculate their relative branching ratios for the $$J/\psi p$$ J / ψ p , $$\eta _c p$$ η c p , $$\chi _{c0} p$$ χ c 0 p , $$\chi _{c1} p$$ χ c 1 p , $$\bar{D}^{(*)0} \varLambda _c^+$$ D ¯ ( ∗ ) 0 Λ c + , $$\bar{D}^{0} \varSigma _c^{+}$$ D ¯ 0 Σ c + , and $$\bar{D}^{-} \varSigma _c^{++}$$ D ¯ - Σ c + + decay channels. We propose to search for the $$P_c(4312)$$ P c ( 4312 ) in the $$\eta _c p$$ η c p channel and the $$P_c(4440)/P_c(4457)$$ P c ( 4440 ) / P c ( 4457 ) in the $$\bar{D}^{0} \varLambda _c^+$$ D ¯ 0 Λ c + channel.

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34

Mullen, C., S. Gardner, D. I. Glazier, S. J. D. Kay, K. Livingston, I. I. Strakovsky, R. L. Workman, et al. "Single $$\pi ^0$$ production off neutrons bound in deuteron with linearly polarized photons." European Physical Journal A 57, no. 6 (June 2021). http://dx.doi.org/10.1140/epja/s10050-021-00521-9.

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AbstractThe quasifree $$\overrightarrow{\gamma } d\rightarrow \pi ^0n(p)$$ γ → d → π 0 n ( p ) photon beam asymmetry, $$\varSigma $$ Σ , has been measured at photon energies, $$E_\gamma $$ E γ , from 390 to 610 MeV, corresponding to center of mass energy from 1.271 to 1.424 GeV, for the first time. The data were collected in the A2 hall of the MAMI electron beam facility with the Crystal Ball and TAPS calorimeters covering pion center-of-mass angles from 49$$^\circ $$ ∘ to 148$$^\circ $$ ∘ . In this kinematic region, polarization observables are sensitive to contributions from the $$\varDelta (1232)$$ Δ ( 1232 ) and N(1440) resonances. The extracted values of $$\varSigma $$ Σ have been compared to predictions based on partial-wave analyses (PWAs) of the existing pion photoproduction database. Our comparison includes the SAID, MAID and Bonn–Gatchina analyses; while a revised SAID fit, including the new $$\varSigma $$ Σ measurements, has also been performed. In addition, isospin symmetry is examined as a way to predict $$\pi ^0n$$ π 0 n photoproduction observables, based on fits to published data in the channels $$\pi ^0p$$ π 0 p , $$\pi ^+n$$ π + n and $$\pi ^-p$$ π - p .

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35

Jia, Duojie, Ji-Hai Pan, and Cheng-Qun Pang. "A mixing coupling scheme for spectra of singly heavy baryons with spin-1 diquarks in P-waves." European Physical Journal C 81, no. 5 (May 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09205-6.

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AbstractA new scheme of state classification is proposed and applied to analyze masses of the heavy baryons $$\varOmega _{Q}$$ Ω Q , $$\varSigma _{Q}$$ Σ Q and $$\varXi _{Q}^{\prime }$$ Ξ Q ′ in P-waves. The results confirm all excited $$\varOmega _{c}$$ Ω c and $$\varOmega _{b}$$ Ω b baryons reported recently by LHCb to be bound states of a P-wave ss-diquark and a respective charm or bottom quark, and thereby predict Regge trajectories for more excited $$\varOmega _{c}$$ Ω c and $$\varOmega _{b}$$ Ω b baryons. We suggest one excited $$J^{P}=5/2^{-}$$ J P = 5 / 2 - $$\varOmega _{b}$$ Ω b state to be unseen by LHCb around 6352 MeV, and predict P-wave masses of all spin-partners of the odd-parity baryons $$\varSigma _{c}(2800)/\varXi _{c}^{\prime }(2942)$$ Σ c ( 2800 ) / Ξ c ′ ( 2942 ) and $$\varSigma _{b}(6097)$$ Σ b ( 6097 ) /$$\varXi _{b}^{\prime }(6227)$$ Ξ b ′ ( 6227 ) . A computation is further given in a relativized potential quark models to explain matched values of spin couplings of all considered baryons, by which a scaling law for these spin couplings is discussed.

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36

Fishta, Markeljan, and Franco Fiori. "Decimation of Delta-Sigma-Modulated Signals Using a Low-Cost Microcontroller." Circuits, Systems, and Signal Processing, July 5, 2021. http://dx.doi.org/10.1007/s00034-021-01772-z.

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Abstract$$\varDelta \varSigma $$ Δ Σ analog-to-digital converters (ADCs) are largely used in sensor acquisition applications. In the last few years, standalone $$\varDelta \varSigma $$ Δ Σ modulators have become increasingly available as off-the-shelf parts. To build a complete ADC, a standalone modulator has to be paired with some advanced elaboration unit, such as a field programmable gate array (FPGA) or a digital signal processor (DSP), which is needed for the implementation of the decimation filter. This work investigates the use of low-cost, general-purpose microcontrollers for the decimation of $$\varDelta \varSigma $$ Δ Σ -modulated signals. The main challenge is given by the clock frequency of the modulator, which can be in the range of a few $$\hbox {MHz}$$ MHz . The proposed technique deals with this limitation by employing two serial peripheral interface (SPI) modules in a time-interleaved configuration. This approach allows for continuous acquisition and elaboration of relatively high-speed, digital signals. The technique has been applied to a case study, and a data conversion system has been practically realized. The performance of the proposed filter is compared to that of a digital filter, present on board a commercial microcontroller, and the results of experimental tests are provided.

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37

Klempt, E., V. Burkert, U. Thoma, L. Tiator, and R. Workman. "$$\varLambda $$ and $$\varSigma $$ Excitations and the Quark Model." European Physical Journal A 56, no. 10 (October 2020). http://dx.doi.org/10.1140/epja/s10050-020-00261-2.

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AbstractThe spectrum of $$\varLambda $$ Λ and $$\varSigma $$ Σ excitations is reviewed taking into account (nearly) all hyperon resonances which were seen in early analyses or in one of the recent partial-wave analyses. The spectrum is compared with the old Isgur–Karl model and the Bonn model. These models allows us to discuss the SU(3) structure of the observed resonances. The SU(3) decomposition is compared with SU(6) relations between the different decay modes. Seven $$\varLambda $$ Λ states are proposed to be classified as SU(3) singlet states. The hyperon spectrum is compared with the spectrum of N and $$\varDelta $$ Δ resonances.

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38

Björklund, Johanna, and Loek Cleophas. "Aggregation-based minimization of finite state automata." Acta Informatica, January 6, 2020. http://dx.doi.org/10.1007/s00236-019-00363-5.

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AbstractWe present a minimization algorithm for non-deterministic finite state automata that finds and merges bisimulation-equivalent states. The bisimulation relation is computed through partition aggregation, in contrast to existing algorithms that use partition refinement. The algorithm simultaneously generalises and simplifies an earlier one by Watson and Daciuk for deterministic devices. We show the algorithm to be correct and run in time $$ O \left( n^2 r^2 \left| \varSigma \right| \right) $$On2r2Σ, where n is the number of states of the input automaton $$M$$M, r is the maximal out-degree in the transition graph for any combination of state and input symbol, and $$\left| \varSigma \right| $$Σ is the size of the input alphabet. The algorithm has a higher time complexity than derivatives of Hopcroft’s partition-refinement algorithm, but represents a promising new solution approach that preserves language equivalence throughout the computation process. Furthermore, since the algorithm essentially computes the maximal model of a logical formula derived from $$M$$M, optimisation techniques from the field of model checking become applicable.

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39

Visser, Albert. "The absorption law." Archive for Mathematical Logic, December 16, 2020. http://dx.doi.org/10.1007/s00153-020-00752-5.

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AbstractIn this paper, we show how to construct for a given consistent theory U a $$\varSigma ^0_1$$ Σ 1 0 -predicate that both satisfies the Löb Conditions and the Kreisel Condition—even if U is unsound. We do this in such a way that U itself can verify satisfaction of an internal version of the Kreisel Condition.

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40

Ackerman, Nathanael, Cameron Freer, and Rehana Patel. "On computable aspects of algebraic and definable closure." Journal of Logic and Computation, December 23, 2020. http://dx.doi.org/10.1093/logcom/exaa070.

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Abstract We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most $n$, in any given computable structure, both algebraic and definable closure with respect to that collection are $\varSigma ^0_{n+2}$ sets. We further show that these bounds are tight.

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41

Hanson, James. "Analog reducibility." Journal of Logic and Computation, June 14, 2021. http://dx.doi.org/10.1093/logcom/exab036.

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Abstract In this paper we introduce and characterize two ‘analog reducibility’ notions for $[0,1]$-valued oracles on $\omega $ obtained by applying the syntactic characterizations of Turing and enumeration reducibility in terms of (positive) relatively $\varSigma _1$ and $\varPi _1$ formulas to formulas in continuous logic (Ben Yaacov, Berenstein, Henson and Usvyatsov, 2008, Model Theory for Metric Structures, vol. 2 of London Mathematical Society Lecture Note Series, pp. 315–427. Cambridge University Press.). The resulting analog and analog enumeration degree structures, $\mathscr {D}_a$ and $\mathscr {D}_{ae}$, naturally extend $\mathscr {D}_T$ and $\mathscr {D}_e$ in a compatible way. To show that these extensions are proper we prove that a sufficiently generic total $[0,1]$-valued oracle does not ‘analog enumerate’ any non-c.e. discrete set and that a sufficiently generic positive $[0,1]$-valued oracle neither ‘analog enumerates’ a non-c.e. discrete set nor ‘analog computes’ a non-trivial total $[0,1]$-valued oracle. We also provide a characterization of the continuous degrees among $\mathscr {D}_{ae}$ as precisely $\mathscr {D}_e \cap \mathscr {D}_a$. Finally we characterize a generalization of r.i.c.e. relations to metric structures via $\varSigma _1$ formulas in the ‘hereditarily compact superstructure’, which was the original motivation for the concepts in this paper.

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42

Husek, Tomáš, and Stefan Leupold. "Radiative corrections for the decay $$\varSigma ^0\rightarrow \varLambda e^+e^-$$." European Physical Journal C 80, no. 3 (March 2020). http://dx.doi.org/10.1140/epjc/s10052-020-7710-7.

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43

Kakadiya, Amee, Zalak Shah, Keval Gandhi, and Ajay Kumar Rai. "Spectra and Decay Properties of $$\varLambda _b$$ and $$\varSigma _b$$ Baryons." Few-Body Systems 63, no. 2 (March 10, 2022). http://dx.doi.org/10.1007/s00601-022-01729-1.

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44

Smeulders, B., D. A. M. P. Blom, and F. C. R. Spieksma. "Identifying optimal strategies in kidney exchange games is $$\varSigma _2^p$$-complete." Mathematical Programming, January 21, 2022. http://dx.doi.org/10.1007/s10107-021-01748-6.

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45

Huang, Yin, and Lisheng Geng. "Strong decays of the $$\varXi (1620)^0$$ as a $$\varLambda {\bar{K}}$$ and $$\varSigma {\bar{K}}$$ molecule." European Physical Journal C 80, no. 9 (September 2020). http://dx.doi.org/10.1140/epjc/s10052-020-8421-9.

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AbstractIn this work, we study the strong decays of the newly observed $$\varXi (1620)^0$$ Ξ ( 1620 ) 0 assuming that it is a meson-baryon molecular state of $$\varLambda {\bar{K}}$$ Λ K ¯ and $$\varSigma {\bar{K}}$$ Σ K ¯ . We consider four possible spin-parity assignments $$J^P=1/2^{\pm }$$ J P = 1 / 2 ± and $$3/2^{\pm }$$ 3 / 2 ± for the $$\varXi (1620)^0$$ Ξ ( 1620 ) 0 , and evaluate its partial decay width into $$\varXi \pi $$ Ξ π and $$\varXi \pi \pi $$ Ξ π π via hadronic loops with the help of effective Lagrangians. In comparison with the Belle data, the calculated decay width favors the spin-party assignment $$1/2^-$$ 1 / 2 - while the other spin-parity assignments do not yield a decay width consistent with data in the molecule picture. We find that about 52–68% of the total width comes from the $${\bar{K}}\varLambda $$ K ¯ Λ channel, while the rest is provided by the $${\bar{K}}\varSigma $$ K ¯ Σ channel. As a result, both channels are important in explaining the strong decay of the $$\varXi (1620)^0$$ Ξ ( 1620 ) 0 . In addition, the transition $$\varXi (1620)^0\rightarrow \pi \varXi $$ Ξ ( 1620 ) 0 → π Ξ is the main decay channel in the $$J^{P}=1/2^{-}$$ J P = 1 / 2 - case, which almost saturates the total width. These information are helpful to further understand the nature of the $$\varXi (1620)^0$$ Ξ ( 1620 ) 0 .

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46

Mikec, Luka. "Complexity of the interpretability logics ILW and ILP." Logic Journal of the IGPL, April 7, 2022. http://dx.doi.org/10.1093/jigpal/jzac042.

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Abstract The interpretability logic ILP is the interpretability logic of all sufficiently strong $\varSigma _1$-sound finitely axiomatised theories, such as the Gödel-Bernays set theory. The interpretability logic IL is a strict subset of the intersection of the interpretability logics of all so-called reasonable theories, IL(All). It is known that both ILP and ILW are decidable, however their complexity has not been resolved previously. In [10] it was shown that the basic interpretability logic IL is PSPACE-complete. Here we prove the same for ILP and ILW.

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47

Kuznetsov, Stepan L. "Commutative action logic." Journal of Logic and Computation, March 24, 2022. http://dx.doi.org/10.1093/logcom/exac008.

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Abstract We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, i.e. the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic, the equational theory of *-continuous commutative action lattices. Namely, we prove that the former is $\varSigma _1^0$-complete and the latter is $\varPi _1^0$-complete. Thus, the situation is the same as in the more well-studied non-commutative case. The methods used, however, are different: we encode infinite and circular computations of counter (Minsky) machines.

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48

Chamolly, Alexander, and Neil M. Ribe. "Fluid mechanics of free subduction on a sphere. Part 1. The axisymmetric case." Journal of Fluid Mechanics 929 (October 27, 2021). http://dx.doi.org/10.1017/jfm.2021.871.

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To understand how a spherical geometry influences the dynamics of gravity-driven subduction of the oceanic lithosphere on Earth, we study a simple model of a thin and dense axisymmetric shell of thickness $h$ and viscosity $\eta _1$ sinking in a spherical body of fluid with radius $R_0$ and a lower viscosity $\eta _0$ . Using scaling analysis based on thin viscous shell theory, we identify a fundamental length scale, the ‘bending length’ $l_b$ , and two key dimensionless parameters that control the dynamics: the ‘flexural stiffness’ $St = (\eta _1/\eta _0)(h/l_b)^3$ and the ‘sphericity number’ $\varSigma = (l_b/R_0)\cot \theta _t$ , where $\theta _t$ is the angular radius of the subduction trench. To validate the scaling analysis, we obtain a suite of instantaneous numerical solutions using a boundary-element method based on new analytical point-force Green functions that satisfy free-slip boundary conditions on the sphere's surface. To isolate the effect of sphericity, we calculate the radial sinking speed $V$ and the hoop stress resultant $T_2$ at the leading end of the subducted part of the shell, both normalised by their ‘flat-Earth’ values (i.e. for $\varSigma = 0$ ). For reasonable terrestrial values of $\eta _1/\eta _0$ ( $\approx$ several hundred), sphericity has a modest effect on $V$ , which is reduced by $< 7\,\%$ for large plates such as the Pacific plate and by up to 34 % for smaller plates such as the Cocos and Philippine Sea plates. However, sphericity has a much greater effect on $T_2$ , increasing it by up to 64 % for large plates and 240 % for small plates. This result has important implications for the growth of longitudinal buckling instabilities in subducting spherical shells.

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49

Nanamura, T., K. Miwa, Y. Akazawa, R. Honda, Y. Nakada, and T. Sakao. "The Analysis Status of $${\varSigma }^+ p$$ Scattering Events in the J-PARC E40 Experiment." Few-Body Systems 62, no. 4 (October 17, 2021). http://dx.doi.org/10.1007/s00601-021-01698-x.

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50

Rybakov, Mikhail, and Dmitry Shkatov. "Undecidability of the Logic of Partial Quasiary Predicates." Logic Journal of the IGPL, May 20, 2021. http://dx.doi.org/10.1093/jigpal/jzab018.

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Abstract We obtain an effective embedding of the classical predicate logic into the logic of partial quasiary predicates. The embedding has the property that an image of a non-theorem of the classical logic is refutable in a model of the logic of partial quasiary predicates that has the same cardinality as the classical countermodel of the non-theorem. Therefore, we also obtain an embedding of the classical predicate logic of finite models into the logic of partial quasiary predicates over finite structures. As a consequence, we prove that the logic of partial quasiary predicates is undecidable—more precisely, $\varSigma ^0_1$-complete—over arbitrary structures and not recursively enumerable—more precisely, $\varPi ^0_1$-complete—over finite structures.

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