The Mehler-Fock transform of general order and arbitrary index and its inversion by Cyril Nasim

“…In this present note, we define a general Mehler-Fock transform involving, as the kernel, the Legendre function P−12+tμ(x), of general order μ and an arbitrary index −12+t, t=σ+iτ, −∞<τ<∞. Then we develop a symmetric inversion formulae for these transforms. …”
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Depth-Based Classification for Distributions with Nonconvex Support by Daniel Hlubinka, Ondrej Vencalek

“…The data depth approach is used instead of the linear discriminant analysis mostly to avoid the parametric assumptions and to get better classifier for data whose distribution is not elliptically symmetric, for example, skewed data. In our paper, we suggest to use weighted version of halfspace depth rather than the halfspace depth itself in order to obtain lower misclassification rate in the case of “nonconvex” distributions. …”
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On the Jeans Theorem and the “Tolman–Oppenheimer–Volkoff Equation” in R2 Gravity by Rishabh Jain, Burra G. Sidharth, Christian Corda

“…Corda, Mosquera Cuesta, and Lorduy Gòmez have shown that spherically symmetric stationary states can be used as a model for galaxies in the framework of the linearized R2 gravity. …”
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The Chini integrability condition in second order Lovelock gravity by Mohammed O. E. Ismail, Sunil D. Maharaj, Byron P. Brassel

“…Abstract We analyse neutral and charged matter distributions in second order Lovelock gravity, also known as Einstein–Gauss–Bonnet gravity, in arbitrary dimensions for a static, spherically symmetric spacetime. We first transform the charged condition of pressure isotropy, an Abel differential equation of the second kind, into canonical form. …”
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Induced Unbalanced Linguistic Ordered Weighted Average and Its Application in Multiperson Decision Making by Lucas Marin, Aida Valls, David Isern, Antonio Moreno, José M. Merigó

“…Some aggregation operators for linguistic variables force the use of a symmetric and uniformly distributed set of terms. The need to relax these conditions has recently been posited. …”
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Starlikeness associated with certain strongly functions by Afis Saliu, Kanwal Jabeen, Jianhua Gong, Sarfraz Nawaz Malik, Hala Alaqad

“…Then κ∈K(λ) if and only if κ(t)≺ϕλ(t), where ≺ is a subordination relation and the function ϕλ(t):=(1+t)λ, for 0<λ<1, maps U to a symmetric domain about the real axis in the right-half plane. …”
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A Bis-Glycosylamine Strategy for the Synthesis of Dimeric Iminosugars Based on a DAB-1 Scaffold by Kamilia Ould Lamara, Nathan Noël, Fabien Massicot, Jean-Luc Vasse, Stéphane P. Vincent, Jean-Bernard Behr

“…Moreover, an additional substituent (allyl, ethynyl) may be inserted into the structure via nucleophilic addition of an organometallic reagent to the starting bis-glycosylamine. A symmetrical ethynyl-iminosugar proved susceptible to intramolecular Glaser coupling, affording the corresponding macrocyclic structure. …”
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Numerical Laser Energy Deposition on Supersonic Cavity Flow and Sensor Placement Strategies to Control the Flow by Ibrahim Yilmaz, Selin Aradag

“…Laser is numerically modeled using a spherically symmetric temperature distribution. By using the POD results, the effects of laser energy on the flow mechanism are presented. …”
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Mutual Correlation in the Shock Wave Geometry by Xiao-Xiong Zeng, Hong-Bo Shao, Ling Li, Xian-Ming Liu

“…We probe the shock wave geometry with the mutual correlation in a spherically symmetric Reissner-Nordström AdS black hole on the basis of the gauge/gravity duality. …”
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Granulomatosis with Polyangiitis as a Cause of Sudden-Onset Bilateral Sensorineural Hearing Loss: Case Report and Recommendations for Initial Assessment by Paul R. Ratmeyer, Benjamin R. Johnson, Luis P. Roldan, Tania L. Kraai

“…Here, we present a case of bilateral sudden sensorineural hearing loss (SSNHL) and distal symmetric polyneuropathy as the first presenting signs of GPA. …”
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Load-Balanced Secure Routing Protocol for Wireless Sensor Networks by Wang Xin-sheng, Zhan Yong-zhao, Wang Liang-min

“…Data breach is prevented by data encryption, and data security is realized by one-way hash key chain and symmetric key authentication. LSRP offers preventions against usual attacks, and it also takes into account traffic load balance. …”
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Method for the Calculation of DPA in the Reactor Pressure Vessel of Atucha II by J. A. Mascitti, M. Madariaga

“…It was determined that the maximum DPA rate in the RPV wall with fresh fuel element (FE) is 3.76(3) × 10-12 s-1, it takes place in front of FEs BA42 and BL43, and it is symmetrical about the central channel, LG04, and LH03.…”
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Study on Environmental Effects Induced by Quasirectangle Shield Tunnelling with Analytical Stiffness Matrix by Jianguo Xu, Fengyang Miao, Lei Kou, Jinpeng Zhang

“…Finally, the horizontal settlement groove of the quasirectangle shield is roughly symmetrical and parabolic along the tunnel axis, with a groove width range of about 20m. …”
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Unified reference system for geometric characteristics dimensional elements of details. Part II. Geometric characteristics of cylindrical elements of parts by V. I. Glukhov, L. G. Varepo

“…The accuracy of coordinating dimensions should be specified by symmetrical tolerances for linear and angular coordinates of elements.…”
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An exact symmetry in λ-deformed CFTs by George Georgiou, Eftychia Sagkrioti, Konstantinos Sfetsos, Konstantinos Siampos

“…Finally, we extend the above results to λ-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.…”
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Regular black holes from pure gravity by Pablo Bueno, Pablo A. Cano, Robie A. Hennigar

“…The theories we consider have two key properties that ensure the results are general and robust: (1) they provide a basis for (vacuum) gravitational effective field theory in five and higher-dimensions, (2) for each value of the mass, they have a unique static spherically symmetric solution. We present several exact solutions of the theories that include the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones. …”
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Analysis of Rattleback Chaotic Oscillations by Michael Hanias, Stavros G. Stavrinides, Santo Banerjee

“…Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. …”
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Pulmonary Alveolar Microlithiasis and Rheumatoid Arthritis: A Case Report and Review of the Literature by Waleed Hafiz, Ahmedhusam Alahmed, Mohammed Alahmadi, Rakan Alotaibi, Abdullah Alsharif, Safwan Alim, Mohammed Mokhtar, Kholoud Al-Maabdi, Omaima Badr

“…Rheumatoid arthritis (RA) is a chronic systemic autoimmune disease characterized by chronic seropositive symmetrical inflammatory polyarthritis with numerous extra-articular manifestations. …”
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Quasi-topological fractons: a 3D dipolar gauge theory by Erica Bertolini, Alberto Blasi, Nicola Maggiore

“…Abstract We consider the theory of a generic rank-2 tensor field in three spacetime dimensions, which involves a symmetric tensor field transforming under infinitesimal diffeomorphisms, and a vector field, whose gauge transformation depends on a local vector parameter. …”
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Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning by Luca Bergamaschi, Angeles Martínez, Giorgio Pini

“…The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse-approximate-inverse- (FSAI-) type preconditioners. …”
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