Simultaneous Bilateral Rupture of the Patellar Tendon and Medial Collateral Ligament: A Case Report and Literature Review by Jean G. Louka, Damien Pourre

“…The clinical case is described and discussed following a review of the literature. The symmetrical knee injury was treated with a primary direct repair of the MCL tears and using a suture anchor fixation of the patellar tendon ruptures, which was reinforced by a stainless steel wire and an autograft of the ipsilateral quadriceps tendon.…”
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Criterion for Unbounded Synchronous Region in Complex Networks by Jin Zhou

“…A main result is that, when the coupling strength is sufficiently strong, the dynamical network achieves synchronization provided that the symmetric part of the inner-coupling matrix is positive definite. …”
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Interactivity gratifications by Adwoa Sikayena Amankwah, Blessing Mbatha

“…The findings indicate that the interactive features of the technologies produced emerging social and psychological gratifications in millennials by projecting them as purposeful, and active in deploying symmetric political communication repertoires. The practical implication of this is that political leaders need to invigorate their electoral communication repertoires both in substance and in depth by deploying the heuristic attributes of the new technologies to facilitate the awakening of visceral responses in millennials and get them to engage in e-politics. …”
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The edge of random tensor eigenvalues with deviation by Nicolas Delporte, Naoki Sasakura

“…Abstract The largest eigenvalue of random tensors is an important feature of systems involving disorder, equivalent to the ground state energy of glassy systems or to the injective norm of quantum states. For symmetric Gaussian random tensors of order 3 and of size N, in the presence of a Gaussian noise, continuing the work [1], we compute the genuine and signed eigenvalue distributions, using field theoretic methods at large N combined with earlier rigorous results of [2]. …”
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Nonlinear eigenvalue problems in Sobolev spaces with variable exponent by Teodora-Liliana Dinu

“…Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a ℤ2-symmetric version for even functionals of the Mountain Pass Lemma and some adequate variational methods.…”
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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. …”
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New Investigation of Millimeter-Wave Rotational Spectrum of CCl3CN in Ground, v7 = 1 and v8 = 1 States by Masoud Motamedi, Tahere Zohrevand

“…The millimeter-wave rotational spectra of the ground and excited vibrational states v7 =1 and v8 =1 of the symmetric top molecule, CCl3CN, have been analyzed again. …”
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Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals by Caishi Wang, Beiping Wang

“…By using the Bernoulli annihilators, we first define in a dense subspace of L2-space of Bernoulli functionals a positive, symmetric, bilinear form Ew associated with w. And then we prove that Ew is closed and has the contraction property; hence, it is a Dirichlet form. …”
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Topological Indices of Pent-Heptagonal Nanosheets via M-Polynomials by Hafiza Bushra Mumtaz, Muhammad Javaid, Hafiz Muhammad Awais, Ebenezer Bonyah

“…In this paper, we used the M-polynomial-based TIs such as 1st Zagreb, 2nd Zagreb, modified 2nd Zagreb, symmetric division deg, general Randi c´, inverse sum, harmonic, and augmented indices to study the chemical structures of pent-heptagonal nanosheets of VC5C7 and HC5C7. …”
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Effective metric descriptions of quantum black holes by Manuel Del Piano, Stefan Hohenegger, Francesco Sannino

“…Abstract In a recent work (Del Piano et al. in Phys Rev D 109(2):024045, 2024), we have described spherically symmetric and static quantum black holes as deformations of the classical Schwarzschild metric that depend on the physical distance to the horizon. …”
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Localized RG flows on composite defects and C $$ \mathcal{C} $$ -theorem by Dongsheng Ge, Tatsuma Nishioka, Soichiro Shimamori

“…Focusing on the case where the symmetry group O(N) is broken to a subgroup O(m) × O(N − m) on the line defect, there is an O(N) symmetric fixed point for all N, while two additional O(N) symmetry breaking ones appear for N ≥ 23. …”
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Paraná Pine, Araucaria angustifolia: An Ancient-Looking Conifer for Modern Landscapes by Gary W. Knox

“… Paraná pine is a primitive-looking conifer valued for its unusual horizontal branching, interesting triangular-shaped needles, and neat, symmetrical form. The primitive appearance of this evergreen tree results from its resemblance to and relationship with an ancient group of Araucaria-related conifers that dominated forests more than 145 million years ago. …”
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Assignment of O–O and Mo=O Stretching Frequencies of Molybdenum/Tungsten Complexes Revisited by Choon Wee Kee

“…We found that M06 functional is unsuitable for assignment of Mo=O and O–O stretches in CpMo(η2-O2)OCH3 and we found that MP2 and even the def2-TZVP do not give accurate order of asymmetric and symmetric Mo=O stretching. We recommend the M06L, which is a good compromise between speed and accuracy, for works involving these complexes. …”
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On Optimal Progressive Censoring Schemes from Models with U-Shaped Hazard Rate: A Comparison between Conventional and Fuzzy Priors by Navid Feroze, Muhammad Noor-ul-Amin, Maryam Sadiq, Md. Moyazzem Hossain

“…We have used conventional and fuzzy priors for the estimation. Further, the symmetric and asymmetric loss functions have been considered for the estimation. …”
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Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation by Kai Ma

“…This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential.…”
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Molecular Descriptors on Line Graphs of Cactus Chains and Rooted Products Graphs by Iftikhar Ahmad, Maqbool Ahmad Chaudhry, Tarkan Öner, Tariq Mahmood, Muhammad Hussain

“…To predict the biological activity of a compound, the generalized Zagreb index, the first Zagreb index M1G, the second Zagreb index M2G, the F-index, the general Randic index, the symmetric division, the atom bond connectivity (ABC), and the geometric arithmetic (GA) descriptors are created.…”
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Process Monitoring for Gamma Distributed Product under Neutrosophic Statistics Using Resampling Scheme by Abdullah M. Almarashi, Muhammad Aslam

“…The control chart coefficients, probability of in-control, probability of out-of-control, and average run lengths have been determined under the assumption of the symmetrical property of the normal distribution using the neutrosophic interval method. …”
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Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods by Abdelaziz Alsubie

“…The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. …”
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Coalescing hardcore-boson condensate states with nonzero momentum by C. H. Zhang, Z. Song

“…Under open boundary conditions, the condensate states become coalescing states when the non-Hermitian $\mathcal{PT}$-symmetric boundary gives rise to the EPs. The fundamental mechanism behind this phenomenon is uncovered through analyzing the scattering dynamics of many-particle wavepackets at the non-Hermitian boundaries. …”
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Economic Policy Uncertainty and Conditional Dependence between China and U.S. Stock Markets by Xinyu Wu, Meng Zhang, Mengqi Wu, Hao Cui

“…The empirical analysis based on the Shanghai Stock Exchange Composite (SSEC) index in China and the S&P 500 index in the U.S. shows that the tail dependence between China and U.S. stock markets is symmetrical, and the t Copula outperforms alternative Copulas in terms of in-sample goodness of fit. …”
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