Substitutions with Vanishing Rotationally Invariant First Cohomology by Juan García Escudero

“…The rank of the rational first cohomology, in the tiling space formed by the closure of a translational orbit, equals the Euler totient function evaluated at 𝑁 if the underlying rotation group is 𝐙𝑁. …”
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Comment on “Analysis of Risk Factors Causing Adjacent Disc Degeneration After Percutaneous Kyphoplasty for Osteoporotic Vertebral Compression Fractures” [Letter] by Zeng X, Wang Y

“…Xuefan Zeng,1,* Yiwei Wang2,* 1Chongqing Medical University, Chongqing, People’s Republic of China; 2Tianjin University of Traditional Chinese Medical, Chongqing, People’s Republic of China*These authors contributed equally to this workCorrespondence: Xuefan Zeng, Chongqing Medical University, No. 21,Mid University Town Road, Chongqing, 400016, People’s Republic of China, Email zxfcqmu@163.com…”
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Kamilla’s Letter to Aleksandra, or Not Just a Letter by Reda Griškaitė

“…It explores the issues of gender equality, woman’s freedom(s) and powers, as well as questions of women’s education, which are closely related to the still-sensitive problem of a writing woman. …”
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Miyaoka–Yau inequalities and the topological characterization of certain klt varieties by Greb, Daniel, Kebekus, Stefan, Peternell, Thomas

“…Ball quotients, hyperelliptic varieties, and projective spaces are characterized by their Chern classes, as the varieties where the Miyaoka–Yau inequality becomes an equality. Ball quotients, Abelian varieties, and projective spaces are also characterized topologically: if a complex, projective manifold $X$ is homeomorphic to a variety of this type, then $X$ is itself of this type. …”
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Individual Differences in Placebo Analgesia: Functional Connectivity and Neural Mechanisms [Letter] by Cao H, Zhang Y, Bai L, Ma X

“…Haixing Cao,* Yujie Zhang,* Lingfeng Bai, Xiang Ma The First Affiliated Hospital of Dalian Medical University, Dalian, Liaoning Province, People’s Republic of China*These authors contributed equally to this workCorrespondence: Xiang Ma, The First Affiliated Hospital of Dalian Medical University, 222 Zhongshan Road, Dalian City, Liaoning Province, People’s Republic of China, Email xma9467@vip.sina.com…”
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Stabilized Multiscale Nonconforming Finite Element Method for the Stationary Navier-Stokes Equations by Tong Zhang, Shunwei Xu, Jien Deng

“…This method is based on the enrichment of the standard polynomial space for the velocity component with multiscale function and the nonconforming lowest equal-order finite element pair. Stability and existence uniqueness of the numerical solution are established, optimal-order error estimates are also presented. …”
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Pd-Au Electrocatalysts for Hydrogen Evolution Reaction at Neutral pH by Elitsa Chorbadzhiyska, Mario Mitov, Georgi Hristov, Nina Dimcheva, Lori Nalbandian, Antigoni Evdou, Yolina Hubenova

“…The highest hydrogen evolution rate was achieved with the electrocatalysts, produced from electrolyte with equal Pd and Au content.…”
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DEFINITION AND ANALYSIS OF THE RATIO «PRICE / EARNINGS» OF ACQUIRING AND ACQUIRED COMPANIES by O. Zemlyanskiy

“…This formula allow determining the maximum value of the ratio at which the cost of shares of the combined company for a period of one year, would be equal to the value of the shares of the acquiring company, under certain forecast profit growth of the company after the acquisition. …”
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CURRENT ISSUES OF ARRANGING POST-GRADUATE EDUCATION FOR ACADEMIC STAFF TRAINING by Petr I. Kasatkin, Maxim I. Inozemtsev

“…Special attention is paid to working out post-graduate courses of double training with international partner universities to make it possible for the national educational organizations to join on equal terms the world's academic community.…”
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COMPRESENZE: DONNE E RELIGIONI A SUD by Irene Strazzeri

“…Religious identity ceases to be the difference trough which single persons can continue to exist in equal relationship. Gender identity reveals, on the contrary, all the problems and conflicts rooted in the respective cultural, religious, social and political spheres. …”
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THE CHALLENGES FACED BY NIGERIAN WOMEN IN AGRICULTURAL ACTIVITIES: STUDY OF FORON WOMEN, 2010- 2023 by GUMAR MANJI KEFAS, MUTTANG S. FWANGMUN, UCHECHUKWU F. MUTBAM

“… This paper is an attempt to appreciate the contribution of women in agricultural activities in Foron, thereby unleashing the full potential of women in agriculture which is not only a matter of gender equality but also a critical step towards achieving sustainable development goals, by recognizing and amplifying their roles in the agricultural sector. …”
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Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation by Wen-Xiu Ma

“…Let k be a nonnegative integer and c a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c),  n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.…”
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Gap Phenomenon of an Abstract Willmore Type Functional of Hypersurface in Unit Sphere by Yanqi Zhu, Jin Liu, Guohua Wu

“…Its critical point is called the Wn,F-Willmore hypersurface, for which the variational equation and Simons’ type integral equalities are obtained. Moreover, we construct a few examples of Wn,F-Willmore hypersurface and give a gap phenomenon characterization by use of our integral formula.…”
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Structure of the antieigenvectors of a strictly accretive operator by K. C. Das, M. Das Gupta, K. Paul

“…A sort of uniqueness is also established for the values of Re(Af,f) and ‖Af‖ if the first antieigenvalue, which is equal to min Re(Af,f)/(‖Af‖‖f‖) is attained at the unit vector f.…”
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Phase angle synchronization system of synchronous generators for parallel operation by V. V. Sushkov, E. E. Revyakin

“…This happens due to the voltage frequency of the synchronized generator is not equal to its synchronous value when the phase angle is controlled. …”
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A survey on the positive mass theorem for asymptotically flat initial data sets by Huang, Lan-Hsuan

“…We review seminal contributions as well as recent advances, and then we focus our discussions on the equality case and the counter-examples arising from pp-wave spacetimes.…”
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Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate by Zizhen Zhang, Limin Song

“…In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. …”
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On the Resistance-Harary Index of Graphs Given Cut Edges by Hongzhuan Wang, Hongbo Hua, Libing Zhang, Shu Wen

“…The resistance distance between any two vertices is equal to the resistance between the two points of an electrical network. …”
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New Convergence Properties of the Primal Augmented Lagrangian Method by Jinchuan Zhou, Xunzhi Zhu, Lili Pan, Wenling Zhao

“…New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. …”
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CHOOSING OF OPERATING FREQUENCY OF EDDY CURRENT THICKNESS METER WITH SUPERIMPOSED TRANSDUCER by A. V. Chernyshev

“…It is shown that when using eddy current thickness meter with superimposed transducer the maximal thickness of the conductive sheets or conductive surface layers of a two-layer wares, which may be controlled with selected frequency of excitation current of the transducer, can be estimated based on the magnitude of the penetration depth of a plane electromagnetic wave in the half-space, the specific electrical conductivity and the relative magnetic permeability of which is equal to the values of these parameters in a controlled surface layer or sheet of two-layer ware.…”
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