Special Kähler geometry and holomorphic Lagrangian fibrations by Li, Yang, Tosatti, Valentino

“…Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. …”
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Duality by reproducing kernels by A. Shlapunov, N. Tarkhanov

“…Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write 𝒮A(𝒟) for the space of solutions of the system Au=0 in a domain 𝒟⋐X. …”
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Dynamic Analysis on a Diffusive Two-Enterprise Interaction Model with Two Delays by Yanxia Zhang, Long Li

“…In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. …”
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Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems by Chein-Shan Liu

“…To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA) as well as a globally optimal algorithm (GOA), by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly. An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven. …”
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What is TEI Conformance, and Why Should You Care? by Lou Burnard

“…The recommendations of the Text Encoding Initiative (TEI) seem to have become a defining feature of the methodological framework of the Digital Humanities, despite recurrent concerns that the system they define is at the same time both too rigorous for the manifold variability of humanistic text, and not precise enough to guarantee interoperability of resources defined using it. …”
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Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms by Yanlin Li, Ali H. Alkhaldi, Akram Ali

“…In this study, we develop a general inequality for warped product semi-slant submanifolds of type Mn=NTn1×fNϑn2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. …”
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Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations by M. Enstedt, M. Melgaard

“…The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.…”
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Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting by Karima Mokni, Mohamed Ch-Chaoui

“…This analysis utilizes bifurcation theory and the center manifold theorem. The chaos influenced by NSB is stabilized. …”
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Some Qualitative Properties of Traveling Wave Fronts of Nonlocal Diffusive Competition-Cooperation Systems of Three Species with Delays by Meiping Yao, Pengzhi Qiao, Yang Wang

“…In order to obtain more information of the asymptotic behavior of such solutions at positive infinity, for the special kernels, we discuss the asymptotic behavior of such solutions of such system without delays, via the stable manifold theorem. In addition, by using the sliding method, the strict monotonicity and uniqueness of traveling wave fronts are also obtained.…”
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Inflation is not an Effective Remedy for High Public Debt Ratio by Michael Grömling, Jürgen Matthes

“…Only under very specific conditions — and by simultaneously ignoring the manifold knock-on effects of inflation — does a higher inflation rate bring about a decline in the government debt ratio. …”
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Normalized ground state solutions for the Chern–Simons–Schrödinger equations with mixed Choquard-type nonlinearities by Yipeng Qiu, Yingying Xiao, Yan Zhao, Shengyue Xu

“…Moreover, we also get the relationship between the minimizer and the ground state solution under the Pohožaev–Nehari manifold of the Chern–Simons–Schrödinger equations.…”
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Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection by Xinchao Yang, Xiju Zong, Xingong Cheng, Zhenlai Han

“…The explicit formulae which determine the direction of the bifurcations, stability, and the other properties of the bifurcating periodic solutions are given by using the normal form theory and the center manifold theorem. Numerical simulation verifies the theoretical results.…”
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Miyaoka–Yau inequalities and the topological characterization of certain klt varieties by Greb, Daniel, Kebekus, Stefan, Peternell, Thomas

“…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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Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate by Yingying Zhang, Ruohan Wang, Yanan Cai

“…By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. …”
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Hopf bifurcation analysis in a diffusive predator-prey system with delay and surplus killing effect by Zuolin Shen, Junjie Wei

“…Furthermore, an algorithm for determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions is derived by using the theory of normal form and center manifold. Finally, some numerical simulations are presented to illustrate the analytical results obtained.…”
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Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays by Yunxian Dai, Yiping Lin, Huitao Zhao

“…We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays τ1≠τ2.…”
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Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays by Zizhen Zhang, Huizhong Yang

“…In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory. Some numerical examples are also presented to verify the theoretical analysis.…”
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Some New Characterizations of Trivial Ricci–Bourguignon Solitons by Hana Al-Sodais, Nasser Bin Turki, Sharief Deshmukh, Bang-Yen Chen, Hemangi Madhusudan Shah

“…Each trivial Ricci–Bourguignon soliton is an Einstein manifold. The main purpose of this paper is to discover geometric conditions on compact Ricci–Bourguignon solitons for which the solitons are trivial. …”
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Conformally symplectic structures and the Lefschetz condition by Lejmi, Mehdi, Wilson, Scott O.

“…Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mutually compatible almost complex structure.…”
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A Zone-Based Self-Organized Handover Scheme for Heterogeneous Mobile and Ad Hoc Networks by Murad Khan, Kijun Han

“…Uninterrupted internet services are need of the day and their demand will increase in future by manifold. However, providing uninterrupted services under heterogeneous networks environment is a challenging task. …”
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