A simple construction of the Rumin algebra by Case, Jeffrey S.

“…We recover this fact by giving a simple and explicit construction of the Rumin algebra via Markl’s formulation of the Homotopy Transfer Theorem.…”
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Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space by Kangqun Zhang

“…Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.…”
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Factorization of Hankel operators, range inclusion of Toeplitz and Hankel operators on the vector-valued Hardy space by Bhuia, Sudip Ranjan

“…Using Douglas theorem on factorization and range inclusion of bounded linear operators, we give the factorization of Hankel operators, range inclusion of Hankel and Toeplitz operators defined on vector-valued Hardy spaces.…”
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Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator by Zhi-Wei Lv, Xu-Dong Zheng

“…Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results.…”
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Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence by Huiqin Lu

“…By constructing a special cone in C1[0,2π] and the fixed point theorem, this paper investigates second-order singular semipositone periodic boundary value problems with dependence on the first-order derivative and obtains the existence of multiple positive solutions. …”
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Bicubic ribbon surface by V. A. Korotkiy, E. A. Usmanova

“…Theorem 2 contains conditions for the continuity of curvature. …”
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Short and long-range magnetic ordering and emergent topological transition in (Mn1−xNix)2P2S6 by Nasaru Khan, Deepu Kumar, Shantanu Semwal, Yuliia Shemerliuk, Bernd Büchner, Koushik Pal, Saicharan Aswartham, Pradeep Kumar

“…Though, there are some exceptions to Mermin-Wagner theorem in particular low dimensional magnetic systems with topologically ordered phase transitions. …”
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On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c0 and c by Bilâl Altay, Feyzı Başar

“…We determine the fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ, and includes as other special cases the right shift and the Zweier matrices.…”
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Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays by Qiming Liu, Sumin Yang

“…Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.…”
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Derived categories and the analytic approach to general reciprocity laws. Part I by Michael Berg

“…We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. …”
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Invertibility-preserving maps of C∗-algebras with real rank zero by Istvan Kovacs

“…We also generalize a theorem of Russo.…”
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Generalization Contractive Mappings on Rectangular b-Metric Space by Jayshree Patil, Basel Hardan, Ahmed A. Hamoud, Amol Bachhav, Homan Emadifar, Hatira Günerhan

“…Finally, an example is presented to clarify our theorem.…”
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A Class of Fuzzy Variational Inequality Based on Monotonicity of Fuzzy Mappings by Zezhong Wu, Jiuping Xu

“…The existence of a solution to the fuzzy variational-like inequality is discussed, and the existence theorem can be achieved. Furthermore, some extended properties of the fuzzy variational-like inequality are researched. …”
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Eigenvalues and ranges for perturbations of nonlinear accretive and monotone operators in Banach spaces by Zhou Haiyun, Athanassios G. Kartsatos

“…The eigenvalue results improve and extend some recent results by Guan and Kartsatos, while the range theorem gives an affirmative answer to a recent problem of Kartsatos.…”
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Global Attractivity of a Periodic Delayed N-Species Model of Facultative Mutualism by Ahmadjan Muhammadhaji, Zhidong Teng

“…Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.…”
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Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. …”
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Borel Directions and Uniqueness of Meromorphic Functions by Keyu Zhang, HongYan Xu, Hongxun Yi

“…Our result is an improvement of a recent theorem given by Long and Wu (2012).…”
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Solving Partial Integro-Differential Equations via Double Formable Transform by Bayan Ghazal, Rania Saadeh, Abdelilah K. Sedeeg

“…Several properties and theorems related to existing conditions, partial derivatives, the double convolution theorem, and others are presented. …”
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Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem by Yongping Sun, Qian Sun, Xiaoping Zhang

“…The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.…”
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Successive Iteration and Positive Solutions for Nonlinear m-Point Boundary Value Problems on Time Scales by Yanbin Sang

“…Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.…”
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