Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM by Reza Abazari, Adem Kılıcman

“…We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮(𝑡)=𝑓(𝑡,𝐮(𝑡),𝐮(𝑡)) and subject to initial conditions 𝐮(𝑎)=𝐮0,𝐮(𝑎)=𝐮1 and boundary conditions 𝐮(𝑎)=𝐮0,𝐮(𝑏)=𝐮1, where 𝐮0,𝐮1∈𝑅𝑟×𝑞. …”
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Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations by Mujeeb Ur Rehman, Rahmat Ali Khan

“…We study existence of positive solutions to nonlinear higher-order nonlocal boundary value problems corresponding to fractional differential equation of the type 𝑐𝒟𝛿0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0, 𝑡∈(0,1), 0<𝑡<1. 𝑢(1)=𝛽𝑢(𝜂)+𝜆2, 𝑢(0)=𝛼𝑢(𝜂)−𝜆1, 𝑢(0)=0, 𝑢(0)=0⋯𝑢(𝑛−1)(0)=0, where, 𝑛−1<𝛿<𝑛, 𝑛(≥3)∈ℕ, 0<𝜂,𝛼,𝛽<1, the boundary parameters 𝜆1,𝜆2∈ℝ+ and 𝑐𝐷𝛿0+ is the Caputo fractional derivative. …”
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Convergence of Locally Square Integrable Martingales to a Continuous Local Martingale by Andriy Yurachkivsky

“…It is assumed that the discontinuities of 𝑋𝑛 are in a sense asymptotically small as 𝑛→∞ and the relation 𝖤(𝑓(⟨𝑧𝑋𝑛⟩(𝑡))|ℱ𝑛(𝑠))−𝑓(⟨𝑧𝑋𝑛⟩(𝑡))𝖯→0 holds for all 𝑡>𝑠>0, row vectors 𝑧, and bounded uniformly continuous functions 𝑓. …”
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Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities by Xionghua Wu, Yeong-Cheng Liou, Zhitao Wu, Pei-Xia Yang

“…Let {𝑡𝑛}⊂(0,1) be such that 𝑡𝑛→1 as 𝑛→∞, let 𝛼 and 𝛽 be two positive numbers such that 𝛼+𝛽=1, and let 𝑓 be a contraction. …”
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On the Abstract Subordinated Exit Equation by Hassen Mejri, Ezzedine Mliki

“…Let ℙ=(𝑃𝑡)𝑡>0 be a 𝐶0-contraction semigroup on a real Banach space ℬ. …”
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A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components by Louis Aimé Fono, Gilbert Njanpong Nana, Maurice Salles, Henri Gwet

“…This enables us to determine necessary and sufficient conditions on a 𝒯-transitive IFR 𝑅 under which a strict component of 𝑅 satisfies pos-transitivity and negative transitivity.…”
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A Nice Separation of Some Seiffert-Type Means by Power Means by Iulia Costin, Gheorghe Toader

“…We add to these inequalities two new results obtaining the following nice chain of inequalities 𝒜0<ℒ<𝒜1/2<𝒫<𝒜1<ℳ<𝒜3/2<𝒯<𝒜2, where the power means are evenly spaced with respect to their order.…”
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Inversion of the Laplace Transform from the Real Axis Using an Adaptive Iterative Method by Sapto W. Indratno, Alexander G. Ramm

“…This method is based on a quadrature formula. We assume that the unknown function 𝑓(𝑡) is continuous with (known) compact support. …”
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Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations by Delin Wu

“…Assuming 𝑓=𝑓(𝑥,𝑡)∈𝐿2loc((0,𝑇);𝐷(𝐴−1/2)), we establish the existence of the uniform attractors in 𝐷(𝐴1/2) and 𝐷(𝐴). …”
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Existence of Positive Solutions to Singular 𝑝-Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity by Qiying Wei, You-Hui Su, Subei Li, Xing-Xue Yan

“…These results are new even for the corresponding differential (𝕋=ℝ) and difference equations (𝕋=ℤ), as well as in general time scales setting. …”
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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {𝑇(𝑡)}𝑡≥0). …”
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Oscillation for a Nonlinear Dynamic System with a Forced Term on Time Scales by Xinli Zhang, Shanliang Zhu

“…Our results not only unify the oscillation of two-dimensional differential systems and difference systems but also improve the oscillation results that have been established by Saker, 2005, since our results are not restricted to the case where b(t)≠0 for all t∈𝕋 and g(u)=u. …”
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The 𝐶-Version Segal-Bargmann Transform for Finite Coxeter Groups Defined by the Restriction Principle by Stephen Bruce Sontz

“…We apply a special case, the restriction principle (for which we give a definition simpler than the usual one), of a basic result in functional analysis (the polar decomposition of an operator) in order to define 𝐶𝜇,𝑡, the 𝐶-version of the Segal-Bargmann transform, associated with a finite Coxeter group acting in ℝ𝑁 and a given value 𝑡>0 of Planck's constant, where 𝜇 is a multiplicity function on the roots defining the Coxeter group. …”
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Left Baire-1 Compositors and Continuous Functions by Jonald P. Fenecios, Emmanuel A. Cabral

“…Moreover, based on the above result we provide a new proof that the class of functions ℬ𝒮,𝒯 where 𝒮 is the class of all positive continuous functions and 𝒯 is the class of all positive constants as defined in the work by Bakowska and Pawlak (2010) is exactly the class of all continuous functions.…”
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Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations by Rong Cheng, Jianhua Hu

“…The existence of multiple periodic solutions of the following differential delay equation 𝑥(𝑡)=−𝑓(𝑥(𝑡−𝑟)) is established by applying variational approaches directly, where 𝑥∈ℝ, 𝑓∈𝐶(ℝ,ℝ) and 𝑟>0 is a given constant. …”
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Investigation of a CDDW Hamiltonian to Explore Possibility of Magneto-Quantum Oscillations in Electronic Specific Heat of Hole-Doped Cuprates by Partha Goswami, Manju Rani

“…For ́𝜀=0, with the chemical potential 𝜇=−0.27 eV for 10% doping level and |𝑣0|≥|𝑡| (where |𝑡|=0.25 eV is the first neighbor hopping), at zero/non-zero magnetic field (𝐵), the FS on the first Brillouin zone is found to correspond to electron pockets around antinodal regions and barely visible patches around nodal regions. …”
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Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source by R. T. Al-Khairy, Z. M. AL-Ofey

“…Laser heating is modeled as an internal heat source, whose capacity is given by 𝑔(𝑥,𝑡)=𝐼(𝑡)(1−𝑅)𝜇𝑒−𝜇𝑥 while the semi-infinite body has insulated boundary. …”
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Multiplication Operators between Lipschitz-Type Spaces on a Tree by Robert F. Allen, Flavia Colonna, Glenn R. Easley

“…Let ℒ be the space of complex-valued functions 𝑓 on the set of vertices 𝑇 of an infinite tree rooted at 𝑜 such that the difference of the values of 𝑓 at neighboring vertices remains bounded throughout the tree, and let ℒ𝐰 be the set of functions 𝑓∈ℒ such that |𝑓(𝑣)−𝑓(𝑣−)|=𝑂(|𝑣|−1), where |𝑣| is the distance between 𝑜 and 𝑣 and 𝑣− is the neighbor of 𝑣 closest to 𝑜. …”
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A Limit Theorem for Random Products of Trimmed Sums of i.i.d. Random Variables by Fa-mei Zheng

“…Under some suitable conditions, we show that (∏[𝑛𝑡]𝑘=1(𝑇𝑘(𝑎)/𝜇𝑘))𝜇/𝑉𝑛𝑑∫→exp{𝑡0(𝑊(𝑥)/𝑥)𝑑𝑥}𝑖𝑛𝐷[0,1], as 𝑛→∞, where 𝑇𝑘(𝑎)=𝑆𝑘−𝑆𝑘(𝑎) is the trimmed sum and {𝑊(𝑡);𝑡≥0} is a standard Wiener process.…”
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Preirradiation Graft Polymerization of Styrene in a Poly(tetrafluoroethylene) Film Investigated by Time-Resolved Small-Angle Neutron Scattering by Hiroki Iwase, Shin-ichi Sawada, Tetsuya Yamaki, Yasunari Maekawa, Satoshi Koizumi

“…SANS elucidated that graft polymerization proceeds by two reaction processes (I) and (II). In process (I) at 0<𝑡<200 min, graft polymerization occurs at an interface between crystalline and amorphous PTFE domains and the grafted polystyrene segregates from PTFE, forming a thin layer with a sharp interface. …”
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