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Abstract: Abstract In this paper, we extend the concept of s-convexity from the case where the functions are with real variables to the case where the functions are with operator arguments. Afterwards, we investigate some related properties and operator inequalities. As an application, some inequalities of Hermite-Hadamard and Jensen types involving some operator means are established. PubDate: 2023-12-23

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Abstract: Abstract In this paper, we construct Carathéodory type and exponential Carathéodory type schemes for Caputo stochastic fractional differential equations (CSFDEs) of order \(\alpha \in (\frac{1}{2},1)\) in \(L^p\) spaces with \(p \ge 2\) whose coefficients satisfy a standard Lipschitz and a linear growth bound conditions. The strong convergence and the convergence rate of these schemes are also established. PubDate: 2023-12-19

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Abstract: Abstract Let \((R,\mathfrak m,\Bbbk )\) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by \(\mathfrak m\) ; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R/J and compute a partial DG algebra structure on this resolution. We provide the full DG algebra structure in the appendix. We use the products on this resolution to study the Tor algebra of such trimmed ideals and we use the information obtained to prove that recent conjectures of Christensen, Veliche and Weyman on ideals of class \(\textbf{G}\) hold true in our context. Furthermore, we address the realizability question for ideals of class \(\textbf{G}\) . PubDate: 2023-12-13

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Abstract: Abstract The purpose of this paper is to characterize Noetherian local rings \((R, \mathfrak {m})\) such that the Chern numbers of certain \(\mathfrak {m}\) -primary ideals in R are bounded above or range among only finitely many values. Consequently, we characterize the Gorensteinness, Cohen-Macaulayness, and generalized Cohen-Macaulayness of local rings in terms of the behavior of their Chern numbers. PubDate: 2023-12-05

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Abstract: Abstract Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when $$ \{\mathfrak {p}\in {\text {Spec}} (R)\,:\, \mathcal {F}^{E_{\mathfrak {p}}}\text { is finitely generated as a ring over its degree zero piece}\} $$ is an open set in the Zariski topology, where \(\mathcal {F}^{E_{\mathfrak {p}}}\) denotes the Frobenius algebra attached to the injective hull of the residue field of \(R_{\mathfrak {p}}.\) We show that this is true when R is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so. PubDate: 2023-12-05

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Abstract: Abstract In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction. PubDate: 2023-12-01

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Abstract: This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the \(\varepsilon \) -weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the \(\varepsilon \) -weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques. PubDate: 2023-12-01

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Abstract: Abstract Let G be a finite simple connected graph on the vertex set \(V(G)=[d]=\{1,\dots ,d\}\) with edge set \(E(G)=\{e_{1},\dots , e_{n}\}\) . Let \(\mathbb {K}[\textbf{t}]=\mathbb {K}[t_{1},\dots ,t_{d}]\) be the polynomial ring in d variables over a field \(\mathbb {K}\) . The edge ring of G is the affine semigroup ring \(\mathbb {K}[G]\) generated by monomials \(\textbf{t}^{e}:=t_{i}t_{j}\) , for \(e=\{i,j\} \in E(G)\) . In this paper, we will prove that, given integers d and n, where \(d\ge 7\) and \(d+1\le n\le \frac{d^{2}-7d+24}{2}\) , there exists a finite simple connected graph G with \( V(G) =d\) and \( E(G) =n\) , such that \(\mathbb {K}[G]\) is non-normal and satisfies \((S_{2})\) -condition. PubDate: 2023-12-01

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Abstract: Abstract In this paper, we use composite ring extensions to construct a new class of Noetherian rings. Composite ring extensions are examples of pullback constructions, and they are useful in constructing of (counter)-examples. PubDate: 2023-11-11 DOI: 10.1007/s40306-023-00516-2

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Abstract: Abstract This paper is concerned with the inverse medium scattering problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data. PubDate: 2023-11-06 DOI: 10.1007/s40306-023-00513-5

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Abstract: Abstract A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on Hankel matrices. Inversion of the natural parametrization is known as Padé approximation. We study the dimension and defining ideals of Taylor varieties. Taylor hypersurfaces are interesting for projective geometry, since their Hessians tend to vanish. In three and more variables, there exist defective Taylor varieties whose dimension is smaller than the number of parameters. We explain this with Fröberg’s Conjecture in commutative algebra. PubDate: 2023-11-03 DOI: 10.1007/s40306-023-00514-4

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Abstract: Abstract In this paper, we provide the structure of Hopf graphs associated to pairs \((G, \mathfrak {r})\) consisting of groups G together with ramification datas \(\mathfrak {r}\) and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data \(\mathfrak {r}\) and G. PubDate: 2023-09-19 DOI: 10.1007/s40306-023-00511-7

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Abstract: Abstract We study the exploration of an Erdös-Rényi random graph by a respondent-driven sampling method, where discovered vertices reveal their neighbors. Some of them receive coupons to reveal in their turn their own neighborhood. This leads to the study of a Markov chain on the random graph that we study. For sparse Erdös-Rényi graphs of large sizes, this process correctly renormalized converges to the solution of a deterministic curve, solution of a system of ODEs absorbed on the abscissa axis. The associated fluctuation process is also studied, providing a functional central limit theorem, with a Gaussian limiting process. Simulations and numerical computation illustrate the study. PubDate: 2023-09-12 DOI: 10.1007/s40306-023-00510-8

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Abstract: Abstract In this paper, we investigate local derivations and local generalized derivations on path algebras associated with finite acyclic quivers. We show that every local derivation on a path algebra is a derivation, and every local generalized derivation on a path algebra is a generalized derivation. Also, we apply main results on several related maps to local derivations. The established results generalize several ones on some known algebras such as incidence algebras. PubDate: 2023-09-01 DOI: 10.1007/s40306-023-00499-0

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Abstract: Abstract In this note, we give some results on maximal subextensions of plurisubharmonic functions on hyperconvex domains in \(\mathbb C^n\) and introduce the notion about cone of maximal subextensions of plurisubharmonic functions. Furthermore, we establish the invariant of this cone through proper holomorphic surjections. PubDate: 2023-08-05 DOI: 10.1007/s40306-023-00509-1

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Abstract: Abstract Motivated by the Jacobian problem, this article is concerned with the density of the image set \(F( \mathbb {Z}^n)\) of polynomial maps \(F\in \mathbb {Z}[X_1,\dots ,X_n]^n\) with \(\det DF\equiv 1\) . It is shown that if such a map F is not invertible, its image set \(F( \mathbb {Z}^n)\) must be very thin in the lattice \( \mathbb {Z}^n\) : (1) for almost all lines l in \( \mathbb {Z}^n\) the numbers \(\texttt {\#}(F^{-1}(l) \cap \mathbb {Z}^n)\) are uniformly bounded; (2) \(\texttt {\#}\{ z\in F( \mathbb {Z}^n): \vert z_i\vert \le B\} \ll B^{n-1}\) as \(B\rightarrow +\infty \) , where the implicit constants depend on F. PubDate: 2023-07-25 DOI: 10.1007/s40306-023-00504-6

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Abstract: Abstract In this paper we prove the existence of initial data satisfying the constraint equations corresponding to the 1+3 formulation of asymptotically flat spherically symmetric Einstein-Vlasov-Maxwell system, when the charge of the particles is either low or large, the initial distribution function is compactly supported, the shift vector is non-zero and the isotropic metric ansatz is not diagonal. This result extends the work (Rein and Rendall, Commun. Math. Phys. 150(3), 561–583 1992) concerning the existence of solutions to the constraint equations for chargeless particles. PubDate: 2023-07-19 DOI: 10.1007/s40306-023-00507-3

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Abstract: Abstract In this work, we propose a new method for solving a bilevel split variational inequality problem (BSVIP) in Hilbert spaces. The proposed method is inspired by the subgradient extragradient method for solving a monotone variational inequality problem. A strong convergence theorem for an algorithm for solving such a BSVIP is proved without knowing any information of the Lipschitz and strongly monotone constants of the mappings. Moreover, we do not require any prior information regarding the norm of the given bounded linear operator. Special cases are considered. Two numerical examples are given to illustrate the performance of our algorithm. PubDate: 2023-07-18 DOI: 10.1007/s40306-023-00508-2

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Abstract: Abstract In this paper, we establish a decomposition theorem for strong martingale Hardy space \(sH_p^\sigma \) , which is based on its atomic decomposition theorem. By using of this decomposition theorem, we investigate the real interpolation spaces between \(sH_p^\sigma \;(0<p\le 1)\) and \(sL_2\) . Furthermore, with the help of the decomposition theorem and the real interpolation method, a sufficient condition to ensure the boundedness of a sublinear operator defined on strong martingale Hardy-Lorentz spaces is given. PubDate: 2023-07-17 DOI: 10.1007/s40306-023-00505-5

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Abstract: Abstract We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the PDE under consideration. To find this fixed point, we define a recursive sequence with an arbitrary initial term using the same manner as in the proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution. On the other hand, we also show that our method delivers reliable solutions even when the given data are noisy. Numerical examples are presented. PubDate: 2023-04-20 DOI: 10.1007/s40306-023-00500-w