Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces. Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators. Moreover, some parameters are relaxed to accommodate a larger range of values for the step sizes. Under some mild conditions on the control parameters and without prior knowledge of the operator norms, we obtain strong convergence result for the proposed method. Finally, we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method. Several of the existing results in the literature could be viewed as special cases of our result in this paper. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data ρ0 without vacuum state. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract An extension of slant Hankel operator, namely, the k-th-order λ-slant Hankel operator on the Lebesgue space \(L^{2}(\mathbb{T}^{n})\) , where \(\mathbb{T}\) is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially k-th-order λ-slant Hankel operators on \(L^{2}(\mathbb{T}^{n})\) . PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we prove that for each positive k ≡ 1 mod m there exists a P-symmetric kmτ-periodic solution xk for asymptotically linear mτ-periodic Hamiltonian systems, which are nonautonomous and endowed with a P-symmetry. If the P-symmetric Hamiltonian function is semi-positive, one can prove, under a new iteration inequality of the Maslov-type P-index, that \({x_{{k_1}}}\) and \({x_{{k_2}}}\) are geometrically distinct for k1/k2 ≥ (2n + 1)m + 1; and \({x_{{k_1}}}\) , \({x_{{k_2}}}\) are geometrically distinct for k1/k2 ≥ m + 1 provided \({x_{{k_1}}}\) is non-degenerate. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball \({\mathbb{B}_2}\) . It is proved that each minimal reducing subspace M is finite dimensional, and if dim M ≥ 3, then M is induced by a monomial. Furthermore, the structure of commutant algebra \(\nu ({T_{\overline w {N_z}N}}): = {\{ M_{{w^N}}^ * {M_{{z^N}}},M_{{z^N}}^ * {M_{{w^N}}}\} ^\prime }\) is determined by N and the two dimensional minimal reducing subspaces of \({T_{\overline w {N_z}N}}\) . We also give some interesting examples. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously, but these existing methods may fail to be consistent for the setting with highly correlated covariates. In this paper, the semi-standard partial covariance (SPAC) method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates, and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions. Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Pseudo-differential operators (PDO) \(Q(x,{{\cal L}_{a,x}})\) and \({\cal Q}(x,{{\cal L}_{a,x}})\) involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space L 2 a (ℝ+;ma(x)dx) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on ℌ α,2 r are proven with the help of the Weinstein transform technique. PubDate: 2024-04-15

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements. Let Λ′, Λ, Λ″ be artin algebras such that (mod Λ′, mod Λ, mod Λ′) is a recollement, and let \(\cal{D}^{\prime}\) and \(\cal{D}^{\prime\prime}\) be subcategories of mod Λ′ and mod Λ″ respectively. For any n, m ≥ 0, under some conditions, we get \(\text{dim}\Omega^{k}(\cal{D})\leq \text{dim}\Omega^{n}(\cal{D}^{\prime})+\text{dim}\Omega^{m}(\cal{D}^{\prime\prime})+1\) , where k = max{m, n} and \(\cal{D}\) is the subcategory of mod Λ glued by \(\cal{D}^{\prime}\) and \(\cal{D}^{\prime\prime}\) ; moreover, we give a sufficient condition such that the converse inequality holds true. As applications, some results for Igusa–Todorov subcategories and syzygy finite subcategories are obtained. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Similar to Nomizu–Pinkall’s geometric characterization of the Cayley surface and Hu–Li–Zhang’s characterization of the Cayley hypersurface, how can one characterize the generalized Cayley hypersurfaces' In this paper, by the affine α-connection of statistical manifolds, we study affine hypersurfaces with parallel cubic form relative to the affine α-connection. As the main results, we complete the classification of such hypersurfaces if its affine metric is either definite, or Lorentzian with α ≠ −1. Moreover, we give a new characterization of the generalized Cayley hypersurfaces to answer the question. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Recurrent event data are commonly encountered in many scientific fields, including biomedical studies, clinical trials and epidemiological surveys, and many statistical methods have been proposed for their analysis. In this paper, we consider to use a weighted composite endpoint of recurrent and terminal events, which is weighted by the severity of each event, to assess the overall effects of covariates on the two types of events. A flexible additive-multiplicative model incorporating both multiplicative and additive effects on the rate function is proposed to analyze such weighted composite event process, and more importantly, the dependence structure among the recurrent and terminal events is left unspecified. For the estimation, we construct the unbiased estimating equations by virtue of the inverse probability weighting technique, and the resulting estimators are shown to be consistent and asymptotically normal under some mild regularity conditions. We evaluate the finite-sample performance of the proposed method via simulation studies and apply the proposed method to a set of real data arising from a bladder cancer study. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this article, we construct free centroid hom-associative algebras and free centroid hom-Lie algebras. We also construct some other relatively free centroid hom-associative algebras by applying the Gröbner–Shirshov basis theory for (unital) centroid hom-associative algebras. Finally, we prove that the “Poincaré–Birkhoff–Witt theorem” holds for certain type of centroid hom-Lie algebras over a field of characteristic 0, namely, every centroid hom-Lie algebra such that the eigenvectors of the map β linearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra, and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, the dynamics (including shadowing property, expansiveness, topological stability and entropy) of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view. It is shown that (1) if f is a hyperbolic endomor-phism then for each ε> 0 there exists a C1-neighborhood \({\cal U}\) of f such that the induced set-valued map \({F_{f,{\cal U}}}\) has the ε-shadowing property, and moreover, if f is an expanding endomorphism then there exists a C1-neighborhood \({\cal U}\) of f such that the induced set-valued map \({F_{f,{\cal U}}}\) has the Lipschitz shadowing property; (2) when a set-valued map F is generated by finite expanding endomorphisms, it has the shadowing property, and moreover, if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable; (3) if f is an expanding endomorphism then for each ε> 0 there exists a C1-neighborhood \({\cal U}\) of f such that \(h({F_{f,{\cal U}}},\varepsilon) = h(f)\) (4) when F is generated by finite expanding endomorphisms with no coincidence point, the entropy formula of F is given. Furthermore, the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let \(\{{{\boldsymbol{X}}_{ni}},{{\cal F}_{ni}};1 \le i \le n,\,\,n \ge 1\} \) be an array of \({\mathbb{R}^d}\) martingale difference random vectors and \(\{{{\boldsymbol{A}}_{ni}},1 \le i \le n,\,\,n \ge 1\} \) be an array of m × d matrices of real numbers. In this paper, the Marcinkiewicz–Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th (1 < p < 2) moments. Moreover, the complete convergence and strong law of large numbers are established under some mild conditions. An application to multivariate simple linear regression model is also provided. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we show the scattering of the radial solution for the nonlinear Schrödinger equation with combined power-type and Choquard-type nonlinearities $$\rm{i}u_{t}+\Delta u=\lambda_{1}\vert u\vert^{p_{1}-1}u+\lambda_{2}(I_{\alpha}\ast\vert u\vert^{p_{2}})\vert u\vert^{p_{2}-2}u.$$ in the energy space H1(ℝN) for λ1λ2 = −1. We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory. Results show that the defocusing perturbation terms does not determine the scattering solution in energy space. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality (DEHVI) which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space. First, by applying surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke’s subgradient, we show the nonempty of the solution set for the parabolic hemivariational inequality. Then, some topological properties of the solution set are established such as boundedness, closedness and convexity. Furthermore, we explore the upper semicontinuity of the solution mapping. Finally, we prove the solution set of the system (DEHVI) is nonempty and the set of all trajectories of (DEHVI) is weakly compact in C(I, X). PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we prove two supercongruences conjectured by Z.-W. Sun via the Wilf–Zeilberger method. One of them is, for any prime p > 3, $$_4{F_3}{\left[{\left. {\matrix{{{7 \over 6}} & {{1 \over 2}} & {{1 \over 2}} & {{1 \over 2}} \cr {} & {{1 \over 6}} & 1 & 1 \cr}} \right - {1 \over 8}} \right]_{{{p - 1} \over 2}}} \equiv p\left({{{- 2} \over p}} \right) + {{{p^3}} \over 4}\left({{2 \over p}} \right){E_{p - 3}}\,\,\,\,\,(\bmod \,\,{p^4}),$$ where \(({\cdot \over p})\) stands for the Legendre symbol, and En is the n-th Euler number. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this article, we consider the long-time behavior of extensible beams with nonlocal weak damping: \(\varepsilon(t)u_{tt}+\Delta^{2}u-m(\Vert\nabla u\Vert^{2})\Delta u+\Vert u_{t}\Vert^{p}u_{t}+f(u)=h\) , where ε(t) is a decreasing function vanishing at infinity. Within the theory of process on time-dependent spaces, we investigate the existence of the time-dependent attractor by using the Condition (Ct) method and more detailed estimates. The results obtained essentially improve and complete some previous works. PubDate: 2024-04-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝd with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝd, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived. PubDate: 2024-04-01