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Abstract: We define and study approximate versions of σ-biflatness and σ-biprojectivity of a Banach algebra A where σ ∈Hom(A). We generalize the concepts pseudo amenability and pseudo contractibility via homomorphisms. We investigate their relations. PubDate: 2021-10-09

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Abstract: We prove a regularity theorem for the solutions of the Donaldson geometric flow equation on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. The minimal initial conditions lay in the Besov space \(B^{1,p}_{2}(M, {\varLambda }^{2})\) for p > 4. The Donaldson geometric flow was introduced by Simon Donaldson in Donaldson (Asian J. Math. 3, 1–16 1999). For a detailed exposition see Krom and Salamon (J. Symplectic Geom. 17, 381–417 2019). PubDate: 2021-10-02

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Abstract: We prove upper bounds for the graded Betti numbers of Stanley-Reisner rings of balanced simplicial complexes. Along the way we show bounds for Cohen-Macaulay graded rings S/I, where S is a polynomial ring and \(I\subseteq S\) is a homogeneous ideal containing a certain number of generators in degree 2, including the squares of the variables. Using similar techniques we provide upper bounds for the number of linear syzygies for Stanley-Reisner rings of balanced normal pseudomanifolds. Moreover, we compute explicitly the graded Betti numbers of cross-polytopal stacked spheres, and show that they only depend on the dimension and the number of vertices, rather than also the combinatorial type. PubDate: 2021-10-01

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Abstract: Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if and only if Ann(f) + I = R for all f ∈ I. If J is the trace of a projective R-module M, we prove that J is generated by the “coordinates” of M and JM = M. These lead to a few new results and alternative proofs for some known results. PubDate: 2021-09-30

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Abstract: Our goal is to give Schmidt’s subspace theorem for moving hypersurface targets in subgeneral position in projective varieties. PubDate: 2021-09-29

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Abstract: In this paper, we investigate maximal subgroups of an almost subnormal subgroup G in a division ring D whose center is infinite. Among results, we prove that if M is such a maximal subgroup, then M is abelian provided M is either locally finite or FC-group, and D is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup M in such a G. PubDate: 2021-09-27

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Abstract: We give an explicit description of all irreducible components and their dimensions of mixed commuting varieties over nilpotent 3 × 3 matrices, hence describing the varieties of 3-dimensional modules for certain quotients of polynomial algebras over an algebraically closed field. Our results also provide insights on support varieties of simple modules over Frobenius kernels of SL3. PubDate: 2021-09-22

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Abstract: Let D be a division ring with involution ⋆ and S the set of all symmetric elements of D. Assume that the center F of D is uncountable and K is a division subring of D containing F. The main aim of this note is to show that S is right algebraic over K if and only if so is D. This result allows us to construct an example of division rings K ⊂ D such that D is right algebraic but not left algebraic over K. PubDate: 2021-09-02

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Abstract: Let \(\mathfrak {p}\) be the defining ideal of the monomial curve \({\mathcal {C}}(2q+1, 2q+1+m, 2q+1+2m)\) in the affine space \(\mathbb {A}_{k}^{3}\) parameterised by (x2q+ 1,x2q+ 1+m,x2q+ 1 + 2m), where \(\gcd (2q+1,m)=1\) . In this paper we compute the resurgence of \(\mathfrak {p}\) , the Waldschmidt constant of \(\mathfrak {p}\) and the Castelnuovo-Mumford regularity of the symbolic powers of \(\mathfrak {p}\) . PubDate: 2021-09-01

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Abstract: In this paper, we compute the regularity and Hilbert series of symbolic powers of cover ideal of a graph G when G is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover ideals in terms of the number of edges. PubDate: 2021-09-01

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Abstract: This note is about a certain 16-dimensional family of surfaces of general type with pg = 2 and q = 0 and K2 = 1, called “special Horikawa surfaces”. These surfaces, studied by Pearlstein–Zhang and by Garbagnati, are related to K3 surfaces. We show that special Horikawa surfaces have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, the Chow ring of special Horikawa surfaces displays K3-like behavior. PubDate: 2021-09-01

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Abstract: We introduce, in this paper, the harmonic analysis associated with the Heckman-Opdam-Jacobi operator on \(\mathbb {R}^{d+1}\) in the W -invariant case. Next, we study the generalized wavelets and the generalized wavelet transform associated with this operator and we establish their properties. In particular, we prove for the generalized wavelet transform Plancherel and inversion formulas. PubDate: 2021-09-01

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Abstract: In this paper, we prove, for a fairly general class of domains, that the Bergman kernel of a domain is closely related to the normal derivative of the Szegő kernel. Such a result is useful in passing back and forth between estimates for the Bergman projection and estimates for the Szegő projection. We also make some remarks about comparability of the singularity of the Bergman kernel and the singularity of the Szegő kernel. PubDate: 2021-09-01

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Abstract: We prove the existence of pullback attractors in various spaces for the following non-autonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators on \(\mathbb {R}^{N}\) $$ \frac{\partial u}{\partial t}-\text{div}(\sigma(x) \nabla u ^{p-2}\nabla u)+\lambda u ^{p-2}u+f(u)=g(x,t), $$ under a new condition concerning a variable non-negative diffusivity σ(x), an arbitrary polynomial growth order of the non-linearity f, and an exponential growth of the external force. To overcome the essential difficulty arising due to the unboundedness of the domain, the results are proved by combining the tail estimates method and the asymptotic a priori estimate method. PubDate: 2021-09-01

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Abstract: We study the minimax properties and the artinianness of the generalized local cohomology modules \(H^{i}_{I,J}(M,N)\) with respect to a pair of ideals (I,J). We also show some results on top generalized local cohomology modules. PubDate: 2021-09-01

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Abstract: This paper is devoted to investigate implicit differential equations with boundary condition, which involves the composite fractional derivative in weighted space. The existence and uniqueness of the solution are obtained using the classic fixed point theorems. As an application, an example is presented to illustrate the main results. PubDate: 2021-09-01

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Abstract: In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of a split variational inequality and fixed point problem. Strong convergence of the iterative process is proved. In particular, the problem of finding a common solution to a variational inequality with pseudomonotone mapping and a fixed point problem involving demicontractive mapping is also studied. Besides, we get a strongly convergent algorithm for finding the minimum-norm solution to the split feasibility problem, which requires only two projections at each step. A simple numerical example is given to illustrate the proposed algorithm. PubDate: 2021-09-01

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Abstract: Given a fat point scheme \(\mathbb {W}=m_{1}P_{1}+\cdots +m_{s}P_{s}\) in the projective n-space \(\mathbb {P}^{n}\) over a field K of characteristic zero, the modules of Kähler differential k-forms of its homogeneous coordinate ring contain useful information about algebraic and geometric properties of \(\mathbb {W}\) when \(k\in \{1,\dots , n+1\}\) . In this paper, we determine the value of its Hilbert polynomial explicitly for the case k = n + 1, confirming an earlier conjecture. More precisely this value is given by the multiplicity of the fat point scheme \(\mathbb {Y} = (m_{1}-1)P_{1} + {\cdots } + (m_{s}-1)P_{s}\) . For n = 2, this allows us to determine the Hilbert polynomials of the modules of Kähler differential k-forms for k = 1,2,3, and to produce a sharp bound for the regularity index for k = 2. PubDate: 2021-09-01

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Abstract: An explicit expression for the Kohn-Nirenberg symbol of a Weyl-Heisenberg frame operator on \(L^{2}(\mathbb {R})\) is obtained directly from the Gabor atom coming from new classes of window functions. This new approach, using only elementary Fourier analysis, is independent of the theory of distributions and works strictly inside \(L^{2}(\mathbb {R})\) . Kohn-Nirenberg operators are introduced and are shown to be Weyl-Heisenberg frame operators in suitable cases. PubDate: 2021-09-01

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Abstract: In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents $$ \begin{array}{@{}rcl@{}} &&u_{tt}-M\left( \left\vert \nabla u\left( t\right) \right\vert^{2}\right) {\Delta} u+{{\int}_{0}^{t}}g\left( t-s\right) {\Delta} u\left( s\right) ds+\gamma_{1}u_{t}+\left\vert u_{t}\right\vert^{k\left( x\right) -1}u_{t}\\ &=&\left\vert u\right\vert^{p\left( x\right) -1}u \text{ in }{\Omega} \times \mathbb{R}^{+} \end{array} $$ with simply supported boundary condition, where Ω is a bounded domain of \(\mathbb {R}^{n}\) , g > 0 is a memory kernel that decays exponentially, and M(s) is a locally Lipschitz function. This kind of problem without the memory term when k(.) and p(.) are constants models viscoelastic Kirchhoff equation. PubDate: 2021-09-01