We prove that generalized loop spaces of Hartogs manifolds are Hilbert–Hartogs. We prove also that Hilbert–Hartogs manifolds possess a better extension properties than it is postulated in their definition. Finally, we give a list of examples of Hilbert–Hartogs manifolds.

Let \(S={\textsf {k}}[X_1,\dots , X_n]\) be a polynomial ring, where \({\textsf {k}}\) is a field. This article deals with the defining ideal of the Rees algebra of a squarefree monomial ideal generated in degree \(n-2\). As a consequence, we prove that Betti numbers of powers of the cover ideal of the complement graph of a tree do not depend on the choice of the tree. Further, we study the regularity

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

We use the notion of the optimal plan associated with the Fuglede p-modulus of a family of Borel measures to derive formulas for the p-modulus and the extremal function in many special cases. Among others, we deduce Rodin’s formula for a family of Hausdorff measures associated with leaves of a foliation defined by a single chart.

A connected Lie group admitting an expansive automorphism is known to be nilpotent, but not all nilpotent Lie groups admit expansive automorphisms. In this article, we find sufficient conditions for a class of nilpotent Lie groups to admit expansive automorphisms.

We show that the center set of reversible cubic systems, close to the symmetric Hamiltonian system \(x'=y, y'= x-x^3\), has two irreducible components of co-dimension two in the parameter space. One of them corresponds to the Hamiltonian stratum, the other to systems which are a polynomial pull back of an appropriate linear system.

A subgroup H of a group G is said to be complemented in G if there exists a subgroup K of G such that \(G=HK\) and \(H \cap K=1\). We prove that, for a locally soluble group G, all cyclic subgroups are complemented if and only if it is the semidirect product of groups \(A= {{\,\mathrm{Dr}\,}}_{i \in I} A_i\) by \(B={{\,\mathrm{Dr}\,}}_{j \in J} B_j\), where all factors \(A_i\) and \(B_j\) are finite

We discuss certain geometric properties for area stationary currents and currents with integrable mean curvature, so called “enclosure theorems”. As a consequence, we obtain non-existence results for currents with connected support. Finally, we extend these results to currents in submanifolds and state a non-existence result for stationary currents in spheres.

We consider the control problem of the heat equation on bounded and unbounded domains, and more generally the corresponding inhomogeneous equation for the Schrödinger semigroup. We show that if the sequence of null-controls associated to an exhaustion of an unbounded domain converges, then the solutions do in the same way, and that the control cost estimate carries over to the limiting problem on the

We consider Mergelyan sets and Farrell sets for \(H^p\)\((1\le p < \infty )\) spaces in the unit disc for both the weak topology and the norm topology, and give a short proof of a theorem of Pérez-González which answers a question proposed by Rubel and Stray (J Approx Theory 37:44–50, 1983).

An open problem about finite geometric progressions in syndetic sets leads to a family of diophantine equations related to the commutativity of translation and multiplication by squares.

We consider the Cauchy problem for the dissipative nonlinear Schrödinger equation with a cubic nonlinear term \(\lambda |u|^2u\), where \(\lambda \in {\mathbb {C}}\) with Im \(\lambda < 0\). We prove the global existence of a unique solution and obtain the uniform estimate in the Gevrey class. Using the uniform regularity estimate, we show the \(L^2\)-decay rate for the solution which has the Gevrey

The heart of a cotorsion pair, which is a generalization of the heart of a t-structure, has been proven to be abelian on triangulated, exact, and extriangulated categories. On the other hand, the heart of a twin cotorsion pair is not always abelian (it is only semi-abelian). In this article, we study a special kind of hearts of twin cotorsion pairs induced by d-cluster tilting subcategories. We will

We define Rankin–Selberg series on general linear groups and study its growth rate by counting lattice points.

It is well-known that the side length of a regular hexagon is half the length of its longest diagonals. From this property, one can easily see that for every positive integer \(m>1\), any regular 6m-gon contains two non-congruent diagonals that are commensurable. In this paper, we show that if n is not a multiple of 6, then all pairs of diagonals of different lengths of a regular n-gon are incommensurable

Let A be a positive bounded linear operator acting on a complex Hilbert space \({\mathcal {H}}\). Our aim in this paper is to prove some A-numerical radius inequalities of bounded linear operators acting on \({\mathcal {H}}\) when an additional semi-inner product structure induced by A is considered. In particular, an alternative proof of a recent result proved in Moslehian et al. (Linear Algebra Appl

We generalize results of Alladi, Dawsey, and Sweeting and Woo for Chebotarev densities to general densities of sets of primes. We show that if K is a number field and S is any set of prime ideals with natural density \(\delta (S)\) within the primes, then $$\begin{aligned} -\lim _{X \rightarrow \infty }\sum _{\begin{array}{c} 2 \le {\text {N}}(\mathfrak {a})\le X\\ \mathfrak {a} \in D(K,S) \end{array}}\frac{\mu

We generalize the recent work of Viazovska by constructing infinite families of Schwartz functions, suitable for Cohn–Elkies style linear programming bounds, using quasi-modular and modular forms. In particular, for dimensions \(d \equiv 0 \pmod {8}\), we give new constructions for obtaining sphere packing upper bounds via modular forms. In dimension 8 and 24, these exactly match the functions constructed

This note deals with the existence and uniqueness of a minimiser of the following Grötzsch type problem $$\begin{aligned} \inf _{f\in {\mathcal {F}}}\mathop {\iint }\limits _{Q_{1}}\psi ({\mathbb {K}}(z,f))dxdy \end{aligned}$$ under some conditions, where \({\mathcal {F}}\) denotes the set of all orientation preserving homeomorphisms f with the boundary correspondence. As an application, we consider

For a \(C^{\infty }\)-function f on \(\mathbb {R}\), \(S_n(f)\) denotes the n-th partial sum of the Taylor series of f with center at 0. Let \(f_1,f_2\) be two \(C^{\infty }\)-functions. We prove that even if the union \(\{S_n(f_1):n\in \mathbb {N}\}\cup \{S_n(f_2):n\in \mathbb {N}\}\) is dense in the space of continuous functions on \([-1,1]\) vanishing at 0 endowed with the topology of uniform convergence

We study the periodic \(L_2\)-discrepancy of point sets in the d-dimensional torus. This discrepancy is intimately connected with the root-mean-square \(L_2\)-discrepancy of shifted point sets, with the notion of diaphony, and with the worst-case error of cubature formulas for the integration of periodic functions in Sobolev spaces of mixed smoothness. In discrepancy theory, many results are based

In Emamirad et al. (in: Semigroups of Operators - Theory and Applications, Springer, 2014; and Proc. Amer. Math. Soc. 140:2043–2052, 2012), the Black–Scholes semigroup was studied in various Banach spaces of continuous functions regarding chaotic behavior and the null volatility limit. Here we let the volatility and the interest rates be continuous functions on the half line \([0,\infty )\), and we

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, we prove the Besse conjecture for compact manifolds with pinched Weyl curvature. Moreover, we shall conclude that such a conjecture is true if its Weyl curvature tensor and the

In this paper, we shall investigate a semilinear elliptic boundary blow-up problem \(\Delta u=a(x)|u|^{p-1}u+h(x)\) in \(\Omega \) and \(u|_{\partial \Omega }=\infty \), where \(\Omega \) is a smooth bounded domain of \(\mathbb {R}^{N}\). The weight a(x) and the nonhomogeneous term h(x) may be unbounded near the boundary. Furthermore, h(x) may change sign and a(x) may vanish in \(\Omega \). The existence

In this paper, we consider a truncated version of the Timoshenko beam model and we prove an inverse inequality in order to obtain the controllability of the total system. The present system is new in the control and stabilization setting according to recent contributions due to Almeida Júnior and Ramos (Z Angew Math Phys 68(145):31, 2017). The advantage here relies on mathematical results which do

We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle \(\frac{\pi }{2}\) on the space of continuous functions on a compact manifold with boundary.

In this paper, it is proved that the finite group G is solvable if cod\((\chi ) \le p_{\chi }\cdot \chi (1)\) for any nonlinear irreducible character \(\chi \) of G, where \(p_{\chi }\) is the largest prime divisor of \(|G:\mathrm{ker} \chi |\).

For a locally compact group G and \(1

We establish an estimate related to the \(H^1-BMO\) duality in the dyadic setting. Specifically, for any Hilbert space \({\mathcal {H}}\) over \({\mathbb {R}}\) and any functions \(\varphi ,\,\psi :{\mathbb {R}}\rightarrow {\mathcal {H}}\), we have $$\begin{aligned} \mathop {\int }\limits _{{\mathbb {R}}} \varphi \cdot \psi \,\text{ d }u\le \sqrt{2}\Vert \varphi \Vert _{H^1}\Vert \psi \Vert _{BMO}

We explicitly calculate the cohomologies of all G-lattices, where G is the Kleinian 4-group.

For a smooth projective quadric X, Alexander Vishik introduced the notion of connections. He discovered connections arising from the splitting pattern of X as well as the so-called excellent connections. Recently, Victor Petrov and Nikita Semenov found new connections arising from the J-invariantJ(X), which is a layer of the elementary discrete invariant\(ED(X)\), both further Vishik’s inventions.

Let D be a commutative domain with identity, and let \({\mathcal {L}}(D)\) be the lattice of nonzero ideals of D. Say that D is ideal upper finite provided \({\mathcal {L}}(D)\) is upper finite, that is, every nonzero ideal of D is contained in but finitely many ideals of D. Now let \(\kappa >2^{\aleph _0}\) be a cardinal. We show that a domain D of cardinality \(\kappa \) is ideal upper finite if

Let P be a positive rational number. A function \(f:\mathbb {R}\rightarrow \mathbb {R}\) has the finite gaps property mod P if the following holds: for any positive irrational \(\alpha \) and positive integer M, when the values of \(f(m\alpha )\), \(1\le m\le M\), are inserted mod P into the interval [0, P) and arranged in increasing order, the number of distinct gaps between successive terms is bounded

Let L be the generalized mixed product ideal induced by a monomial ideal I. We characterize the unmixed generalized mixed product ideals. Furthermore, we show that I is normal if and only if L is normal.

For every prime \(p\ge 5\), we give examples of Beauville p-groups whose Beauville structures are never strongly real. This shows that there are nilpotent purely non-strongly real Beauville groups. On the other hand, we determine infinitely many Beauville 2-groups which are purely strongly real. This answers two questions formulated by Fairbairn (Arch Math. https://doi.org/10.1007/s00013-018-1288-4)

We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.

Let G be a connected reductive algebraic group over an algebraically closed field k. We consider the strata in G defined by Lusztig as fibers of a map given in terms of truncated induction of Springer representations. We elaborate on the existing proof of the following two results in order to show that it extends to arbitrary characteristic: Lusztig’s strata are locally closed and the irreducible components

Given any group G, the multiple holomorph \(\mathrm {NHol}(G)\) is the normalizer of the holomorph \(\mathrm {Hol}(G) = \rho (G)\rtimes \mathrm {Aut}(G)\) in the group of all permutations of G, where \(\rho \) denotes the right regular representation. The quotient \(T(G) = \mathrm {NHol}(G)/\mathrm {Hol}(G)\) has order a power of 2 in many of the known cases, but there are exceptions. We shall give

Let d be a non-square positive integer such that the period of the continued fraction expansion of \(\sqrt{d}\) is even. We give some relations between some properties of partial quotients of the continued fraction expansion of \(\sqrt{d}\), which emerge from numerical experiments.

Let \({\mathscr {G}}\) be the class of all finite groups and consider the function \(\psi '':{\mathscr {G}}\longrightarrow (0,1]\), given by \(\psi ''(G)=\frac{\psi (G)}{|G|^2}\), where \(\psi (G)\) is the sum of element orders of a finite group G. In this paper, we show that the image of \(\psi ''\) is a dense set in [0, 1]. Also, we study the injectivity and the surjectivity of \(\psi ''\).

For unital \(C^*\)-algebras A and B, we completely characterize the isometric (\(*\)-) automorphisms of their Banach space projective tensor product \(A\otimes ^\gamma B\). This leads to the characterization of inner and outer isometric \(*\)-automorphisms of \(A\otimes ^\gamma B\) as well. As an application, we provide a partial affirmative answer to a question posed by Kaijser and Sinclair, viz.

We prove the following theorem. Let G be a finite group generated by unitary reflections in a complex Hermitian space \(V={\mathbb {C}}^\ell \) and let \(G'\) be any reflection subgroup of G. Let \({\mathcal {H}}={\mathcal {H}}(G)\) be the space of G-harmonic polynomials on V. There is a degree preserving isomorphism \(\mu :{\mathcal {H}}(G')\otimes {\mathcal {H}}(G)^{G'}\overset{\sim }{{\longrightarrow

We characterize the blocks of finite group algebras with the property that the radical of their center is an ideal in the block. We also consider related properties of blocks of symmetric algebras and of group algebras.

We introduce a wide class of bounded Hartogs domains in \({\mathbb {C}}^n\), which contains some generalizations of the classical Hartogs triangle. A sharp criterion for the \(L^p-L^q\) boundedness of the Toeplitz operator with the symbol \(K^{-t}\) is obtained on these domains, where K is the Bergman kernel on the diagonal and \(t\ge 0\). It generalizes the results by Beberok and Chen in the case

We show that, for any n ≠ 2, most orientation preserving homeomorphisms of the sphere S2n have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do not have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere S2n+1 have a Cantor set of fixed points for any