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Pre-Schwarzian and Schwarzian norm estimates for subclasses of univalent functions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-20 Xiaoyuan Wang, Huijie Li, Jinhua Fan
In the present article, we are focused to study the sharp estimates of the pre-Schwarzian and Schwarzian norms for subclasses of univalent functions. We will generalize the results of Carrasco and Hernández (Anal Math Phys 13(2):22, 2023) to the case of Janowski convex mappings in terms of the value \(h^{\prime \prime }(0)\). We will also derive the sharp bound of pre-Schwarzian norm for a subclass
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Uniqueness and stability of nonnegative solutions for a class of nonpositone problems in a ball Monatshefte Math. (IF 0.9) Pub Date : 2024-04-11 Hajar Chahi, Said Hakimi
In this article, we study the uniqueness and stability of nonnegative solutions for a class of semilinear elliptic problems in a ball, when the nonlinearity has more than one zero, negative at the origin and concave.
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Weighted periodic and discrete pseudo-differential Operators Monatshefte Math. (IF 0.9) Pub Date : 2024-04-11 Aparajita Dasgupta, Lalit Mohan, Shyam Swarup Mondal
In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class \(M_{\rho , \Lambda }^m({\mathbb {T}}\times {\mathbb {Z}})\) (associated to a suitable weight function \(\Lambda \) on \({\mathbb {Z}}\)) by deriving formulae for the asymptotic sums, composition, adjoint, transpose. We also construct the parametrix of M-elliptic pseudo-differential
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Well-posedness and non-uniform dependence on initial data for the Fornberg–Whitham-type equation in Besov spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-04-09 Xueyuan Qi
In this paper, we first establish the local well-posedness for the Fornberg–Whitham-type equation in the Besov spaces \(B^{s}_{p,r}({\mathbb {R}})\) with \( 1\le p,r\le \infty \) and \(s> max\{1+\frac{1}{p},\frac{3}{2}\}\), which improve the previous work in Sobolev spaces \( H^{s}({\mathbb {R}})= B^{s}_{2,2}({\mathbb {R}})\) with \( s>\frac{3}{2}\) (Lai and Luo in J Differ Equ 344:509–521, 2023).
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On the Gauss-Kuzmin-Lévy problem for nearest integer continued fractions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-09 Florin P. Boca, Maria Siskaki
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Hardy’s uncertainty principle for Gabor transform on compact extensions of $$\mathbb {R}^n$$ Monatshefte Math. (IF 0.9) Pub Date : 2024-04-08 Kais Smaoui
We prove in this paper a generalization of Hardy’s theorem for Gabor transform in the setup of the semidirect product \(\mathbb {R}^n\rtimes K\), where K is a compact subgroup of automorphisms of \(\mathbb {R}^n\). We also solve the sharpness problem and thus obtain a complete analogue of Hardy’s theorem for Gabor transform. The representation theory and Plancherel formula are fundamental tools in
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On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations Monatshefte Math. (IF 0.9) Pub Date : 2024-04-08 Harald Grobner, Sonja Žunar
In this paper we describe several new aspects of the foundations of the representation theory of the space of smooth-automorphic forms (i.e., not necessarily \(K_\infty \)-finite automorphic forms) for general connected reductive groups over number fields. Our role model for this space of smooth-automorphic forms is a “smooth version” of the space of automorphic forms, whose internal structure was
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Some questions about complex harmonic functions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-07 Luis E. Benítez-Babilonia, Raúl Felipe
In this paper, we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here, we begin the study of the iterations of the functions of this class showing briefly its potential to be a topic of future research. In parallel, we define and study composition operators on a Hardy type space denoted
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Explicit solution for a Sea-Breeze flow model with special viscosity functions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-07 Zhuohao Li, JinRong Wang
In this paper, we are concerned with determining the explicit solution of a Sea-Breeze flow model by selecting a special viscosity function. Firstly, we examine the exact solution when the viscosity function is related to a nonnegative constant coefficient. Further, by employing suitable transformations and forcing terms, we transform the original second order differential equation corresponding to
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Multiplicity results for system of Pucci’s extremal operator Monatshefte Math. (IF 0.9) Pub Date : 2024-04-06
Abstract This article deals with the existence of multiple positive solutions to the following system of nonlinear equations involving Pucci’s extremal operators: $$\begin{aligned} \left\{ \begin{aligned} -\mathcal {M}_{\lambda _1,\Lambda _1}^+(D^2u_1)&=f_1(u_1,u_2,\dots ,u_n)~~~{} & {} \textrm{in}~~\Omega ,\\ -\mathcal {M}_{\lambda _2,\Lambda _2}^+(D^2u_2)&=f_2(u_1,u_2,\dots ,u_n)~~~{} & {} \textrm{in}~~\Omega
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Minimal extensions in smooth dynamics Monatshefte Math. (IF 0.9) Pub Date : 2024-04-06
Abstract A classical result of Fathi and Herman from 1977 states that a smooth compact connected manifold without boundary admitting a locally free action of a 1-torus, respectively, an almost free action of a 2-torus, admits a minimal diffeomorphism, respectively, a minimal flow. In the first part of our paper we study the existence of locally free and almost free actions of tori on homogeneous spaces
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Unique double base expansions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-06
Abstract For two real bases \(q_0, q_1 > 1\) , we consider expansions of real numbers of the form \(\sum _{k=1}^{\infty } i_k/(q_{i_1}q_{i_2}\ldots q_{i_k})\) with \(i_k \in \{0,1\}\) , which we call \((q_0,q_1)\) -expansions. A sequence \((i_k)\) is called a unique \((q_0,q_1)\) -expansion if all other sequences have different values as \((q_0,q_1)\) -expansions, and the set of unique \((q_0,q_1)\)
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A measurable spectral decomposition Monatshefte Math. (IF 0.9) Pub Date : 2024-04-05 Bomi Shin
introduce the spectral decomposition property for measures and prove that a homeomorphism has the spectral decomposition property if and only if every Borel probability measure has the property too. Furthermore, we show that all shadowable measures for expansive homeomorphisms have the spectral decomposition property. Additionally, we provide illustrative examples relevant to these results.
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Magic squares, the symmetric group and Möbius randomness Monatshefte Math. (IF 0.9) Pub Date : 2024-04-04 Ofir Gorodetsky
Diaconis and Gamburd computed moments of secular coefficients in the CUE ensemble. We use the characteristic map to give a new combinatorial proof of their result. We also extend their computation to moments of traces of symmetric powers, where the same result holds but in a wider range. Our combinatorial proof is inspired by gcd matrices, as used by Vaughan and Wooley and by Granville and Soundararajan
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Monotonicity of the period map for the equation $$-\varphi ''+\varphi -\varphi ^{k}=0$$ Monatshefte Math. (IF 0.9) Pub Date : 2024-04-04 Giovana Alves, Fábio Natali
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Counting geodesics on compact symmetric spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-04-02
Abstract We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting in the tangent space at the basepoint. We show how their dimensions (infinitesimal data) and connected components (topological data) are encoded in the
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Blow-up, global existence and propagation speed for a modified Camassa–Holm equation both dissipation and dispersion in $$H^{s,p}(\mathbb {R})$$ Monatshefte Math. (IF 0.9) Pub Date : 2024-04-02
Abstract In this essay, we investigate the blow-up scenario, global solution and propagation speed for a modified Camassa–Holm (MCH) equation both dissipation and dispersion in Sobolev space \(H^{s,p} (\mathbb {R})\) , \(s\ge 1\) , \(p\in (1,\infty )\) . First of all, by the mathematical induction of index s, we establish the precise blow-up criteria, which extends the result obtained by Gui et al
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Stability of singular solutions to the b-family of equations Monatshefte Math. (IF 0.9) Pub Date : 2024-04-02 Shou-Jun Huang, Li-Fan Wu
In this paper, we first construct some explicit solutions to the b-family of equations, which will become unbounded in a finite time. Then, we investigate the asymptotic stability of the aforementioned singular solutions of the b-family of equations in the Sobolev space \(H^s\) with \(s>\frac{7}{2}\). It is also interesting to point out that this stability highly depends on the values of parameter
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New contributions to a complex system of quadratic heat equations with a generalized kernels: global solutions Monatshefte Math. (IF 0.9) Pub Date : 2024-04-01 Sarah Otsmane, Abdelaziz Mennouni
In this work, we propose new contributions to a complex system of quadratic heat equations with a generalized kernel of the form: \(\partial _t z=\mathfrak {L}\,z+ \widetilde{z}^{2},\;\partial _t \widetilde{z}=\mathfrak {L}\,\widetilde{z}+ z^2,\;t>0,\) with initial conditions \(z_{0}=u_0+v_0,\;\widetilde{z}_{0}=\widetilde{u}_0+\widetilde{v}_0\), and \(\mathfrak {L}\) is a linear operator with \(e^{t\mathcal
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On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations Monatshefte Math. (IF 0.9) Pub Date : 2024-03-30
Abstract We deal with a class of nonlocal Fokker–Planck equations subject to nonlinear force fields and perturbations, where the questions of global solvability and regularity of solutions will be addressed. A representation of solutions to the Cauchy problem is first derived. Then by using the embeddings of fractional Sobolev spaces and fixed point arguments, we show the existence and Hölder regularity
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On profinite groups admitting a word with only few values Monatshefte Math. (IF 0.9) Pub Date : 2024-03-30 Pavel Shumyatsky
A group-word w is called concise if the verbal subgroup w(G) is finite whenever w takes only finitely many values in a group G. It is known that there are words that are not concise. The problem whether every word is concise in the class of profinite groups remains wide open. Moreover, there is a conjecture that every word w is strongly concise in profinite groups, that is, w(G) is finite whenever
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Weighted distribution approach for a class of nonlinear elliptic equations associated to Schrödinger-type operators Monatshefte Math. (IF 0.9) Pub Date : 2024-03-30 Minh-Phuong Tran, Thanh-Nhan Nguyen, Quang-Vinh Tran, Phuoc-Nguyen Huynh
This paper makes a contribution to the field of regularity theory for a class of nonlinear elliptic equations associated with Schrödinger-type operators with potential belonging to a certain reverse Hölder class. Inspired by a very recent paper (Lee and Ok in \(L^{q}\)-regularity for nonlinear elliptic equations with Schrödinger-type lower order terms, arXiv:2108.13779) on the \(L^p\)-regularity estimates
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Small time characterization of heat kernels in a weighted setting Monatshefte Math. (IF 0.9) Pub Date : 2024-03-30 Tan Duc Do, Le Xuan Truong, Nguyen Ngoc Trong
We provide a small time characterization for the Gaussian bounds on the heat kernel of the \(C_0\)-semigroup generated by a second-order degenerate elliptic operator on the weighted Lebesgue space \(L^2_w(\mathbb {R}^d)\), where w belongs to the class \(\mathcal {A}_1\) of Muckenhoupt weights. The result extends (Elst in Proc Am Math Soc 134:707–714, 2005, Thereom 1) to a weighted setting.
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Well-posedness of short time solutions and non-uniform dependence on the initial data for a shallow water wave model in critical Besov space Monatshefte Math. (IF 0.9) Pub Date : 2024-03-30 Changtai Zhou, Honglin Xiao, Shaoyong Lai
A nonlinear shallow water wave equation containing the famous Degasperis-Procesi and Fornberg-Whitham equations is investigated. The well-posedness of short time solutions is established to illustrate that the solution map of the equation is continuous in the critical Besov space \(B^{1}_{\infty ,1}(\mathbb {R})\). Using the methods to construct high and low frequency functions, we prove that the solution
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Wave-breaking phenomena for a new weakly dissipative quasilinear shallow-water waves equation Monatshefte Math. (IF 0.9) Pub Date : 2024-03-28 Xiaofang Dong, Xianxian Su, Kai Wang
In this paper, we mainly study a new weakly dissipative quasilinear shallow-water waves equation, which can be formally derived from a model with the effect of underlying shear flow from the incompressible rotational two-dimensional shallow water in the moderately nonlinear regime by Wang, Kang and Liu (Appl Math Lett 124:107607, 2022). Considering the dissipative effect, the local well-posedness of
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New results on spectral synthesis Monatshefte Math. (IF 0.9) Pub Date : 2024-03-13 László Székelyhidi
In our former paper we introduced the concept of localization of ideals in the Fourier algebra of a locally compact Abelian group. It turns out that localizability of a closed ideal in the Fourier algebra is equivalent to the synthesizability of the annihilator of that closed ideal which corresponds to this ideal in the measure algebra. This equivalence provides an effective tool to prove synthesizability
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Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions Monatshefte Math. (IF 0.9) Pub Date : 2024-03-12 Guangshi Lü, Qiang Ma
We describe a new method to obtain upper bounds for exponential sums with multiplicative coefficients without the Ramanujan conjecture. We verify these hypothesis for (with mild restrictions) the Rankin–Selberg L-functions attached to two cuspidal automorphic representations.
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On a construction method of new moment sequences Monatshefte Math. (IF 0.9) Pub Date : 2024-03-05 Seunghwan Baek, Hayoung Choi, Seonguk Yoo
In this paper we provide a way to construct new moment sequences from a given moment sequence. An operator based on multivariate positive polynomials is applied to get new moment sequences. A class of new sequences is corresponding to a unique symmetric polynomial; if this polynomial is positive, then the new sequence becomes again a moment sequence. We will see for instance that a new sequence generated
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Spectrum of self-affine measures on the Sierpinski family Monatshefte Math. (IF 0.9) Pub Date : 2024-02-29
Abstract In this study, a spectrum \(\Lambda \) for the integral Sierpinski measures \(\mu _{M, D}\) with the digit set \( D= \left\{ \begin{pmatrix} 0\\ 0 \end{pmatrix}, \begin{pmatrix} 1\\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \end{pmatrix}\right\} \) is derived for a \(2 \times 2\) diagonal matrix M with entries as \(3\ell _1\) and \(3\ell _4\) and for off-diagonal matrix M with both the off-diagonal
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a-Weyl’s theorem and hypercyclicity Monatshefte Math. (IF 0.9) Pub Date : 2024-02-29 Ying Liu, Xiaohong Cao
Let H be a complex infinite dimensional Hilbert space, B(H) be the algebra of all bounded linear operators acting on H, and \(\overline{HC(H)}\) \((\overline{SC(H)})\) be the norm closure of the class of all hypercyclic operators (supercyclic operators) in B(H). An operator \(T\in B(H)\) is said to be with hypercyclicity (supercyclicity) if T is in \(\overline{HC(H)}\) \((\overline{SC(H)})\). Using
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A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations Monatshefte Math. (IF 0.9) Pub Date : 2024-02-21 Jaroslav Jaroš
A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity
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On polynomials in primes, ergodic averages and monothetic groups Monatshefte Math. (IF 0.9) Pub Date : 2024-02-17 Jaroslav Hančl, Radhakrishnan Nair, Jean-Louis Verger-Gaugry
Let G denote a compact monothetic group, and let \(\rho (x) = \alpha _k x^k + \ldots + \alpha _1 x + \alpha _0\), where \(\alpha _0, \ldots , \alpha _k\) are elements of G one of which is a generator of G. Let \((p_n)_{n\ge 1}\) denote the sequence of rational prime numbers. Suppose \(f \in L^{p}(G)\) for \(p> 1\). It is known that if $$\begin{aligned} A_{N}f(x):= {1 \over N} \sum _{n=1}^{N} f(x +
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Pair correlation of real-valued vector sequences Monatshefte Math. (IF 0.9) Pub Date : 2024-02-04 Sneha Chaubey, Shivani Goel
In this article, we investigate the fine-scale statistics of real-valued arithmetic sequences. In particular, we focus on real-valued vector sequences, generalizing previous works of Boca et al. and the first author on the local statistics of integer-valued and rational-valued vector sequences, respectively. As the main results, we prove the Poissonian behavior of the pair correlation function for
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Zero-filter limit issue for the Camassa–Holm equation in Besov spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-02-04 Yuxing Cheng, Jianzhong Lu, Min Li, Xing Wu, Jinlu Li
In this paper, we focus on zero-filter limit problem for the Camassa-Holm equation in the more general Besov spaces. We prove that the solution of the Camassa-Holm equation converges strongly in \(L^\infty (0,T;B^s_{2,r}(\mathbb {R}))\) to the inviscid Burgers equation as the filter parameter \(\alpha \) tends to zero with the given initial data \(u_0\in B^s_{2,r}(\mathbb {R})\). Moreover, we also
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The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of sech $$^2$$ solutions Monatshefte Math. (IF 0.9) Pub Date : 2024-02-01 Bashar Khorbatly
In the context of the initial data and an amplitude parameter \(\varepsilon \), we establish a local existence result for a highly nonlinear shallow water equation on the real line. This result holds in the space \(H^k\) as long as \(k>5/2\). Additionally, we illustrate that the threshold time for the occurrence of wave breaking in the surging type is on the order of \(\varepsilon ^{-1},\) while plunging
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Aron–Berner extensions of almost Dunford–Pettis multilinear operators Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30 Geraldo Botelho, Luis Alberto Garcia
We study when Aron–Berner extensions of (separately) almost Dunford–Pettis multilinear operators between Banach lattices are (separately) almost Dunford–Pettis. For instance, for a \(\sigma \)-Dedekind complete Banach lattice F containing a copy of \(\ell _\infty \), we characterize the Banach lattices \(E_1, \ldots , E_m\) for which every continuous m-linear operator from \(E_1 \times \cdots \times
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Linear and bilinear Fourier multipliers on Orlicz modulation spaces Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30 Oscar Blasco, Serap Öztop, Rüya Üster
Let \(\Phi _i, \Psi _i\) be Young functions, \(\omega _i\) be weights and \(M^{\Phi _i,\Psi _i}_{\omega _i}(\mathbb {R} ^{d})\) be the corresponding Orlicz modulation spaces for \(i=1,2,3\). We consider linear (respect. bilinear) multipliers on \(\mathbb {R} ^{d}\), that is bounded measurable functions \(m(\xi )\) (respect. \(m(\xi ,\eta )\)) on \(\mathbb {R} ^{d}\) (respect. \(\mathbb {R} ^{2d}\))
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Sharp bounds of nodes for Sturm–Liouville equations Monatshefte Math. (IF 0.9) Pub Date : 2024-01-30
Abstract A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the \(L^1\) norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem
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Quadratic Crofton and sets that see themselves as little as possible Monatshefte Math. (IF 0.9) Pub Date : 2024-01-29
Abstract Let \(\Omega \subset \mathbb {R}^2\) and let \(\mathcal {L} \subset \Omega \) be a one-dimensional set with finite length \(L =|\mathcal {L}|\) . We are interested in minimizers of an energy functional that measures the size of a set projected onto itself in all directions: we are thus asking for sets that see themselves as little as possible (suitably interpreted). Obvious minimizers of the
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Existence and regularity results for some nonlinear singular parabolic problems with absorption terms Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Mounim El Ouardy, Youssef El Hadfi, Abdelaaziz Sbai
In this paper, we prove the existence of a nonnegative solution to nonlinear parabolic problems with two absorption terms and a singular lower order term. More precisely, we analyze the interaction between the two absorption terms and the singular term to get a solution for the largest possible class of the data. Also, the regularizing effect of absorption terms on the regularity of the solution of
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Existence and stability for a nonlinear model describing arctic gyres Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Jin Zhao
This paper is concerned with the bounded solutions for a nonlinear second-order differential equation with asymptotic conditions and boundary condition which arise from the study of Arctic gyres. In the case of Lipschitz continuous nonlinearities, we prove the existence, uniqueness and stability of the bounded solution. An existence result for the general nonlinear vorticity term is also obtained.
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On lattice extensions Monatshefte Math. (IF 0.9) Pub Date : 2024-01-27 Maxwell Forst, Lenny Fukshansky
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Wave-breaking and persistence properties in weighted $$L^p$$ spaces for a Camassa–Holm type equation with quadratic and cubic nonlinearities Monatshefte Math. (IF 0.9) Pub Date : 2024-01-25 Wenguang Cheng, Ji Lin
We consider the Cauchy problem of a Camassa–Holm type equation with quadratic and cubic nonlinearities. We establish a new sufficient condition on the initial data that leads to the wave-breaking for this equation. Moreover, we obtain the persistence results of solutions for the equation in weighted \(L^p\) spaces.
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Groups in which all involutions are 3-transvections Monatshefte Math. (IF 0.9) Pub Date : 2024-01-25 Egle Bettio, Enrico Jabara
Let G be a group which is generated by the set of its involutions, and assume that the set of integers which occur as orders of products of two involutions in G is \(\{1,2,3,4\}\). It is shown that \(G\simeq \textrm{PSL}(2,7)\) or \(G\simeq \textrm{PSU}(3,3)\) or G is a \(\{2,3\}\)-group and \(G/O_{2}(G) \simeq S_{3}\).
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On the deductive strength of the Erdős–Dushnik–Miller theorem and two order-theoretic principles Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24 Eleftherios Tachtsis
We provide answers to open questions from Banerjee and Gopaulsingh (Bull Pol Acad Sci Math 71: 1–21, 2023) about the relationship between the Erdős–Dushnik–Miller theorem (\(\textsf{EDM}\)) and certain weaker forms of the Axiom of Choice (\(\textsf{AC}\)), and we properly strengthen some results from Banerjee and Gopaulsingh (2023). We also settle a part of an open question of Lajos Soukup (stated
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Uniform density topology Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24
Abstract Main results of the paper are: the Lebesgue Density Theorem does not hold for the uniform density points and the uniform density topology is completely regular.
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A sharp two-weight estimate for the maximal operator under a bump condition Monatshefte Math. (IF 0.9) Pub Date : 2024-01-24 Adam Osękowski
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On some special subspaces of a Banach space, from the perspective of best coapproximation Monatshefte Math. (IF 0.9) Pub Date : 2024-01-23
Abstract We study the best coapproximation problem in Banach spaces, by using Birkhoff–James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets–Klee
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Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit Monatshefte Math. (IF 0.9) Pub Date : 2024-01-22 Jinlu Li, Yanghai Yu, Weipeng Zhu
In this short note, we prove that given initial data \(u_0\in H^s(\mathbb {R})\) with \(s>\frac{3}{2}\) and for some \(T>0\), the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in \(L^\infty (0,T;H^s(\mathbb {R}))\) to the inviscid Burgers equation as the filter parameter \(\alpha \) tends to zero. This is a complement of our recent result on the
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On spectral measures and convergence rates in von Neumann’s Ergodic theorem Monatshefte Math. (IF 0.9) Pub Date : 2024-01-22
Abstract We show that the power-law decay exponents in von Neumann’s Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value 1. In this work we also prove that, under an assumption of weak convergence, in the absence of a spectral gap, the convergence rates of the time-average in von Neumann’s Ergodic Theorem depend on sequences of time
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A central limit theorem for integer partitions into small powers Monatshefte Math. (IF 0.9) Pub Date : 2023-12-15 Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy
The study of the well-known partition function p(n) counting the number of solutions to \(n = a_{1} + \dots + a_{\ell }\) with integers \(1 \le a_{1} \le \dots \le a_{\ell }\) has a long history in number theory and combinatorics. In this paper, we study a variant, namely partitions of integers into $$\begin{aligned} n=\left\lfloor a_1^\alpha \right\rfloor +\cdots +\left\lfloor a_\ell ^\alpha \right\rfloor
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Solvability of some integro-differential equations with the double scale anomalous diffusion in higher dimensions Monatshefte Math. (IF 0.9) Pub Date : 2023-12-13 Vitali Vougalter, Vitaly Volpert
The article is devoted to the studies of the existence of solutions of an integro-differential equation in the case of the double scale anomalous diffusion with the sum of the two negative Laplacians raised to two distinct fractional powers in \({\mathbb R}^{d}, \ d=4, 5\). The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for the non-Fredholm elliptic
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Some inequalities for self-mappings of unit ball satisfying the invariant Laplacians Monatshefte Math. (IF 0.9) Pub Date : 2023-11-27 Deguang Zhong, Meilan Huang, Dongping Wei
In this paper, we study those mappings in unit ball satisfying the Dirichlet problem of the following differential operators $$\begin{aligned} \Delta _{\gamma }=\big (1-|x|^{2}\big )\cdot \left[ \frac{1-|x|^{2}}{4}\cdot \sum _{i}\frac{\partial ^{2}}{\partial x_{i}^{2}}+\gamma \sum _{i}x_{i}\cdot \frac{\partial }{\partial x_{i}}+\gamma \left( \frac{n}{2}-1-\gamma \right) \right] . \end{aligned}$$ Our
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Strong tree properties, Kurepa trees, and guessing models Monatshefte Math. (IF 0.9) Pub Date : 2023-11-25 Chris Lambie-Hanson, Šárka Stejskalová
We investigate the generalized tree properties and guessing model properties introduced by Weiß and Viale, as well as natural weakenings thereof, studying the relationships among these properties and between these properties and other prominent combinatorial principles. We introduce a weakening of Viale and Weiß’s Guessing Model Property, which we call the Almost Guessing Property, and prove that it
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Cohomology of quasi-abelianized braid groups Monatshefte Math. (IF 0.9) Pub Date : 2023-11-24 Filippo Callegaro, Ivan Marin
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Infinite products involving the period-doubling sequence Monatshefte Math. (IF 0.9) Pub Date : 2023-11-24 John M. Campbell
We explore the evaluation of infinite products involving the automatic sequence \((d_{n}: n \in \mathbb {N}_{0})\) known as the period-doubling sequence, inspired by the work of Allouche, Riasat, and Shallit on the evaluation of infinite products involving the Thue–Morse or Golay–Shapiro sequences. Our methods allow for the application of integral operators that result in new product expansions for
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A short note on coproducts of Abelian pro-Lie groups Monatshefte Math. (IF 0.9) Pub Date : 2023-11-19 Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo
The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.
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A Voronoi summation formula for non-holomorphic Maass forms of half-integral weight Monatshefte Math. (IF 0.9) Pub Date : 2023-11-18 Olga Balkanova, Dmitry Frolenkov
We prove a Voronoi summation formula for non-holomorphic half-integral weight Maass forms on \(\Gamma _0(4)\) without any restrictions on the denominator of a fraction in the exponential function. As an application we obtain a Voronoi summation formula for the values of Zagier L-series.
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An extension of Aigner’s theorem Monatshefte Math. (IF 0.9) Pub Date : 2023-11-18 Nguyen Xuan Tho
In 1957, Aigner (Monatsh Math 61:147–150, 1957) showed that the equations \(x^6+y^6=z^6\) and \(x^9+y^9=z^9\) have no solutions in any quadratic number field with \(xyz\ne 0\). We show that Aigner’s result holds for all equations \(x^{3n}+y^{3n}=z^{3n}\), where \(n\ge 2\) is a positive integer. The proof combines Aigner’s idea with deep results on Fermat’s equation and its variants.
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Eigenvalues of truncated unitary matrices: disk counting statistics Monatshefte Math. (IF 0.9) Pub Date : 2023-11-16 Yacin Ameur, Christophe Charlier, Philippe Moreillon