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Description of the symmetric $$H_q$$ -Laguerre–Hahn orthogonal q-polynomials of class one Period. Math. Hung. (IF 0.8) Pub Date : 2024-03-06 Sobhi Jbeli
We study the \(H_{q}\)-Laguerre–Hahn forms u, that is to say those satisfying a q-quadratic q-difference equation with polynomial coefficients (\(\Phi , \Psi , B\)): \( H_{q}(\Phi (x)u) +\Psi (x) u+B(x) \, \big (x^{-1}u(h_{q}u)\big )=0,\) where \(h_q u\) is the form defined by \(\langle h_{q} u,f\rangle =\langle u, f(qx)\rangle \) for all polynomials f and \(H_{q}\) is the q-derivative operator. We
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Linear independence on simple abelian varieties Period. Math. Hung. (IF 0.8) Pub Date : 2024-02-22 Duc Hiep Pham
In this paper, we establish new results on complex and p-adic linear independence on general simple abelian varieties defined over the field of algebraic numbers \(\overline{{\mathbb {Q}}}\). In particular, these results extend some previous results on that concerning elliptic curves and simple abelian varieties with complex multiplication defined over \(\overline{{\mathbb {Q}}}\).
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Spanning trees of $$K_{1,4}$$ -free graphs whose reducible stems have few leaves Period. Math. Hung. (IF 0.8) Pub Date : 2024-02-19 Pham Hoang Ha, Le Dinh Nam, Ngoc Diep Pham
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On the q-statistical convergence of double sequences Period. Math. Hung. (IF 0.8) Pub Date : 2024-01-19 Mohammad Mursaleen, Sabiha Tabassum, Ruqaiyya Fatma
In this paper, we study q-statistical convergence for double sequences. The definitions of q-analog of statistical Cauchy and statistical pre-Cauchy for double sequences are given. The necessary and sufficient condition for a double sequence to have different statistical limits is also obtained. We show that a q-statistical convergent sequence is q-statistical Cauchy and vice-versa.
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Non-vanishing and cofiniteness of generalized local cohomology modules Period. Math. Hung. (IF 0.8) Pub Date : 2024-01-02 Tran Tuan Nam, Nguyen Minh Tri
In this paper, we show some results on the non-vanishing of the generalized local cohomology modules \(H^i_I(M,N)\). In a Cohen–Macaulay local ring \((R,\mathop {\mathfrak {m}})\), we prove, by using induction on \(\dim N\), that if M, N are two finitely generated R-modules with \({\text {id}}\,M<\infty \) and \({\text {Gid}}\,N<\infty \), then \(H^{\dim R-grade _R({\text {Ann}}_RN,M)}_{\mathop {\mathfrak
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On the boundedness of general partial sums Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-24 Vakhtang Tsagareishvili
From S. Banach’s results it follows that even for the function \(f(x)=1\) \((x\in [0,1])\) the general partial sums of its general Fourier series are not bounded a.e. on [0, 1]. In the present paper, we find conditions for the functions \(\varphi _n\) of an orthonormal system \((\varphi _n\)) under which the partial sums of functions from some differentiable class are bounded. We prove that the obtained
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Bifurcation and hybrid control in a discrete predator–prey model with Holling type-IV functional response Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-16 Wenxian Zhang, Shengfu Deng
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Sums of divisors on arithmetic progressions Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-15 Prapanpong Pongsriiam
For each \(s\in {\mathbb {R}}\) and \(n\in {\mathbb {N}}\), let \(\sigma _s(n) = \sum _{d\mid n}d^s\). In this article, we study the number of sign changes in the difference \(\sigma _s(an+b)-\sigma _s(cn+d)\) where a, b, c, d, s are fixed, the vectors (a, b) and (c, d) are linearly independent over \({\mathbb {Q}}\), and n runs over all positive integers. We also give several examples and propose
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On a class of Lebesgue-Ramanujan-Nagell equations Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-14 Azizul Hoque
We deeply investigate the Diophantine equation \(cx^2+d^{2m+1}=2y^n\) in integers \(x, y\ge 1, m\ge 0\) and \(n\ge 3\), where c and d are coprime positive integers satisfying \(cd\not \equiv 3 \pmod 4\). We first solve this equation for prime n under the condition \(\gcd (n, h(-cd))=1\), where \(h(-cd)\) denotes the class number of the imaginary quadratic field \({\mathbb {Q}}(\sqrt{-cd})\). We then
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Extensions of a Diophantine triple by adjoining smaller elements II Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-14 Mihai Cipu, Andrej Dujella, Yasutsugu Fujita
Let \(\{a_1,b,c\}\) and \(\{a_2,b,c\}\) be Diophantine triples with \(a_1
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The ascending chain condition on principal right ideals for semigroup constructions Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-14 Craig Miller
We call a semigroup \({\mathcal {R}}\)-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on \({\mathcal {R}}\)-classes. We investigate the behaviour of the property of being \({\mathcal {R}}\text {-noetherian}\) under the following standard semigroup-theoretic constructions: semidirect products, Schützenberger products
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On some maximal and minimal sets Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-12 Jin-Hui Fang, Xue-Qin Cao
A set A of positive integers is called 3-free if it contains no 3-term arithmetic progression. Furthermore, such A is called maximal if it is not properly contained in any other 3-free set. In 2006, by confirming a question posed by Erdős et al., Savchev and Chen proved that there exists a maximal 3-free set \(\{a_1
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The c-differential uniformity of the perturbed inverse function via a trace function $$ {{\,\textrm{Tr}\,}}\big (\frac{x^2}{x+1}\big )$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-09 Kübra Kaytancı, Ferruh Özbudak
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On Greenberg’s conjecture for certain real biquadratic fields Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-09 Abdelakder El Mahi, M’hammed Ziane
In this paper, we give the structure of the Iwasawa module \(X=X(k_{\infty })\) of the \(\mathbb {Z}_{2}\)-extension of infinitely many real biquadratic fields k. Denote by \(\lambda , \mu \) and \(\nu \) the Iwasawa invariants of the cyclotomic \(\mathbb {Z}_{2}\)-extension of k. Then \(\lambda =\mu =0 \) and \(\nu =2\).
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A degenerate Kirchhoff-type problem involving variable $$s(\cdot )$$ -order fractional $$p(\cdot )$$ -Laplacian with weights Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-07 Mostafa Allaoui, Mohamed Karim Hamdani, Lamine Mbarki
This paper deals with a class of nonlocal variable s(.)-order fractional p(.)-Kirchhoff type equations: $$\begin{aligned} \left\{ \begin{array}{ll} {\mathcal {K}}\left( \int _{{\mathbb {R}}^{2N}}\frac{1}{p(x,y)}\frac{|\varphi (x)-\varphi (y)|^{p(x,y)}}{|x-y|^{N+s(x,y){p(x,y)}}} \,dx\,dy\right) (-\Delta )^{s(\cdot )}_{p(\cdot )}\varphi (x) =f(x,\varphi ) \quad \text{ in } \Omega , \\ \varphi =0 \quad
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On Three Problems of Y.–G. Chen Period. Math. Hung. (IF 0.8) Pub Date : 2023-12-07 Yuchen Ding
In this short note, we answer two questions of Chen and Ruzsa negatively and answer a question of Ma and Chen affirmatively.
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On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods Period. Math. Hung. (IF 0.8) Pub Date : 2023-11-23 Teshome Bayleyegn, István Faragó, Ágnes Havasi
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A regular Tóth identity and a Menon-type identity in residually finite Dedekind domains Period. Math. Hung. (IF 0.8) Pub Date : 2023-11-24 Tianfang Qi
In this paper, we define the s-dimensional regular generalized Euler function and give a variant of Tóth’s identity in residually finite Dedekind domains, which can be viewed as a multidimensional version of the results by Wang, Zhang, Ji (2019) and Ji, Wang (2020).
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Inverse results for restricted sumsets in $${\mathbb {Z}/p\mathbb {Z}}$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-11-22 Mario Huicochea
Let p be a prime, A and B be subsets of \({\mathbb {Z}/p\mathbb {Z}}\) and S be a subset of \(A\times B\). We write \(A{{\mathop {+}\limits ^{S}}}B:=\{a+b:\;(a,b)\in S\}\). In the first inverse result of this paper, we show that if \(\left| A{{\mathop {+}\limits ^{S}}}B\right| \) and \(|(A\times B)\setminus S|\) are small, then A has a big subset with small difference set. In the second theorem of
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Unlimited accumulation by Shelah’s PCF operator Period. Math. Hung. (IF 0.8) Pub Date : 2023-11-14 Mohammad Golshani
Modulo the existence of large cardinals, there is a model of set theory in which, for some set B of regular cardinals, the sequence \(\langle \textrm{pcf}^\alpha (B): \alpha \in \textrm{Ord}\rangle \) is strictly increasing. The result answers a question from Tsukuura (Tsukuba J Math 45(2):83–95, 2021).
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On Arestov’s inequalities concerning the Shur–Szegő composition of polynomials Period. Math. Hung. (IF 0.8) Pub Date : 2023-11-11 Mudassir A. Bhat, Ravinder Kumar, Suhail Gulzar
In this paper, a wide range of Bernstein-type polynomial inequalities involving the Hardy space norm, obtained over the last thirty years, is derived directly from Arestov’s inequalities concerning the Shur–Szegő composition of polynomials.
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Singular value and norm inequalities for products and sums of matrices Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-23 Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
In this paper, we give singular value and norm inequalities involving convex functions of positive semidefinite matrices. Our results generalize some known inequalities for the spectral norm and for the Schatten p-norms for \( p\ge 1\).
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Ringel–Hall polynomials associated to a quiver of type $${\tilde{D}}_{4}$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-19 Csaba Szántó, István Szöllősi
Let k be a finite field and Q an acyclic quiver of tame type \({\tilde{D}}_{4}\). Consider the path algebra kQ and the category of finite-dimensional right modules \(\textrm{mod}\)-kQ. We determine all Ringel–Hall polynomials associated to indecomposable modules in \(\textrm{mod}\)-kQ.
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Metric convolution and frames Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-16 R. Pasupathi, M. A. Navascués, A. K. B. Chand, R. N. Mohapatra
The fractal convolution of two mappings is a binary operation in some space of functions. In previous papers we extracted the main properties of this association and defined a new type of inner operations in metric spaces, not necessarily linked to fractal theory. This operation has been called metric convolution, though it does not agree with the classical convolution of functions. In this paper we
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A class of wide neighborhood interior-point algorithms based on the algebraic equivalent transformation technique with specific functions Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-15 Jianbin Wang, Jianhua Yuan, Wenbao Ai
In this paper, we generalize the identity function and the square root function used in the algebraic equivalent transformation (AET) technique to a class of AET functions with an arbitrary positive integer parameter p. Based on this class of AET functions, we propose a class of wide neighborhood primal–dual interior-point algorithms for linear programming. For each function in this class of AET functions
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Parallel covering a rhombus with squares Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-11 Chen-Yang Su, Xue Li
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Frucht’s theorem in Borel setting Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-11 Onur Bilge, Burak Kaya
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Asymptotics on a class of $${\mathcal {S}}$$ -unit integers Period. Math. Hung. (IF 0.8) Pub Date : 2023-09-14 Florian Luca, Pantelimon Stănică
In this paper we consider a (non)congruence generalizing the so-called good/bad numbers introduced by Moree (Acta Arith LXXX 3:197–212, 1997) and give asymptotics for their counting functions. In addition, we give heuristics for some conjectured bounds on primes belonging to such a class.
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A special family of non-symmetric semi-classical forms of class one Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-22 Mohamed Zaatra
A form (linear functional) v is called regular if there exists a sequence of polynomials \(\{S_{n}\}_{n\ge 0}\), \(\deg (S_{n})=n\), which is orthogonal with respect to v. \(\{S_{n}\}_{n\ge 0}\) is fully characterized by the following recurrence relation: \(S_{n+2}(x)=(x-\beta _{n+1})S_{n+1}(x)-\gamma _{n+1}S_{n}(x)\), \(n\ge 0\), with \(S_{0}(x)=1\), \(S_{1}(x)=x-\beta _{0}\) and \(\gamma _{n+1}\ne
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On relations between partial moduli of smoothness in mixed metrics Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-23 B. V. Simonov, A. A. Jumabayeva
In this paper we obtain Ulyanov-type inequalities between partial moduli of smoothness of positive orders in mixed metrics.
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A measure-theoretic representation of graphs Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-21 Raffaella Mulas, Giulio Zucal
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Existence and nonexistence results for fractional mixed boundary value problems via a Lyapunov-type inequality Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-18 Barbara Łupińska
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A new small Dowker space Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-17 Assaf Rinot, Roy Shalev, Stevo Todorcevic
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Bounded meromorphic functions on the complex 2-disc Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-17 János Kollár
We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.
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On the number of weighted zero-sum subsequences Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-16 A. Lemos, B. K. Moriya, A. O. Moura, A. T. Silva
Let G be a finite additive abelian group with exponent \(d^kn, d,n>1,\) and k a positive integer. For a sequence S over G and \(A=\{1,2,\ldots ,d^kn-1\}\setminus \{d^kn/d^i:i\in [1,k]\}, \) we investigate the lower bound of the number \(N_{A,0}(S)\), which denotes the number of A-weighted zero-sum subsequences of S. In particular, we prove that \(N_{A,0}(S)\ge 2^{|S|-D_A(G)+1},\) where \(D_A(G)\) is
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Tiltan and graphs with no infinite paths Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-14 Shimon Garti
We prove the consistency of tiltan with the positive relation \(\omega ^*\cdot \omega _1 \rightarrow (\omega ^*\cdot \omega _1,\text {infinite path})^2\).
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A Munn type representation for DRC-restriction semigroups Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-12 Shoufeng Wang
The class of P-Ehresmann semigroups has been proposed by Jones as a common generalization of the classes of Ehresmann semigroups and regular \(^*\)-semigroups, and the class of DRC semigroups introduced by Stokes contains the class of P-Ehresmann semigroups as a proper subclass. Jones has introduced P-ample conditions for P-Ehresmann semigroups by which P-restriction semigroups are distinguished from
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The exceptional set for integers of the form $$[p_1^c]+[p_2^c]$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-12 Roger Baker
Let \(1< c < 24/19\). We show that the number of integers \(n \le N\) that cannot be written as \([p_1^c] + [p_2^c]\) (\(p_1\), \(p_2\) primes) is \(O(N^{1-\sigma +\varepsilon })\). Here \(\sigma \) is a positive function of c (given explicitly) and \(\varepsilon \) is an arbitrary positive number.
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On perfect powers that are sum of two balancing numbers Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-09 Pritam Kumar Bhoi, Sudhansu Sekhar Rout, Gopal Krishna Panda
Let \(B_k\) denote the k-th term of balancing sequence. In this paper we find all positive integer solutions of the Diophantine equation \(B_n+B_m = x^q\) in variables (m, n, x, q) under the assumption \(n\equiv m \pmod 2\). Furthermore, we study the Diophantine equation $$\begin{aligned}B_n^{3}\pm B_m^{3} = x^q\end{aligned}$$ with positive integer \(q\ge 3\) and \(\gcd (B_n, B_m) =1\).
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New characterizations of ruled real hypersurfaces in complex projective space Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-10 Juan de Dios Pérez, David Pérez-López
We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections. For any nonnull constant k and any symmetric tensor field of type (1, 1) L on M, we can define two tensor fields of type (1, 2) on M, \(L_F^{(k)}\) and \(L_T^{(k)}\), related to both connections. We study the behaviour of the structure operator \(\phi \) with respect
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On the consecutive k-free values for certain classes of polynomials Period. Math. Hung. (IF 0.8) Pub Date : 2023-08-10 Haihong Fan, Wenguang Zhai
In the present paper we propose an asymptotic formula for R(H, k), the number of triples of positive integers \(x, y, z\le H\) such that \(x^{2}+ y^{2}+ z^{2}+ 1, x^{2}+ y^{2}+ z^{2}+ 2\) are k-free with \(k\ge 2.\) Especially, in the case of \(k= 2\) we prove that \(R(H, 2)= \sigma _{2} H^{3}+ O(H^{9/4+ \varepsilon }),\) where \(\sigma _{2}\) is an absolute constant and \(\varepsilon \) is an arbitrary
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On the denominators of harmonic numbers, III Period. Math. Hung. (IF 0.8) Pub Date : 2023-06-09 Xiao-Hui Yan, Bing-Ling Wu
Let \(H_n=1+1/2 +1/3 +\cdots +1/n\) be the n-th harmonic number and let \(v_n\) be its denominator. Let S be the set of positive integers n such that \(v_n\) is not equal to the least common multiple of \(1, 2, \dots , n\). In this paper, we obtain lower bounds for asymptotic densities \(\underline{d}(S)\) and \(\overline{d}(S)\).
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Regularity and symbolic defect of points on rational normal curves Period. Math. Hung. (IF 0.8) Pub Date : 2023-06-05 Iman Bahmani Jafarloo, Grzegorz Malara
In this paper we study ideals of points lying on rational normal curves defined in projective plane and projective 3-space. We give an explicit formula for the value of Castelnuovo–Mumford regularity for their ordinary powers. Moreover, we compare the m-th symbolic and ordinary powers for such ideals in order to show whenever the m-th symbolic defect is non-zero.
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On integer values of sum and product of three positive rational numbers Period. Math. Hung. (IF 0.8) Pub Date : 2023-06-05 M. Z. Garaev
In 1997 we proved that if n is of the form $$\begin{aligned} 4k, \quad 8k-1\quad {\textrm{or}} \quad 2^{2m+1}(2k-1)+3, \end{aligned}$$ where \(k,m\in {\mathbb {N}} \), then there are no positive rational numbers x, y, z satisfying $$\begin{aligned} xyz = 1, \quad x+y+z = n. \end{aligned}$$ Recently, N. X. Tho proved the following statement: let \(a\in \mathbb N\) be odd and let either \(n\equiv 0\pmod
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On the smallest area $$(n-1)$$ -gon containing a convex n-gon Period. Math. Hung. (IF 0.8) Pub Date : 2023-06-05 David E. Hong, Dan Ismailescu, Alex Kwak, Grace Y. Park
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Existence of ground states for fractional Choquard–Kirchhoff equations with magnetic fields and critical exponents Period. Math. Hung. (IF 0.8) Pub Date : 2023-06-02 Zhenyu Guo, Lujuan Zhao
In this paper, we consider the following fractional Choquard–Kirchhoff equation with magnetic fields and critical exponents $$\begin{aligned} M([u]_{s,A}^{2})(-\Delta )_{A}^{s}u+V(x)u=[|x|^{-\alpha }*|u|^{2^{*}_{\alpha ,s}}]|u|^{2^{*}_{\alpha ,s}-2}u+\lambda f(x,u) \quad \text {in } {\mathbb {R}}^{N}, \end{aligned}$$ where \(N>2s\) with \(00\), \(A=(A_{1},A_{2},\ldots ,A_{n})\in ({\mathbb {R}}^{N}
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On the single partial Caputo derivatives for functions of two variables Period. Math. Hung. (IF 0.8) Pub Date : 2023-05-29 Rafał Kamocki, Cezary Obczyński
In this work we propose definitions (distinguishable from the standard ones) of single partial derivatives in a Caputo sense of functions of two variables on the rectangle \(P=[0,a]\times [0,b]\). Next, we give an integral representation of functions possessing such derivatives. Finally, we apply these derivatives to the study of the existence and uniqueness of solutions and the continuous dependence
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Integrality and Thurston rigidity for bicritical PCF polynomials Period. Math. Hung. (IF 0.8) Pub Date : 2023-05-22 Heidi Benham, Alexander Galarraga, Benjamin Hutz, Joey Lupo, Wayne Peng, Adam Towsley
We give an algebraic proof of an important consequence of Thurston rigidity for bicritical PCF polynomials with periodic critical points under certain mild assumptions. The key result is that when the family of bicritical polynomials is parametrized using dynamical Belyi polynomials, the PCF solutions are integral at certain special primes, which we term “index divisor free primes.” We prove the existence
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On general divisor problems of Hecke eigenvalues of cusp forms Period. Math. Hung. (IF 0.8) Pub Date : 2023-05-12 Guodong Hua
Let f be a primitive holomorphic cusp form of even integral weight k for the full modular group \(\Gamma =SL(2,{\mathbb {Z}})\). Let \(\lambda _{f}(n)\) denote the nth normalized Fourier coefficient of f. In this paper, we consider the general divisor problem of higher moments of \(\lambda _{f}(n)\), and also consider the same problem over sums of two squares.
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Indecomposability of top local cohomology modules and Falting’s finiteness dimension of modules Period. Math. Hung. (IF 0.8) Pub Date : 2023-05-05 Saeed Yazdani, Jafar A’zami, Yasin Sadegh
Let \((R, {\mathfrak {m}})\) be a commutative Noetherian local ring, I a proper ideal of R and M a finitely generated R-module of dimension d. We investigate Falting’s finiteness dimension \(f_I(M)\) and the equidimensionalness of certain quotients of M. It is seen, under some conditions, that \(f_I (M)= \max \lbrace 1, {\text {grade}}(I, M)\rbrace .\) To achieve this, we first study the indecomposability
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Global gradient estimates of porous medium equations under the Finsler-geometric flow Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-27 Shahroud Azami
In this paper, we consider a compact n-dimensional Finsler manifold \((M^{n},F(t),m)\) evolving under the Finsler-geometric flow and prove global gradient estimates for positive solutions of porous medium equations \(\partial _{t}u=\Delta _{m}u^{p}\) on \(M^{n}\) where \(\Delta _{m}\) is the Finsler-Laplacian. As applications, by integrating the gradient estimates, we derive Harnack type inequalities
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Complete solutions of the simultaneous Pell’s equations $$x^2-(a^2-2)y^2=2$$ and $$y^2-bz^2=1$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-24 Dou Cencen, Luo Jiagui
In this paper, we consider the simultaneous Pell equations \(x^2-(a^2-2)y^2=2\) and \(y^2-bz^2=1\) where \(a>1\) is an integer and \(b>1\) is squarefree and has at most three prime divisors. We obtain necessary and sufficient conditions for the above simultaneous Pell equations have positive integer solutions by using only the elementary methods of factorization, congruence, the quadratic residue and
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A note on noncompact collectively coincidence point theory Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-17 Donal O’Regan
In this paper we present a variety of collectively fixed point and coincidence point results where the maps are not necessarily compact. Our arguments are based on a very general fixed point result in the literature.
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On the local cohomology of powers of ideals in idealizations Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-14 Pham Hong Nam
Let \((R, {\mathfrak {m}})\) be a Noetherian local ring and M a finitely generated R-module. Let \(A=R\ltimes M\) be the idealization of M over R and Q an ideal in A. Set \({\mathfrak {q}}=\rho (Q)\), where \(\rho : R\ltimes M\rightarrow R\) is the canonical projection defined by \(\rho (a,x)=a\). We show that \(H^i_{{\mathfrak {m}}\times M}(A/Q^{n+1}A)\simeq H^i_{{\mathfrak {m}}}(R/{\mathfrak {q}}^{n+1})\oplus
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On weakly prime-additive numbers of the form $$2^l+p^2+q^2$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-14 Xing-Wang Jiang
A positive integer n is called weakly prime-additive if n is not a prime power and there exist distinct prime divisors \(p_1\), \(p_2\), ..., \(p_t\) of n and positive integers \(\alpha _1\), \(\alpha _2\), ..., \(\alpha _t\) such that \(n=p_1^{\alpha _1}+p_2^{\alpha _2}+\cdots +p_t^{\alpha _t}\). Clearly, \(t\ge 3\). Recently, Fang found all weakly prime-additive numbers n with \(n=2^2+p^2+q^2\),
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On the size of a linear combination of two linear recurrence sequences over function fields Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-13 Sebastian Heintze
Let \( G_n \) and \( H_m \) be two non-degenerate linear recurrence sequences defined over a function field F in one variable over \( \mathbb {C}\), and let \( \mu \) be a valuation on F. We prove that under suitable conditions there are effectively computable constants \( c_1 \) and \( C' \) such that the bound $$\begin{aligned} \mu (G_n - H_m) \le \mu (G_n) + C' \end{aligned}$$ holds for \( \max
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Tauberian theorems concerning weighted mean summable integrals Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-13 Sefa Anıl Sezer, İbrahim Çanak
Let p be a positive real-valued continuous function on \(\mathbb {R_{+}}\) such that the function $$\begin{aligned} P(x)=\int _{0}^{x} p(t) \,dt, \quad x>0, \end{aligned}$$ is regularly varying with a positive index in the Karamata sense. For a real- or complex-valued continuous function f on \(\mathbb {R_{+}}\), we define $$\begin{aligned} s(x)=\int _{0}^{x}f(y) \,dy \ \ \text {and} \ \ \sigma _p
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On the distribution of large values of $$|\zeta (1+\textrm{i}t)|$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-12 Zikang Dong
In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved distribution function concerning large values, holding in the same range as that given by Granville and Soundararajan.
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Supercongruences involving Apéry-like sequences $$\{m^nG_n(x)\}$$ and $$\{m^nV_n(x)\}$$ Period. Math. Hung. (IF 0.8) Pub Date : 2023-04-08 Guo-Shuai Mao, Jun-Jun Yang
In this paper, we mainly obtain some congruences involving Apéry-like sequences \(\{m^nG_n(x)\}\) and \(\{m^nV_n(x)\}\) modulo \(p^3\) and \(p^4\), respectively.