Periodica Mathematica Hungarica最新文献

We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in ({mathbb {Z}}), equal to 1 or (-1). Furthermore, we give the exact number of Pascal-like (n times m) matrices over a commutative ring with finite group of units.

For a sequence (M=(m_{i})_{i=0}^{infty }) of integers such that (m_{0}=1), (m_{i}ge 2) for (ige 1), let (p_{M}(n)) denote the number of partitions of n into parts of the form (m_{0}m_{1}cdots m_{r}). In this paper we show that for every positive integer n the following congruence is true:

where (mathcal {M}(m,r):=frac{m}{textrm{gcd}big (m,textrm{lcm}(1,ldots ,r)big )}). Our result answers a conjecture posed by Folsom, Homma, Ryu and Tong, and is a generalisation of the congruence relations for m-ary partitions found by Andrews, Gupta, and Rødseth and Sellers.

Recently, the level two analogue of the multiple polylogarithm function (textrm{A}(k_1,ldots ,k_r;z)) and the Arakawa–Kaneko zeta function (psi (k_1,ldots ,k_r;s)) have been introduced by M. Kaneko and H. Tsumura for (k_1,ldots ,k_rin mathbb {Z}_{ge 1}). In this paper, we investigate some of their special relations. In particular, we prove some explicit forms of (textrm{A}(k_1,ldots ,k_r;z)) and (psi (k_1,ldots ,k_r;s)). Also, we introduce a level m analogue of the Arakawa–Kaneko zeta functions.

Motivated by applications in geomorphology, the aim of this paper is to extend Morse–Smale theory from smooth functions to the radial distance function (measured from an internal point), defining a convex polyhedron in 3-dimensional Euclidean space. The resulting polyhedral Morse–Smale complex may be regarded, on one hand, as a generalization of the Morse–Smale complex of the smooth radial distance function defining a smooth, convex body, on the other hand, it could be also regarded as a generalization of the Morse–Smale complex of the piecewise linear parallel distance function (measured from a plane), defining a polyhedral surface. Beyond similarities, our paper also highlights the marked differences between these three problems and it also relates our theory to other methods. Our work includes the design, implementation and testing of an explicit algorithm computing the Morse–Smale complex on a convex polyhedron.

We introduce the Hardy and Hardy–Littlewood–Pólya operators on local fields and show that they are bounded on weighted Lebesgue spaces with power weights. Moreover, we compute the precise norms of these operators on these spaces. Further, we prove the boundedness of the commutators generated by these operators and functions with central mean oscillation on Herz spaces, and in particular, on the weighted Lebesgue spaces.

Let ({a_{n}: nin mathbb {P}}) be an increasing sequence of positive integers. For every (nin mathbb {P}) let ({t_{k,a_{n}}: 1le kle a_{n}, kin mathbb {P}}) be a finite sequence of non-negative numbers such that

holds and

is satisfied for any fixed k. Our main result (Theorem 6.5) is that we prove (L_{1})-norm convergence

(for example, but not limited to (a_{n}:=2^{n}), see Corollary 6.6 and Sect. 7) with weaker conditions than it was known before for matrix transform means and for some special means, namely Nörlund and weighted ones.

In this article we give a molecular reconstruction theorem for (H_{omega }^{p(cdot )}(mathbb {R}^{n})). As an application of this result and the atomic decomposition developed in Ho (Tohoku Math J 69 (3), 383–413, 2017) we show that classical singular integrals can be extended to bounded operators on (H_{omega }^{p(cdot )}(mathbb {R}^{n})). We also prove, for certain exponents (q(cdot )) and certain weights (omega ), that the Riesz potential (I_{alpha }), with (0< alpha < n), can be extended to a bounded operator from (H^{p(cdot )}_{omega }(mathbb {R}^{n})) into (H^{q(cdot )}_{omega }(mathbb {R}^{n})), for (frac{1}{p(cdot )}:= frac{1}{q(cdot )} + frac{alpha }{n}).

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,frangle =langle u, f(qx)rangle ) for all polynomials f and (H_{q}) is the q-derivative operator. We give the definition of the class s of such a form and the characterization of its corresponding orthogonal q-polynomials sequence ({P_n}_{nge 0}) by the structure relation. As a consequence, we establish the system fulfilled by the coefficients of the structure relation, those of the polynomials (Phi , Psi , B) and the recurrence coefficient (gamma _{n+1}, , n ge 0), of ({P_n}_{nge 0}) for the class one in the symmetric case. In addition, we present the complete description of the symmetric (H_{q})-Laguerre–Hahn forms of class (s=1.) The limiting cases are also covered.

In the last decade, Europe has seen a rise in natural disasters. Due to climate change, an increase of such events is predicted for the future. While natural disasters have been a rare phenomenon in Europe so far, other regions of the world, such as Central and North America or Southeast Asia, have regularly been affected by Hurricanes and Tsunamis. The aim of the current study is to synthesize the literature on child development in immediate stress, prolonged reactions, trauma, and recovery after natural disasters with a special focus on trajectories of (mal-)adaptation. In a literature search using PubMed, Psychinfo and EBSCOhost, 15 studies reporting about 11 independent samples, including 11,519 participants aged 3-18 years, were identified. All studies identified resilience, recovery, and chronic trajectories. There was also evidence for delayed or relapsing trajectories. The proportions of participants within each trajectory varied across studies, but the more favorable trajectories such as resilient or recovering trajectory were the most prevalent. The results suggested a more dynamic development within the first 12 months post-disaster. Female gender, a higher trauma exposure, more life events, less social support, and negative coping emerged as risk factors. Based on the results, a stepped care approach seems useful for the treatment of victims of natural disasters. This may support victims in their recovery and strengthen their resilience. As mental health responses to disasters vary, a coordinated screening process is necessary, to plan interventions and to detect delayed or chronic trauma responses and initiate effective interventions.

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}}}).