Proceedings - Mathematical Sciences
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New families of graceful banana trees
Proceedings - Mathematical Sciences - Tập 106 - Trang 201-216 - 1996
Consider a family of stars. Take a new vertex. Join one end-vertex of each star to this new vertex. The tree so obtained is known as abanana tree. It is proved that the banana trees corresponding to the family of stars
...... hiện toàn bộ
Lifshitz tails for random perturbations of periodic Schrödinger operators
Proceedings - Mathematical Sciences - Tập 112 - Trang 147-162 - 2002
The present paper is a non-exhaustive review of Lifshitz tails for random perturbations of periodic Schrödinger operators. It is not our goal to review the whole literature on Lifshitz tails; we will concentrate on a single model, the continuous Anderson model.
On qualitative analysis of delay systems and x Δ = f(t, x, x σ ) on time scales
Proceedings - Mathematical Sciences - Tập 120 - Trang 249-258 - 2010
Here we solve two problems presented in paper [9] (C C Tisdell and A Zaidi, Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal.
68 (2008) 3504–3524). We study existence and uniqueness of solutions for delay systems and first-order dynamic equations of the form x
...... hiện toàn bộ
Set of periods of a subshift
Proceedings - Mathematical Sciences - Tập 128 - Trang 1-8 - 2018
In this article, subsets of
$${\mathbb {N}}$$
that can arise as sets of periods of the following subshifts are characterized: (i) subshifts of finite type, (ii) transitive subshifts of finite type, (iii) sofic shifts, (iv) transitive sofic shifts...... hiện toàn bộ
ξζrelation
Proceedings - Mathematical Sciences - Tập 109 - Trang 379-383 - 1999
In this note we prove a relation between the Riemann Zeta function, ζ and the ξ function (Krein spectral shift) associated with the harmonic oscillator in one dimension. This gives a new integral representation of the zeta function and also a reformulation of the Riemann hypothesis as a question inL
1(ℝ).
On the numbers of ward and bernoulli
Proceedings - Mathematical Sciences - Tập 3 - Trang 193-200 - 1936
Proof of a supercongruence conjectured by Sun through a $${\varvec{q}}$$ -microscope
Proceedings - Mathematical Sciences - Tập 130 - Trang 1-7 - 2020
In 2011, Sun (Sci. China Math. 54 (2011) 2509–2535) made the following conjecture: for any odd prime p and odd integer m,
$$\begin{aligned}&\qquad \frac{1}{m^2{m-1\atopwithdelims ()(m-1)/2}}\Bigg (\sum _{k=0}^{(mp-1)/2}\frac{{2k\atopwithdelims ()k}}{8^k} -\left( \frac{2}{p}\right) \sum _{k=0}^{(m-1)/2}\frac{{2k\atopwithdelims ()...... hiện toàn bộ
Primes of the form x 2 + d y 2 with x ≡ 0(mod N) or y ≡ 0(mod N)
Proceedings - Mathematical Sciences - Tập 127 - Trang 35-43 - 2016
In this paper, we characterize primes of the form x
2 + d
y
2 with x≡0(mod N) or y≡0(mod N) for positive integers N and d with d being square free.
Multiplicity of summands in the random partitions of an integer
Proceedings - Mathematical Sciences - Tập 123 - Trang 101-143 - 2013
In this paper, we prove a conjecture of Yakubovich regarding limit shapes of ‘slices’ of two-dimensional (2D) integer partitions and compositions of n when the number of summands m ~An
α
for some A > 0 and
$\alpha < \frac{1}{2}$
. We prove that the proba...... hiện toàn bộ
On a generalization of B 1 (Ω) on C ∗ -algebras
Proceedings - Mathematical Sciences - Tập 124 - Trang 243-253 - 2014
We discuss the unitary classification problem of a class of holomorphic curves on C
∗-algebras. It can been regarded as a generalization of Cowen–Doulgas operators with index one.
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