Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

We obtain an asymptotic behavior of the loss probability for the GI/M/1/K queue as K for cases of <1, >1 and =1.     

Ternary univariate curvature-preserving subdivision

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original (in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Cobalt Based Nanoparticles Embedded Reduced Graphene Oxide Aerogel for Hydrogen Evolution Electrocatalyst

Efficient water electrolysis catalyst is highly demanded for the production of hydrogen as a sustainable energy fuel. It is reported that cobalt derived nanoparticle (CoS₂, CoP, CoS|P) decorated reduced graphene oxide (rGO) composite aerogel catalysts for highly active and reliable hydrogen evolution reaction electrocatalysts. 7 nm level cobalt derived nanoparticles are synthesized over graphene aerogel surfaces with excellent surface coverage and maximal expose of active sites. CoS|P/rGO hybrid aerogel composites show an excellent catalytic activity with overpotential of ≈169 mV at a current density of ≈10 mA cm^?2. Accordingly, efficient charge transfer is attained with Tafel slope of ≈52 mV dec^?1 and a charge transfer resistance (R_ct) of ≈12 Ω. This work suggests a viable route toward ultrasmall, uniform nanoparticles decorated graphene surfaces with well‐controlled chemical compositions, which can be generally useful for various applications commonly requiring large exposure of active surface area as well as robust interparticle charger transfer.     

Surface structure of low-coveraged Cs on Si(0 0 1)-() system

Alkali metals (AM) on semiconductors have been investigated as a simple model system for the metal-semiconductor interfaces due to their simple electronic structures. Especially, cesium (Cs) on Si(0 0 1) surface has been studied with various experimental techniques. In this study, we investigated the atomic structure of initial Cs adsorption on Si(0 0 1)-(2×1) surface using coaxial impact collision ion scattering spectroscopy. When Cs atoms are adsorbed on Si(0 0 1)-(2×1) up to 0.2 ML at room temperature, the initial adsorption site is on-top T3 site with poor periodicity and the length of Si dimer is reserved as in the clean Si(0 0 1) surface. It is also found that Cs atoms adsorbed on Si(0 0 1) surface with a height of 2.83±0.05 Å from the second layer of Si(0 0 1) surface.     

Effect of Ni doping on the phase stability and conductivity of scandia-stabilized zirconia

The effect of Ni doping on the phase stability and conductivity of scandia-stabilized zirconia (SSZ) thick film was studied. A free-standing 10SSZ thick-film (10 mol% Sc₂O₃-stabilized zirconia, ~ 10 μm thick) that was previously in contact with a Ni layer during co-firing was fabricated. The 10SSZ thick-film showed a cubic phase in contrast to the rhombohedral phase shown for a bulk 10SSZ sample. The Ni content in the SSZ thick film was ~ 1.7 mol%. The effect of Ni on the cubic phase formation was also confirmed by the similar observation of the cubic phase in the Ni-doped bulk 10SSZ sample. The observed conductivity behavior also supported the XRD observation. Ni was found to hinder the transformation of the cubic phase to the rhombohedral on cooling in 10SSZ samples after a reduction treatment.     

G/M/1 queues with delayed vacations

We considerG/M/1 queues with multiple vacation discipline, where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vacation time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.     

An old conjecture of Erdos-Turán on additive bases

There is a 1941 conjecture of Erdos and Turán on what is now called additive basis that we restate:

Conjecture 0.1(Erdos and Turán). Suppose that is an increasing sequence of integers and

Suppose that

If 0$"> for all , then is unbounded.

Our main purpose is to show that the sequence cannot be bounded by . There is a surprisingly simple, though computationally very intensive, algorithm that establishes this.

     

Limsup results and LIL for partial sum processes of a Gaussian random field

Let {ξ _j ; j ∈ ℤ₊ ^d be a centered stationary Gaussian random field, where ℤ₊ ^d is the d-dimensional lattice of all points in d-dimensional Euclidean space ℝ^d, having nonnegative integer coordinates. For each j = (j ₁ , ..., jd) in ℤ₊ ^d , we denote |j| = j ₁ ... j _d and for m, n ∈ ℤ₊ ^d , define S(m, n] = Σ _m<j≤n ζ _j , σ²(|n−m|) = ES ² (m, n], S _n = S(0, n] and S ₀ = 0. Assume that σ(|n|) can be extended to a continuous function σ(t) of t > 0, which is nondecreasing and regularly varying with exponent α at b ≥ 0 for some 0 < α < 1. Under some additional conditions, we study limsup results for increments of partial sum processes and prove as well the law of the iterated logarithm for such partial sum processes. Research supported by NSERC Canada grants at Carleton University, Ottawa     

Cohomological relation between Jacobi forms and skew‐holomorphic Jacobi forms

Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito‐Kurokawa conjecture. Later Skoruppa introduced skew‐holomorphic Jacobi forms, which play an important role in understanding liftings of modular forms and Jacobi forms. In this paper, we explain a relation between Jacobi forms and skew‐holomorphic Jacobi forms in terms of a group cohomology. More precisely, we introduce an isomorphism from the direct sum of the space of Jacobi cusp forms on and the space of skew‐holomorphic Jacobi cusp forms on with the same half‐integral weight to the Eichler cohomology group of with a coefficient module coming from polynomials.