The impact of order batching and picking area zoning on order picking system performance

This paper proposes an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. The model includes the sorting process needed to sort the batch again by order. Service times at pick zones are assumed to follow general distributions. The first and second moments of service times at zones and the visiting probability of a batch of orders to a pick zone are derived. Based on this information, the mean throughput time of an arbitrary order in the order picking system is obtained. Results from a real application and simulation show that this approximation model provides acceptable accuracy for practical purposes. Furthermore, the proposed method is simple and fast and can be easily applied in the design and selection process of order picking systems.     

Gauss Rigidity and Volume Preservation Under Preserving Curvature Deformations for Hedgehogs

We consider Gauss rigidity and Gauss infinitesimal rigidity for hedgehogs of ${\mathbb{R}^{3}}$ (regarded as Minkowski differences of closed convex surfaces of ${\mathbb{R}^{3}}$ with positive Gaussian curvature). Besides, we prove under an appropriate differentiability condition that whenever we perform a deformation of a hedgehog so that its curvature function remains constant, its algebraic volume also remains constant.     

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order 2, showing that the latter characterize the proof-theoretic ordinal $1^{\infty }$ of the fragment ${\mathrm{\Pi }}_1^1$–${\mathrm{CA}}_0$ of second order number theory, or equivalently the set theory $\mathrm{KP}{?}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order 2 implies transfinite induction up to the ordinal $1^{\infty }$. We expect that our approach will facilitate analysis of more powerful systems of patterns.     

Almost fixed-point-free automorphisms of order 2

Let φ be an automorphism of order 2 of the group G with C _G (φ) finite. We prove the following. If G has finite Hirsch number then G is (nilpotent of class at most 2)-by-finite but need not be abelian-by-finite. If G is a finite extension of a soluble group with finite abelian ranks, then G is abelian-by-finite.     

Quasinormal subgroups of order p 2

The location of quasinormal subgroups in a group is not particularly well known. Maximal ones always have to be normal, but little has been proved about the minimal ones. In finite groups, the difficulties arise in the p-groups. Here we prove that, for every odd prime p, a quasinormal subgroup of order p ² in a finite p-group G contains a quasinormal subgroup of G of order p. S. Stonehewer is grateful to the Australian National University for financial support during the preparation of this paper.     

A new semifield of order 2

In [G. Lunardon, Semifields and linear sets of PG(1,q^t), Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order q²ⁿ,n>1 and n odd, with left nucleus F_qⁿ, middle and right nuclei both F_q² and center F_q. When n=3 this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1-34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87-104]. For n>3, no example of a semifield belonging to this family is known.In this paper we first prove that, when n>3, any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 2¹⁰ belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield.     

Regular maps of 2-power order

Journal of Algebraic Combinatorics - In this paper, we consider the possible types of regular maps of order $$2^n$$ , where the order of a regular map is the order of automorphism group of the map....     

The area of an exponential random walk and partial sums of uniform order statistics

Let S_i be a random walk with standard exponential increments. The sum ∑ _i=1 ^k S_i is called the k-step area of the walk. The random variable ∑ _i=1 ^k S_i plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of this variable and prove that

Opial's inequality and oscillation of 2nd order equations

For a second-order differential equation, we obtain from Opial's inequality lower bounds for the spacing between two zeros of a solution or between a zero of a solution and a zero of its derivative. These bounds are expressed in terms of antiderivatives of the potential, and in particular we derive some new Liapunov type inequalities from them.

     

Nonlinear elliptic equations of order 2m and subdifferentials

LetA be an operator of the calculus of variations of order 2m onW ^m,p (Ω) andj a normal convex integrand. Forf ∈L ^p (Ω), the equation $$\mathcal{A}u + \partial j(x,u) \ni f, in \Omega , u - \phi \in W_0^{m,p} (\Omega ),$$ may have no strong solutions whenm>1, even ifj is independent ofx and φ=0. However, we obtain existence results whenj is everywhere finite and $$\int_\Omega {j(x,\phi ) dx< + \infty ,} $$ by the study of the subdifferential of the function $$\upsilon \mapsto \int_\Omega {j(x,\upsilon + \phi ) dx on W_0^{m,p} (\Omega ).} $$      

4p阶群及2p2阶群的自同构群

给出了4p阶群和2p^2阶群的自同构群的结构,这里P是奇素数。     

A structure theory for two-dimensional translation planes of order q 2 that admit collineation groups of order q 2

This paper is devoted to the study of translation planes of order q ² and kernel GF(q) that admit a collineation group of order q ² in the linear translation complement. We give a representation of this group by a suitable set of matrices depending on some functions over GF(q). Using this representation we obtain several results concerning the existence and the collineation group of the plane.     

Semisymmetric graphs of order 6p 2 and prime valency

In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 and valency k is semisymmetric if and only if k = 3 and either Γ is the Gray graph, or p ≡ 1 (mod 6) and Γ is isomorphic to one known graph.