The Haemers partial geometry and the Steiner system S(5, 8, 24)

Haemers has constructed a partial geometry with parameters s = 4, t = 17, and α = 2, using properties of the Hoffman-Singleton graph. We describe this geometry in terms of the Steiner system S(5, 8, 24).     

Orthogonal resolutions of lines in AG(n,q)

A resolution of the lines of AG(n,q) is a partition of the lines classes (called resolution classes) such that every point of the geometry is on exactly one line of each resolution class. Two resolutions R,R' of AG(n,q) are orthogonal if any resolution class from R has at most one line in common with any class from R'. In this paper, we construct orthogonal resolutions on AG(n,q) for all n=2ⁱ⁺¹, i=1,2,…, and all q>2 a prime power. The method involves constructing AG(n,q) from a finite projective plane of order q^n-1 and using the structure of the plane to display the orthogonal resolutions.     

Laplacian integral graphs in S(a, b)

Let G_n,m be the family of graphs with n vertices and m edges, when n and m are previously given. It is well-known that there is a subset of G_n,m constituted by graphs G such that the vertex connectivity, the edge connectivity, and the minimum degree are all equal. In this paper, S(a, b)-classes of connected (a, b)-linear graphs with n vertices and m edges are described, where m is given as a function of a,b∈N/2. Some of them have extremal graphs for which the equalities above are extended to algebraic connectivity. These graphs are Laplacian integral although they are not threshold graphs. However, we do build threshold graphs in S(a, b).     

A variational problem with lack of compactness for H(S;S) maps of prescribed degree

We consider, for maps in H^1/2(S¹;S¹), a family of (semi)norms equivalent to the standard one. We ask whether, for such a norm, there is some map in H^1/2(S¹;S¹) of prescribed topological degree equal to 1 and minimal norm. In general, the answer is no, due to concentration phenomena. The existence of a minimal map is sensitive to small perturbations of the norm. We derive a sufficient condition for the existence of minimal maps. In particular, we prove that, for every given norm, there are arbitrarily small perturbations of it for which the minimum is attained. In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences. We prove that, for such minimizing sequences, the energy concentrates near a point of S¹. We describe this concentration in terms of bubbling-off of circles.     

Solving stochastic differential equations on Homeo(S)

The Brownian motion with respect to the metric H^3/2 on Diff(S¹) has been constructed. It is realized on the group of homeomorphisms Homeo(S¹). In this work, we shall resolve the stochastic differential equations on Homeo(S¹) for a given drift Z.     

Eine charakterisierung des steinersystems S(5, 8, 24)

S(5, 8, 24) is characterized as the unique Steiner system S(t, k, n) satisfying n = (t + 1)(k ? t + 1) and k ? t + 2 ? 4.     

Constraint programming for computing non-stationary (R, S) inventory policies

This paper proposes a constraint programming model for computing the finite horizon single-item inventory problem with stochastic demands in discrete time periods with service-level constraints under the non-stationary version of the “periodic review, order-up-to-level” policy (i.e., non-stationary (R, S) or, simply (R_n, S_n)). It is observed that the modeling process is more natural and the required number of variables is smaller compared to the MIP formulation of the same problem. The computational tests show that the CP approach is more tractable than the conventional MIP formulation. Two different domain reduction methods are proposed to improve the computational performance of solution algorithms. The numerical experiments confirmed the effectiveness of these methods.     

On the empirical performance of (T, s, S) heuristics

The periodic (T,s,S)$(T\text{,}s\text{,}S)$ policies have received considerable attention from the academic literature. Determination of the optimal parameters is computationally prohibitive, and a number of heuristic procedures have been put forward. However, these heuristics have never been compared in an extensive empirical study. Such an investigation on 3055 SKUs is carried out in this paper. Our study provides insights into the performance of (T,s,S)$(T\text{,}s\text{,}S)$ heuristics, also in relation to demand forecasting. The results show that Naddor’s heuristic is best able to minimize the total cost. However, the normal and power approximations achieve more efficient solutions in that backorder volumes are smaller at the same inventory levels, indicating the potentially superior performance of these methods if the balancing of holding and backorder costs can be improved. The results also show that, for all heuristics, the SBA variant of the Croston forecasting method significantly outperforms Croston as well as Single Exponential Smoothing (SES).     

Weakly compact operators and multipliers on C0(S, A)

The problem of defining a convolution of operator-valued measures defined on a locally compact semitopological semigroup which represent weakly compact operators is considered in this paper. Convolution of the corresponding weakly compact operators is then defined. A characterization of multipliers on function spaces is given in terms of their representing measures.     

The Banach algebra l1(S)

Let S be the free semigroup with a finite or countably infinite set of generators plus an identity. It is shown that there is a natural involution 1 on the convolution Banach algebra l¹(S) such that (l¹(S), 1) has a separating family of finite-dimensional star representations. The star representations of the l¹-algebra of some other semigroups are also considered. The spectrum of every element of l¹(S) which is not a scalar multiple of the identity is shown to be a connected set with interior.     

On sufficient conditions for cost rate function unimodality in periodic review (s, S) inventory models

The cost rate function that arises in the stationary analysis of a class of periodic review regenerative inventory systems is known to be unimodal if the renewal density of the underlying demand sequence is decreasing. We prove that the same result holds, under zero leadtimes, if the renewal density is concave increasing.     

L-Poisson integral representations of solutions of the Hua system on the bounded symmetric domain SU(n,n)/S(U(n)×U(n))

Let positive definite} be the matrix ball of rank n and let H_D be the associated Hua operator. For a complex number λ, such that Reiλ>n−1 we give a necessary and sufficient condition on solutions F of the following Hua system of differential equations on D:

     

Homotopy decomposition of a group of symplectomorphisms of S×S

We continue the analysis started by Abreu, McDuff and Anjos of the topology of the group of symplectomorphisms of S²×S² when the ratio of the area of the two spheres lies in the interval (1,2]. We express the group, up to homotopy, as the pushout (or amalgam) of certain of its compact Lie subgroups. We use this to compute the homotopy type of the classifying space of the group of symplectomorphisms and the corresponding ring of characteristic classes for symplectic fibrations.     

On 1-rotational Sλ(2, 3, ν) designs

In this paper, the necessary and sufficient condition for the existence of a 1-rotational S_λ (2, 3, ν) design is obtained, and it is shown that an S_λ (2, 3, ν) design, if it exists, can be always constructed cyclically.     

New uniqueness proofs for the (5, 8, 24), (5, 6, 12) and related Steiner systems

New elementary proofs of the uniqueness of certain Steiner systems using coding theory are presented. In the process some of the codes involved are shown to be unique.The uniqueness proof for the (5, 8, 24) Steiner system is due to John Conway. The blocks of the system are used to generate a length 24 binary code. Any two such codes are then shown to be equivalent up to a permutation of the coordinates. This code turns out to be the extended Golay code.In the uniqueness proof for the (4, 7, 23) system, the blocks generate a length 23 code which is extended to a length 24 code. The minimum weight vectors of this larger code hold a (5, 8, 24) Steiner system. This result together with the previous one completes the proof. At this point it is also possible to conclude that the codes involved are unique and hence equivalent to the binary perfect Golay code and its extension.Continuing with the uniqueness result for the (3, 6, 22) Steiner system, the blocks generate a length 22 code which is extended to the same length 24 code by the addition of two coordinates and one additional vector. This extension ultimately requires the computation of the coset weight distribution of the length 22 code, a result heretofore unknown. The complete coset weight distribution for a specific (22, 11, 6) self-dual code is computed using the CAMAC computer system.The (5, 6, 12) and (4, 5, 11) Steiner systems are treated differently. It is shown that each system is completely determined by the choice of six blocks which may be assumed to lie in any such design. These six blocks in fact form a basis for length 12 (and 11) ternary codes corresponding to the two systems and may be generated by an algorithm independent of the designs. This algorithm is presented and the minimum weight vectors of the resulting codes, the perfect ternary Golay code and its extension, are calculated by the CAMAC system.     

On the existence of 2-designs S2(2,3,v) without repeated blocks

The necessary condition of 2 (mod 3) is sufficient for the existence of a 2-design S₂(2,3,v) without repeated blocks.     

Weak solution of (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0))u′(0) = ku(0), r(L, u(L))u′ (L) = hu(L) and k, h are suitable elements of [0, ∞]

We consider weak solutions to the nonlinear boundary value problem (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0)) u′(0) = ku(0), r(L, u(L)) u′(L) = hu(L) and k, h are suitable elements of [0, ∞]. In addition to studying some new boundary conditions, we also relax the constraints on r(x, u) and (Fu)(x). r(x, u) > 0 may have a countable set of jump discontinuities in u and r(x, u)^?1?L_q((0, L) × (0, p)). F is an operator from a suitable set of functions to a subset of L_p(0, L) which have nonnegative values. F includes, among others, examples of the form (Fu)(x) = (1 ? H(x ? x₀)) u(x₀), (Fu)(x) = ∫_x^Lf(y, u(y)) dy where f(y, u) may have a countable set of jump discontinuities in u or F may be chosen so that (Fu)′(x) = ? g(x, u(x)) u′(x) ? q(x) u(x) ? f(x, u(x)) where q is a distributional derivative of an L₂(0, L) function.     

Some topological and geometrical properties of the sequence space e (u,p)

In this paper, we introduce the sequence space e^r(u,p) and investigate its some topological and geometrical properties such as basis, α-, β-, γ- duals and the uniform Opial property.