We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An (n 1), Bn (n 3), Cn (n 2), Dn (n 4), En (n = 6,7,8), F4 and G2 are shown to...

We investigate context-free languages with respect to the measure Var of descriptional complexity, which gives the minimal number of nonterminals which is necessary to generate the language. Especially, we consider the behaviour of this measure with respect to operations. For given numbers c1, c2, . . . , cn and an nary operation τ on languages we discuss the range of Var(τ(L1, L2, . . . , Ln))...

By invoking the existence of a general custodial O(2) symmetry, a minimal Left-Right symmetric model based on the gauge group G = SU(2)L ⊗ SU(2)R ⊗ U(1)B−L is shown to require the existence of only two physical Higgs bosons. The lighter Higgs is predicted to have a small mass which could be evaluated by standard perturbation theory. The fermionic mass matrices are recovered by insertion of ad h...

Machines at customers have to be provided with spare parts upon failure. Consider a number of groups of machines, for each of which a target aggregate fill rate or target average response time (waiting time) should be met. Between groups, commonality exists, i.e., some parts occur in the material breakdown structure of machines in multiple groups. Instead of using separate stocks per group of m...

This paper addresses an inventory control problem when common components are allowed and the goal is to minimize the expected units shortage subject to a budget constraint. A two-level assemble-to-order product structure is analyzed when the demands for two end products follow independent mixtures of Erlang distributions. Closed form expressions for the objective function under various scenari...

We consider the upper bounds of the finite block length capacity Cn,FB(P ) of the discrete time Gaussian channel with feedback. We also let Cn(p) the nonfeedback capacity. We prove the relations Cn(P ) ≤ Cn,FB(P ) ≤ Cn(αP ) + 1 2 ln(1 + 1 α ) and Cn(P ) ≤ Cn,FB(P ) ≤ (1 + 1 α )Cn(αP ) for any P > 0 and any α > 0, which induce the half-bit and factor-of two bounds given by Cover and Pombra in th...

superconformal Wn+1 minimal models that appear in the context of the supersymmetric higher-spin AdS3/CFT2 duality. These models are constructed as Kazama-Suzuki coset models of the form SU(n+1)/U(n). We determine a family of boundary conditions in the limit theories, and use the modular bootstrap to obtain the full bulk spectrum of N = 2 super-Wn+1 primaries in the theory. We also confirm the i...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...