The least common multiple of random sets in polynomial rings over finite fields

The Ramanujan Journal - In this paper we investigate the distribution of degrees of the least common multiples of random subsets of monic polynomials of degree n in $${\mathbb {F}}_q[t]$$ . We...     

Composition series of generalized principal series; the case of strongly positive discrete series

In this paper we determine the composition series of the generalized principal seriesδ⋊σ assuming thatσ is strongly positive discrete series.     

Beiträge zur Ringofenmethodik. V

Zusammenfassung Nach Abtrennung von Cu(II)-Ionen mit Hilfe der Ringofentechnik ist es möglich, Ultramikromengen Kupfer(II) mit 0,001-m ÄDTA gegen PAN als Indikator zu titrieren. Eine dazu geeignete Arbeitsweise wird angegeben.

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Contributions to the ring furnace methodology. V

Summary Following separation of the Cu(II) ions with the aid of the ring furnace technique, it is possible to titrate ultramicro amounts of copper(II) with 0.001M EDTA in the presence of PAN as indicator. A suitable procedure is given.

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IV. Teil: Mikrochim. Acta [Wien]1969, 25.     

Implications of a light Higgs scalar

Phenomenological consequences of a light neutral Higgs scalar S (mass < 3.7 GeV) are explored in various two-Higgs-doublet models where some of the couplings are strongly enhanced. In one class of models the two-gluon decay mode is predominant, and decays into two muons are quite suppressed. A detailed analysis of the decay b → s + S is given. The consequences a light scalar for supersymmetric models are discussed.     

A simple solution to the strongCP-problem

We suggest soft breaking of Peccei-Quinn symmetry as a simple solution to the strongCP problem without the presence of the axion. In the context of theSU(2) _L ×U(1) model, it is shown how settingθ _tree=0 keeps θ calculable and, furthermore, extremely small: θ?10^?16. Unlike in the case of the axion the model is free from the cosmological domain wall problem. Possible extension of this idea to grand unification is discussed.     

Elastic bag model for molecular dynamics simulations of solvated systems: application to liquid water and solvated peptides

The fluctuating elastic boundary (FEB) model for molecular dynamics has recently been developed and validated through simulations of liquid argon. In the FEB model, a flexible boundary which consists of particles connected by springs is used to confine the solvated system, thereby eliminating the need for periodic boundary conditions. In this study, we extend this model to the simulation of bulk water and solvated alanine dipeptide. Both the confining potential and boundary particle interaction functions are modified to preserve the structural integrity of the boundary and prevent the leakage of the solute-solvent system through the boundary. A broad spectrum of structural and dynamic properties of liquid water are computed and compared with those obtained from conventional periodic boundary condition simulations. The applicability of the model to biomolecular simulations is investigated through the analysis of conformational population distribution of solvated alanine dipeptide. In most cases we find remarkable agreement between the two simulation approaches.     

Robust optimization of contaminant sensor placement for community water systems

We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected. We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of near-optimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.     

Bases of Feigin–Stoyanovsky’s type subspaces for $$C_\ell ^{(1)}$$

In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level k affine Lie algebra \(C_\ell ^{(1)}\). We prove spanning by using annihilating field \(x_\theta (z)^{k+1}\) of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.