Search results for "Multiplier"
showing 10 items of 338 documents
An equivalent definition of the vector-valued McShane integral by means of partitions of unity
2002
An integral for vector-valued functions on a σ-finite outer regular quasi-radon measure space is defined by means of partitions of unity and it is shown that it is equivalent to the McShane integral. The multipliers for both the McShane and Pettis integrals are characterized
A presentation and a representation of the Held group
1996
In this note we give a brief description of a new presentation of the Held group, which is deduced only from the original work of D. Held in 1969, who shows that a finite simple group, having the same centralizer of a 2-central involution as in the Mathieu group M24, is M24, L5(2) or a group of order 4.030.387.200. The first complete uniqueness proof for the latter case was given by L. Soicher in 1991. The generators and relations occurring here are easy to verify by a simple Todd–Coxeter algorithm. It is an easy task to get a new uniqueness and existence proof of the Held group from this result. Also basic facts like the Schur Multiplier or the automorphism group of the Held group follow f…
The IceCube prototype string in Amanda
2006
The Antarctic Muon And Neutrino Detector Array (Amanda) is a high-energy neutrino telescope. It is a lattice of optical modules (OM) installed in the clear ice below the South Pole Station. Each OM contains a photomultiplier tube (PMT) that detects photons of Cherenkov light generated in the ice by muons and electrons. IceCube is a cubic-kilometer-sized expansion of Amanda currently being built at the South Pole. In IceCube the PMT signals are digitized already in the optical modules and transmitted to the surface. A prototype string of 41 OMs equipped with this new all-digital technology was deployed in the Amanda array in the year 2000. In this paper we describe the technology and demonst…
Nonradial normalized solutions for nonlinear scalar field equations
2018
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
First year performance of the IceCube neutrino telescope
2006
The first sensors of the IceCube neutrino observatory were deployed at the South Pole during the austral summer of 2004-2005 and have been producing data since February 2005. One string of 60 sensors buried in the ice and a surface array of eight ice Cherenkov tanks took data until December 2005 when deployment of the next set of strings and tanks began. We have analyzed these data, demonstrating that the performance of the system meets or exceeds design requirements. Times are determined across the whole array to a relative precision of better than 3 ns, allowing reconstruction of muon tracks and light bursts in the ice, of air-showers in the surface array and of events seen in coincidence…
Position-sensitive neutron detector
2002
Abstract A position-sensitive neutron detector has been developed for use in nuclear physics research. The detector consists of a ∅5.5 cm×100 cm long quartz tube filled with liquid scintillator viewed from both ends by photomultipliers and enclosed in a light-tight titanium container. The properties of the detector were determined both experimentally and by Monte Carlo simulations (EFEN code). A time resolution of 0.4 ns was reached resulting in the position resolution of less than 4 cm. The neutron registration efficiency varies from 36% to 20% within neutron energy range 1–10 MeV and is practically independent of the position along the detector length. Good n–γ separation is achieved for …
Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties
2014
An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for…
Commuting powers and exterior degree of finite groups
2011
In [P. Niroomand, R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335-343] it is introduced a group invariant, related to the number of elements $x$ and $y$ of a finite group $G$, such that $x \wedge y = 1_{G \wedge G}$ in the exterior square $G \wedge G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m \wedge k$ of $H \wedge K$ such that $h^m \wedge k = 1_{H \wedge K}$, where $m \ge 1$ and $H$ and $K$ are arbitrary subgroups of $G$.
Extension of a Schur theorem to groups with a central factor with a bounded section rank
2013
Abstract A well-known result reported by Schur states that the derived subgroup of a group is finite provided its central factor is finite. Here we show that if the p-section rank of the central factor of a locally generalized radical group is bounded, then so is the p-section rank of its derived subgroup. We also give an explicit expression for this bound.
A note on the exterior centralizer
2009
The notion of the exterior centralizer \({C_G^{^\wedge}(x)}\) of an element x of a group G is introduced in the present paper in order to improve some known results on the non-abelian tensor product of two groups. We study the structure of G by looking at that of \({C_G^{^\wedge}(x)}\) and we find some bounds for the Schur multiplier M(G) of G.