The co-degrees of irreducible characters

LetG be a finite group. The co-degree of an irreducible character χ ofG is defined to be the number |G|/χ(1). The set of all prime divisors of all the co-degrees of the nonlinear irreducible characters ofG is denoted by Σ(G). First we show that Σ(G)=π(G) (the set of all prime divisors of |G|) unlessG is nilpotent-by-abelian. Then we make Σ(G) a graph by adjoining two elements of Σ(G) if and only if their product divides a co-degree of some nonlinear character ofG. We show that the graph Σ(G) is connected and has diameter at most 2. Additional information on the graph is given. These results are analogs to theorems obtained for the graph corresponding to the character degrees (by Manz, Staszewski, Willems and Wolf) and for the graph corresponding to the class sizes (by Bertram, Herzog and Mann). Finally, we investigate groups with some restriction on the co-degrees. Among other results we show that ifG has a co-degree which is ap-power for some primep, then the corresponding character is monomial andO _p (G)≠1. Also we describe groups in which each co-degree of a nonlinear character is divisible by at most two primes. These results generalize results of Chillag and Herzog. Other results are proved as well. The paper was written during this author’s visit at the Technion and the University of Tel Aviv. He would like to thank the departments of mathematics at the Technion and the University of Tel Aviv for their hospitality and support.     

An addition theorem for the elementary Abelian group of type (p,p)

In this paper we prove that every element in the finite Abelian groupZ _p ×Z _p ,p>3,p prime, can be written as a sum over a subset of the setA, whereA is any set of non-zero elements ofZ _p ×Z _p with |A|=2p–2.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday     

New results on elements 111 and 112

Experiments on the synthesis and identification of the nuclei ²⁷²111 and ²⁷⁷112 were performed in order to confirm previous results. Three additional decay chains were measured in the reaction ⁶⁴Ni + ²⁰⁹Bi →²⁷³111^*. The study revealed considerably improved data on the decay chain originating from ²⁷²111. One additional chain was measured in the reaction ⁷⁰Zn + ²⁰⁸Pb →²⁷⁸112^*. The decay properties of the chain starting at ²⁷⁷112 are in excellent agreement with the second chain of the first experiment down to ²⁶⁵Sg, where the new chain ends by a previously unknown spontaneous-fission branch. A re-analysis of all the data on elements 110, 111, and 112 measured at GSI since 1994 (a total of 34 decay chains was investigated) revealed that for 2 chains (the second chain of ²⁶⁹110 measured in 1994 and the first chain of ²⁷⁷112 measured in 1996) the results of the new analysis differed from the previous one. In all other cases the earlier data are exactly reproduced. Received: 21 December 2001 / Accepted: 15 January 2002     

Characterization of the ξ-carbide in ex-service 1Cr-0.5 Mo steels

The ξ-carbide, also described as Fe₂MoC and M_aC_b, has been identified at ferrite grain boundaries in 1Cr-0.5Mo steels exposed to elevated temperatures (500–530°C) for prolonged periods (65,000–170,000 hr). The structure and composition of the phase have been characterized using electron microdiffraction and energy-dispersive X-ray spectroscopy (EDXS) respectively. Analysis of microdiffraction patterns supports the proposal that the ξ-carbide has a monoclinic unit cell, rather than the orthorhombic unit cell first proposed. The ranges of metallic element concentrations in the ξ-carbide (i.e. 48–59 at.% Fe, 22–29 at.% Mo, 7–16 at.% Cr, 4–7 at.% Mn and 3–6 at.% Si) are unique compared to those of other carbide precipitates identified in the 1Cr-0.5Mo steels, which means that the ξ-carbide may be identified rapidly on extraction replicas using qualitative EDXS.     

183 GHz double diode subharmonically pumped mixer

A double diode subharmonically pumped mixer is described. A diode-whisker contacting arrangement has been developed which avoids many of the problems associated with whisker contacts. Early tests indicate that the circuit structure is rugged and capable of good electrical performance.     

MM-Wave Band Transversal Filter with Improved Spurious Characteristics

A spurious-suppressed transversal filter using the multiple-coupled line is proposed. The frequency characteristics of the multiple-coupled line are analyzed in detail. In order to compare the performances, the novel spurious-suppressed transversal filter using triple-coupled half-wavelength directional couplers is designed at 30 GHz. The spurious-suppression characteristics of the proposed transversal filter are verified by the full wave analysis and the measurement. The spurious response of the fabricated filter is effectively suppressed and the large attenuation is obtained in the stopband.     

Dynamics of milling processes with variable time delays

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.     

Multivalent binding motifs for the noncovalent functionalization of graphene

Single-layer graphene is a newly available conductive material ideally suited for forming well-defined interfaces with electroactive compounds. Aromatic moieties typically interact with the graphene surface to maximize van der Waals interactions, predisposing most compounds to lie flat on its basal plane. Here we describe a tripodal motif that binds multivalently to graphene through three pyrene moieties and projects easily varied functionality away from the surface. The thermodynamic and kinetic binding parameters of a tripod bearing a redox-active Co(II) bis-terpyridyl complex were investigated electrochemically. The complex binds strongly to graphene and forms monolayers with a molecular footprint of 2.3 nm(2) and a ΔG(ads) = -38.8 ± 0.2 kJ mol(-1). Its monolayers are stable in fresh electrolyte for more than 12 h and desorb from graphene 1000 times more slowly than model compounds bearing a single aromatic binding group. Differences in the heterogeneous rate constants of electron transfer between the two compounds suggest that the tripod projects its redox couple away from the graphene surface.