665 research outputs found
On the metric dimension of corona product graphs
Given a set of vertices of a connected graph , the
metric representation of a vertex of with respect to is the vector
, where ,
denotes the distance between and . is a resolving set for if
for every pair of vertices of , . The metric
dimension of , , is the minimum cardinality of any resolving set for
. Let and be two graphs of order and , respectively. The
corona product is defined as the graph obtained from and by
taking one copy of and copies of and joining by an edge each
vertex from the -copy of with the -vertex of . For any
integer , we define the graph recursively from
as . We give several results on the metric
dimension of . For instance, we show that given two connected
graphs and of order and , respectively, if the
diameter of is at most two, then .
Moreover, if and the diameter of is greater than five or is
a cycle graph, then $dim(G\odot^k H)=n_1(n_2+1)^{k-1}dim(K_1\odot H).
Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets
An identifying code of a (di)graph is a dominating subset of the
vertices of such that all distinct vertices of have distinct
(in)neighbourhoods within . In this paper, we classify all finite digraphs
which only admit their whole vertex set in any identifying code. We also
classify all such infinite oriented graphs. Furthermore, by relating this
concept to a well known theorem of A. Bondy on set systems we classify the
extremal cases for this theorem
Nonthermal fragmentation of C60
A theoretical study of the subpicosecond fragmentation of C60 clusters in
response to ultrafast laser pulses is presented. We simulate the laser
excitation and the consequent nonequilibrium relaxation dynamics of the
electronic and nuclear degrees of freedom. The first stages of the
nonequilibrium dynamics are dominated by a coherent breathing mode followed by
the cold ejection of single C atoms, in contrast to the dimer emission which
characterizes the thermal relaxation. We also determine the nonequilibrium
damage thresholds as a function of the pulse duration.Comment: 5 pages, 4 figures, submitted to Chem. Phys. Let
Majorana solutions to the two-electron problem
A review of the known different methods and results devised to study the
two-electron atom problem, appeared in the early years of quantum mechanics, is
given, with particular reference to the calculations of the ground state energy
of helium. This is supplemented by several, unpublished results obtained around
the same years by Ettore Majorana, which results did not convey in his
published papers on the argument, and thus remained unknown until now.
Particularly interesting, even for current research in atomic and nuclear
physics, is a general variant of the variational method, developed by Majorana
in order to take directly into account, already in the trial wavefunction, the
action of the full Hamiltonian operator of a given quantum system. Moreover,
notable calculations specialized to the study of the two-electron problem show
the introduction of the remarkable concept of an effective nuclear charge
different for the two electrons (thus generalizing previous known results), and
an application of the perturbative method, where the atomic number Z was
treated effectively as a continuous variable, contributions to the ground state
energy of an atom with given Z coming also from any other Z. Instead,
contributions relevant mainly for pedagogical reasons count simple broad range
estimates of the helium ionization potential, obtained by suitable choices for
the wavefunction, as well as a simple alternative to Hylleraas' method, which
led Majorana to first order calculations comparable in accuracy with well-known
order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure
Unravelling the transport mechanism of pore-filled membranes for hydrogen separation
The permeation characteristics of palladium pore filled (PF) membranes have been investigated with gas permeation and structural characterization of the membranes. PF membranes have been prepared by filling with Pd the nanoporous γ-Al2O3/YSZ (or pure YSZ) layer supported onto porous α-Al2O3 and ZrO2. The number of nanoporous layers and the applied vacuum level during the electroless plating process have been studied. Gas permeation properties of the PF membranes have been determined in a temperature range of 300-550 °C. The measured hydrogen permeances have been found to be lower than previously reported for similar membranes. It has been found that the hydrogen fluxes do not depend on the thickness of the nanoporous layers (γ-Al2O3/YSZ or pure YSZ) or on the vacuum pump employed for filling with Pd. The physicochemical characterization performed showed that the palladium deposited does not form a percolated network across the mesoporous layer(s), leading to low hydrogen permeances and thus low H2/N2 perm-selectivities.The presented work is funded within FERRET project as part of European Union’s Seventh
Framework Programme (FP7/2007-2013) for the Fuel Cells and Hydrogen Joint Technology
Initiative under grant agreement n° 621181.
The Talos TEM was funded as part of HEFCE funding in the UK
Research Partnership Investment Funding (UKRPIF) Manchester RPIF Round 2
Geometric phases for non-degenerate and degenerate mixed states
This paper focuses on the geometric phase of general mixed states under
unitary evolution. Here we analyze both non-degenerate as well as degenerate
states. Starting with the non-degenerate case, we show that the usual procedure
of subtracting the dynamical phase from the total phase to yield the geometric
phase for pure states, does not hold for mixed states. To this end, we furnish
an expression for the geometric phase that is gauge invariant. The parallelity
conditions are shown to be easily derivable from this expression. We also
extend our formalism to states that exhibit degeneracies. Here with the
holonomy taking on a non-abelian character, we provide an expression for the
geometric phase that is manifestly gauge invariant. As in the case of the
non-degenerate case, the form also displays the parallelity conditions clearly.
Finally, we furnish explicit examples of the geometric phases for both the
non-degenerate as well as degenerate mixed states.Comment: 23 page
Young women with a disorder of sex development: learning to share information with health professionals, friends and intimate partners about bodily differences and infertility
Aim: To understand the experiences of young women with a disorder of sex development when sharing information about their body with healthcare professionals, friends and intimate partners. Background: Disorders of sex development are lifelong conditions that create bodily difference such as absence of reproductive organs which can impact on young women's fertility and sexual experiences. Design: Interpretive phenomenological analysis with thirteen young women (14-19 years old) with a disorder of sex development. Methods: The young women chose to participate in either a face-to-face semi-structured interview or to complete a paper diary between 2011-2012. Results: A superordinate theme focusing on the meaning bodily differences held for these young women is presented through three themes: self-awareness and communicating this to others; actualizing intimacy; and expressing meaning of altered fertility to self or professionals or partners. During early adolescence, the young women were guarded and reticent about sharing personal information about their disorder of sex development but as they moved towards adulthood, some of the young women learnt to engage in conversations with more confidence. Frustrations about their bodily differences and the limitations of their bodies were talked about as factors which limited physical spontaneity, impacted on their perceived sexual fulfilment and challenged the development or sustainability of close friendships or intimate partnerships. The young women wanted empathic, sensitive support from knowledgeable health professionals to help them understand their bodies. Conclusion: Attachment and a 'sense of being' were the concepts that were closely linked to the young women's development of a secure identity
Uhlmann's geometric phase in presence of isotropic decoherence
Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)]
is analyzed in the case of a qubit affected by isotropic decoherence treated in
the Markovian approximation. It is demonstrated that this phase decreases
rapidly with increasing decoherence rate and that it is most fragile to weak
decoherence for pure or nearly pure initial states. In the unitary case, we
compare Uhlmann's geometric phase for mixed states with that occurring in
standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]
and show that the latter is more robust to reduction in the length of the Bloch
vector. We also describe how Uhlmann's geometric phase in the present case
could in principle be realized experimentally.Comment: New ref added, refs updated, journal ref adde
Relation between geometric phases of entangled bi-partite systems and their subsystems
This paper focuses on the geometric phase of entangled states of bi-partite
systems under bi-local unitary evolution. We investigate the relation between
the geometric phase of the system and those of the subsystems. It is shown that
(1) the geometric phase of cyclic entangled states with non-degenerate
eigenvalues can always be decomposed into a sum of weighted non-modular pure
state phases pertaining to the separable components of the Schmidt
decomposition, though the same cannot be said in the non-cyclic case, and (2)
the geometric phase of the mixed state of one subsystem is generally different
from that of the entangled state even by keeping the other subsystem fixed, but
the two phases are the same when the evolution operator satisfies conditions
where each component in the Schmidt decomposition is parallel transported
Non-western contexts: the invisible half
Like many other disciplines within the broad area of social sciences (e.g., anthropology, gender studies, psychology, sociology, etc.), consumer research is also highly navigated by scholars from Western countries. This, however, does not mean, by any means, that consumer research is devoted to studying Western contexts only. As evident from the ever-increasing number of regional conferences (e.g., Asia-Pacific and Latin American conferences of the Association for Consumer Research) and non-Western students' enrolment in doctoral programs at Western universities, there are many more researchers (from non-Western countries) who are entering the field and enriching it by their colourful contributions. Yet, given the low number of publications on consumer research in non-Western contexts, it seems that our current knowledge in these societies has a long way to go to flourish. More specifically, and in the domain of consumption culture research, this gap is even further widened by the fact that the culture of consumption in such contexts is largely interpreted with reference to the 'grand narratives' of Western scholars (e.g., Foucault, Mafessoli, Bourdieu, Deleuze, Baudrillard, Nietzsche, Durkheim, Derrida, etc.). Therefore, from an ontological perspective, it seems that our existing knowledge about non-Western societies lies heavily on the 'theoretical structures' that are 'constructed' by Western philosophy as a set of ideas, beliefs, and practices (Said, 1978). As Belk (1995) reminds us, consumption culture always existed in all human societies. What makes contemporary societies different from that of our predecessors' is not the fact that consumption culture did not exist in those societies, but that consumption culture has become a prevailing feature in modern society (Slater, 1997; Lury, 1996; Fırat and Venkatesh, 1995; McCracken, 1988). Therefore, the nature and dynamics of consumption culture in each society should be studied not only against the sociocultural, historical, and economic background of a given context (Western or non-Western) but also with reference to the philosophical and epistemological viewpoints that analyse and interpret cultural practices of that society from within that culture. Addressing such issues, this paper discusses some of the key reasons for lack of theory development in the field from non-western contexts. The paper invites scholars in non-Western contexts to introduce the less articulated, and sometime hidden, body of knowledge from their own contexts into the field of marketing in general and consumer research in particular
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