3,200 research outputs found
Optimal mean value estimates beyond Vinogradov's mean value theorem
We establish improved mean value estimates associated with the number of
integer solutions of certain systems of diagonal equations, in some instances
attaining the sharpest conjectured conclusions. This is the first occasion on
which bounds of this quality have been attained for Diophantine systems not of
Vinogradov type. As a consequence of this progress, whenever we
obtain the Hasse principle for systems consisting of cubic and
quadratic diagonal equations in variables, thus attaining the
convexity barrier for this problem.Comment: Our original treatment of systems with degrees contained a
fatal flaw (thanks to S. T. Parsell for alerting us to this). The revised
version gives an adapted treatment, leading to different results for . All results involving only quadratic and cubic equations remain
unaffecte
Vinogradov systems with a slice off
Let denote the number of integral solutions of the modified
Vinogradov system of equations with .
By exploiting sharp estimates for an auxiliary mean value, we obtain bounds for
for . In particular, when
satisfy and , we establish the essentially
diagonal behaviour .Comment: 19 page
Phase Transitions in Generalised Spin-Boson (Dicke) Models
We consider a class of generalised single mode Dicke Hamiltonians with
arbitrary boson coupling in the pseudo-spin - plane. We find exact
solutions in the thermodynamic, large-spin limit as a function of the coupling
angle, which allows us to continuously move between the simple dephasing and
the original Dicke Hamiltonians. Only in the latter case (orthogonal static and
fluctuating couplings), does the parity-symmetry induced quantum phase
transition occur.Comment: 6 pages, 5 figue
Warhogs: A History of War Profits in America
The Puritans condemned war profiteering as a Provoking Evil, George Washington feared that it would ruin the Revolution, and Franklin D. Roosevelt promised many times that he would never permit the rise of another crop of war millionaires. Yet on every occasion that American soldiers and sailors served and sacrificed in the field and on the sea, other Americans cheerfully enhanced their personal wealth by exploiting every opportunity that wartime circumstances presented.
In Warhogs, Stuart D. Brandes masterfully blends intellectual, economic, and military history into a fascinating discussion of a great moral question for generations of Americans: Can some individuals rightly profit during wartime while others sacrifice their lives to protect the nation?
Drawing upon a wealth of manuscript sources, newspapers, contemporary periodicals, government reports, and other relevant literature, Brandes traces how each generation in financing its wars has endeavored to assemble resources equitably, to define the ethical questions of economic mobilization, and to manage economic sacrifice responsibly. He defines profiteering to include such topics as price gouging, quality degradation, trading with the enemy, plunder, and fraud, in order to examine the different guises of war profits and the degree to which they have existed from one era to the next.
This far-reaching discussion moves beyond a linear narrative of the financial schemes that have shaped this nation\u27s capacity to make war to an in-depth analysis of American thought and culture. Those scholars, students, and general readers interested in the interaction of legislative, economic, social, and technological events with the military establishment will find no other study that so thoroughly surveys the story of war profits in America.
Stuart D. Brandes is professor of history at the University of Wisconsin-Rock County.
Stuart D. Brandes has written a solid, thoroughly researched, and exceedingly unemotional and restrained history of a neglected subject, carrying it through World War II with a limited consideration of the Cold War. . . . [H]is book is not to be ignored by either economic or military historians. —American Historical Review
Offers a treasure of information on greed and selfishness during crises in America. —Reviews in American History
A valuable addition to the historiography of the United States munitions industry and its relationship to American democracy and capitalism. —Journal of Southwest Georgia History
The only comprehensive attempt to deal with the many facets of government contracting during time of military crisis through World War II. . . . This balanced account is must reading for anyone interested in American military history. —Military History of the West
Stuart D. Brandes is the first scholar to tackle the complex and ever-shifting issue of war profits across nearly the entire scope of American history. This highly readable narrative asks the right questions and supplies cogent, well-reasoned answers based on impressive research and careful reflection. —Daniel E. Sutherlandhttps://uknowledge.uky.edu/upk_united_states_history/1106/thumbnail.jp
Non-equilibrium correlations and entanglement in a semiconductor hybrid circuit-QED system
We present a theoretical study of a hybrid circuit-QED system composed of two
semiconducting charge-qubits confined in a microwave resonator. The qubits are
defined in terms of the charge states of two spatially separated double quantum
dots (DQDs) which are coupled to the same photon mode in the microwave
resonator. We analyze a transport setup where each DQD is attached to
electronic reservoirs and biased out-of-equilibrium by a large voltage, and
study how electron transport across each DQD is modified by the coupling to the
common resonator. In particular, we show that the inelastic current through
each DQD reflects an indirect qubit-qubit interaction mediated by off-resonant
photons in the microwave resonator. As a result of this interaction, both
charge qubits stay entangled in the steady (dissipative) state. Finite shot
noise cross-correlations between currents across distant DQDs are another
manifestation of this nontrivial steady-state entanglement.Comment: Final versio
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
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