53,994 research outputs found
Nuove classi di funzioni scalari quasi concave generalizzate ed applicazioni a problemi di ottimizzazione
In this paper new classes of generalized-concave functions are introduced and studied. Moreover some properties about optimization are provided
On Asymptotic Optimality of Dual Scheduling Algorithm In A Generalized Switch
Generalized switch is a model of a queueing system where parallel servers are interdependent and have time-varying service capabilities. This paper considers the dual scheduling algorithm that uses rate control and queue-length based scheduling to allocate resources for a generalized switch. We consider a saturated system in which each user has infinite amount of data to be served. We prove the asymptotic optimality of the dual scheduling algorithm for such a system, which says that the vector of average service rates of the scheduling algorithm maximizes some aggregate concave utility functions. As the fairness objectives can be achieved by appropriately choosing utility functions, the asymptotic optimality establishes the fairness properties of the dual scheduling algorithm.
The dual scheduling algorithm motivates a new architecture for scheduling, in which an additional queue is introduced to interface the user data queue and the time-varying server and to modulate the scheduling process, so as to achieve different performance objectives. Further research would include scheduling with Quality of Service guarantees with the dual scheduler, and its application and implementation in various versions of the generalized switch model
Some inequalities involving ratios and products of the gamma function
In this paper, we establish some generalized inequalities for the gamma function using the properties of logarithmically convex/concave functions
The Legendre Transform in Non-additive Thermodynamics and Complexity
We present an argument which purports to show that the use of the standard
Legendre transform in non-additive Statistical Mechanics is not appropriate.
For concreteness, we use as paradigm, the case of systems which are
conjecturally described by the (non-additive) Tsallis entropy. We point out the
form of the modified Legendre transform that should be used, instead, in the
non-additive thermodynamics induced by the Tsallis entropy. We comment on more
general implications of this proposal for the thermodynamics of "complex
systems".Comment: 23 pages. LaTeX2e. No figure
Generalized canonical ensembles and ensemble equivalence
This paper is a companion article to our previous paper (J. Stat. Phys. 119,
1283 (2005), cond-mat/0408681), which introduced a generalized canonical
ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous
function of the Hamiltonian . We provide here a simplified introduction
to our previous work, focusing now on a number of physical rather than
mathematical aspects of the generalized canonical ensemble. The main result
discussed is that, for suitable choices of , the generalized canonical
ensemble reproduces, in the thermodynamic limit, all the microcanonical
equilibrium properties of the many-body system represented by even if this
system has a nonconcave microcanonical entropy function. This is something that
in general the standard () canonical ensemble cannot achieve. Thus a
virtue of the generalized canonical ensemble is that it can be made equivalent
to the microcanonical ensemble in cases where the canonical ensemble cannot.
The case of quadratic -functions is discussed in detail; it leads to the
so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title
changed, references updated, new paragraph added, minor differences with
published versio
Geometric convexity of the generalized sine and the generalized hyperbolic sine
In the paper, the authors prove that the generalized sine function
and the generalized hyperbolic sine function
are geometrically concave and geometrically convex, respectively. Consequently,
the authors verify a conjecture posed in the paper "B. A. Bhayo and M.
Vuorinen, On generalized trigonometric functions with two parameters, J.
Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at
\url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".Comment: 5 page
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