129 research outputs found
On the variance of the number of occupied boxes
We consider the occupancy problem where balls are thrown independently at
infinitely many boxes with fixed positive frequencies. It is well known that
the random number of boxes occupied by the first n balls is asymptotically
normal if its variance V_n tends to infinity. In this work, we mainly focus on
the opposite case where V_n is bounded, and derive a simple necessary and
sufficient condition for convergence of V_n to a finite limit, thus settling a
long-standing question raised by Karlin in the seminal paper of 1967. One
striking consequence of our result is that the possible limit may only be a
positive integer number. Some new conditions for other types of behavior of the
variance, like boundedness or convergence to infinity, are also obtained. The
proofs are based on the poissonization techniques.Comment: 34 page
CsMgPO4
Caesium magnesium orthophosphate is built up from MgO4 and PO4 tetrahedra (both with . m. symmetry) linked together by corners, forming a three-dimensional framework. The Cs atoms have .m. site symmetry and are located in hexagonal channels running along the a- and b-axis directions
Phase Splitting for Periodic Lie Systems
In the context of the Floquet theory, using a variation of parameter
argument, we show that the logarithm of the monodromy of a real periodic Lie
system with appropriate properties admits a splitting into two parts, called
dynamic and geometric phases. The dynamic phase is intrinsic and linked to the
Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric
phase is represented as a surface integral of the symplectic form of a
co-adjoint orbit.Comment: (v1) 15 pages. (v2) 16 pages. Some typos corrected. References and
further comments added. Final version to appear in J. Phys. A
Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for the nonstationary
Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic
potential. The asymptotic parameter is 1/T, where is the adiabatic
evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Gross-Pitaevskii equation. For the solutions constructed,
the Berry phases are found in explicit form.Comment: 13 pages, no figure
Instability of coherent states of a real scalar field
We investigate stability of both localized time-periodic coherent states
(pulsons) and uniformly distributed coherent states (oscillating condensate) of
a real scalar field satisfying the Klein-Gordon equation with a logarithmic
nonlinearity. The linear analysis of time-dependent parts of perturbations
leads to the Hill equation with a singular coefficient. To evaluate the
characteristic exponent we extend the Lindemann-Stieltjes method, usually
applied to the Mathieu and Lame equations, to the case that the periodic
coefficient in the general Hill equation is an unbounded function of time. As a
result, we derive the formula for the characteristic exponent and calculate the
stability-instability chart. Then we analyze the spatial structure of the
perturbations. Using these results we show that the pulsons of any amplitudes,
remaining well-localized objects, lose their coherence with time. This means
that, strictly speaking, all pulsons of the model considered are unstable.
Nevertheless, for the nodeless pulsons the rate of the coherence breaking in
narrow ranges of amplitudes is found to be very small, so that such pulsons can
be long-lived. Further, we use the obtaned stability-instability chart to
examine the Affleck-Dine type condensate. We conclude the oscillating
condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review
SPERMATOGENIC TESTICULAR FUNCTION IN MEN WITH CHRONIC UROGENITAL MONOTRICHOMONIASIS AND PATHOSPERMIA
We did not observed significant differences in levels of inhibin B and follicle-stimulating hormone in serum samples of men with chronic urogenital trichomoniasis and different spermogram. It confirmed that spermatogenic testicular function in these men is preserved
Современная лекарственная терапия и прогностические факторы при хроническом лимфолейкозе. Обзор литературы и собственные данные
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Synthesis of an adaptive regulator in the stabilization of an uncertain discrete linear system
Synthesis of an adaptive regulator in the stabilization of an uncertain discrete linear system
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