3,619 research outputs found
On Pairs of Difference Operators Satisfying: [P,Q] = Id
Different finite difference replacements for the derivative are analyzed in
the context of the Heisenberg commutation relation. The type of the finite
difference operator is shown to be tied to whether one can naturally consider
and to be self-adjoint and skew self-adjoint or whether they have to be
viewed as creation and annihilation operators. The first class, generalizing
the central difference scheme, is shown to give unitary equivalent
representations. For the second case we construct a large class of examples,
generalizing previously known difference operator realizations of .Comment: 32 pages, plain Te
String theory extensions of Einstein-Maxwell fields: the static case
We present a new approach for generation of solutions in the four-dimensional
heterotic string theory with one vector field and in the five-dimensional
bosonic string theory starting from the static Einstein-Maxwell fields. Our
approach allows one to construct the solution classes invariant with respect to
the total subgroup of the three-dimensional charging symmetries of these string
theories. The new generation procedure leads to the extremal
Israel-Wilson-Perjes subclass of string theory solutions in a special case and
provides its natural continuous extension to the realm of non-extremal
solutions. We explicitly calculate all string theory solutions related to
three-dimensional gravity coupled to an effective dilaton field which arises
after an appropriate charging symmetry invariant reduction of the static
Einstein-Maxwell system.Comment: 19 pages in late
Symplectic Gravity Models in Four, Three and Two Dimensions
A class of the gravity models describing a coupled system of
Abelian vector fields and the symmetric matrix generalizations of
the dilaton and Kalb-Ramond fields is considered. It is shown that the
Pecci-Quinn axion matrix can be entered and the resulting equations of motion
possess the symmetry in four dimensions. The stationary case is
studied. It is established that the theory allows a -model
representation with a target space which is invariant under the
group of isometry transformations. The chiral matrix of the coset is constructed. A K\"ahler formalism based on the use of the Ernst
complex symmetric matrix is developed. The stationary
axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending
on the original field variables is obtained. The Kramer-Neugebauer
transformation, which algebraically maps the original variables into the target
space ones, is presented.Comment: 21 pages, RevTex, no figurie
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
We consider a Hamiltonian quantum theory of spherically symmetric,
asymptotically flat electrovacuum spacetimes. The physical phase space of such
spacetimes is spanned by the mass and the charge parameters and of the
Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical
momenta. In this four-dimensional phase space, we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner.
The classical Hamiltonian written in terms of these variables and their
conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian
operator, and an eigenvalue equation for the ADM mass of the hole, from the
point of view of a distant observer at rest, is obtained. Our eigenvalue
equation implies that the ADM mass and the electric charge spectra of the hole
are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of
the quantity is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of the quantity are of the form , where
is an integer. It turns out that this result is closely related to
Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure
Left atrial strain in assessing heart failure with preserved ejection fraction in hypertensive patients
Aim. To compare the results of diagnosing heart failure with preserved ejection fraction (HFpEF) in patients with hypertension (HTN) according left atrial (LA) strain values with the results obtained using the H2FPEF score and diastolic stress testing (DST).Material and methods. The study included 293 patients with previously established HTN who were examined due to complaints of shortness of breath and/or palpitations (men, 97 (33,5%), mean age, 62,0 (55,0; 67,0) years). All patients underwent transthoracic echocardiography with the assessment of LA strain parameters and probability of HFpEF using the H2FPEF score. Eighty five patients with an intermediate probability of HFpEF underwent DST.Results. A low probability of HFpEF according to the H2FPEF score was registered in 35 (11,9%) patients, uncertain — in 206 (70,3%), high — in 52 (17,7%). DST was negative in 43 (50,6%) and positive in 42 (49,4%) patients with an intermediate probability of HFpEF. LA strain in the reservoir phase in patients with a low probability of HFpEF averaged (median and interquartile interval) 28,0 (23,6; 31,5)%, while in patients with an intermediate probability and negative DST — 24,0 (22,0; 26,8)%, with an intermediate probability and positive DST — 20,0 (18,0; 21,0)%, and with a high probability of HFpEF — 19,6 (16,9; 21,8)%. HFpEF was diagnosed in 94 patients, including 52 with a high probability on the H2FPEF score and 42 with an intermediate probability and positive DST. The diagnosis of HFpEF was ruled out in 78 patients, including 35 with a low probability on the H2FPEF score and 43 with an intermediate probability and negative DST. Further, 172 patients with confirmed or excluded HFpEF were randomly divided into two equal cohorts. In the training cohort, HFpEF was diagnosed in 44 (51,2%) patients, in the validation cohort — in 50 (58,1%). ROC analysis performed on the training cohort for the LA strain in reservoir phase showed AUC of 0,920 (95% confidence interval (CI), 0,842-0,968) and cut-off point of 21,5%. In the training cohort, the results of HFpEF diagnosis using the indicated criterion coincided with those using H2FPEF score and DST in 86,1% (95% CI, 77,2-91,8) of cases. The Cohen’s kappa was 0,721 (95% C,I 0,575-0,868). In the validation cohort, agreement was observed in 84,9% (95% CI 75,8-91,0) of cases with Cohen’s kappa of 0,702 (95% CI 0,553-0,851).Conclusion. In hypertensive patients, the diagnosis of HFpEF made on the basis of a decrease in the LA strain in reservoir phase to ≤21,5%, is in good agreement with the diagnosis made using the H2FPEF score and DST
Building blocks of a black hole
What is the nature of the energy spectrum of a black hole ? The algebraic
approach to black hole quantization requires the horizon area eigenvalues to be
equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be
exponentially degenerate with respect to the area quantum number if one is to
understand black hole entropy as reflecting degeneracy of the observable
states. Here we construct the black hole states by means of a pair of "creation
operators" subject to a particular simple algebra, a slight generalization of
that for the harmonic oscillator. We then prove rigorously that the n-th area
eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole
entropy qua logarithm of the number of states for fixed horizon area comes out
proportional to that area.Comment: PhysRevTeX, 14 page
Morphophysiological peculiarities of productivity formation in columnar apple varieties
Received: December 30th, 2021 ; Accepted: February 22nd, 2022 ; Published: March 4th, 2022 ; Correspondence: [email protected] of generative buds is one of the most important biological processes of
plant transition from vegetative to generative state. This process is key to the problem of creating
regular fruit-bearing and early-fruiting plantations. The article provides information on the
organogenesis of buds in plants of columnar apple varieties in the Forest-Steppe of Ukraine,
which allows establishing the features of this process in complex fruit formations of different
ages, and the levels of their productivity and longevity. Research to study the organogenesis of
different-age fruit formations of columnar apple varieties was conducted in the northern part of
the Forest-Steppe of Ukraine during 2016–2020. The efficiency of realization the plants biological
potential of all studied columnar apple varieties at III–IV and V–IX stages of organogenesis was
high: the largest number of buds from their total number differentiated into generative on trees
varieties ‘Sparta’, ‘President’, ‘Bilosnizhka’, ‘Valuta’ and ‘Tantsivnytsia’ (37–51%), the smallest
in ‘Favoryt’ and ‘Bolero’. The biggest number of flowers per one potentially generative bud was
formed by plants of ‘Tantsivnytsia’ and ‘Bilosnizhka’ varieties. The lowest level of ovarian loss
during the X stage of organogenesis was observed on plants of ‘Valuta’, ‘President’, and
‘Tantsivnytsia’ varieties (41–49%), and the highest - in ‘Favoryt’ variety (up to 83%). More
effective realization of potential productivity at the XI stage of organogenesis occurred in plants
of ‘President’, ‘Valuta’ and ‘Tantsivnytsia’ varieties; their trees on one potentially generative bud
formed - 0.27–0.38 fruits. The coefficient of determination indicates that the influence of
meteorological conditions of the year on the passage of III–IV stages of organogenesis is 46%;
V–IX stages - 42%; Stage X - 17%; Stage XI - 24%
Perturbation theory for self-gravitating gauge fields I: The odd-parity sector
A gauge and coordinate invariant perturbation theory for self-gravitating
non-Abelian gauge fields is developed and used to analyze local uniqueness and
linear stability properties of non-Abelian equilibrium configurations. It is
shown that all admissible stationary odd-parity excitations of the static and
spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have
total angular momentum number , and are characterized by
non-vanishing asymptotic flux integrals. Local uniqueness results with respect
to non-Abelian perturbations are also established for the Schwarzschild and the
Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly
stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable
modes with are also excluded for the static and spherically
symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure
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