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 $P$ and $X$ 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 $[P,X]=Id$.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 $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n \times n$ 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 $Sp(2n, R)$ symmetry in four dimensions. The stationary case is studied. It is established that the theory allows a $\sigma$-model representation with a target space which is invariant under the $Sp[2(n+1), R]$ group of isometry transformations. The chiral matrix of the coset $Sp[2(n+1), R]/U(n+1)$ is constructed. A K\"ahler formalism based on the use of the Ernst $(n+1) \times (n+1)$ 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 $M$ and $Q$ 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 $M^2-Q^2$ is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where $n$ 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 $\ell = 1$, 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 $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure