We find a sharp estimate for the pre-Schwarzian derivative on the class of holomorphic functions in the unit disk with derivatives subordinate to linear-fractional functions from the family ...parametrized by the Janowski triangle. Applications deal with the uniqueness conditions for the critical point of a conformal radius and with the norm estimates for the pre-Schwarzian derivative.
A
bstract
The two-loop anomalous dimension of the chiral matter superfields is calculated for a general
N
= 1 supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both ...the anomalous dimension defined in terms of the bare couplings, and the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription. For the one-loop finite theories we find a simple relation between the higher derivative regulators under which the anomalous dimension defined in terms of the bare couplings vanishes in the considered approximation. In this case the one-loop finite theory is also two-loop finite in the HD+MSL scheme. Using the assumption that with the higher covariant derivative regularization the NSVZ equation is satisfied for RGFs defined in terms of the bare couplings, we construct the expression for the three-loop
β
-function. Again, the result is written both for the
β
-function defined in terms of the bare couplings and for the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription.
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A mechanism for the origin of Kuiper belt (KB) bodies different from the hitherto known mechanisms is proposed. The distributions of the orbital elements of most of the bodies of the hot component ...of the KB are analyzed. The shape of the distributions indicates that all of these bodies could have appeared as a result of the destruction of a single massive body (Kuiper belt planet, KBP). The separation velocities of the fragments were determined mainly by the linear velocities of the parts of the KBP at different depths and latitudes. The maximum separation velocity corresponded to the linear velocity on the surface of the KBP near the equator and could be 2.4 km/s. The size of the KBP could be either slightly smaller or larger than the size of the Earth. The spin period was approximately 4 h. The KBP spin axis was inclined at a slight angle to the ecliptic plane, and it was directed toward the Sun at the time of destruction. This mechanism is in good agreement with current observational data. It can explain the large number of bodies with satellites in the KB as well as the revealed dependence of the average density of bodies on their size. According to this mechanism, the spin axes of the formed debris (primarily large ones) should be inclined at small angles to the ecliptic plane. The spin axes of the dwarf planets Pluto and Haumea are inclined to the ecliptic plane at angles of 23° and 10°, respectively. The future data on the coordinates of the poles of other large KB bodies can become the final confirmation of the proposed mechanism.
We obtain a number of the uniqueness criteria for the critical point of the conformal radius in the form of the subordination of pre-Schwarzian derivative both to functions of well-known subclasses ...in the geometric function theory and to the images of such functions under the action of some classical operators.
ABSTRACT
We present the results of an investigation of the giant radio pulse (GRP) generation rate from five radio pulsars (B0301+19, B0950+08, B1112+50, B1133+16, and B1237+25) and anomalous ...intensity pulse generation rate from B0809+74. All data used were obtained with the Large Phased Array radio telescope at the Pushchino Radio Astronomy Observatory at 111 MHz from 2012 to 2021. In addition to the analysis of the rate of generation of bright pulses, we analyse the distribution of bright pulses in the phase of the pulsar period and search for clusters of bright pulses – several bright pulses emitted in adjacent pulsar periods. It is found that pulsars B0301+19, B1112+50, B1133+16, and B1237+25 demonstrate different generation rates and generation of clusters. Pulsar B1112+50 generates GRP clusters more often than the other pulsars studied. The longest cluster of GRPs containing four single pulses is detected from this pulsar. GRPs from the pulsars studied are distributed along the longitudes of the main components of the average pulses of these pulsars. This distribution is 1.5–2 times narrower than the phase distribution of non-giant pulses. It is found that the distance between the components of the average GRP profile and the distance between the components of the average non-giant profile differ substantially for pulsars with multicomponent average profiles.
A
bstract
We investigate a recently proposed new form of the exact NSVZ
β
-function, which relates the
β
-function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ...ghosts, and of the chiral matter superfields. Namely, for the general renormalizable
N
= 1 supersymmetric gauge theory, regularized by higher covariant derivatives, the sum of all three-loop contributions to the
β
-function containing the Yukawa couplings is compared with the corresponding two-loop contributions to the anomalous dimensions of the quantum superfields. It is demonstrated that for the considered terms both new and original forms of the NSVZ relation are valid independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings. This result is obtained from the equality relating the loop integrals, which, in turn, follows from the factorization of the integrals for the β-function into integrals of double total derivatives. For the renormalization group functions defined in terms of the renormalized couplings we verify that the NSVZ scheme is obtained with the higher covariant derivative regularization supplemented by the subtraction scheme in which only powers of ln Λ
/μ
are included into the renormalization constants.
This article presents the results of processing observations of 26 radio pulsars of the Northern Hemisphere, obtained as part of the search and study of giant pulses at the Large Phased Array of the ...Pushchino Radio Astronomy Observatory at 111 MHz. Individual pulses with peak flux density 30 and more times higher than the peak flux density of dynamic average profile were found from the pulsars B0011+47, B0450+55, B0525+21, B0751+32, B0823+26, and B0917+63. Pulsars B0450+55, B0525+21, and B0751+32 generate individual pulses that meet the main criteria for giant pulses of pulsars. The analysis of the distributions of individual pulses of pulsars by the peak flux density relative to the average flux density in the session is carried out. From the analyzed sample, for 5 pulsars the distribution is lognormal, for 10 it is a combination of log-normal and power-law distributions. In other cases, it cannot be unambiguously approximated only by the lognormal distribution or by a combination of the lognormal and power-law distributions.
This paper presents a novel algorithm, CrystalOptimizer, for the minimization of the lattice energy of crystals formed by flexible molecules. The algorithm employs isolated-molecule quantum ...mechanical (QM) calculations of the intramolecular energy and conformation-dependent atomic multipoles in the course of the lattice energy minimization. The algorithm eliminates the need to perform QM calculations at each iteration of the minimization by using Local Approximate Models (LAMs), with a minimal impact on accuracy. Additional computational efficiencies are achieved by storing QM-derived components of the lattice energy model in a database and reusing them in subsequent calculations whenever possible. This makes the approach particularly well suited to applications that involve a sequence of lattice energy evaluations, such as crystal structure prediction. The algorithm is capable of handling efficiently complex systems with considerable conformational flexibility. The paper presents examples of the algorithm’s application ranging from single-component crystals to cocrystals and salts of flexible molecules with tens of intramolecular degrees of freedom whose optimal values are determined by the interplay of conformational strain and packing forces. For any given molecule, the degree of flexibility to be considered can vary from a few torsional angles to relaxation of the entire set of torsion angles, bond angles, and bond lengths present in the molecule.
Sirtuins comprise a unique class of nicotinamide adenine dinucleotide (NAD⁺)-dependent deacetylases that target multiple protein substrates to execute diverse biological functions. These enzymes are ...key regulators of clinically important cellular and organismal processes, including metabolism, cell division and aging. The desire to understand the important determinants of human health and lifespan has resulted in a firestorm of work on the seven mammalian sirtuins in less than a decade. The implication of sirtuins in medically important areas such as diabetes, cancer, cardiovascular dysfunction and neurodegenerative disease has further catapulted them to a prominent status as potential targets for nutritional and therapeutic development. Here, we present a review of published results on sirtuin biology and its relevance to human disease.
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