On the Endomorphisms of Weyl Modules over Affine Kac–Moody Algebras at the Critical Level

We present an independent short proof of the recently established result that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity and residue determined by the highest weight of the Weyl module. We derive this from our results about the shift of argument subalgebras.     

Analysis of Transverse-Momentum Distributions of Charged Particles in Proton–Proton Collisions at Energies in the Range of $$\boldsymbol{(s_{nn})^{1/2}=2.76}$$ –7 TeV at the LHC

Physics of Atomic Nuclei - Experimental transverse-momentum distributions measured by the ALICE Collaboration for charged pions and kaons, protons, and antiprotons at midrapidities in inelastic...     

Production of High-Transverse-Momentum Deuterons and Tritons at an Angle of 40 $${{}^{\circ}}$$ in Proton–Nucleus Interactions at a Beam Energy of 50 GeV

Physics of Atomic Nuclei - Data on the production of positively charged particles emitted at an angle of 40 $${}^{\circ}$$ (in the laboratory frame) with transverse momenta of up to 2.7 GeV $$/c$$...     

Production of ϒ meon in pp colliion at $$\qrt $$ = 7 and 8 TeV in the LHCb experiment

The LHCb results on the production of ? mesons in pp collisions at \(\sqrt s\) = 7 and 8 TeV are briefly reviewed.     

Hypergeometric Solutions for the q-Painlevé Equation of Type {E^{(1)}_6} by the Padé Method

The q-Painlevé equation of type ${E^{(1)}_6}$ is obtained by the Padé method. Special solutions in a determinant formula to the q-Painlevé equations are presented. A relation between the Padé method and Bäcklund transformations of type ${E^{(1)}_6}$ is given.     

Kolmogorov’s Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in $${\mathbb {R}^3}$$

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in \mathbb R³{\mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α ^th -order fractional derivatives of the velocity for some α > 0 in the space variables in L ², which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the L ²-equicontinuity in the time variable and the uniform bound in L ^q , for some q > 2, of the velocity independent of μ > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations in \mathbb R³{\mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of μ > 0, that is in the high Reynolds number limit.     

The theoretical character of the X^1∑^＋ and A^1∑^＋ states of ScN

This paper calculates the potential energy curves (PECs) of the ground state (X 1 Σ + ) and excited state (A 1 Σ + ) of ScN molecule by multireference configuration interaction method. The correct character of the PECs has been gripped while they had been improperly reported in the literature. Based on the PECs, the spectroscopic parameters and vibrational energy levels are determined, and compared with experimental data and other theoretical works available at the present.     

Determination of the spatial dependence of the complex components of the tensor \hat \chi ^{(2)} (z, ω 1 + ω 2; ω 1, ω 2) of a medium with one-dimensional inhomogeneity using a biharmonic wave

It is proven that the spatial profiles of different components of the complex quadratic susceptibility tensor $\hat \chi ^{(2)}$ (z,?? ₁+?? ₂; ?? ₁, ?? ₂), which is responsible for the generation of sum-frequency wave in a plate with one-dimensional inhomogeneity, can be reconstructed unambiguously. A reconstruction technique is proposed. To implement it, one has to direct a plane biharmonic wave with monochromatic components at frequencies ?? ₁ and ?? ₂ onto a plate and measure (in some range of the angles of incidence) the complex amplitude of the sum-frequency wave reflected from the plate. Changing the plane of incidence of the initial wave and (or) the polarization of its monochromatic components, one can determine the coordinate dependences for more than half of the components of $\hat \chi ^{(2)}$ (z,?? ₁+?? ₂; ?? ₁, ?? ₂). This reconstruction can be performed if the symmetry of the plate medium provides a diagonal form for its linear permittivity tensor. The technique proposed implies measurement of the intensities of the sum-frequency waves generated under special conditions using an auxiliary reference plate; this approach allows one to do without complex phase measurements.     

On the contribution of interference of electromagnetic and chromomagnetic dipole operators in the $$ \bar B $$ → Xsγ decay at O(αs2)

The contribution of c-quark loops into the interference of the electromagnetic and chromomagnetic dipole operators in the \(\bar B\) → X _s γ decay is calculated to O(α _s ² ) within the framework of the Standard Model (SM). Several new calculation techniques, such as Laporta’s automated algorithm, the second order decomposition method, and Mellin-Barnes representation, have been used.     

The Local Gromov–Witten Theory of $${\mathbb{C}\mathbb{P}^1}$$ and Integrable Hierarchies

In this paper we begin the study of the relationship between the local Gromov–Witten theory of Calabi–Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full-descendent genus zero theory. Our main tool is the application of Dubrovin’s formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold in the equivariantly Calabi–Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz–Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g ≤ 1; our methods are based on establishing, analogously to the case of KdV, a “quasi-triviality” property for the Ablowitz–Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz–Ladik correspondence at higher genus by testing it successfully in the primary sector for g = 2.     

Reconstruction of the coordinate dependences of quadratic susceptibility tensor \hat \chi ^{(2)} (z, ω1 ± ω2; ω1, ±ω2) components for the one-dimensionally inhomogeneous absorbing medium

A method for the unambiguous reconstruction of the spatial profiles of all components (except for ?? _zzz ) of the quadratic susceptibility complex tensor {ie165-2} (z, ??₁ + ??₂; ??₁, ??₂), which is responsible for the sumfrequency generation in a one-dimensionally inhomogeneous plate is proposed and proven for the first time. Such reconstruction is possible if the symmetry of the medium provides the diagonal character of the linear permittivity tensor {ie165-3} (z, ??). The procedure involves the measurement of the complex amplitude of the new wave with the frequency ??₁ + ??₂ that is reflected from the plate for a certain interval of the angles of incidence of the wave with the frequency ??₂. The reflected wave results from the nonlinear interaction of the wave with frequency ??₂ and the wave with frequency ??₁ that exhibits the normal incidence. A similar approach can be used to determine the profiles of the components of the quadratic susceptibility tensor {ie165-4}(z, ??₁ ? ??₂; ??₁, ? ??₂), which is responsible for the difference-frequency generation.     

Features of the Crystal Structure of Tm1–xYbxB12 Dodecaborides near a Quantum Critical Point and at a Metal–Insulator Transition

JETP Letters - The magnetic phase diagram of Tm1–xYbxB12 antiferromagnets is determined from the specific heat measurements performed at low and ultralow temperatures (0.07–10 K)....     

Uniform in N global well-posedness of the time-dependent Hartree–Fock–Bogoliubov equations in $$\mathbb {R}^{1+1}$$

We prove the global well-posedness of the time-dependent Hartree–Fock–Bogoliubov (TDHFB) equations in \(\mathbb {R}^{1+1}\) with two-body interaction potential of the form \(N^{-1}v_N(x) = N^{\beta -1} v(N^\beta x)\) where \(v\ge 0\) is a sufficiently regular radial function, i.e., \(v \in L^1(\mathbb {R})\cap C^\infty (\mathbb {R})\). In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24–67, 2017), we are able to show for any scaling parameter \(\beta >0\) the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree–Fock–Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).     

Determination of the spatial profiles of all components of the quadratic susceptibility tensor \hat \chi ^{(2)} (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2??; ??, ?? responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of the wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.     

Study of Events with an Electron,Muon, and Two Hadron Jets in the Final State with an Integrated Luminosity of a 139 fb–1 in pp Collisions at $$\sqrt s $$ = 13 TeV with the ATLAS Detector at the LHC

Physics of Atomic Nuclei - To investigate the Higgs boson properties in the h → WW* → еνμν decay channel, events with an electron, muon, and two hadron jets in the...     

Estimation of the $$boldsymbol{p+textrm{He}}$$ Fraction in the Mass Composition of Primary Cosmic Radiation the Energy Range of $$boldsymbol{E_{0}=1}$$ –100 PeV according to Gamma-Ray Families Featuring Halo

Physics of Atomic Nuclei - The present article reports on an analysis of the properties that gamma-ray families featuring a halo exhibit in the cores of extensive air showers (EAS). The events...     

The Feasibility of Testing the Inverse Square Law of Gravitation at Newtonian Strength and at Mass Separations of 1 μm

We examine the feasibility of searching for violations of the inverse square law of gravitation with Newtonian strength and at particle separations of 1 m. We discuss systematic uncertainties, such as spurious forces due to the Casimir force, and various sources of random uncertainty, including those due to patch fields and detector noise. Our analysis suggests that a cryogenic, drag-free space environment is necessary to make the experiment feasible, as thermal and vibrational noise could potentially be reduced to the required level in such an environment.     

Lie point symmetries,conservation laws and exact solutions of ($$1+ n$$)-dimensional modified Zakharov–Kuznetsov equation describing the waves in plasma physics

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the \(\alpha {-}\alpha \) system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.     

Critical points and points of the bifurcation of the rotating magnetized newtonian polytropes with a 1 ⩽ n ⩽ 1.6 index

The presence of critical points and the bifurcation points of rotating Newtonian polytropes with an index of 1 ? n ? 1.6 has been shown for the first time in this paper. The symbolic-numerical calculation error in metric L ₂ has reached the size of the 10^?4 order. The approximate analytical solution to the problem to the abovementioned accuracy has been set forth. A critical value of the polytropes index n = n _k = 1.51025 has been calculated which is the highest among the critical points and bifurcation points. The value n _k corresponds to the infinitely slow polytropes rotation. Furthermore, in this paper the presence of the period jump at the bifurcation point T _b has been predicted and the relative value of this jump ΔT _b /T _b ～ B _0in ^4/3 has been estimated.