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Using the skew-Hopf pairing, we obtain ℛ -matrix for the two-parameter quantum algebra U v , t . We further construct a strict monoidal functor from the tangle category (OTa , ⊗ , ∅) to the category (Mod , ⊗ , ℚ (v , t)) of U v , t -modules. As a consequence, the quantum knot invariant of the tangle L of type (n , n) is obtained by the action of on the closure L ̃ of L. [ABSTRACT FROM AUTHOR]

Due to the availability of fuel, favorable kinetics, and high output energy, the deuterium-tritium (D-T) fusion reaction is dominantly used in thermonuclear fusion. This paper presents a detailed, step-by-step theoretical calculation of the D-T fusion cross-section within the framework of the phenomenological R-matrix method. The fundamental principles of the phenomenological R-matrix method are outlined. Nuclear and Coulomb interactions are addressed by the R-matrix formalism, which classifies the configuration space into internal and external regions, respectively. Precise Coulomb functions are utilized in the calculations, essential for the accurate determination of the penetration and shift factors. Precise Coulomb functions for the D+T, 4He+12C systems have been calculated. The penetration and shift factors for the D+T system for a given angular momentum have been obtained. Two different R-matrix models with parameters from recent scientific papers are employed to calculate D-T fusion cross-sections and reaction rates, which are then compared with those obtained from the ENDF/B-VIII.0 library data. Within a crucial low-energy range (from 0 to 0.1 MeV), important for fusion technology, our results show quite good agreement with experimental data, while in a high-energy range, the obtained results are slightly underestimated due to non-resonant 5He levels not being taken into account. These findings indicate that the models can be used for future thermonuclear fusion applications. [ABSTRACT FROM AUTHOR]

We study minimal triangular structures on abelian extensions. In particular, we construct a family of minimal triangular semisimple Hopf algebras and prove that the Hopf algebra H b : y in the semisimple Hopf algebras of dimension 16 classified by Y. Kashina in 2000 is minimal triangular Hopf algebra with smallest dimension among non-trivial semisimple triangular Hopf algebras (i.e. not group algebras or their dual). [ABSTRACT FROM AUTHOR]

Based on work related to the R-matrix theory, we first abstract the Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, a generalized zero-curvature equation expressed by the Poisson bracket is exhibited. As an application of this theory, a generalized (2+1)-dimensional integrable system is obtained, from which a resulting generalized Davey–Stewartson (DS) equation and a generalized Pavlov equation (gPe) are further obtained. Via the use of a nonisospectral zero-curvature-type equation, some (3+1) -dimensional integrable systems are produced. Next, we investigate the recursion operator of the gPe using an approach under the framework of the R-matrix theory. Furthermore, a type of solution for the resulting linearized equation of the gPe is produced by using its conserved densities. In addition, by applying a nonisospectral Lax pair, a (3+1)-dimensional integrable system is generated and reduced to a Boussinesq-type equation in which the recursion operators and the linearization are produced by using a Lie symmetry analysis; the resulting invertible mappings are presented as well. Finally, a Bäcklund transformation of the Boussinesq-type equation is constructed, which can be used to generate some exact solutions. [ABSTRACT FROM AUTHOR]

In the paper we present the angular distributions of photoelectrons in ionization of neon atom by a field of several multiple frequencies. The considered setup is referred to the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) spectroscopy under condition that the field frequencies are selected in such a way that resonant transitions through discrete states play an important role. The role of the phase of the seeding infrared field on the angular distributions of photoemission is analyzed. A significant difference in the anisotropy parameters at the near-threshold sideband caused by transitions through discrete states is shown. Two methods are compared: numerical solution of the rate equations with continuum discretization and third-order perturbation theory. [ABSTRACT FROM AUTHOR]

The isotope 1 6 O is one of the most abundant light isotopes, and therefore the process 1 6 O (n , γ) 1 7 O reaction plays a critical role in stellar nucleosynthesis. Reaction cross-sections and rates for neutron capture by 1 6 O at astrophysical energies have been calculated with special attention to low-lying, narrow resonances while implementing R -matrix formalism during integration. [ABSTRACT FROM AUTHOR]

We provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang–Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our neural network on the spin chains of difference form with two-dimensional local space. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an Explorer , scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains with higher dimensional local space and in more general settings where no analytical methods are available.

An extensive study of photoionization from neon excited states was performed. The R-matrix approach was applied to calculate a photoionization cross-section from the metastable 2 p 5 (2 P J f) 3 s [ K ] 0 , 2 and dipole-allowed 2 p 5 (2 P J f) 3 s [ K ] 1 states. The resonance structures and Cooper minimum accessible in photoionization from the excited states by the photons with energy below 30 eV were analyzed. The parameters of the lowest autoionizing states (AISs) of even parity were extracted by fitting of the photoionization cross-section. For the dipole-allowed states, calculations are presented for unpolarized, linearly and circularly polarized radiation. [ABSTRACT FROM AUTHOR]

Based on work related to the R-matrix theory, we first abstract the Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, a generalized zero-curvature equation expressed by the Poisson bracket is exhibited. As an application of this theory, a generalized (2+1)-dimensional integrable system is obtained, from which a resulting generalized Davey–Stewartson (DS) equation and a generalized Pavlov equation (gPe) are further obtained. Via the use of a nonisospectral zero-curvature-type equation, some (3+1) -dimensional integrable systems are produced. Next, we investigate the recursion operator of the gPe using an approach under the framework of the R-matrix theory. Furthermore, a type of solution for the resulting linearized equation of the gPe is produced by using its conserved densities. In addition, by applying a nonisospectral Lax pair, a (3+1)-dimensional integrable system is generated and reduced to a Boussinesq-type equation in which the recursion operators and the linearization are produced by using a Lie symmetry analysis; the resulting invertible mappings are presented as well. Finally, a Bäcklund transformation of the Boussinesq-type equation is constructed, which can be used to generate some exact solutions.

Over an algebraically closed field k of characteristic zero, the Drinfeld double D n of the Taft algebra that is defined using a primitive n th root of unity q ∈ k for n ≥ 2 is a quasitriangular Hopf algebra. Kauffman and Radford have shown that D n has a ribbon element if and only if n is odd, and the ribbon element is unique; however there has been no explicit description of this element. In this work, we determine the ribbon element of D n explicitly. For any n ≥ 2 , we use the R-matrix of D n to construct an action of the Temperley-Lieb algebra TL k (ξ) with ξ = − (q 1 2 + q − 1 2 ) on the k -fold tensor power V ⊗ k of any two-dimensional simple D n -module V. This action is known to be faithful for arbitrary k ≥ 1. We show that TL k (ξ) is isomorphic to the centralizer algebra End D n (V ⊗ k) for 1 ≤ k ≤ 2 n − 2. [ABSTRACT FROM AUTHOR]

The typical energy range for charge particle interactions in stellar plasmas corresponds to a few 10s or 100s of keV. At these low energies, the cross sections are so vanishingly small that they cannot be measured directly with accelerator based experimental techniques. Thus, indirect studies of the compound structure near the threshold are used in the framework of reaction models to complement the direct data in order to extrapolate the cross section into the low energy regime. However, at the extremely small cross sections of interest, there maybe other quantum effects that modify the such extracted cross section. These may result from additional nuclear interactions associated with the threshold itself or could be due to other processes, such as electron screening. Measurements in plasma environments like at the OMEGA or National Ignition Facility facilities offer an entirely new set of experimental conditions for studying these types of reactions, often directly at the energies of interest. In this paper, we examine three reaction, 10B(p,α)7Be, 12C(p,γ)13N and 14N(p,γ)15O, which have all been measured at very low energies using accelerator based methods. All three reactions produce relatively long-lived radioactive nuclei, which can be collected and analyzed at plasma facilities using a variety of collection and identification techniques.

The broadly applied notions of Lie bialgebras, Manin triples, classical r-matrices and 풪 -operators of Lie algebras owe their importance to the close relationships among them. Yet these notions and their correspondences are mostly understood as classes of objects and maps among the classes. To gain categorical insight, this paper introduces, for each of the classes, a notion of homomorphisms, uniformly called coherent homomorphisms, so that the classes of objects become categories and the maps among the classes become functors or category equivalences. For this purpose, we start with the notion of an endo Lie algebra, consisting of a Lie algebra equipped with a Lie algebra endomorphism. We then generalize the above classical notions for Lie algebras to endo Lie algebras. As a result, we obtain the notion of coherent endomorphisms for each of the classes, which then generalizes to the notion of coherent homomorphisms by a polarization process. The coherent homomorphisms are compatible with the correspondences among the various constructions, as well as with the category of pre-Lie algebras. [ABSTRACT FROM AUTHOR]

Electron collision cross-sections of c-C4F8 were investigated at low energies by using the R-matrix method. The static exchange (SE), static exchange with polarization (SEP), and close-coupling (CC) models of the R-matrix method were used for the calculation of the scattering cross-section. The shape resonance was detected with all the models at around 3~4 eV, and a Feshbach resonance was detected with the SEP model at 7.73 eV, in good agreement with the previous theoretical calculation. The resonance detected was also associated with the experimental dissociative electron attachment of c-C4F8, which displayed the resonances at the same energy range. The cross-sections calculated are important for plasma modeling and applications. [ABSTRACT FROM AUTHOR]

The quantum Sugawara operators associated with a simple Lie algebra g are elements of the center of a completion of the quantum affine algebra U q (g ˆ) at the critical level. By the foundational work of Reshetikhin and Semenov-Tian-Shansky (1990), such operators occur as coefficients of a formal Laurent series ℓ V (z) associated with every finite-dimensional representation V of the quantum affine algebra. As demonstrated by Ding and Etingof (1994), the quantum Sugawara operators generate all singular vectors in generic Verma modules over U q (g ˆ) at the critical level and give rise to a commuting family of transfer matrices. Furthermore, as observed by E. Frenkel and Reshetikhin (1999), the operators are closely related with the q -characters and q -deformed W -algebras via the Harish-Chandra homomorphism. We produce explicit quantum Sugawara operators for the quantum affine algebra of type A which are associated with primitive idempotents of the Hecke algebra and parameterized by Young diagrams. This opens a way to understand all the related objects via their explicit constructions. We consider one application by calculating the Harish-Chandra images of the quantum Sugawara operators. The operators act by scalar multiplication in the q -deformed Wakimoto modules and we calculate the eigenvalues by identifying them with the Harish-Chandra images. [ABSTRACT FROM AUTHOR]

Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ2-based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3He (α,γ)7Be and 3He (α,α)3He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

Shapovalov elements θ β , m of the classical or quantized universal enveloping algebra of a simple Lie algebra g are parameterized by a positive root β and a positive integer m. They relate the highest vector of a reducible Verma module with highest vectors of its submodules. We obtain a factorization of θ β , m to a product of θ β , 1 and calculate θ β , 1 as a residue of a matrix element of the inverse Shapovalov form via a generalized Nagel-Moshinsky algorithm. This way we explicitly express θ β , m of a classical simple Lie algebra through the Cartan-Weyl basis in g. In the case of quantum groups, we give an analogous formulation through the entries of the R-matrix (quantum L -operator) in fundamental representations. [ABSTRACT FROM AUTHOR]

We have investigated C-rich linear molecule (H–C C–C C–C N), which is detected in many regions of space, especially on Titan atmosphere [ Astron. Astrophys. 2015 , 578, A111 ]. The present study helps us to understand the chemistry associated with the C-rich linear molecules. This study presents the multichannel quantum calculation to analyze the resonant scattering of low to high energy electrons with cyanodiacetylene (HC 5 N). We conducted a detailed structural analysis and explored their unoccupied molecular orbitals structure. We found that low energy electronic resonances are due to trapping of electron in their respective unoccupied molecular orbitals. In this study, we confirmed the presence of three π* resonances along with one σ* resonances. Additionally, differential, momentum transfer, electronic excitation, and total electron scattering cross sections are reported for the first time. This work provides comprehensive theoretical data of electron scattering, which would be useful for understanding the molecular chemistry involving this molecule. • Comprehensive theoretical study of the dissociative electron attachment of acrylonitrile. • The present theoretical DEA calculations for CN− and C 3 N− are in excellent agreement with the data available in literature. • Both the anions studied here are abundant in Titan's ionosphere. • This is the maiden theoretical attempt to provide dissociative electron attachment cross-section for acrylonitrile. • These data are useful for understanding its chemistry in the interstellar medium and as well as for industrial applications. [ABSTRACT FROM AUTHOR]

We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE . It has an interpretation in terms of representations of Dynkin quivers and can be proved in a unified way using geometry of the graded quiver varieties. As a by-product, we obtain a geometric interpretation of Kang–Kashiwara–Kim's generalized quantum affine Schur–Weyl duality functor when it arises from a family of the fundamental modules. We also study several cases when the graded quiver varieties are isomorphic to unions of the graded nilpotent orbits of type A . [ABSTRACT FROM AUTHOR]

In this second part of a two part paper (first part: Zawadzki et al (2020 J. Phys. B: At. Mol. Opt. Phys. 53 165201)) we present differential scattering cross sections for excitation of several Rydberg electronic states of carbon monoxide by electron impact. The first part concerned the low-lying valence states of CO. In the present study cross sections are obtained experimentally using low-energy electron energy-loss spectroscopy and theoretically using the R-matrix method. Incident electron energies range from near-threshold of 12.5 eV to 20 eV while the scattering angles range from 20° to 120°. The R-matrix calculations use three distinct close-coupling models and their results are compared to available experimental and theoretical cross sections. The overall comparison leads to significantly improved description of the excitation cross sections for this target. [ABSTRACT FROM AUTHOR]

The differential cross section of the deuteron elastic scattering on oxygen was studied, experimentally, in the energy range of 1.5 – 2.5 MeV, in order for the theoretical study to be accomplished in the energy range 1.9–2.5 MeV for the scattering angles of 130°, 140°, 150°, 160° and 170°.The experiment was performed at the Tandem 5.5 MV Accelerator of the N.C.S.R. "Demokritos" in Athens, Greece. The theoretical study was accomplished in order to extend the pre-existing evaluation, which stopped at 1.98 MeV, up to 2.5 MeV. The used code implements the R-matrix theory along with optical model calculations. [ABSTRACT FROM AUTHOR]

The electron scatterings from isovalent molecules like O 3 , S 3 , OSO and SOS are studied using single centre expansion (SCE) approximation. The elastic differential cross-sections, integral and momentum transfer cross-sections are computed for these targets from ionisation threshold to 5 keV. The molecular wave functions of the targets were obtained from the multicentre expansion of the Gaussian-type orbitals within the single determinant Hartree–Fock self-consistent field scheme. The multipole expansion of the target at the centre of mass includes the dipole and quadrupole terms. The target interactions are modelled within the local potential approximation and consist of static, correlation-polarisation and exchange effects. The results are in good agreement with the available experimental and theoretical results. The SCE results match smoothly near the ionisation threshold with the ab-initioR-matrix results. This helped in estimating the scattering cross-section data from 0.1 to 5 keV energy. The total cross-sections obtained by summing the elastic and inelastic cross-sections are also in excellent agreement with the available results. The scattering study from isovalent molecules further helped in understanding the effects of dipole moment, polarisation and geometrical size while evaluating the collision problem. [ABSTRACT FROM AUTHOR]

The quantum scattering calculations for ultra-cold collisions are performed using a variational procedure based on the R-matrix theory for unbound states employing the finite element method (FEM) for expansion of the wave-function in terms of a finite set of local basis functions. The proposed FEM implementation presents as advantages the possibility of the development of an efficient matrix inversion algorithm which significantly reduces the computation time to calculate the R matrix and makes it numerically competitive. As test cases, we have determined the scattering length for the elastic collision between two alkali atoms using the one- and two-channel formalisms. The efficiency of the methodology is evaluated by comparing our results with several ones previously published in the literature. [ABSTRACT FROM AUTHOR]

We construct a family of q deformations of E (2) group for nonzero complex parameters | q | < 1 as locally compact braided quantum groups over the circle group 𝕋 viewed as a quasitriangular quantum group with respect to the unitary R -matrix R (m , n) : = (q / q ̄) m n for all m , n ∈ ℤ. For real 0 < | q | < 1 , the deformation coincides with Woronowicz's E q (2) groups. As an application, we study the braided analogue of the contraction procedure between SU q (2) and E q (2) groups in the spirit of Woronowicz's quantum analogue of the classic Inönü–Wigner group contraction. Consequently, we obtain the bosonization of braided E q (2) groups by contracting U q (2) groups. [ABSTRACT FROM AUTHOR]

We prove that the singularities of the R -matrix R (k) of the minimal quantization of the adjoint representation of the Yangian Y (𝔤) of a finite dimensional simple Lie algebra 𝔤 are the opposite of the roots of the monic polynomial p (k) entering in the OPE expansions of quantum fields of conformal weight 3 / 2 of the universal minimal affine W -algebra at level k attached to 𝔤. [ABSTRACT FROM AUTHOR]

Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G 2 (1) , E 6 (1) , and Tp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside. [ABSTRACT FROM AUTHOR]

The 1 2 C( 2 0 Ne, 1 6 O) 1 6 O reaction has been used for the first time to determine ANC of 1 6 O levels. The 1 2 C( 2 0 Ne, 1 6 O) 1 6 O α -transfer angular distributions are measured at E lab = 1 5 0 MeV and used to determine the ANC of the ground, 6.05 MeV ( 0 + ), 6.13 MeV ( 3 − ), 6.92 MeV ( 2 + ) and 7.12 MeV ( 1 − ) states of 1 6 O. The ANC values are C 2 (0 +) = (2 2. 2 ± 7. 1) × 1 0 4 fm − 1 , C 2 (0 +) = (1. 4 0 ± 0. 5 4) × 1 0 6 fm − 1 , C 2 (3 −) = (2. 3 0 ± 0. 9 2) × 1 0 4 fm − 1 , C 2 (2 +) = (1. 0 7 ± 0. 3 2) × 1 0 1 0 fm − 1 and C 2 (1 −) = (3 2. 2 9 ± 1 0. 1 4) × 1 0 2 8 fm − 1 . Astrophysical S-factors at 300 keV are extracted { S E 1 3 0 0 = (7 9. 1 8 ± 2 6. 6 0) keV b and S E 2 3 0 0 = (5 2. 5 1 ± 2 4. 3) keV b } using these ANC values by R-matrix theory. [ABSTRACT FROM AUTHOR]

The present study focuses on electron collision with bromine molecule, employing ab-initio scattering calculations. Using the R-matrix method, we calculated elastic and inelastic cross-sections using two different scattering models: static exchange with polarization and close-coupling. Our findings reveal total three low energy resonances for e-Br 2 scattering which are primarily formed through transient negative ions. This observation is supported by dissociative electron attachment cross-section analysis, potential energy curves, and molecular orbital diagrams. Out of these three, first is at zero-energy, the electron attachment is recognized as shape-resonance and further two π* resonances as core-excited resonances. Present computation becomes more important as many cross-sections are reported as bench mark results in absence of any reported data. For instance: elastic, differential, momentum transfer, excitation and total cross-section. Comparing our results with sparse existing literature, we find good agreement. • This is a maiden theoretical attempt to provide low-energy scattering cross-section data using ab-initio R-matrix method. • These calculations provide insights into the electronic structure and dynamics of Br 2 during low-energy electron collisions. • We computed DEA along with potential energy curve of Br 2. • We confirmed zero-energy electron attachment along with various low energy resonances manifested by TNI. • This study stands relevant in: radiation chemistry, gas discharges, plasmas, mass spectrometry and planetary atmospheres. [ABSTRACT FROM AUTHOR]

In this paper, atomistic-level quantum mechanical simulations are performed for nanoscale field-effect transistors (FETs) with lateral or vertical heterojunction, within the non-equilibrium Green's function formalism. For efficient simulation of such heterostructure FETs, a novel approach is developed where the Green's functions are calculated by complementarily using the two algorithms of the recursive Green's function and the R -matrix. The R -matrix algorithm is extended to seamlessly combine the two methods on the open system and an algorithm for the electron correlation function based on the extended R -matrix algorithm is also developed. The proposed method significantly reduces simulation time, making rigorous atomistic simulations of heterojunction FETs possible. As an application, device simulations are performed for the germanane/InSe vertical tunneling FET (VTFET) modeled through the first-principles density functional theory. Our simulation results reveal that the germanane/InSe VTFET is a promising candidate for future low power applications.

Electron collision cross-sections of c-C4F8 were investigated at low energies by using the R-matrix method. The static exchange (SE), static exchange with polarization (SEP), and close-coupling (CC) models of the R-matrix method were used for the calculation of the scattering cross-section. The shape resonance was detected with all the models at around 3~4 eV, and a Feshbach resonance was detected with the SEP model at 7.73 eV, in good agreement with the previous theoretical calculation. The resonance detected was also associated with the experimental dissociative electron attachment of c-C4F8, which displayed the resonances at the same energy range. The cross-sections calculated are important for plasma modeling and applications.

Let g0 be a simple Lie algebra of type ADE and let U′q(g) be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group B(g0) on the quantum Grothendieck ring Kt(g) of Hernandez-Leclerc's category C0g. Focused on the case of type AN-1, we construct a family of monoidal autofunctors {fi}i∈Z on a localization TN of the category of finite-dimensional graded modules over the quiver Hecke algebra of type A∞. Under an isomorphism between the Grothendieck ring K(TN) of TN and the quantum Grothendieck ring Kt(A(1)N-1), the functors {fi}1≤i≤N-1 recover the action of the braid group B(AN-1). We investigate further properties of these functors. [ABSTRACT FROM AUTHOR]

The Gukov–Manolescu series, denoted by F K , is a conjectural invariant of knot complements that, in a sense, analytically continues the colored Jones polynomials. In this paper we use the large color R -matrix to study F K for some simple links. Specifically, we give a definition of F K for positive braid knots, and compute F K for various knots and links. As a corollary, we present a class of "strange identities" for positive braid knots. [ABSTRACT FROM AUTHOR]

An expression for the R-matrix associated with U q (e 8 ^) in its 249-dimensional representation is given using the diagrammatic calculus of U q (e 8) invariants. [ABSTRACT FROM AUTHOR]

The Big Bang Nucleosynthesis (BBN) model is a great success of nuclear astrophysics due to the outstanding agreement between observational and predicted light elements abundances. One exception, however, is the so-called “lithium problem.” In this context, experimental efforts to measure the relevant reactions have been brought to an increased level of accuracy in measuring primordial abundances, and the introduction of indirect methods has allowed researchers to overcome the natural limitations of direct measurements in the energy range of interest for BBN. Here we review the results obtained from the application of the Trojan Horse Method to some of the most influential reactions of the standard network, such as 2H(d,p)3H, 2H(d,n)3He, 3He(d,p)4He, 7Li(p,α)4He, and 7Be(n,α)4He. The relevant cross sections have been then used as new inputs to a classical BBN code, resulting in important constraints that make suggestions for a possible solution for the lithium problem outside of nuclear physics.

I met Oleg Zatsarinny in 2001, and he then worked with me at Western Michigan University for two years. From 2003 to 2013, we were coauthors of 15 papers on theoretical atomic physics, and maintained a friendly relationship over twenty years, meeting and socializing often at conferences. Further elaboration follows below.

The formation and decay of double-core-hole (DCH) states of the neon ion irradiated by an intense electromagnetic x-ray field are studied theoretically. In the present research DCH formation is the result of sequential absorption of two photons with the creation of an intermediate ion. Detailed calculations of the partial decays and probabilities of shake-ups at the atomic and ionic ionization stages are presented. The angular distribution of photoelectrons corresponding to various residual ionic states are calculated. Specifically, we predict the lack of any photoelectrons corresponding to the residual ionic state 1s12s22pnmpn′2Sf+1D in the direction of the electric field polarization. Dynamical competition between single-core-hole state decay and excitation is analyzed and pulse parameters corresponding to various dynamical regimes are found.

We compute the rational s l 2 R-matrix acting in the product of two spin- ℓ 2 ( ℓ ∈ N ) representations, using a method analogous to the one of Maulik and Okounkov, i.e., by studying the equivariant (co)homology of certain algebraic varieties. These varieties, first considered by Nekrasov and Shatashvili, are typically singular. They may be thought of as the higher spin generalizations of A 1 Nakajima quiver varieties (i.e., cotangent bundles of Grassmannians), the latter corresponding to ℓ = 1 . [ABSTRACT FROM AUTHOR]

Postnikov's plabic graphs in a disk are used to parametrize totally positive Grassman- nians. In recent years plabic graphs have found numerous applications in mathematics and physics. One of the key features of the theory is the fact that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this paper we undertake a comprehensive study of a certain semilocal transformation of weights for plabic networks on a cylinder that preserve boundary measurements. We call this a plabic R-matrix. We show that plabic R-matrices have underlying cluster algebra structure, generalizing recent work of Inoue-Lam-Pylyavskyy. Special cases of transformations we consider include ge- ometric R-matrices appearing in Berenstein-Kazhdan theory of geometric crystals, and also certain transformations appearing in a recent work of Goncharov-Shen. [ABSTRACT FROM AUTHOR]

Using the description of multiline queues as functions on words, we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues. We show that the spectral weight of a word is invariant under a natural action of the symmetric group, giving a proof of the commutativity conjecture of Arita, Ayyer, Mallick, and Prolhac. We give a determinant formula for the spectral weight of a word, which gives a proof of a conjecture of the first author and Linusson. [ABSTRACT FROM AUTHOR]