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Many threatened species require ongoing management, which is often funded through short project cycles. Evaluating whether the management is effective in protecting a species is important to inform future management investments. For migratory species, management may affect only part of a species' annual cycle, and reversing a population decline is challenging to achieve and demonstrate. Here, we evaluate whether conservation management projects funded by the European LIFE programme to safeguard a migratory vulture population achieved their major objective of stabilizing the target breeding population. Between 2012 and 2022, an international alliance of conservation organizations implemented multiple actions to reduce poisoning, direct persecution, and electrocution and collision with power lines along the Eastern Mediterranean flyway. We monitored breeding territories of the Balkan population of the globally endangered Egyptian Vulture Neophron percnopterus between 2006 and 2022, and tracked 60 young birds with GPS transmitters since 2010. We used these data to examine whether population growth rate and survival probability had increased since project implementation. The mean annual survival probability of adult territorial birds increased by 1.9% since 2014 from 0.937 to 0.955, and the monthly survival probability of wild juvenile birds increased by 9.7% from 0.833 to 0.914 since 2018. The population growth rate across the Balkans increased by 6.9% from 0.939 before 2018 to 1.005 since 2018. This indicates that the Egyptian Vulture population has remained stable for the past 5 years (2018–2022), but at a population size that is only half (105 adult territorial birds in 2022) than at the beginning of the time series (204 in 2006). We caution that ongoing management along the flyway and reinforcement are required to ensure that the Egyptian Vulture population on the Balkans can recover, but we show that flyway‐scale collaboration of direct conservation actions can have lasting benefits for migratory species. [ABSTRACT FROM AUTHOR]

In this paper, we continue the project of systematic construction of invariant differential operators (IDOs) on the example of the noncompact algebras s p (n , 1). Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which are of split rank one, of which class the other cases were studied, some long time ago. We concentrate on the case n = 2. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations (ER) for, including the necessary data for all relevant invariant differential operators. We also present explicit expressions for the singular vectors and the intertwining differential operators. [ABSTRACT FROM AUTHOR]

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra s o ∗ (10) . We use the maximal Heisenberg parabolic subalgebra P = M ⊕ A ⊕ N with M = s u (3 , 1) ⊕ s u (2) ≅ s o ∗ (6) ⊕ s o (3) . We give the main and the reduced multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERS. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebras s o (p , q) (with p + q = 10 , p ≥ q ≥ 2 ) with maximal Heisenberg parabolic subalgebra: P ′ = M ′ ⊕ A ′ ⊕ N ′ , M ′ = s o (p − 2 , q − 2) ⊕ s l (2 , I R) , M ′ C ≅ M C . [ABSTRACT FROM AUTHOR]

In this paper, we construct explicitly the intertwining differential operators for the Jacobi algebra 2 . For the construction, we use the singular vectors of the Verma modules over 2 which we have constructed earlier. We construct the function spaces on which the operators act. We find two versions of the left (representation) action and the right action. These actions are combined with the singular vectors to provide the intertwining differential operators. [ABSTRACT FROM AUTHOR]

In the present paper we study the representations of the Jacobi algebra. More concretely, we define, analogously to the case of semi-simple Lie algebras, the Verma modules over the Jacobi algebra G 2 . We study their reducibility and give explicit construction of the reducible Verma modules exhibiting the corresponding singular vectors. Using this information we give a complete classification of the reducible Verma modules. More than this we exhibit their interrelation of embeddings between these modules. These embeddings are illustrated by diagrams of the embedding patterns so that each reducible Verma module appears in one such diagram. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups G and Lie algebras 𝒢. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi-like decompositions. The same analysis is applied to the exceptional real semisimple Lie algebras. [ABSTRACT FROM AUTHOR]

We propose a unified algebraic approach for the practical application and preconditioning of static condensation and hybridization, two popular techniques in finite element discretizations. We demonstrate the use of this algebraic framework for the construction of scalable solvers for problems involving H(div)-spaces discretized by conforming (Raviart--Thomas) elements of arbitrary order. We illustrate through numerical experiments the relative performance of the two (in some sense dual) techniques in comparison with a state-of-the-art parallel solver, ADS [T. V. Kolev and P. S. Vassilevski, SIAM J. Sci. Comput., 34 (2012), pp. A3079--A3098], available at http://www.llnl.gov/casc/hypre and http://mfem.org. Based on these results, we recommend the use of the hybridization technique in practice, due to its clearly demonstrated superior performance with increased benefit for higher-order elements. [ABSTRACT FROM AUTHOR]

We construct representations of the quantum algebras Uq,q(gl(n)) and Uq,q(sl(n)) which are in duality with the multiparameter quantum groups GLqq(n), SLqq(n), respectively. These objects depend on n(n − 1)/2+ 1 deformation parameters q, qij (1 ≤ i< j ≤ n) which is the maximal possible number in the case of GL(n). The representations are labelled by n − 1 complex numbers ri and are acting in the space of formal power series of n(n − 1)/2 non-commuting variables. These variables generate quantum flag manifolds of GLqq(n), SLqq(n). The case n = 3 is treated in more detail. [ABSTRACT FROM AUTHOR]

We show how a scalable preconditioner for the primal discontinuous Petrov{Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence which allows us to exploit existing AMG algorithms and software. We show how these algebraic preconditioners can be applied directly to a Schur complement system arising from the DPG method. One of our intermediate results shows that a generic stable decomposition implies a stable decomposition for the Schur complement. This justifies the application of algebraic solvers directly to the interface degrees of freedom. Combining such results, we obtain the first massively scalable algebraic preconditioner for the DPG system. [ABSTRACT FROM AUTHOR]

We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions. [ABSTRACT FROM AUTHOR]

In this paper we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source package [XBraid: Parallel Multigrid in Time, http://llnl.gov/casc/xbraid]. MGRIT is a scalable and multilevel approach to parallel-in-time simulations that nonintrusively uses existing time-stepping schemes, and in a specific two-level setting it is equivalent to the widely known parareal algorithm. The goal of this paper is twofold. First, we present a two-level MGRIT convergence analysis for linear problems where the spatial discretization matrix can be diagonalized, and then apply this analysis to our two basic model problems, the heat equation and the advection equation. One important assumption is that the coarse and fine time-grid propagators can be diagaonalized by the same set of eigenvectors, which is often the case when the same spatial discretization operator is used on the coarse and fine time grids. In many cases, the MGRIT algorithm is guaranteed to converge, and we demonstrate numerically that the theoretically predicted convergence rates are sharp in practice for our model problems. Second, we explore how the convergence of MGRIT compares to the stability of the chosen time-stepping scheme. In particular, we demonstrate that a stable time-stepping scheme does not necessarily imply convergence of MGRIT, although MGRIT with FCF-relaxation always converges for the diffusion dominated problems considered here. [ABSTRACT FROM AUTHOR]

In this work we present a FCT- like Maximum-Principle Preserving (MPP) method to solve the transport equation. We use high-order polynomial spaces; in particular, we consider up to 5th order spaces in two and three dimensions and 23rd order spaces in one dimension. The method combines the concepts of positive basis functions for discontinuous Galerkin finite element spatial discretization, locally defined solution bounds, element-based flux correction, and non-linear local mass redistribution. We consider a simple 1D problem with non-smooth initial data to explain and understand the behavior of different parts of the method. Convergence tests in space indicate that high-order accuracy is achieved. Numerical results from several benchmarks in two and three dimensions are also reported. [ABSTRACT FROM AUTHOR]

In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic. [ABSTRACT FROM AUTHOR]

Earlier we have proposed new q-Maxwell equations which are the first members of an infinite new hierarchy of q-difference equations. We have used an indexless formulation in which all indices are traded for two conjugate variables, z; z. We proposed also new q-Minkowski coordinates which together with z; z can be interpreted as the six local coordinates of a SUq(2, 2) flag manifold. In the present paper we generalise the main ingredients of this construction to the multiparameter case using the seven-parameter quantum group deformation of GL(4) and U(gl(4)) and the four-parameter quantum group deformation of SL(4) and U(sl(4)). The main result is the explicit presentation of the multiparameter quantum Minkowski space-time within the corresponding deformed flag manifold. [ABSTRACT FROM AUTHOR]

In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G0 that have the same complexification and possess maximal parabolic subalgebras with the same complexification. In the present paper we consider in detail the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n - 1, 1) and its analogs so(p - 1, q - 1). [ABSTRACT FROM AUTHOR]

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed. [ABSTRACT FROM AUTHOR]

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D = 4 conformal superalgebras su(2, 2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N = 1 and for several important examples for N = 2 and N = 4. [ABSTRACT FROM AUTHOR]

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras su( n, n). Our choice of these algebras is motivated by the fact that for n = 2 this is the conformal algebra of 4-dimensional Minkowski space-time. Furthermore for general n these algebras belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of n-dimensional Minkowski space-time. We give the main multiplets of indecomposable elementary representations for n = 2, 3, 4, including the necessary data for all relevant invariant differential operators. [ABSTRACT FROM AUTHOR]

The singular vectors in Verma modules over the Schrödinger algebra ŝ( n) in ( n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schrödinger algebras are constructed. [ABSTRACT FROM AUTHOR]

In the present paper, we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients — the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalized to the supersymmetric and quantum group settings and is necessary for applications to string theory and integrable models. [ABSTRACT FROM AUTHOR]

The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given. [ABSTRACT FROM AUTHOR]

We use character formulae for the positive-energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2, 2/ N) that were derived earlier to give decompositions of long superfields as they descend to the unitarity threshold. [ABSTRACT FROM AUTHOR]

We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n, R).© 2005 Pleiades Publishing, Inc. [ABSTRACT FROM AUTHOR]

We propose aq-deformed model of anharmonic vibrations in diatomic molecules. We study the applicability of the model to the phenomenological Dunham expansion by comparison with experimental data. In contrast with other applications where it is difficult to find a physical interpretation for the deformation parameter,q, in our analysis it is directly related to the third-order coefficient in the Dunham expansion. We study the consistency of the parameters that determine theq-deformed system by comparing them with the vibrational terms fitted to 161 electronic states of diatomic molecules. We show how to include both positive and negative anharmonicities in a simple and systematic way. [ABSTRACT FROM AUTHOR]

We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the study of quantum linear conformal (Weyl) gravity by writing the corresponding q-deformed equations. [ABSTRACT FROM AUTHOR]

We construct induced infinite-dimensional representations of the two-parameter quantum algebra Ug,h( gl(2)) which is in duality with the deformation GLg,h(2). The representations depend on two representation parameters, but split into one-parameter representations of a one-generator central subalgebra and the three-generator Jordanian quantum subalgebra U $$_{\tilde g} $$ ( sl(2)), $$\tilde g$$ = g + h. The representations of the latter can be mapped to representations in one complex variable, which give a new deformation of the standard one-parameter vector-field realization of sl(2). These infinite-dimensional representations are reducible for some values of the representation parameters, and then we obtain canonically the finite-dimensional representations of U $${\tilde g}$$ ( sl(2)). [ABSTRACT FROM AUTHOR]

We give solutions of the quantum conformal deformations of the Maxwell and potential equations in terms of deformations of the plane wave. Compatibility of the equations leads to an asymmetry between the q deformations of the fixed helicity constituents F[sup ±] = E ± iH of the Maxwell field. Namely, only one of F[sup ±] can be written in terms of the q-plane wave, while the other can be expressed only through the components of the q-plane wave. This asymmetry and possible alternatives are discussed. [ABSTRACT FROM AUTHOR]

We propose an infinite family of difference equations, which are derived from the first principle that they are invariant with respect to the Schrödinger algebra. The first member of this family is a difference analogue of the free Schrödinger equation. These equations are obtained via a purely algebraic construction from a corresponding family of singular vectors in Verma modules over the Schrödinger algebra. The crucial moment in the construction is the realization of the Schrödinger algebra through additive difference vector fields, i.e. vector fields with difference operators instead of differential operators. Our method produces also differential-difference equations in which only space- or time-differentiation is replaced with the corresponding difference operators. [ABSTRACT FROM AUTHOR]

A new approach to the theory of polynomial solutions of q-difference equations is proposed. The approach is based on the representation theory of simple Lie algebras G and their q-deformations and is presented here for Uq(sl(n)). First a q-difference realization of Uq(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters, ri, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well-known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q-difference equations, i.e., these are kernels of invariant q-difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally, the states in all subrepresentations are depicted graphically via the so-called Newton diagrams. [ABSTRACT FROM AUTHOR]

Representations πr,r of a Lorentz quantum algebra U are constructed. They are labeled by two complex numbers r,r and act in the space of formal power series of two noncommuting variables η,η. These variables are built from elements of the matrix Lorentz quantum group L which is dual to U. The conditions for reducibility of πr,r are given. q-difference intertwining operators in η, η, which realize partial equivalences of the representations πr,r , are constructed explicitly. The whole construction is a generalization of a known procedure for q=1. The case when q is a root of unity is also considered in detail. [ABSTRACT FROM AUTHOR]

It is shown that the algebra Up,q dual to GLp,q(2,C) is isomorphic to U(pq)1/2(sl(2,C)) x Z as a commutation algebra, where Z is a subalgebra central in Up,q. The subalgebra Z is a Hopf subalgebra of Up,q, while the commutation subalgebra U(pq)1/2(sl(2,C)) is not a Hopf subalgebra. [ABSTRACT FROM AUTHOR]

The structure of the groups SL(4,R) and GL(4,R) and their universal cover- ing groups SL(4,R) and GL(4,R), respectively, and Lie algebras sl(4,R) and gl(4,R), respectively, are studied. The parabolic subgroups and subalgebras are identified and the cuspidal parabolic subgroups singled out. The Iwasawa and Bruhat decompositions are given explicitly. All elementary representations (ER) of SL(4,R) are explicitly given in two equivalent realizations. Using the preceding detailed structural analysis the SL(4,R) constructions are used for the explicit realization of all ER of SL(4,R), GL(4,R), and GL(4,R). The results shall be applied (among other things) elsewhere for the construction of all irreducible representations of the above groups. [ABSTRACT FROM AUTHOR]

The structure of the group SU(2, 2) and of its Lie algebra is studied in detail. The results will be applied in subsequent parts devoted to the explicit construction of elementary representations of SU(2, 2) induced from different parabolic subgroups and of the intertwining operators between these representations. A summary of some results of Parts II and III is given. [ABSTRACT FROM AUTHOR]

We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original. [ABSTRACT FROM AUTHOR]

We refute a recent claim in the literature [Czech. J. Phys. 56, 1191 (2006)] of a “new" quantum deformation of GL(2). [ABSTRACT FROM AUTHOR]

An explicit realization of the normalized Gel'fand-(Weyl)-Zetlin (GWZ) basis for U[sub q](sl(3)) in terms of polynomial functions in three variables (real or complex) is given. The construction uses two different realizations of the U[sub q](sl(3)) unnormalized GWZ basis which were given previously, and whose transformation properties were not known. It turns out that finding these properties enables us to find the (GWZ-dependent) proportionality constant between these two realizations. The scalar product is also fixed by this in both unnormalized realizations, and then, by normalization, the normalized GWZ states are obtained. As by-products new summation formulas are obtained which seem new also for q=1. The main new formula is a double sum which is given in terms of the proportionality constant mentioned above. This double sum can be written as single sum over a q-[sub 3]F[sub 2] hypergeometric function, or as a q-hypergeometric function of two variables. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Reprints portions of the papers 'The most general magnetized Kerr-Newman metric' and 'Structural analysis and elementary representations of SL(4,R) and GL(4,R) and their covering groups,' published in a 1986 issue of the 'Journal of Mathematical Physics.'

The exotic bialgebras that arise from a 9 × 9 unitary braid matrix are constructed. The dual bialgebra of one of these exotic bialgebras is presented. [ABSTRACT FROM AUTHOR]

A class of (2n)2×(2n)2 multiparameter braid matrices are presented for all n(n>=1). Apart from the spectral parameter θ, they depend on 2n2 free parameters mij(±), i,j=1,...,n. For real parameters, the matrices R(θ) are nonunitary. For purely imaginary parameters, they became unitary. Thus, a unification is achieved with odd dimensional multiparameter solutions presented before. [ABSTRACT FROM AUTHOR]

We construct (2n)2×(2n)2 unitary braid matrices R⁁ for n>=2 generalizing the class known for n=1. A set of (2n)×(2n) matrices (I,J,K,L) is defined. R⁁ is expressed in terms of their tensor products (such as KxJ), leading to a canonical formulation for all n. Complex projectors P± provide a basis for our real, unitary R⁁. Baxterization is obtained. Diagonalizations and block diagonalizations are presented. The loss of braid property when R⁁ (n>1) is block diagonalized in terms of R⁁ (n=1) is pointed out and explained. For odd dimension (2n+1)2×(2n+1)2, a previously constructed braid matrix is complexified to obtain unitarity. R⁁LL and R⁁TT algebras, chain Hamiltonians, potentials for factorizable S matrices, and complex noncommutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements. [ABSTRACT FROM AUTHOR]

We study the geometric aspects of two exotic bialgebras S03 and S14 introduced in math.QA/0206053. These bialgebras are obtained by the Faddeev–Reshetikhin–Takhtajan RTT prescription with non-triangular R-matrices which are denoted R[sub 03] and R[sub 14] in the classification of Hietarinta, and they are not deformations of either GL(2) or GL(1|1). We give the spectral decomposition which involves two, respectively, three, projectors. These projectors are then used to provide the baxterization procedure with one, respectively, two, parameters. Further, the projectors are used to construct the noncommutative planes together with the corresponding differentials following the Wess–Zumino prescription. In all these constructions there appear nonstandard features which are noted. Such features show the importance of systematic study of all bialgebras of four generators. [ABSTRACT FROM AUTHOR]

We find the exotic matrix bialgebras which correspond to the two nontriangular nonsingular 4 × 4 R-matrices in the classification of Hietarinta, namely, R[sub S0,3] and R[sub S1,4]. We find two new exotic bialgebras S03 and S14 which are not deformations of the classical algebras of functions on GL(2) or GL(I/1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of R[sub S1,4] in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GL[sub p,q](2). [ABSTRACT FROM AUTHOR]

Combined (q,h)-deformations proposed by Kupershmidt and BallesterosHerranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard q-deformation. We briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric (p, q)-deformations to nonhybrid but biparametric nonstandard (g, h) ones. Finally a case of hybrid (q,h)-deformation is recalled, related to the superalgebra GL(11). [ABSTRACT FROM AUTHOR]