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This article, published in the Journal of Mathematical Sciences, discusses the concept of dimension polynomials and their applications in inversive difference fields. It introduces various definitions and notations related to dimension polynomials and their properties. The text also discusses the reduction of inversive difference polynomials and the concept of E-reduction. It provides definitions and explanations of terms such as leaders, coleaders, effective orders, and rank. The text concludes with remarks and examples illustrating the concepts discussed. [Extracted from the article]

AbstractLet K be a differential field with algebraically closed field of constants CK. Let KPV∞ be the (iterated) Picard-Vessiot closure of K. Let G be a linear differential algebraic group over K, and X a differential algebraic torsor for G over K. We prove that X(KPV∞) is Kolchin dense in X. In the special case that G is finite-dimensional we prove that X(KPV∞)=X(Kdiff) (where Kdiff is the differential closure of K). We also give close relationships between Picard-Vessiot extensions of K and the category of torsors for suitable finite-dimensional linear differential algebraic groups over K. [ABSTRACT FROM AUTHOR]

As a continuation of the work of the third author in [5], we make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable automorphism group. We then use a method of twisting cohomology (inspired by Serre's algebraic twisting) to describe arbitrary fibres in cohomology sequences—yielding a useful "finiteness" result on cohomology sets. Applied to the special case of differential fields and Kolchin's constrained cohomology, we complete results from [3] by proving that the first constrained cohomology set of a differential algebraic group over a bounded, differentially large, field is countable. [ABSTRACT FROM AUTHOR]

To enable reliable power delivery through transmission tie‐lines, total transfer capability (TTC) must be calculated and regulated to accommodate the transferred amount. However, the traditional optimal power flow (OPF)‐based total transfer capability calculation is computationally expensive for efficient total transfer capability control due to the inclusion of a large set of differential‐algebraic equations (DAEs) to verify transient stability constraints. In order to enable practicable total transfer capability regulation, a novel risk‐aware deep learning‐assisted paradigm is proposed here. First, a deep belief network (DBN) is employed to establish the total transfer capability predictor and surrogate the computation‐intensive differential‐algebraic equations in original optimal power flow formulas, simplifying the high‐dimensional and intractable constraints deep belief networks without loss of nonlinearity. Particularly, in order to be aware of control risk from the predictive error of the deep belief networks, prediction intervals (PIs) are produced improved by using ensemble learning and used to disclose the probability of insufficient actions, further guaranteeing the sufficient and cost‐effective control by compromising the tradeoff between cost and risk. Symbiotic organisms search (SOS) is then applied to solve the proposed risk‐aware deep belief network‐assisted total transfer capability control problem globally. The numerical studies testify that the proposed method enables economical, reliable, and full nonlinearity‐retained dynamic total transfer capability regulation control within a risk‐free surrogate‐assisted and tractable physical model‐driven hybrid framework. [ABSTRACT FROM AUTHOR]

For a connected reductive algebraic group over an arbitrary number field, we consider a finite dimensional algebraic, irreducible representation of the group of its real points. Each adelic locally symmetric space corresponding to a level structure constructed using the group has an associated sheaf induced by this representation. The purpose of this note is to estimate the rate of growth of the total dimension of the pertinent cohomology with coefficients as either of the level structure or the associated sheaf varies. We obtain an upper bound on this total dimension. We also obtain a lower bound under certain topological conditions. Both the bounds are consistent with several classical dimension formulae as well as other known results. [ABSTRACT FROM AUTHOR]

For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially closed. This cohomological triviality condition is also known to be equivalent to the uniqueness up to an isomorphism of a Picard–Vessiot extension of a linear differential equation with parameters. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the "reduction mod p " method, which constructs large classes of representations for a semisimple algebraic group G from representations for the corresponding Lusztig quantum group U ζ at a p r -th root of unity. The G -modules arising in this way include the Weyl modules, the induced modules, and various reduced versions of these modules. We present a relation between Ext G n (V , W) and Ext U ζ n (V ′ , W ′) , when V , W are obtained from V ′ , W ′ by reduction mod p. Since the dimensions of Ext n -spaces for U ζ -modules are known in many cases, our result guarantees the existence of many new extension classes and homomorphisms between rational G -modules. One application is a new proof of James Franklin's result on certain homomorphisms between two Weyl modules. We also provide some examples which show that the p -th root of unity case and a general p r -th root of unity case are essentially different. [ABSTRACT FROM AUTHOR]

Abstract We show that for every conjugacy class O in a connected semisimple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice Σ to the set of conjugacy classes in G such that O intersects Σ and dim O = codim Σ. [ABSTRACT FROM AUTHOR]

Abstract In this paper we suggest an approach to study actions of semisimple (or reductive) algebraic groups in their algebraic complex representations. We use differential-geometric methods instead of classical algebraic constructions. Namely, according to Borel–Weil–Bott theorem, every algebraic representation of semisimple algebraic group is isomorphic to the action of this group on the module of holomorphic sections of some reductive bundle over homogeneous space. Using this, we give a complete description of the field of differential invariants for this action and obtain a criterion, which separates regular orbits. [ABSTRACT FROM AUTHOR]

Abstract We study the Frobenius base change of a torsor under a smooth algebraic group over a field of positive characteristic by relating it to the pushforward of the torsor under the Frobenius homomorphism. As an application, we determine the change of the multiplicity of a closed fiber of an elliptic surface by purely inseparable base changes with respect to the base curve in the case where the generic fiber is supersingular. [ABSTRACT FROM AUTHOR]

The AISI T1 steel was hardened by the solid boriding process in the temperature range 1123–1273 K for a time duration of 2 to 8 h. A kinetic model, based on the integral method, was applied to the growth of a single boride layer (Fe2B) at the surface of AISI T1 steel. This diffusion model has been validated experimentally by considering two additional boriding conditions. A numerical solution was then obtained after solving the set of differential algebraic equations in order to compare the experimental thicknesses of Fe2B layers with the predicted values. The activation energy for boron diffusion in AISI T1 steel was estimated as 212.76 kJ mol−1 and a comparison was made with other values available in the literature. The formed boride layers with a saw-tooth morphology were examined by scanning electron microscopy (SEM). X-ray diffraction confirmed that the borided layer was composed of only Fe2B. The Daimler-Benz Rockwell-C indentation technique was employed to assess the cohesion of Fe2B layers on AISI T1 steel. In addition, the pin-on-disc and wear scratch tests were carried out for investigating the wear behaviour of borided AISI T1 steel. [ABSTRACT FROM AUTHOR]

Abstract This work presents new implementation of an iterative method proposed by Temimi and Ansari namely (TAM) for approximate solutions of differential algebraic equations that arises in many engineering and applied sciences applications. The solution is obtained with easy computed components without any restrictive assumptions to deal with the nonlinear terms. The numerical results obtained by TAM are better accuracy and faster convergence in comparison to the homotopy perturbation method. Error analysis of the approximate solution is studied using the absolute error and high convergence is achieved. A symbolic manipulator Mathematica®10 was used to evaluate terms in the iterative process. [ABSTRACT FROM AUTHOR]

The conditions of solvability and the structure of a generalized Green operator of the Cauchy problem for a linear differential-algebraic system are found. The sufficient conditions of reducibility of a differential-algebraic equation to a sequence of systems joining differential and algebraic equations are constructed. An original classification and a single scheme of construction of the solutions of differentialalgebraic equations are proposed. [ABSTRACT FROM AUTHOR]

This work presents a new methodology for computing parameter sensitivities of differential algebraic system of equations with higher differential index. This methodology is particularly adequate for performing sensitivity analysis of object-oriented models described by modern universal modelling languages. By employing the same concepts and tools adopted by these languages for structural analysis of systems of equations, it is shown that the computational graphs of a differential algebraic system of equations and its corresponding sensitivity equation are structurally isomorphic. As a consequence, the structural index of both systems of equations are proven to be equal. Based on this result, an efficient strategy for index reduction of sensitivity equations is designed. [ABSTRACT FROM AUTHOR]

We consider an irregular (singular) semilinear differential-algebraic equation ddtAx+Bx=ftx and prove the theorems on Lagrange stability and instability. These theorems give sufficient conditions for the existence, uniqueness, and boundedness of the global solution to the Cauchy problem for a semilinear differential-algebraic equation and sufficient conditions for the existence and uniqueness of the solution with finite escape time for the analyzed Cauchy problem (this solution is defined on a finite interval and unbounded). The proposed theorems do not contain constraints similar to the global Lipschitz condition. This enables us to use them for the solution of more general classes of applied problems. Two mathematical models of radio-engineering filters with nonlinear elements are studied as applications. [ABSTRACT FROM AUTHOR]

Let G be a simply connected semisimple algebraic groups over ℂ and let ρ:G→GL(Vλ) be an irreducible representation of G of highest weight λ. Suppose that ρ has finite kernel. Springer defined an adjoint-invariant regular map with Zariski dense image from the group to the Lie algebra, 휃λ:G→픤, which depends on λ. This map, 휃λ, takes the maximal torus T of G to its Lie algebra 픱. Thus, for a given simple group G and an irreducible representation Vλ, one may write , where we take the simple coroots as a basis for 픱. We give a complete determination for these coefficients ci(t) for any simple group G as a sum over the weights of the torus action on Vλ. [ABSTRACT FROM AUTHOR]

Abstract: Strong approximation with Brauer–Manin obstruction is established for smooth varieties containing a connected linear algebraic group as an open subset with a compatible action. [ABSTRACT FROM AUTHOR]

This paper presents a kinematic and dynamic model which can be used to simulate telescopic crane slewing, luffing, telescoping, lifting and pulling load movements. The crane joint motion can be described as smooth continuous sine cosine function. The crane dynamic equations are derived by Lagrange method. The lifting rope length from boom tip to hooks described as a time-variant constraint equation. The dynamic equations and the constraint equation form differential algebraic equations which can be solved by constraint stabilization method. The validity and correctness of the telescopic crane model is verified through an example. We prospect the model can be used for the research on compound motion control and lifting scheme design of telescopic crane in the virtual reality. [ABSTRACT FROM AUTHOR]

In this study, an alternative approach based on the integral method was proposed to estimate the values of boron diffusion coefficients in the Fe2B layers grown at the surface of Armco iron. The set of differential algebraic equations (DAE) system was obtained to estimate the value of activation energy for boron diffusion when pack-boriding of Armco iron in the range of 1123 to 1273 K taking into account the boride incubation time. The present model has been validated by making a comparison between the experimental value of Fe2B layer thickness obtained at 1253 K for 5 h and the predicted results by using two different approaches. A good agreement was observed between these two set of data. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of $$H_\infty$$ observer-based control design for descriptor systems. A new concept of dynamical observer-based control is introduced for linear descriptor systems. The main advantage of this concept is the structure of this dynamical observer, which is more general than those founded in the literature. By using this general structure, particular cases such as the proportional and the proportional-integral observers (PIOs)can be directly deduced. Necessary and sufficient conditions under which the controlled output converges asymptotically to zero are given in a set of linear matrix inequalities formulation. Numerical examples comparing our approach with the proportional and the PIO (deduced from the dynamical observer), and with a functional filter-based controller previously reported in the literature, are respectively presented. [ABSTRACT FROM AUTHOR]

We introduce a class of strongly étale difference algebras , whose role in the study of difference equations is analogous to the role of étale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem. [ABSTRACT FROM AUTHOR]

This article advocates a nonsmooth differential-algebraic equations (DAEs) modeling paradigm for dynamic simulation and optimization of process operations. A variety of systems encountered in chemical engineering are traditionally viewed as exhibiting hybrid continuous and discrete behavior. In many cases such discrete behavior is nonsmooth (i.e. continuous but nondifferentiable) rather than discontinuous, and is appropriately modeled by nonsmooth DAEs. A computationally relevant theory of nonsmooth DAEs (i.e. well-posedness and sensitivity analysis) has recently been established ( Stechlinski and Barton, 2016a, 2017 ) which is suitable for numerical implementations that scale efficiently for large-scale dynamic optimization problems. Challenges posed by competing hybrid modeling approaches for process operations (e.g. hybrid automata) are highlighted as motivation for the nonsmooth DAEs approach. Several examples of process operations modeled as nonsmooth DAEs are given to illustrate their wide applicability before presenting the appropriate mathematical theory. [ABSTRACT FROM AUTHOR]

Abstract: Let G be a split semisimple algebraic group over an arbitrary field F, let E be a G‐torsor over F, and let P be a parabolic subgroup of G. The quotient variety X : = E / P, known as a flag variety, is generically split, if the parabolic subgroup P is special. It is generic, provided that the G‐torsor E over F is a standard generic G k‐torsor for a subfield k ⊂ F and a split semisimple algebraic group G k over k with ( G k ) F = G. For any generically split generic flag variety X, we show that the Chow ring CH X is generated by Chern classes (of vector bundles over X). This implies that the topological filtration on the Grothendieck ring of X coincides with the computable gamma filtration. The results were already known in some cases including the case where P is a Borel subgroup. We also provide a complete classification of generically split generic flag varieties and, equivalently, of special parabolic subgroups for split simple groups. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear control algorithm based on differential flatness approach for controlling a servo permanent magnet synchronous motor (PMSM) drive. The differential flatness approach is a model-based estimation. Subsequently, two state-observers are introduced to calculate a load torque disturbance and a stator resistance (representing losses in an inverter and motor) using its voltage drop. This can enable the improvement of the PMSM drive system and its efficiency. Using the flatness approach, we propose simple solutions to the dynamics and stabilization problems of the PMSM drive structure. In order to evaluate the proposed control algorithm, a hardware system is realized in a laboratory and digital estimation is obtained using a dSPACE controller DS1104 platform. Simulation and experimental results with a small-scale motor of 1000 W and 3000 r/min in a laboratory corroborate the excellent control scheme during motor-drive cycles. [ABSTRACT FROM PUBLISHER]

Let G be a simple algebraic group of adjoint type over the field C of complex numbers, B be a Borel subgroup of G containing a maximal torus T of G . Let w be an element of the Weyl group W and X ( w ) be the Schubert variety in G / B corresponding to w . In this article we show that given any parabolic subgroup P of G containing B properly, there is an element w ∈ W such that P is the connected component, containing the identity element of the group of all algebraic automorphisms of X ( w ) . [ABSTRACT FROM AUTHOR]

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the symmetry algebra of the wave equation, which in turn are used to determine a large class of invariant solutions of the wave equation. The algorithms are also illustrated for the symmetry algebra of a classical system of differential equations considered by Cartan in the context of contact geometry. [ABSTRACT FROM AUTHOR]

In a nonlinear system, impasse points are singularities beyond which solutions are not continuable. In this article, we study two families of nonlinear electrical circuits, which can be represented by nonlinear Implicit Differential Equations. We set conditions that ensure the existence of impasse points in both families of circuits. In the literature, there exist general results to analyse the presence of such singularities in given differential equations of this type. However, the method proposed in this work allows detecting their existence in these electrical topologies in an extremely straightforward way, as illustrated by the examples of application. [ABSTRACT FROM AUTHOR]

Increasing focus exists on process intensification of pharmaceuticals production by developing continuous manufacturing (CM) processes. However, efficient and economical CM is challenged by the short campaign times prevailing in this industry, resulting in significant transients, often exhibiting nonsmooth behavior, such as changes in flow or thermodynamic phase regimes. Thus, process intensification should be coupled with optimizing its dynamic operation . In this series we investigate the optimal dynamic operation of a continuous process that includes several reaction and separation steps to produce an active pharmaceutical ingredient at final dosage from advanced intermediates, inspired by a pilot plant previously tested at MIT. This paper, the first in a two-part series, illustrates the use of nonsmooth differential-algebraic equations (DAEs) as a new paradigm for modeling dynamic process systems in an equation-oriented approach. Such a formulation has been recently shown to admit a unique solution and computationally tractable sensitivity analysis, facilitating its embedding in optimization schemes to find optimal operational procedures. The nonsmooth dynamics of several units are demonstrated from start-up. The nominal overall campaign performance is characterized in terms of on-specification productivity and yield, showing significant room for improvement. The optimization is then discussed in detail in the second part of this series. [ABSTRACT FROM AUTHOR]

We investigate theoretical optimal campaigns in a continuous process of pharmaceuticals production. The simulated process, inspired by a pilot plant previously tested at MIT, includes several reaction and separation steps to produce final tablets. This paper, demonstrates the use of nonsmooth differential-algebraic equations (DAEs) framework for such optimal campaigns design. We embed the model developed in the first part of this series in a dynamic optimization problem formulated as a hybrid discrete/continuous and nonsmooth problem. We enforce the quality constraints only on an interior epoch (on-spec) and optimize its duration. We then use a gradient-based optimization tool (IPOPT) to solve the problem. We consider the on-specification productivity over the entire campaign. Various control valves are chosen as decision variables, as well as the timings of the control switchings. The yield and the productivity of the process are considered as objectives under a constant (short) time horizon. Pareto curves of optimal yield and productivity for various campaign durations are calculated. The results show a significant improvement over a “nominal” operating procedure that only considers steady-state operation. This methodology can be used to guide decision makers, in both the design stage of new plants and the operation of existing configurations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a State Estimator for Plunger Lift wells based on the Extended Kalman Filter (EKF) algorithm. The state estimator is a joint operation of the Plunger Lift (PL) dynamic model in State Space approach and EKF algorithm. The model is constituted by a set of discrete differential algebraic equations (DAEs) discretized and modeled in the form of equations in state space taking into account the measurement signals in the presence of noise. The state estimator is able to process the measurement signal thus providing estimates of the state variables that in this problem are slug velocity and casinghead pressure. The results of the computational simulation performed with data from a real well are predictions of important well performance items such as production rate, average piston upward velocity, cycle time, and pressures with values very close to those found in the well. The State Estimator for Plunger Lift is therefore a robust prediction system for the variables that influence the performance of a PL well since it considers the noises present in the process and in the measurement. The quality of the prediction is influenced by the correct adjustment of the parameters of the EKF algorithm. [ABSTRACT FROM AUTHOR]

In this paper, for any simple, simply connected algebraic groupGof typeAand for any maximal parabolic subgroupPofG, we provide a criterion for a Richardson variety inG∕Pto admit semistable points for the action of a maximal torusTwith respect to an ample line bundle onG∕P. We study the structure of the Geometric invariant theory (GIT) quotient for the action of a maximal torus on the Richardson varieties inG2,nwith respect to a suitable line bundle onG2,n. We also give a criterion for the Richardson varieties into admit a semistable point with respect to the line bundle corresponding to the highest root. [ABSTRACT FROM PUBLISHER]

In this paper, we apply Haar wavelet method for solving seconed order initial value problems of ordinary differential equation. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. We compared this numerical results with the exact solution and other known methods. [ABSTRACT FROM AUTHOR]

Let λ be a primitive root of unity of order ℓ. We introduce a family of finite-dimensional algebras {Dλ, N (sl2)}N∈N0 over the complex numbers, such that Dλ, N (sl2) is a subalgebra of Dλ, M (sl2) if N < M, and Dλ, N-1(sl2) ⊂ Dλ, N (sl2) is a uλ(sl2)-cleft extension. The simple Dλ, N (sl2)-modules (LN(p))0≤p<ℓN+1 are highest weight modules, which admit a tensor product decomposition: the first factor is a simple uλ(sl2)-module and the second factor is a simple Dλ, N-1(sl2)-module. This factorization resembles the corresponding Steinberg decomposition, and the family of algebras resembles the presentation of the algebra of distributions of SL2 as a filtration by finite-dimensional subalgebras. [ABSTRACT FROM AUTHOR]

Let λ be a primitive root of unity of order ℓ. We introduce a family of finite-dimensional algebras {Dλ, N (sl2)}N∈N0 over the complex numbers, such that Dλ, N (sl2) is a subalgebra of Dλ, M (sl2) if N < M, and Dλ, N-1(sl2) ⊂ Dλ, N (sl2) is a uλ(sl2)-cleft extension. The simple Dλ, N (sl2)-modules (LN(p))0≤p<ℓN+1 are highest weight modules, which admit a tensor product decomposition: the first factor is a simple uλ(sl2)-module and the second factor is a simple Dλ, N-1(sl2)-module. This factorization resembles the corresponding Steinberg decomposition, and the family of algebras resembles the presentation of the algebra of distributions of SL2 as a filtration by finite-dimensional subalgebras. [ABSTRACT FROM AUTHOR]

Given an infinite reductive algebraic group , we consider -equivariant coherent sheaves with prescribed multiplicities, called -constellations, for which two stability notions arise. The first one is analogous to the -stability defined for quiver representations by King [Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. 2) 45(180) (1994) 515-530] and for -constellations by Craw and Ishii [Flops of -Hilb and equivalences of derived categories by variation of GIT quotient, Duke Math. J. 124(2) (2004) 259-307], but depending on infinitely many parameters. The second one comes from Geometric Invariant Theory in the construction of a moduli space for -constellations, and depends on some finite subset of the isomorphy classes of irreducible representations of . We show that these two stability notions do not coincide, answering negatively a question raised in [Becker and Terpereau, Moduli spaces of -constellations, Transform. Groups 20(2) (2015) 335-366]. Also, we construct Harder-Narasimhan filtrations for -constellations with respect to both stability notions (namely, the -HN and -HN filtrations). Even though these filtrations do not coincide in general, we prove that they are strongly related: the -HN filtration is a subfiltration of the -HN filtration, and the polygons of the -HN filtrations converge to the polygon of the -HN filtration when grows. [ABSTRACT FROM AUTHOR]

We show that small normal subsets A of finite simple groups grow very rapidly; namely,|A²| ≥ |A|2-ε, where ε > 0 is arbitrarily small. Extensions, consequences, and a rapid growth result for simple algebraic groups are also given. [ABSTRACT FROM AUTHOR]

Let Q be a connected algebraic group with Lie algebra q . Symmetric invariants of q , i.e., the Q -invariants in the symmetric algebra S ( q ) of q , is a first approximation to the understanding of the coadjoint action ( Q : q ⁎ ) and coadjoint Q -orbits. In this article, we study a class of non-reductive Lie algebras, where the description of the symmetric invariants is possible and the coadjoint representation has a number of nice invariant-theoretic properties. If G is a semisimple group with Lie algebra g and V is G -module, then we define q to be the semi-direct product of g and V . Then we are interested in the case, where the generic isotropy group for the G -action on V is reductive and commutative. It turns out that in this case symmetric invariants of q can be constructed via certain G -equivariant maps from g to V (“covariants”). [ABSTRACT FROM AUTHOR]

The notion of a ( G , N ) -slice of a G -variety was introduced by P.I. Katsylo in the early 80's for an algebraically closed base field of characteristic 0. Slices (also known under the name of relative sections) have ever since provided a fundamental tool in invariant theory, allowing reduction of rational or regular invariants of an algebraic group G to invariants of a “simpler” group. We refine this notion for a G -scheme over an arbitrary field, and use it to get reduction of structure group results for G -torsors. Namely we show that any ( G , N ) -slice of a versal G -scheme gives surjective maps H 1 ( L , N ) → H 1 ( L , G ) in fppf-cohomology for infinite fields L containing F . We show that every stabilizer in general position H for a geometrically irreducible G -variety V gives rise to a ( G , N G ( H ) ) -slice in our sense. The combination of these two results is applied in particular to obtain a striking new upper bound on the essential dimension of the simply connected split algebraic group of type E 7 . [ABSTRACT FROM AUTHOR]

We show that certain signal constellations invoked for classic differential encoding result in a phenomenon we term as the unbounded differential constellation size (UDCS). Various existing differential transmission schemes that suffer from this issue are identified. Then, we propose an enhanced algebraic field extension-based differential spatial modulation (AFE-DSM) scheme and its enhanced counterpart that strikes a diversity-rate tradeoff (AFE-DSM-DR), both of which overcome the UDCS issue without compromising its full transmit diversity advantage. Furthermore, the proposed schemes are extended to incorporate amplitude and phase shift keying (APSK) in order to exploit all the available degrees of freedom. Additionally, we propose a pair of detection schemes specially designed for APSK-aided differential transmission schemes. Explicitly, we conceive the buffered minimum mean squared error (B-MMSE) detector and buffered maximum likelihood (B-ML) detector, which exploit the knowledge of previously detected symbols in order to further improve the detection performance. Our simulation results have shown that the proposed detectors are capable of bridging the performance gap between the conventional differential detector (CDD) and the coherent detector that has full channel state information. Specifically, when employing the proposed APSK-aided AFE-DSM scheme operating at a rate of 2 b per channel use, the B-MMSE and B-ML detectors are observed to give about 3- and 3.5-dB signal-to-noise ratio gain with respect to their CDD counterpart at a bit error ratio of 10^-5 . [ABSTRACT FROM AUTHOR]

The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as an operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyze the properties of the Rothe method concerning stability and convergence for this kind of systems. We consider a regularization of the operator DAE and prove the weak convergence of the implicit Euler scheme. Furthermore, we consider perturbations in the semi-discrete systems which correspond to additional errors such as spatial discretization errors. [ABSTRACT FROM AUTHOR]

I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p > 0 and Lusztig's character formula. I explain ideas connecting representations and constructible sheaves (Finkelberg-Mirković conjecture) in the spirit of the Kazhdan-Lusztig conjecture. I also discuss a conjecture with S. Riche (a theorem for GL) which should eventually make computations more feasible. [ABSTRACT FROM AUTHOR]