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Recently, the problem of bounding the sup norms of L2-normalized cuspidal automorphic newforms ϕ on GL2 in the level aspect has received much attention. However at the moment strong upper bounds are only available if the central character χ of ϕ is not too highly ramified. In this paper, we establish a uniform upper bound in the level aspect for general χ. If the level N is a square, our result reduces to ∥ϕ∥∞ ≪ N1/4 + ϵ, at least under the Ramanujan Conjecture. In particular, when χ has conductor N, this improves upon the previous best known bound ∥ϕ∥∞ ≪ N1/2 + ϵ in this setup (due to [A. Saha, Hybrid sup-norm bounds for Maass newforms of powerful level, Algebra Number Theory 11 2017, 1009–1045]) and matches a lower bound due to [N. Templier, Large values of modular forms, Camb. J. Math. 2 2014, 1, 91–116], thus our result is essentially optimal in this case. [ABSTRACT FROM AUTHOR]

This is the last in a series of articles where we are concerned with normal elements of noncommutative Iwasawa algebras over SL n ⁢ (ℤ p) {\mathrm{SL}_{n}(\mathbb{Z}_{p})}. Our goal in this portion is to give a positive answer to an open question in [D. Han and F. Wei, Normal elements of noncommutative Iwasawa algebras over SL 3 ⁢ (ℤ p) \mathrm{SL}_{3}(\mathbb{Z}_{p}) , Forum Math. 31 2019, 1, 111–147] and make up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over SL n ⁢ (ℤ p) \mathrm{SL}_{n}(\mathbb{Z}_{p}) , Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously. Let n ( n ≥ 2 {n\geq 2}) be a positive integer. Let p ( p > 2 {p>2}) be a prime integer, ℤ p {\mathbb{Z}_{p}} the ring of p-adic integers and 𝔽 p {\mathbb{F}_{p}} the finite filed of p elements. Let G = Γ 1 ⁢ (SL n ⁢ (ℤ p)) {G=\Gamma_{1}(\mathrm{SL}_{n}(\mathbb{Z}_{p}))} be the first congruence subgroup of the special linear group SL n ⁢ (ℤ p) {\mathrm{SL}_{n}(\mathbb{Z}_{p})} and Ω G {\Omega_{G}} the mod-p Iwasawa algebra of G defined over 𝔽 p {\mathbb{F}_{p}}. By a purely computational approach, for each nonzero element W ∈ Ω G {W\in\Omega_{G}} , we prove that W is a normal element if and only if W contains constant terms. In this case, W is a unit. Also, the main result has been already proved under "nice prime" condition by Ardakov, Wei and Zhang [Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type, J. Algebra 320 2008, 1, 259–275; Reflexive ideals in Iwasawa algebras, Adv. Math. 218 2008, 3, 865–901]. This paper currently provides a new proof without the "nice prime" condition. As a consequence of the above-mentioned main result, we observe that the center of Ω G {\Omega_{G}} is trivial. [ABSTRACT FROM AUTHOR]

In this paper, we study varieties and characterize convolution operators on the algebras related to the new structures of KPC-hypergroups, which are a generalization of the classical ones. [ABSTRACT FROM AUTHOR]

Let f : ℝ n → ℝ {f\colon\mathbb{R}^{n}\rightarrow\mathbb{R}} be a polynomial and 𝒵 ⁢ (f) {\mathcal{Z}(f)} its zero set. In this paper, in terms of the so-called Newton polyhedron of f, we present a necessary criterion and a sufficient condition for the compactness of 𝒵 ⁢ (f) {\mathcal{Z}(f)}. From this we derive necessary and sufficient criteria for the stable compactness of 𝒵 ⁢ (f) {\mathcal{Z}(f)}. [ABSTRACT FROM AUTHOR]

In a 1966 paper by C.A.B. Smith, the short and long conjunctive sums of games are defined and methods are described for determining the theoretical winner of a game constructed using one type of these sums. In this paper, we develop a method for determining the winner of a game constructed using arbitrary combinations of these sums. [ABSTRACT FROM AUTHOR]

In recent papers [Honda, J. Diff. Geom 82: 411–444, 2009], [Honda, Invent. Math 174, 463–504, 2008], we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of new Moishezon twistor spaces, as conic bundles over some rational surfaces (called minitwistor spaces). These include the twistor spaces studied in the papers as very special cases. [ABSTRACT FROM AUTHOR]

In this paper and its follow-up [Merkulov and Vallette, J. reine angew. Math.], we study the deformation theory of morphisms of properads and props thereby extending Quillen's deformation theory for commutative rings to a non-linear framework. The associated chain complex is endowed with an L∞-algebra structure. Its Maurer-Cartan elements correspond to deformed structures, which allows us to give a geometric interpretation of these results. To do so, we endow the category of prop(erad)s with a model category structure. We provide a complete study of models for prop(erad)s. A new effective method to make minimal models explicit, that extends the Koszul duality theory, is introduced and the associated notion is called homotopy Koszul. As a corollary, we obtain the (co)homology theories of (al)gebras over a prop(erad) and of homotopy (al)gebras as well. Their underlying chain complex is endowed with an L∞-algebra structure in general and a Lie algebra structure only in the Koszul case. In particular, we make the deformation complex of morphisms from the properad of associative bialgebras explicit. For any minimal model of this properad, the boundary map of this chain complex is shown to be the one defined by Gerstenhaber and Schack. As a corollary, this paper provides a complete proof of the existence of an L∞-algebra structure on the Gerstenhaber-Schack bicomplex associated to the deformations of associative bialgebras. [ABSTRACT FROM AUTHOR]

In an earlier paper we proved some results concerning Gross's conjecture on tori. This conjecture, which we call the Minus Conjecture, is closely related to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however Burns' conjecture does not directly imply the Minus Conjecture. The result proved in the earlier paper was concerned with imaginary absolutely abelian extensions K/ℚ of the form K = FK+, with F imaginary quadratic and K+/ℚ being tame, l-elementary and ramified at most at two primes. In the present paper we complement these results by proving the Minus Conjecture for extensions K/ℚ as above but without any restriction on the number s of ramified primes. The price we have to pay for this generality is that our proof only works if the odd prime l is large enough, more precisely if l ≧ 3( s + 1). There is one more restriction, namely . (A similar restriction was already needed in our previous paper.) [ABSTRACT FROM AUTHOR]

In this paper we define a class of stable equivalences, namely, the stable equivalences of adjoint type, and study the Hochschild cohomology groups of algebras that are linked by a stable equivalence of adjoint type. This notion of adjoint type is a special case of Morita type, covers the stable equivalence of Morita type for self-injective algebras, and thus includes the case where Brou's conjecture was made (see for instance [Brou M.: Equivalences of blocks of group algberas. In: Finite dimensional algebras and related topics (V. Dlab and L. L. Scott eds.). Kluwer, 1994, 126]). The main results in this paper are: Let A and B be two artin k-algebras such that A and B are projective over k, and let Hn( A) and Hn( B) be the n-th Hochschild cohomology groups of A and B, respectively. (1) If A and B are stably equivalent of adjoint type, then Hn( A) Hn( B) for all n 1. (2) If A and B are stably equivalent of Morita type, then the absolute values of Cartan determinants of A and B are equal. In particular, two cellular algebras over a field have the same Cartan determinant if they are stably equivalent of Morita type. 2000 Mathematics Subject Classification: 16G10, 16E30; 16G70, 18G05, 20J05. [ABSTRACT FROM AUTHOR]

In the first part of this paper, we characterize generalized quadrangles which have certain smoothness properties by implicit differential-topological conditions. In particular, we give criteria for a generalized quadrangle to be smooth. Conversely, we establish differential-topological properties of smooth generalized quadrangles. In the final section of Part I, we give a characterization of smooth generalized quadrangles within a class of more general smooth incidence structures. In the second part of this paper we apply our results to a special situation in differential geometry: by results of Ferus, Karcher and Münzner a large class of isoparametric hypersurfaces in spheres arises from real representations of Clifford algebras. Thorbergsson proved that the incidence structures associated with these hypersurfaces and their focal manifolds are generalized quadrangles, and he claimed that, as a consequence of his proof, they were even smooth generalized quadrangles. In Part II we give an explicit proof for the smoothness of these generalized quadrangles. Even more, our approach yields a new proof for Thorbergsson's result. [ABSTRACT FROM AUTHOR]

In this paper, we show boundary monotonicity formulae for rectifiable varifolds having a C1,α “boundary”. In particular, we show that the area ratios of balls centered at this “boundary” satisfy a nice monotonicity formula, similar to that for interior balls proved by Allard in [Ann. of Math. (2) 95 (1972), 417–491]. This extends the boundary monotonicity formulae of Allard [Ann. of Math. (2) 101 (1975), 418–446], which require that the boundary is C1,1. As a corollary, the regularity results of [Ann. of Math. (2) 101 (1975), 418–446] extend to this case and provide a regularity result for rectifiable varifolds with a C1,α “boundary”. [ABSTRACT FROM AUTHOR]

In this paper we apply the REFORM method for the deduction of the system of canonical equations K61 for normalized spectral functions of the matrices A + B(U + γH)C. [ABSTRACT FROM AUTHOR]

In this paper we apply the REFORM method for the deduction of the system of canonical equations K60 for normalized spectral functions of the matrices [An + BnUn(ε)Cn][An + BnUn(ε)Cn]*. [ABSTRACT FROM AUTHOR]

R. Coleman and K. McMurdy calculated the stable reduction of X0(p3) (p ≥ 13) on the basis of the rigid geometry in [8]. In the present paper, we determine the stable reduction of X0(p4) for primes p ≥ 13 on the basis of their idea. As irreducible components in the stable reduction of X0(p4), a certain number of copies of the Hermitian curve, with an affine equation ap - a = tp+1, appear. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of generalized Hermite-Legendre polynomials of 2-variables and consequently a new class of Tricomi, Bessel and Hermite polynomials and their generalizations starting from suitable generating functions. The theory of Bessel, Legendre, Hermite and of the associated generating functions and their generalizations is reformulated within the framework of a series rearrangement formalism by using different analytical means on their respective generating functions. [ABSTRACT FROM AUTHOR]

The paper considers operators that map the set E onto itself. If , then ψ preserves some property of the point ϕ (here A is an operator and ). Such an approach to operators may serve as a method of solving some problems of mathematics, including the theory of orthogonal series. [ABSTRACT FROM AUTHOR]

In this paper, we present our recent results on the so-called complex structures in algebras in the context relevant to the following four problems which, at first glance, have nothing in common: (i) solubility of polynomial equations in non-associative algebras, (ii) topological/geometric properties of quadratic maps, (iii) existence of bounded solutions to quadratic differential systems, and (iv) ellipticity of the Dirac equation. The unsolved problems related to (i)-(iv) are formulated as well. [ABSTRACT FROM AUTHOR]

In this paper, we extend the definition of the Nathanson height from points in projective spaces over to points in projective spaces over arbitrary finite fields. If , then the Nathanson height is where with the field norm and the element of congruent to modulo p. We investigate the basic properties of this extended height, provide some bounds, study its image on the projective line and propose some questions for further research. [ABSTRACT FROM AUTHOR]

Let A be a finitely generated algebra over a field K of characteristic p > 0. We introduce a subring W†( A) ⊂ W( A), which we call the ring of overconvergent Witt vectors, and prove its basic properties. In a subsequent paper we use the results to define an overconvergent de Rham-Witt complex for smooth varieties over K whose hypercohomology is the rigid cohomology. [ABSTRACT FROM AUTHOR]

Denote by A θ the rotation algebra corresponding to the rotation 2 πθ. The C*-algebra 픹 θ generated by A θ together with certain spectral projections of the canonical unitary generators is studied. The C*-algebra 픹 θ is shown to have a unique tracial state and to be nuclear provided that θ is irrational. Moreover, we study the ideal structure of the C*-algebra 픹 θ. In particular, it is shown that 픹 θ is simple if neither the commutative sub-C*-algebra generated by the spectral projections of u in question (assumed to be a set invariant under Ad v) nor the corresponding commutative sub-C*-algebra associated to v contains non-zero minimal projections. In the second part of the paper, we study the extended rotation algebra 픹 θ generated by the spectral projections (one for each unitary) corresponding to the half-open interval from 0 to θ. (The spectral projections for each half-open interval from nθ to ( n + 1) θ are then included for each integer n.) Using simplicity of 픹 θ for θ irrational, the natural field of C*-algebras on the unit circle with fibres 픹 θ is shown to be continuous at irrational points. This field is lower semicontinuous on the whole circle. Much more useful is an upper semicontinuous field which is obtained by desingularizing this field at rational points on the circle. The fibres of the desingularized field at rational points are certain (computable) type I C*-algebras. Using this new field, we are able to show that 픹 θ is an AF algebra with K0(픹 θ) ≅ ℤ + θℤ for generic θ, in the sense of Baire category, with the class of the unit being 1 ∈ ℤ. [ABSTRACT FROM AUTHOR]

For , let count the number of -component multipartitions of a nonnegative integer , and let be the usual divisor function. In this paper, we give a combinatorial proof of the recursive formula both for , where is defined as above, and also for , which requires a subtler approach. This formula was used by Gandhi in 1963 to prove several theorems, which yield numerous Ramanujan type congruences for , including some well-known congruences for Ramanujan's -function. [ABSTRACT FROM AUTHOR]

For any group G the involutions ℐ in G form a G-set under conjugation. The corresponding kG-permutation module kℐ is known as the involution module of G, with k an algebraically closed field of characteristic two. In this paper we discuss the involution module of the special linear group SL2(2ƒ). We describe the vertices and the Loewy and Socle Series of all its components. [ABSTRACT FROM AUTHOR]

In this short paper we establish identities involving sums of products of binomial coefficients and coefficients that satisfy the general second-order linear recurrence. We obtain generalizations of identities of Carlitz, Prodinger and Haukkanen. [ABSTRACT FROM AUTHOR]

If * : G → G is an involution on the finite group G, then * extends to an involution on the integral group ring ℤ[ G]. In this paper, we consider whether bicyclic units u ∈ ℤ[ G] exist with the property that the group 〈 u, u*〉 generated by u and u* is free on the two generators. If this occurs, we say that ( u, u*) is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, ℤ[ G] contains a free bicyclic pair. [ABSTRACT FROM AUTHOR]

In this paper, we define B to be a certain subgroup in a classical group over a finite field and use it to construct non-classical BN-pairs. We also show that this construction is different from the classical one. As an application, we give transcendence bases for the fields of rational invariants of their subgroups B and N. [ABSTRACT FROM AUTHOR]

Some results about products of pairwise mutually permutable subgroups are presented in this paper. It is shown that this kind of products behaves well with respect to some well-known classes of groups. For instance, we show that all factors have only simple chief factors if the product has this property. This is necessary but not sufficient: we need that the factors belong to the subclass of PST-groups to make sure that the product has only simple chief factors (see Theorems 5 and 6). [ABSTRACT FROM AUTHOR]

To any connected and simply connected nilpotent Lie group N, one can associate its group of affine transformations Aff ( N). In this paper, we study simply transitive actions of a given nilpotent Lie group G on another nilpotent Lie group N, via such affine transformations. We succeed in translating the existence question of such a simply transitive affine action to a corresponding question on the Lie algebra level. As an example of the possible use of this translation, we then consider the case where dim( G) = dim( N) ≤ 5. Finally, we specialize to the case of abelian simply transitive affine actions on a given connected and simply connected nilpotent Lie group. It turns out that such a simply transitive abelian affine action on N corresponds to a particular Lie compatible bilinear product on the Lie algebra  of N, which we call an LR-structure. [ABSTRACT FROM AUTHOR]

Let FG be the group algebra of a group G without 2-elements over a field F of characteristic p ≠ 2 endowed with the canonical involution induced from the map g ↦ g–1, g ∈ G. Let ( FG)– and ( FG)+ be the sets of skew and symmetric elements of FG, respectively, and let P denote the set of p-elements of G (with P = 1 if p = 0). In the present paper we prove that if either P is finite or G is non-torsion and ( FG)– or ( FG)+ is Lie solvable, then FG is Lie solvable. The remaining cases are also settled upon small restrictions. [ABSTRACT FROM AUTHOR]

The maximal algebra of quotients of a semiprime Lie algebra was introduced recently by M. Siles Molina. In the present paper we answer some natural questions concerning this concept, and describe maximal algebras of quotients of certain Lie algebras that arise from associative algebras. [ABSTRACT FROM AUTHOR]

In this paper we construct, using Stark elements of Rubin [Ann. Inst. Fourier 46: 33–62, 1996], Kolyvagin systems for certain modified Selmer structures (that are adjusted to have core rank one in the sense of [Mazur and Rubin, Mem. Amer. Math. Soc. 168: viii, 96, 2004]) and prove a Gras-type conjecture, relating these Kolyvagin systems to appropriate ideal class groups, refining the results of [Rubin, J. reine angew. Math. 425: 141–154, 1992] (in a sense we explain below), and of [Perrin-Riou, Ann. Inst. Fourier 48: 1231–1307, 1998], [Rubin, Euler systems, Princeton University Press, 2000] applied to our setting. [ABSTRACT FROM AUTHOR]

In this paper, we compute all Gram determinants associated to all cell modules of Birman-Wenzl algebras. As a by-product, we give a necessary and sufficient condition for Birman-Wenzl algebras being semisimple over an arbitrary field. [ABSTRACT FROM AUTHOR]

In this paper we study the question of surjectivity of the power maps g ↦ gn on p-adic algebraic groups. We give a complete solution of this question in terms of the orders of certain compact analytic subgroups. We next study the p-adic one parameter subgroups of p-adic algebraic groups and find conditions, when the union of all such one parameter groups fills up the entire group. We show that there is a close relation between the above two problems. We also obtain similar results on groups defined over rational numbers. [ABSTRACT FROM AUTHOR]

In this paper we determine all algebraic transformation groups G, defined over an algebraically closed field k, which operate transitively, but not primitively, on a variety Ω, subject to the following conditions. We require that the (non-effective) action of G on the variety of blocks is sharply 2-transitive, as well as the action on a block Δ of the normalizer GΔ. Also we require sharp transitivity on pairs ( X, Y) of independent points of Ω, i.e. points contained in different blocks. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the asymptotic behaviour of class numbers h( d) in the case that the class numbers are ordered by the size of the fundamental solution of Pell's equation t2– du2 = 4 and the considered discriminants d belong to an arithmetic progression. As an application of this result we prove a result for the asymptotic behaviour of class numbers for fundamental discriminants. [ABSTRACT FROM AUTHOR]

The Schwarz-Pick lemma readily implies that the derivative of any Blaschke product belongs to all the Bergman spaces Ap with 0 < p < 1. It is also well known that this result is sharp: there exist a Blaschke product whose derivative does not belong to A1. However, the question of whether there exists an interpolating Blaschke product B with B′ ∉ A1 remained open. In this paper we give an explicit construction of such an interpolating Blaschke product B. A result of W. S. Cohn asserts that if and B is an interpolating Blaschke product with sequence of zeros of , then B′ ∈ Hp if and only if (1 – | ak|)1– p < ∞. We prove that Cohn's result is no longer true for . Indeed, we construct: (a) an interpolating Blaschke product B whose sequence of zeros of satisfies (1 – | ak|)1/2 < ∞ but B′ ∉ H1/2, and (b) an interpolating Blaschke products B whose sequence of zeros of satisfies (1 – | ak|)1– p < ∞, for all p ∈ (0, 1/2), whose derivative B′ does not belong to the Nevanlinna class. [ABSTRACT FROM AUTHOR]

In reviewing the foundations of probability, to establish the underpinnings of the Monte Carlo method, I found some basic results for which I could not find a simple, clear, and concise derivation in the literature. This paper is an attempt to present a sufficient collection of such results. The presentation is pitched at the level of Monte Carlo practitioners, rather than mathematical probabilists. [ABSTRACT FROM AUTHOR]

If L is a lattice, a group is called L-free if its subgroup lattice has no sublattice isomorphic to L. It is easy to see that L10, the subgroup lattice of the dihedral group of order 8, is the largest lattice L such that every finite L-free p-group is modular. Therefore in this paper we study finite L10-free groups and show that such a group is soluble and (with rather few exceptions) has metacyclic Fitting factor group. [ABSTRACT FROM AUTHOR]

In this paper we classify irreducible representations of quasi-simple groups with cyclic Sylow p-subgroup P = 〈 g〉 such that ( g) has at least one eigenvalue of multiplicity 1. [ABSTRACT FROM AUTHOR]

The system under consideration is governed by the equation utt = ▽ϰdivu – rot μ rot u in Ω × (0,T); its response operator ("input ↦ output" map) RT plays the role of the inverse data. As in the case of the proper Lamé system, such a model describes a dynamical system with two wave modes (p-waves and s-waves) propagating with different velocities cp = √ϰ and cs = √μ correspondingly. We show that R2T determines ϰ|ΩTp and μ|ΩTs, where ΩTp and ΩTs are the subdomains of Ω filled (at the moment T) with p- and s-waves propagating from ∂Ω. Due to the wave splitting u = ▽p + rot s the problem is reduced to the inverse problems for the acoustical and Maxwell subsystems governed by the equations ptt = ϰΔp and stt = –μ rot rot s with the response operators R2Tp and R2Ts sdetermined by R2T. The first problem can be solved by the BC method (Belishev, 1986), the second one is solved by a version of the method based on a blow up effect. This version is the main subject of the paper. In addition, we derive the inequality, which can be used for approximate determination of the shape of ΩTs. [ABSTRACT FROM AUTHOR]

The article examines Morita equivalences for blocks of the covering groups of the symmetric and alternating groups. The paper shows results that demonstrate the existence of these equivalences from crossovers between blocks of the covering groups. It also discusses Morita cases obtained by using an involution and are parity-preserving. The existence of various functors involving module categories of blocks of the covering groups of the symmetric group and alternating groups has also shown some relevance to crossovers.

This paper is a sequel to [A. M. Cohen and L. Paris. On a theorem of Artin. J. Group Theory 6 (2003), 421–441.]. Let A be an Artin group, let W be its associated Coxeter group, and let CA be its associated coloured Artin group, that is, the kernel of the standard epimorphism μ : A → W. We determine the homomorphisms φ : A → W that satisfy Im φ · Z(W) = W, for A irreducible and of spherical type, and we prove that CA is a characteristic subgroup of A if A is of spherical type but not necessarily irreducible. [ABSTRACT FROM AUTHOR]

In this paper, we consider algorithms to pack rectangles into a strip. As the main result we present an algorithm that packs rectangles online and for which the ratio of expected wasted area to expected occupied area tends to zero as the number of rectangles increases. The research was supported by the Russian Foundation for Basic Research, grants 05–01–00798 and 04–01–00359. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalisation of quadratic residue codes to the cases of higher power residues. Such a generalisation enhances the information transmission rate with the use of such codes as compared with the quadratic-residue codes, at a sacrifice in the lower bound for the code distance, though. We consider the construction of generating polynomials for such codes, which allows to write explicitly their generating matrix. [ABSTRACT FROM AUTHOR]

New formulae for solutions and coefficients of multidimensional kinetic equations are presented in the paper. [ABSTRACT FROM AUTHOR]

The Cayley graph generated by a set A is the graph ΓA(V) on a set of positive integers V such that a pair(u,v) ∈ V×V is an edge of the graph if and only if |u-v| ∈ A or u+v ∈ A. We denote by G2(n,m) the class of graphs G = (V, E) such that G is a union of chains and cycles and |V| = n, |E| = m. In this paper, we present an upper bound for the number of independent sets in Cayley graphs ΓA(V) such that A = {⌈n/2⌉ - t, ⌈n/2⌉ - ƒ}, V &subE; [⌊n/2⌋ + 1, ⌊n/2⌋+t] ∪ [n - t + 1, n], where n, t, ƒ ∈ N and ƒ < t < n/4. We also describe the graph with the maximum number of independent sets in the family g2(n, m). This research was supported by the Russian Foundation for Basic Researches, grant 04–01–00359. [ABSTRACT FROM AUTHOR]

In this paper we present two recent results for matrices arising in the mixed finite element method on triangular meshes. The first result is an algebraic proof for the discrete LBB condition. The second one is a new algorithm for the construction of a two-level spectrally equivalent preconditioner for the condensed matrix. [ABSTRACT FROM AUTHOR]

The aim of this paper is to gain insight into the spectral structure of the discrete analog of hydrodynamic equations linearized at a steady state and discuss how to compute its spectral characteristics connected with the main part of the spectrum. [ABSTRACT FROM AUTHOR]

Let G be a group. A set X of elements of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If |X| ≥ |X′| for any other non-commuting set X′ in G, then X is said to be a maximal non-commuting set. In this paper we obtain upper and lower bounds for the cardinality of a maximal non-commuting set in an extraspecial p-group where p is an odd prime. [ABSTRACT FROM AUTHOR]

In this paper, indecomposable and irreducible weight representations with 1-dimensional weight spaces for simple generalized Witt algebras over any field of characteristic 0 are classified. There are five classes of such nontrivial indecomposable modules. [ABSTRACT FROM AUTHOR]

In this paper, we present the list of minimal sets of systems of parastrophs for all 109 classes of isomorphic loops and 22 classes of isotopic quasigroups of order 6. [ABSTRACT FROM AUTHOR]