Superlocals in Symmetric and Alternating Groups

On Aschbacher's definition, a subgroup N of a finite group is called a -superlocal for a prime if . We describe the -superlocals in symmetric and alternating groups, thereby resolving part way Problem 11.3 in the Kourovka Notebook [3].     

Quasiconformal Mappings and Solutions of the Dispersionless KP Hierarchy

A formalism for studying dispersionless integrable hierarchies is applied to the dispersionless KP (dKP) hierarchy. We relate this formalism to the theory of quasiconformal mappings on the plane and present some classes of explicit solutions of the dKP hierarchy.     

Locally Finite Barely Transitive Groups

Infinite transitive permutation groups all proper subgroups of which have just finite orbits are treated. Under the extra condition of being locally finite, such groups are proved to be primary, and, moreover, soluble if the stabilizer of some point is soluble.     

Sur la cohomologie à supports compacts des variétés de Shimura pour GSp(4)_\mathbb{Q}

In this paper we compute the cohomology with compact supports of a Siegelthreefold as a virtual module over the product of the Galois group of over and the Hecke algebra. We use a method which has been developed by Ihara, Langlands and Kottwitz: comparison of the Grothendieck--Lefschetz formula and the Arthur--Selberg trace formula.     

\mathcal{Q}-Universal Quasivarieties of Graphs

It is proved that a quasivariety K of undirected graphs without loops is -universal if and only if K contains some non-bipartite graph.     

Semiclassical $$\bar \partial $$ -Method: Generating Equations for Dispersionless Integrable Hierarchies

We use the semiclassical -dressing method to derive compact generating equations for dispersionless hierarchies. The considered illustrative examples are the dispersionless Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies.     

Some New Extrapolation Estimates for the Scale of Spaces

Using new extrapolation estimates for the - and -functionals of couples of limit spaces of the -scale , we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces close to and , which depend only on the -norms of a function.     

Evaluation Formulas for a Conditional Feynman Integral Over Wiener Paths in Abstract Wiener Space

In this paper, we introduce a simple formula for conditional Wiener integrals over , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form which are of interest in Feynman integration theories and quantum mechanics.     

Polynomials with All Zeros Real and in a Prescribed Interval

We provide a characterization of the real-valued univariate polynomials that have only real zeros, all in a prescribed interval [a,b]. The conditions are stated in terms of positive semidefiniteness of related Hankel matrices.     

Domination in generalized Petersen graphs

Generalized Petersen graphs are certain graphs consisting of one quadratic factor. For these graphs some numerical invariants concerning the domination are studied, namely the domatic number , the total domatic number and the -ply domatic number for and . Some exact values and some inequalities are stated.     

On microfunctions at the boundary along CR manifolds

Let X be a complex analytic manifold, a C ² submanifold, an openset with C ² boundary .Denote by (resp. ) the microlocalization along M (resp. ) of the sheaf of holomorphic functions.In the literature (cf. [A-G], [K-S 1,2])one encounters two classical results concerning the vanishing of the cohomology groups .The most general gives the vanishing outside a range of indices j whose length is equal to (with being the number of respectively positive, negative and null eigenvalues for themicrolocal Levi form ).The sharpest result gives the concentration in a single degree, provided that the difference is locally constant for near p (with for z the base point of p).The first result was restated for the complex in [D'A-Z 2], in the case codim We extend it here to any codimension and moreover we also restate for the second vanishing theorem.We also point out that the principle of our proof, related to a criterion for constancy of sheaves due to [K-S 1], is a quite new one.     

Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations

We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra . For a discriminantal arrangement in ^k, the skew-symmetric cohomology is nontrivial in dimension k–1 precisely when the 'master function' which defines the local system on the complement has nonisolated criticalpoints. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.     

Initial Segments in Rogers Semilattices of \Sigma _n^0 -Computable Numberings

S. Goncharov and S. Badaev showed that for , there exist infinite families whose Rogers semilattices contain ideals without minimal elements. In this connection, the question was posed as to whether there are examples of families that lack this property. We answer this question in the negative. It is proved that independently of a family chosen, the class of semilattices that are principal ideals of the Rogers semilattice of that family is rather wide: it includes both a factor lattice of the lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semilattice of -degrees generated by immune sets.     

Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

Stability of Hypersurfaces with Constant r-Mean Curvature

We deal with compact hypersurfaces immersed in space forms with constant -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.     

A New \mathcal{N}\mathcal{P} -Complete Problem and Public-Key Identification

The appearance of the theory of zero-knowledge, presented by Goldwasser, Micali and Rackoff in 1985, opened a way to secure identification schemes. The first application was the famous Fiat-Shamir scheme based on the problem of modular square roots extraction. In the following years, many other schemes have been proposed, some Fiat-Shamir extensions but also new discrete logarithm based schemes. Therefore, all of them were based on problems from number theory. Their main common drawback is high computational load because of arithmetical operations modulo large integers. Implementation on low-cost smart cards was made difficult and inefficient.With the Permuted Kernels Problem (PKP), Shamir proposed the first efficient scheme allowing for an implementation on such low-cost smart cards, but very few others have afterwards been suggested.In this paper, we present an efficient identification scheme based on a combinatorial -complete problem: the Permuted Perceptrons Problem (PPP). This problem seems hard enough to be unsolvable even with very small parameters, and some recent cryptanalysis studies confirm that position. Furthermore, it admits efficient zero-knowledge proofs of knowledge and so it is well-suited for cryptographic purposes. An actual implementation completes the optimistic opinion about efficiency and practicability on low-cost smart cards, and namely with less than 2KB of EEPROM and just 100 Bytes of RAM and 6.4 KB of communication.     

Orders on Braid Groups

It is shown that the braid group defies lattice ordering.     

Lp Contraction Semigroups for Vector Valued Functions

Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.     

ℓ1-Minimization with Magnitude Constraints in the Frequency Domain

In this paper, we study the -optimal control problem with additional constraints on the magnitude of the closed-loop frequency response. In particular, we study the case of magnitude constraints at fixed frequency points (a finite number of such constraints can be used to approximate an -norm constraint). In previous work, we have shown that the primal-dual formulation for this problem has no duality gap and both primal and dual problems are equivalent to convex, possibly infinite-dimensional, optimization problems with LMI constraints. Here, we study the effect of approximating the convex magnitude constraints with a finite number of linear constraints and provide a bound on the accuracy of the approximation. The resulting problems are linear programs. In the one-block case, both primal and dual programs are semi-infinite dimensional. The optimal cost can be approximated, arbitrarily well from above and within any predefined accuracy from below, by the solutions of finite-dimensional linear programs. In the multiblock case, the approximate LP problem (as well as the exact LMI problem) is infinite-dimensional in both the variables and the constraints. We show that the standard finite-dimensional approximation method, based on approximating the dual linear programming problem by sequences of finite-support problems, may fail to converge to the optimal cost of the infinite-dimensional problem.