on the maxwell and friedrichs poincare constants in nd we prove that for bounded and convex domains in arbitrary dimensions the maxwell constants are bounded from below and above by friedrichs and poincare s constants respectively especially the second positive maxwell eigenvalues in nd are bounded from below by the square root of the second neumann laplace eigenvalue

unique determination of periodic polyhedral structures by scattered electromagnetic fields this work is concerned with the unique determination of a periodic diffraction grating profile in three dimensions by some scattered electromagnetic fields measured above the grating in general it is well known that global uniqueness may not be true when the measurement is only taken for one incident field our goal is to completely characterize the global uniqueness properties when the periodic structure is of polyhedral type corresponding to each incident plane wave we are able to classify all unidentifiable structures into three classes and show that any periodic polyhedral structure can be uniquely determined by one incident field if and only if it belongs to none of the three classes consequently the minimum number of incident waves required for the unique determination of a periodic polyhedral structure can be easily read

fully simple semihypergroups transitive digraphs and sequence a000712 abstract fully simple semihypergroups have been introduced in 9 motivated by the study of the transitivity of the fundamental relation in semihypergroups here we determine a transversal of isomorphism classes of fully simple semihypergroups with a right absorbing element the structure of that transversal can be described by means of certain transitive acyclic digraphs moreover we prove that if n is an integer 2 then the number of isomorphism classes of fully simple semihypergroups of size n 1 with a right absorbing element is the n 1 th term of sequence a000712 in 20 namely k 0 n p k p n k where p k denotes the number of nonincreasing partitions of integer k

unconditional families in banach spaces it is shown that for every separable banach space x with non separable dual the space x contains an unconditional family of size x the proof is based on ramsey theory for trees and finite products of perfect sets of reals among its consequences it is proved that every dual banach space has a separable quotient

variational approximation of maxwell s equations in biperiodic structures consider a plane wave incident on a biperiodic diffractive structure the diffraction problem may be modeled by maxwell s equations with transparent boundary conditions and solved by a finite element method in this paper a variational approximation is studied the well posedness of the continuous and discretized problems is established in the following sense in the continuous case it is shown that the model problem attains a unique cal h 1 solution for all but possibly a discrete set of frequencies in the discrete case error estimates for the variational finite element approximation of the model problem with or without truncation of the nonlocal boundary operators are obtained

hausdorff measures and functions of bounded quadratic variation to each function f of bounded quadratic variation we associate a hausdorff measure f we show that the map f f is locally lipschitz and onto the positive cone of m 0 1 we use the measures f f v 2 to determine the structure of the subspaces of v 0 2 which either contain c 0 or the square stopping time space s 2

transposition hypergroups noncommutative join spaces the study of various kinds of algebraic hypergroups is unified in the theory of transposition hypergroups the hyperoperation in any hypergroup has two inverses given bya b x a xb andb a x a bx a transposition hypergroup is a hypergroup where transposition b a c d impliesad bc holds the algebra of transposition hypergroups is developed closed subhypergroupsnthat are reflexive a n n a have distinguished structural significance the quotient space of a transposition hypergroup modulo a reflexive closed subhypergroup forms a transposition hypergroup that is a polygroup then generalizations of the isomorphism theorems and the jordan holder theorem of group theory are obtained

ordered regular equivalence relations on ordered semihypergroups abstract in this paper we introduce the concept of ordered regular strongly ordered regular equivalence relation on an ordered semihypergroup moreover we use hyperfilters to construct a strongly ordered regular equivalence relation on an ordered semihypergroup for which the corresponding quotient structure is a semilattice finally we construct an ordered regular equivalence relation on an ordered semihypergroup by hyperideals such that the corresponding quotient structure is also an ordered semihypergroup under a related order relation which is an answer to the open problem given by b davvaz p corsini and t changphas in european journal of combinatorics

fully simple semihypergroups abstract in this paper we consider the class of semihypergroups h such that all subsemihypergroups k h are simple and when k 3 the fundamental relation k is not transitive for these semihypergroups we prove that hyperproducts of elements in h have size 2 and the quotient semigroup h is trivial this last result allows us to completely characterize these semihypergroups in terms of a small set of simple semihypergroups of size 3 finally we solve a problem on strongly simple semihypergroups introduced in 11

electromagnetic waves in an inhomogeneous medium abstract in this paper we consider the electromagnetic wave problem in an inhomogeneous medium we first prove uniqueness of the solution using rellich and cauchy kowalewska theorems then we explicitly compute the dirichlet neumann operator on the sphere we reduce the equations to a problem on a truncated domain and we give a variational formulation this formulation reads as a compact perturbation of a coercive operator which leads to the existence of the solution according to fredholm s alternative

on the subspaces of jf and jt with non separable dual it is proved that every subspace of james tree space jt with non separable dual contains an isomorph of james tree complemented in jt this yields that every complemented subspace of jt with non separable dual is isomorphic to jt a new jt like space denoted as tf is defined it is shown that every subspace of james function space jf with non separable dual contains an isomorph of tf the later yields that every subspace of jf with non separable dual contains isomorphs of c0 and lp for 2 p the analogues of the above results for bounded linear operators are also proved

polygroups derived from cogroups abstract a polygroup is a completely regular reversible in itself multigroup in the sense of dresher and ore 4 these systems occur naturally in the study of algebraic logic 1 2 some algebraic and combinatorial properties were developed in 3 the question of whether or not q 2 group the class of double quotients of groups is the same as the class of all chromatic polygroups is important for many reasons in this paper double quotients of groups are constructed in a natural way from cogroups cogroups were introduced by eaton 5 in an attempt to axiomatize d hypergroups i e systems obtainable from groups by right coset decompositions with respect to not necessarily normal subgroups eaton s axioms apply only to finite systems utumi 7 formulated a general notion and gave an example of a cogroup not isomorphic to a d hypergroup utumi s scalar partition hypergroups appear in section 2 the main results in section 3 show that polygroups derivable from cogroups are chromatic and they include all double quotients of groups

the time harmonic maxwell equations in a doubly periodic structure abstract consider the diffraction of a beam of particles in r 3 when the dielectric coefficient is a constant e1 above a surface s and a different constant e2 below s and the magnetic permeability is constant throughout r 3 s is assumed to be a doubly periodic surface say z f x y with f x ml1 y nl2 f x y for integers m n the existence and uniqueness of a solution satisfying a radiation condition at infinity is reduced to a system of fredholm equations thus for all but a discrete set of e s there exists a unique solution

minimal order semihypergroups of type u on the right ii abstract we prove a new characterization of the heart w h and of the derived d h of a finite semihypergroup h of type u on the right in terms of its hyperproducts consequently we characterize the minimal size of the proper semihypergroups h of type u on the right such that w h d h h w h d h h or w h d h h moreover we obtain new results on the fundamental relations and on finite semihypergroups of type u on the right in particular we prove that is transitive is transitive if h 8 and that there exist semihypergroups of type u on the right of size 9 where is not transitive hence the minimal size for a semihypergroup of type u on the right to have a nontransitive is 9

an inverse problem for scattering by a doubly periodic structure consider scattering of electromagnetic waves by a doubly periodic structure s x3 f xl x2 with f xl nial x2 n2a2 f xl x2 for integers nl n2 above the structure the medium is assumed to be homogeneous with a constant dielectric coefficient the medium is a perfect conductor below the structure an inverse problem arises and may be described as follows for a given incident plane wave the tangential electric field is measured away from the structure say at x3 b for some large b to what extent can one determine the location of the periodic structure that separates the dielectric medium from the conductor in this paper results on uniqueness and stability are established for the inverse problem a crucial step in our proof is to obtain a lower bound for the first eigenvalue of the following problem in a convex domain q l au in q v u 0 in q n xu 0 on q

an inverse cavity problem for maxwellʼs equations abstract consider the scattering of a time harmonic electromagnetic plane wave by an open cavity embedded in a perfect electrically conducting infinite ground plane where the electromagnetic wave propagation is governed by the maxwell equations the upper half space is filled with a lossless homogeneous medium above the flat ground surface while the interior of the cavity is assumed to be filled with a lossy homogeneous medium accounting for the energy absorption the inverse problem is to determine the cavity structure or the shape of the cavity from the tangential trace of the electric field measured on the aperture of the cavity in this paper results on a global uniqueness and a local stability are established for the inverse problem a crucial step in the proof of the stability is to obtain the existence and characterization of the domain derivative of the electric field with respect to the shape of the cavity

inverse problems for scattering by periodic structures suppose the 3 dimensional space is filled with three materials having dielectric constants 1 above s1 x2 f1 x1 x3 arbitrary 2 below s2 x2 f2 x1 x3 arbitrary and o in f2 x1 0 if the measurements for the two pairs are close then tilde s 1 and tilde s 2 are 0 close to s1 and s2 respectively

isomorphism classes of the hypergroups of type u on the right of size five by means of a blend of theoretical arguments and computer algebra techniques we prove that the number of isomorphism classes of hypergroups of type u on the right of order five having a scalar bilateral identity is 14751 in this way we complete the classification of hypergroups of type u on the right of order five started in our preceding papers m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five far east j math sci 26 2 2007 393 418 m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five part two mathematicki vesnik 60 2008 23 45 m de salvo d freni g lo faro on the hypergroups of type u on the right of size five with scalar identity submitted for publication in particular we obtain that the number of isomorphism classes of such hypergroups is 14865

characterizations of strongly ordered regular relations on ordered semihypergroups abstract in this paper we give the fundamental normal homomorphism theorem of ordered semihypergroups moreover we characterize the strongly ordered regular relations on an ordered semihypergroup by means of the chain and obtain that the set of all strongly ordered regular relations on an ordered semihypergroup consists a complete lattice finally the subset of an ordered semihypergroup can serve as some ordered regular ordered semilattice relation class is determined