the treatment of singularities at 90 circ and 270 circ microstrip corners in fdtd by the modification of assigned material parameters it has been recently shown that the efficiency of the finite difference time domain fdtd method for structures containing thin wires and metal edges is much increased by using modified assigned material parameters mamps these parameters may be calculated empirically and in many cases analytically in this contribution the technique is extended to include the case of 90deg and 270deg corners in microstrip which may exist at an arbitrary position within the plane of the mesh a semi analytical method is presented and applied to the analysis of a complex patch antenna results are presented which show that the use of mamps allows a much larger cell size to be used than would be needed to achieve the same accuracy using standard fdtd

semiprime graded algebras of dimension two semiprime noetherian connected graded k algebras r of quadratic growth are described in terms of geometric data a typical example of such a ring is obtained as follows let y be a projective variety of dimension at most one over the base field k and let e be an oy order in a finite dimensional semisimple algebra a over k k y then for any automorphism of a that restricts to an automorphism of y and any ample invertible e bimodule b van den bergh constructs a noetherian twisted homogeneous coordinate ring b h0 y b b n 1 we show that r is noetherian if and only if some veronese ring r m of r has the form k i where i is a left ideal of such a ring b and where i b at each point p y at which has finite order this allows one to give detailed information about the structure of r and its modules

boundedness properties and perturbing lyapunov functions it is well known 1 4 that in investigating uniform boundedness of solutions of a given differential system by means of lyapunov functions it is enough to impose conditions on the complement of a compact set in 1w where as in the case of nonuniform boundedness properties the proofs demand that the assumptions hold everywhere in ky in 2 using the idea of perturbing lyapunov functions the nonuniform boundedness property is discussed without assuming conditions everywhere as in the case of uniform boundedness recently 31 uniform boundedness criteria are studied by using two lyapunov functions together with the theory of differential inequalities to obtain sufficient conditions under weaker assumptions in this paper we investigate nonuniform boundedness properties employing the method of perturbing lyapunov functions and the theory of differential inequalities our results include several existing results as special cases as well as those in 2 33

a resolution of paz s conjecture in the presence of a nonderogatory matrix abstract let m n f be the algebra of n n matrices over the field f and let s be a generating set of m n f as an f algebra the length of a finite generating set s of m n f is the smallest number k such that words of length not greater than k generate m n f as a vector space it is a long standing conjecture of paz that the length of any generating set of m n f cannot exceed 2 n 2 we prove this conjecture under the assumption that the generating set s contains a nonderogatory matrix in addition we find linear bounds for the length of generating sets that include a matrix with some conditions on its jordan canonical form finally we investigate cases when the length 2 n 2 is achieved

generators of matrix algebras in dimension 2 and 3 abstract let k be an algebraically closed field of characteristic zero and consider a set of 2 2 or 3 3 matrices using a theorem of shemesh we give conditions for when the matrices in the set generate the full matrix algebra

golod shafarevich algebras free subalgebras and noetherian images abstract it is shown that golod shafarevich algebras of a reduced number of defining relations contain noncommutative free subalgebras in two generators and that these algebras can be homomorphically mapped onto prime noetherian algebras with linear growth it is also shown that golod shafarevich algebras of a reduced number of relations cannot be nil

electric field singularities at sharp edges of planar conductors the electric field behavior around printed conductors with a polygonal contour as used in antennas and microwave circuit components is investigated the diffraction problem posed by these geometries involves edge and vertex conditions as well as boundary conditions these can collectively be described by means of a simple singularity function that gives the distribution of zeros of the electric field on the flat conductor surfaces and of its singularities along the conductor edges the analysis is based on solving the vector helmholtz equation for the plane sector perfect conductor in a conical coordinate system and the static case is derived from a limit process the values of the singularity function for the electric field components are explicitly reported for the more commonly encountered 90 degrees and 270 degrees sectors and for 90 degrees bitriangular antennas systematic extension to sectors of arbitrary aperture to composite configurations and to their polygonal combinations is also indicated

primitive algebras with arbitrary gelfand kirillov dimension abstract we construct for every real 2 a primitive affine algebra with gelfand kirillov dimension unlike earlier constructions there are no assumptions on the base field in particular this is the first construction over or l given a recursive sequence v n of elements in a free monoid we investigate the quotient of the free associative algebra by the ideal generated by all nonsubwords in v n we bound the dimension of the resulting algebra in terms of the growth of v n in particular if n is less than doubly exponential then the dimension is 2 this also answers affirmatively a conjecture of salwa 1997 comm algebra 25 3965 3972

a class of algebras similar to the enveloping algebra of sl 2 fix f e c x define r c a b h subject to the relations ha ah a hb bh b ab ba f h we study these algebras for different f and in particular show how they are similar to and different from u sl 2 the enveloping algebra of sl 2 c there is a notion of highest weight modules and a category a for such r for each n 0 if f x x 1 n l xn 1 then r has precisely n simple modules in each finite dimension and every finite dimensional r module is semisimple

lengths of quasi commutative pairs of matrices abstract in this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras we consider mainly the sets of two matrices which are quasi commuting it is shown that in this case the length function is linearly bounded we also analyze which particular natural numbers can be realized as the lengths of certain special generating sets and prove that for commuting or product nilpotent pairs all possible numbers are realizable however there are non realizable values between lower and upper bounds for the other quasi commuting pairs in conclusion we also present several related open problems

examples in finite gel fand kirillov dimension for any field f we give an example of a prime finitely generated f algebra of gk dimension 2 for which gk dimension is not finitely partitive for each m 0 1 2 3 we give an example

on the codimension sequence of g simple algebras abstract let f be an algebraically closed field of characteristic zero and let g be a finite group in this paper we will show that the asymptotics of c n g a the g graded codimension sequence of a finite dimensional g simple f algebra a has the form n 1 dim f a e 2 dim f a n as conjectured by e aljadeff d haile and m natapov where is some positive real number and a e denotes the identity component of a in the special case where a is the algebra of m m matrices with an arbitrary elementary g grading we succeeded in calculating the constant explicitly

noetherian connected graded algebras of global dimension 3 abstract let a be a noetherian connected graded algebra of global dimension 3 we show that a is regular in the sense of artin and schelter if one of the following conditions holds 1 a is generated by two elements 2 the graded simple module has a standard resolution 3 the degrees of minimal relations are the same this includes the quadratic case some general properties of a are studied without assuming regularity

associative conformal algebras with finite faithful representation abstract the classification of irreducible subalgebras of the associative conformal algebra cend n is presented in this paper the structure theory of associative conformal algebras with finite faithful representation is developed

on condensed forms for partially commuting matrices abstract two complex n n matrices a and b are said to be partially commuting if a and b have a common eigenvector we propose a condensed form for such matrices that can be obtained from a and b by a finite rational computation the condensed form is a pair of block triangular matrices with the sizes of the blocks being uniquely defined by the original matrices we then show how to obtain additional zeros inside the diagonal blocks of a condensed form by using the generalized lanczos procedure as given by elsner and ikramov this procedure can also be considered as a finite rational process we point out several applications of the constructions above it turns out that for laffey pairs of matrices i e for matrices a b such that rank a b 1 the condensed form is a pair of 2 2 block triangular matrices using this fact we show an economical way to find a spanning set for the matrix algebra generated by laffey matrices a and b another application concerns so called k self adjoint matrices we examine such matrices in the unitary space as well as in a krein space of defect 1 as an appendix we give a new description of the shemesh subspace of matrices a and b this is the maximal common invariant subspace of a and b on which these matrices commute

electric singularity near the tip of a sharp cone the singularity of the electric fields proportional to the radial coordinate value r sup nu 1 is investigated for a very sharp perfectly conducting cone of arbitrary cross section it is shown that in the limit of a very small cone the exponent nu tends to zero in proportion with the inverse of the logarithm of the maximum opening angle results are shown for the circular and elliptic cone with the flat sector as a special case and for the pyramid with n equal faces an expression valid for arbitrary opening angles is presented in the case of a flat sector

a dichotomy result for prime algebras of gelfand kirillov dimension two abstract let k be an uncountable field we show that a finitely generated prime goldie k algebra of quadratic growth is either primitive or satisfies a polynomial identity answering a question of small in the affirmative

an elementary method to compute the algebra generated by some given matrices and its dimension abstract we give an efficient solution to the following problem given x 1 x d and y some n by n matrices can we determine if y is in the unital algebra generated by x 1 x d as a subalgebra of all n by n matrices the solution also gives an easy method for computing the dimension of this algebra

electric field behavior near metallic wedges electric field behavior is determined on perfect metallic wedges of bidimensional conical and three dimensional shape the analytical treatment is based on solving laplace s equation in spherical and conical coordinate systems for both cases the components of the electric field behave like r sup alpha presenting a singularity when alpha

there are no graded domains with gk dimension strictly between 2 and 3 let k be a field and let r n n r n be a finitely generated graded k algebra which is a domain it is shown that r cannot have gelfand kirillov dimension strictly between 2 and 3

on the generalized lienard equation without the signum condition abstract we consider the generalized lienard equation x x h x x g x k x 0 without the signum condition xg x 0 for all x 0 and give a necessary and sufficient condition for the boundedness of all solutions of this equation and their derivatives

on the boundedness of the solutions of the nonlinear oscillating equation abstract we consider the nonlinear oscillating equation x f x h x x g x k x 0 without the common conditions a f x 0 for all x r b xg x 0 for all x 0 and give a set of necessary and sufficient conditions for the boundedness of all solutions of this equation and their derivatives

upper bounds for the length of non associative algebras abstract we introduce the notion of length for non associative finite dimensional unitary algebras and obtain a sharp upper bound for the lengths of algebras belonging to this class we also put forward a new method of characteristic sequences based on linear algebra technique which provides an efficient tool for computing the length function in non associative case then we apply the introduced method to obtain an upper bound for the length of an arbitrary locally complex algebra in the last case the length is bounded in terms of the fibonacci sequence we present concrete examples demonstrating the sharpness of our bounds

the effect of assuming the identity as a generator on the length of the matrix algebra abstract let m n f be the algebra of n n matrices and let s be a generating set of m n f as an f algebra the length of a finite generating set s of m n f is the smallest number k such that words of length not greater than k generate m n f as a vector space traditionally the identity matrix is assumed to be automatically included in all generating sets s and counted as a word of length 0 in this paper we discuss how the problem changes if this assumption is removed

unitarily achievable zero patterns and traces of words in a and a abstract our primary objective is to identify a natural and substantial problem about unitary similarity on arbitrary complex matrices which 0 patterns may be achieved for any given n by n complex matrix via some unitary similarity of it to this end certain restrictions on achievable 0 patterns are mentioned both positional and more important on the maximum number of achievable 0 s prior results fitting this general question are mentioned as well as the first unresolved pattern for 3 by 3 matrices in the process a recent question is answered a closely related additional objective is to mention the best known bound for the maximum length of words necessary for the application of specht s theorem about which pairs of complex matrices are unitarily similar which seems not widely known to matrix theorists in the process we mention the number of words necessary for small size matrices

application of shemesh theorem to quantum channels completely positive maps are useful in modeling the discrete evolution of quantum systems spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to multiple interactions described by the same quantum channel we discuss a connection between the properties of the peripheral spectrum of completely positive and trace preserving map and the algebra generated by its kraus operators a a1 ak by applying the shemesh and amitsur levitzki theorems to analyse the structure of the algebra a a1 ak one can predict the asymptotic dynamics for a class of operations completely positive maps are useful in modeling the discrete evolution of quantum systems spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to multiple interactions described by the same quantum channel we discuss a connection between the properties of the peripheral spectrum of completely positive and trace preserving map and the algebra generated by its kraus operators a a1 ak by applying the shemesh and amitsur levitzki theorems to analyse the structure of the algebra a a1 ak one can predict the asymptotic dynamics for a class of operations

some noncommutative minimal surfaces abstract in the ongoing programme to classify noncommutative projective surfaces connected graded noetherian domains of gelfand kirillov dimension three a natural question is to determine the minimal models within any birational class in this paper we show that the generic noncommutative projective plane corresponding to the three dimensional sklyanin algebra as well as noncommutative analogues of p 1 p 1 and the more general van den bergh quadrics satisfy very strong minimality conditions translated into an algebraic question where one is interested in a maximality condition we prove the following result theorem a let r be a sklyanin algebra or a van den bergh quadric that is infinite dimensional over its centre and let a r be any connected graded noetherian maximal order with the same graded quotient ring as r then up to taking veronese rings a is isomorphic to r let t be an elliptic algebra that is the coordinate ring of a noncommutative surface containing an elliptic curve then under an appropriate homological condition we prove that every connected graded noetherian overring of t is obtained by blowing down finitely many lines line modules of self intersection 1

length realizability for pairs of quasi commuting matrices abstract for the pairs of quasi commuting matrices we completely characterize natural numbers that can be realized as the lengths of these pairs of generators

on irreducible semigroups of matrices with traces in a subfield abstract in this paper we consider irreducible semigroups of matrices over a general field k with traces in a subfield f motivated by a result of omladic radjabalipour radjavi we prove a block matrix representation theorem for the f algebras generated by such semigroups we use our main results to generalize certain classical triangularization results e g those due to guralnick and radjavi some other consequences of our main results are presented

an upper bound for the length of a finite dimensional algebra abstract letfbe a field and letabe a finite dimensionalf algebra writed dimf a and letebe the largest degree of the minimal polynomial for anya a define the function f d e e 2d e 1 1 4 e 2 2 we prove that ifsis any finite generating set foraas anf algebra the words insof length less thanf d e spanaas anf vector space in the special case ofn by nmatrices this bound becomes f n 2 n n 2n 2 n 1 1 4 n 2 2 o n 3 2 this is a substantial improvement over previous bounds which have all beeno n2 we also prove that for particular setssof matrices the bound can be sharpened to one that is linear inn as an application of these results we reprove a theorem of small stafford and warfield about semiprime affinef algebras

boundedness theorems by two liapunov functions on considere le systeme d equations differentielles dx dt f t x y dy dt g t x y avec x r n y r m et f g des fonctions continues sur r r n r m on demontre un theoreme qui donne des criteres pour que des solutions soient uniformement bornees en se servant de deux fonctions de lyapunov et du theoreme de comparaison

simultaneous unitary equivalences abstract let s 1 s 2 s 3 s 4 be given finite sets of pairs of n by n complex matrices we describe an algorithm to determine with finitely many computations whether there is a single unitary matrix u such that each pair of matrices in s 1 is unitarily similar via u each pair of matrices in s 2 is unitarily congruent via u each pair of matrices in s 3 is unitarily similar via u and each pair of matrices in s 4 is unitarily congruent via u

on the boundedness of solution of the generalized lie nard equation without the signum condition on presente des criteres de limitation pour l equation de lienard generalisee x f x x g x 0 ou un systeme equivalent x y f x y g x ou f g r r sont continues et f x 0 x f d

simultaneous similarity and triangularization of sets of 2 by 2 matrices abstract let a a 1 a n be a finite or infinite sequence of 2 2 matrices with entries in an integral domain we show that except in a very special case a is simultaneously triangularizable if and only if all pairs a j a k are triangularizable for 1 j k we also provide a simple numerical criterion for triangularization using constructive methods in invariant theory we define a map with the minimal number of invariants that distinguishes simultaneous similarity classes for non commutative sequences over a field of characteristic 2 we also describe canonical forms for sequences of 2 2 matrices over algebraically closed fields and give a method for finding sequences with a given set of invariants

types of serre subcategories of grothendieck categories abstract every serre subcategory s of an abelian category a is assigned a unique type m n where m resp n counts how many times one can form left resp right adjoints starting from i and q where i s a is the inclusion and q is the quotient functor the main result gives a complete list of all the types of serre subcategories of grothendieck categories 0 0 0 1 1 1 0 2 1 2 2 1 two observations are technically crucial in proving the main result the exactness of all the functors in a recollement of abelian categories forces the recollement to split and any left recollement of a grothendieck category can be extended to a recollement

commutative matrix subalgebras and length function it is proved that if the length of a commutative matrix subalgebra is maximal then this subalgebra is maximal under inclusion the examples are given showing that the converse does not hold to establish this result we prove several fundamental properties of the length function

matrix pencils and a generalized clifford algebra let f be an algebraically closed field and x1 xm be commuting indeterminates over f for a given monic polynomial z f x1 xm z which is homogeneous viewed as an element of f x1 xm z we construct an associative algebra c which we call the generalized clifford algebra of the polynomial this construction generalizes that of roby s clifford algebra and is a universal algebra for the problem of finding matrices a1 am mn f for some n such that z is the minimal polynomial of the matrix pencil x1a1 xmam our main result is that if z is quadratic then c is either a matrix algebra of dimension a power of 2 or a direct sum of two such matrix algebras and we conclude that the problem of finding m matrices in mn f whose pencil has a prescribed quadratic minimal polynomial can be solved if and only if n is an appropriate power of 2 we apply this result to the problem of bounding the lengths of generating sets for matrix algebras and discuss some of the difficulties encountered when the degree of z is 3

unitary and orthogonal equivalence of sets of matrices abstract two matrices a and b are called unitary resp orthogonal equivalent if a u v b for two unitary resp orthogonal matrices u and v using trace identities criteria are given for simultaneous unitary orthogonal or complex orthogonal equivalence between two sets of matrices

zariski cancellation problem for non domain noncommutative algebras we study zariski cancellation problem for noncommutative algebras that are not necessarily domains

h field and j current singularities at sharp edges in printed circuits the magnetic field and related current density behavior on the surface of printed conductors with a polygonal contour used in mic microwave integrated circuit components and antennas are investigated from the rigorous e solution for the plane sector perfect conductor the h singular solution is determined the authors formulate a convenient singularity function that just represents the boundary conditions and the singularity distributed along the conductor edge the singularity function is explicitly reported for the commonly encountered 90 degrees and 270 degrees plane sectors and 90 degrees bitriangular antenna and its systematic generalization is indicated for sectors of arbitrary aperture and composite configurations and polygonal path

rigorous evaluation of the vertex effects on the frequency dependent circuit parameters of an open ended microstrip line this study presents the original inclusion of right singular vertex conditions in integral equations solved by the method of moments for accurate evaluation of the frequency dependent microstrip discontinuity models required in microwave integrated circuits mic and monolithic microwave integrated circuits mmic design the 90 spl deg wedges singularity function for the current density weighted with a novel sampling function for corner cells and the harmonic green s function for shielded structures is accurately and efficiently integrated in the conical geometry of the 90 spl deg sector the frequency dependent effective length and excess equivalent capacitance of a shielded open ended microstrip line are calculated to a higher accuracy with respect to previous two dimensional and three dimensional full wave analyses

representations of solvable lie algebras v on the gelfand kirillov dimension of simple modules abstract examples are given of simple noetherian integral domains which have simple modules of widely differing gk dimensions there is also an example of a simple integral domain whose gk dimension is one

classification of affine prime regular hopf algebras of gk dimension one abstract the classification of affine prime regular hopf algebras of gk dimension one is completed as consequences 1 we give a negative answer to question 7 1 posed in 5 and 2 we show that there do exist prime regular hopf algebras of gk dimension one which are not pointed

lengths of finite dimensional representations of pbw algebras abstract let be a set of n n matrices with entries from a field for n 1 and let c be the maximum length of products in necessary to linearly span the algebra it generates bounds for c have been given by paz and pappacena and paz conjectures a bound of 2n 2 for any set of matrices in this paper we present a proof of paz s conjecture for sets of matrices obeying a modified poincare birkhoff witt pbw property applicable to finite dimensional representations of lie algebras and quantum groups a representation of the quantum plane establishes the sharpness of this bound and we prove a bound of 2n 3 for sets of matrices with this modified pbw property which do not generate the full algebra of all n n matrices this bound of 2n 3 also holds for representations of lie algebras although we do not know whether it is sharp in this case

on structure of domains with quadratic growth abstract let f be a finite field and let r be an affine f algebra which is a domain of gelfand kirillov dimension smaller than 3 let m n be natural numbers assume that x r is transcendental over f and y 1 y n r are such that i j m i j x i y k x j 0 for some i j f not all equal to 0 and each k n it is shown that either r satisfies a polynomial identity or else the subalgebra of r generated by y 1 y 2 y n and x has gelfand kirillov dimension 1 from this we deduce that a finitely generated domain over f with quadratic growth and with an infinite centre satisfies a polynomial identity is a pi domain moreover the centralizer of a non algebraic element in a finitely generated domain with quadratic growth over finite field is a pi domain

electromagnetic excitation of pec slotted cones by elementary radial dipoles a semi inversion analysis a novel method is presented that is based on the use of the kontorovich lebedev integral transform and the semi inversion technique developed for building the efficient and accurate numerical solutions to the boundary value problems of electromagnetic wave scattering by the 3d coaxial slotted cones a generic structure under consideration consists of two semi infinite coaxial circular perfectly electrical conducting and zero thickness cones with periodic longitudinal slots excited by a radial dipole the considered problem is reduced to an infinite set of linear algebraic equations of the fredholm second kind that is truncated and solved numerically a detail analysis of the accuracy and convergence of the method is presented the basic electromagnetic characteristics such as the field behavior near the structure singularities field patterns in the wave zone and field polarization for various problem parameters are investigated for the cones excited by on axis elementary dipoles the slotted cones allow obtaining more directional patterns in wider band than the solid ones

specht s criterion for systems of linear mappings abstract w specht 1940 proved that two n n complex matrices a and b are unitarily similar if and only if trace w a a trace w b b for every word w x y in two noncommuting variables we extend his criterion and its generalizations by n a wiegmann 1961 and n jing 2015 to an arbitrary system a consisting of complex or real inner product spaces and linear mappings among them we represent such a system by the directed graph q a whose vertices are inner product spaces and arrows are linear mappings denote by q a the directed graph obtained by enlarging to q a the adjoint linear mappings we prove that a system a is transformed by isometries of its spaces to a system b if and only if the traces of all closed directed walks in q a and q b coincide