computing ray class groups conductors and discriminants we use the algorithmic computation of exact sequences of abelian groups to compute the complete structure of z k m for an ideal m of a number field k as well as ray class groups of number fields and conductors and discriminants of the corresponding abelian extensions as an application we give several number fields with discriminants less than previously known ones

the computation of sextic fields with a cubic subfield and no quadratic subfield we describe six tables of sixth degree fields k containing a cubic subfield k and no quadratic subfield one for totally real sextic fields one for sextic fields with four real places two for sextic fields with two real places and two for totally imaginary sextic fields depending on whether the cubic subfield is totally real or not the tables provide for each possible discriminant dg of k a quadratic polynomial which defines k k the discriminant of the cubic subfield and the galois group of a galois closure at q of k q

enumeration of quartic fields of small discriminant with the mixed type case now completed all algebraic number fields of degree 4 with absolute discriminant 106 have been enumerated methods from the totally real and totally complex cases were used without major mod ification isomorphism of fields was determined by a method similar to one of lenstra the t2 criterion of pohst was applied to reduce the number of redundant examples

oscillation properties of a logistic equation with several delays abstract for a scalar delay logistic equation y t y t k 1 m r k t 1 y h k t k h k t t the oscillation properties are established which are well known for a linear delay differential equation such as comparison theorems explicit nonoscillation and oscillation conditions dependence of the solution sign on the initial function and the initial value

unstable and nonproper weights in h control an h control problem is examined in which the controller can and need only stabilize a part of the generalized closed loop due to unstable weights the procedure is a simple extension of known results and is computationally the easiest method available

on the computation of totally real quartic fields of small discriminant all totally real quartic fields of discriminant less than 106 are computed the method used to generate the fields is derived from delone and faddeev with corrections and improvements a new method for deciding field i8omorphism is used to eliminate redundant examples integral bases and galois groups are given for each field 1 introduction in 3 pp 184 200 delone and faddeev give a number geometric method for computing generating equations for all totally real quartic fields of discriminant not exceeding a fixed upper bound l e r 0 this method is well suited for implementation on a computer unfortunately the original paper contains many mistakes and the proofs are sometimes hard to understand in the present paper we give a corrected version of the delone faddeev algorithm we describe its implementation and we give a table of all totally real quartic fields of discriminant less than 1 000 000 including their integral bases and the galois groups of their normal closures a different method for computing totally real quartic fields was given by god win 6 and for general algorithms for computing fields of small discriminants see martinet 8 and pohst 9 10

some oscillation problems for a second order linear delay differential equation abstract for the delay differential equation formula a connection between the following properties is established non oscillation of the differential equation and the corresponding differential inequality positiveness of the fundamental function and the existence of a nonnegative solution of a generalized riccati inequality explicit conditions for non oscillation and oscillation and comparison theorems are presented

positive solutions of second order delay differential equations with a damping term in the paper the existence of positive solutions is studied for the second order delay differential equation with a damping term email protected t a t email protected t b t x h t 0 using a comparison with the integro differential equation email protected t email protected t 0 te s t a x d xb s y h s ds 0 explicit non oscillation criteria and comparison type results are derived

extended rm h _ 2 controller synthesis for continuous descriptor systems this technical note presents a complete solution to the nonstandard h2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used in such a problem the desired controller has to satisfy two conditions simultaneously i the closed loop is admissible and has a minimum h2 norm ii only the internal stability of a part of the closed loop is sought the condition of the existence of such a controller is deduced an explicit characterization of the optimal solution is also formulated based on two generalized algebraic riccati equations gares and two generalized sylvester equations a numerical example is included to illustrate the validity of the proposed results

shimura curves of genus at most two we enumerate all shimura curves x d 0 r of genus at most two there are exactly 858 such curves up to equivalence

stability criteria for certain second order delay differential equations with mixed coefficients in this paper we study asymptotic stability of the zero solution of the second order linear delay differential equation y t p1y t p2y t q1y t q2y t where p1p2 q1 and q2 are constants with p1p2 0 and q1q2 0 is a constant in proving our results we make use of pontryagin s theory of quasi polynomials

a fast algorithm to compute cubic fields we present a very fast algorithm to build up tables of cubic fields real cubic fields with discriminant up to 10 11 and complex cubic fields down to 10 11 have been computed

comments on stein s postulated high frequency behavior of h sub infinity optimal controllers g stein 26th ieee conf decision control los angeles ca dec 1987 showed that h sub infinity controller designs often give very unrealistic high frequency behavior the polynomial systems approach to h sub infinity is used by the commenter to demonstrate that the high frequency gain of h sub infinity controllers can be made to fall off at any desired rate provided improper noise and weighting models are chosen

an hp version of the discontinuous galerkin time stepping method for nonlinear second order delay differential equations with vanishing delays abstract we present and analyze an h p version of the discontinuous galerkin dg time stepping method for nonlinear second order delay differential equations with vanishing delays we derive a priori error bounds in the l 2 and l norm that are fully explicit with respect to the local time steps the local approximation orders and the local regularity of the exact solution we further prove that the h p dg scheme based on geometrically refined time steps and on linearly increasing approximation orders attains exponential rates of convergence for analytic solutions with start up singularities moreover we also propose an h p dg scheme for the state dependent delay differential equations we illustrate the theoretical results with a series of numerical experiments

constructing complete tables of quartic fields using kummer theory we explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using kummer theory instead of the traditional and much less efficient method using the geometry of numbers as an application we describe the computation of quartic fields of discriminant up to 107 the corresponding table being available by anonymous ftp

tables of octic fields with a quartic subfield we describe the computation of extended tables of degree 8 fields with a quartic subfield using class field theory in particular we find the minimum discriminants for all signatures and for all the possible galois groups we also discuss some phenomena and statistics discovered while making the tables such as the occurrence of 11 non isomorphic number fields having the same discriminant or several pairs of non isomorphic number fields having the same dedekind zeta function