Theoretische Betrachtungen über die Elektronenoptik einer Ringstrahl-Elektronenkanone

A ring beam electron gun consists of a circular cathode and of focusing and accelerating electrodes arranged concentrically in such a way that the electrons can be accelerated towards the centre of curvature of the ring-cathode. In this system the electron beam is brought to a focus in the centre of the gun in the plane of the circular cathode by cathode curvature, whilst in the perpendicular direction focusing is obtained by the geometry of the focusing electrodes. When the cathode is heated by a direct current the magnetic field of this circular current deflects the electron paths in the symmetry plane of the gun (plane of the ring-cathode) in such a manner that, neglecting the electron gas temperature, no electrons can reach a circular area of certain radius in the centre of the gun. The radius of this dead zone is calculated as a function of the relevant gun parameters according to the laminar theory and then the definition of the dead zone is modified with respect to the Maxwellian distribution of electron velocities and also for heating of the ring-cathode with a. c. If a second circular current concentric with the circular current of the cathode but flowing in the opposite direction is introduced, one can completely eliminate the electron deflection effect in the central part of the gun. The influence of this compensation current is calculated and represented in graphical form. Also some calculations of achievable current densities on a cylindrical object in the centre of the gun are reported both for compensated and partly compensated cases.     

About C-rigid quadrics

In the article strongly nondegenerate (k, n)-quadrics all of whose linear automorphisms are of the formzz, ¦¦2, {0} are considered. Quadrics all of whose linear automorphisms are of this form were calledc-rigid by V. Beloshapka. The main result of the article is the following: anyc-rigid strongly nondegenerate (k, n)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for (k, n)-quadrics is presented.Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 224–229, February, 1996.     

Almost everywhere convergence of riesz means on certain noncompact symmetric spaces

Summary Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f L^p, 1p2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to falmost everywhere for Re(z)>(l, p). The critical index (l, p) is the same as in the classical result of Stein in the Euclidean case.The first author was supported by funds of the Ministero della Pubblica Istruzione. The work was done while the second author was a member of the Mathematical Sciences Research Institute at Berkeley, with a fellowship from the Consiglio Nazionale delle Ricerehe.     

On the abstract Cauchy problem for the operator\frac{{d^2 }}{{dt^2 }} - A.

LetX be a Banach space, A a closed operator with dense domainD(A) and non-void resolvent set; topologized by the semi-norm system. We prove that the Cauchy problem is well posed in the sense of distributions for the operator d²/dt²–A if and only if A restricted toD generates a locally — equicontinuous cosine function of class C inL _S D . This is an extension of Ushijima's smoothness result of distribution semi-groups [10].     

On the Circumference of 2-Connected $$\mathcal{P}_{3}$$-Dominated Graphs

Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P ₃-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P ₃-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs.     

Convexity of Nonlinear Image of a Small Ball with Applications to Optimization

Let f: XY be a nonlinear differentiable map, X,Y are Hilbert spaces, B(a,r) is a ball in X with a center a and radius r. Suppose f (x) is Lipschitz in B(a,r) with Lipschitz constant L and f (a) is a surjection: f (a)X=Y; this implies the existence of >0 such that f (a)^* yy, yY. Then, if r,/(2L), the image F=f(B(a,)) of the ball B(a,) is convex. This result has numerous applications in optimization and control. First, duality theory holds for nonconvex mathematical programming problems with extra constraint x–a. Special effective algorithms for such optimization problems can be constructed as well. Second, the reachability set for small power control is convex. This leads to various results in optimal control.     

The order of approximation to functions of the Zα. Class by means of positive linear operators

Let C_n (, ) be the upper bound for deviations of periodic functions which form the Zygmund class Z,0 0<<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit nC_n(, )=C(, ). An explicit expression is given for the functions C(,).Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 201–210, August, 1968.     

Non-Uniformly Elliptic Equations with Natural Growth in the Gradient

We prove the existence of bounded solutions for a class of nonlinear elliptic problems of type–div(a(x,u,Du))=H(x,u,Du)+f, uW ^1,p ₀()L (),where a(x,,)b(||)|| ^p , b is a continuous monotone decreasing function and |H(x,,)| k()|| ^p , k is a continuous monotone increasing function.     

Existence Condition for the Diffusion Approximations of Multiclass Priority Queueing Networks

In this paper, we extend the work of Chen and Zhang [12] and establish a new sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. This sufficient condition relates to the weak stability of the fluid networks and the stability of the high priority classes of the fluid networks that correspond to the queueing networks under consideration. Using this sufficient condition, we prove the existence of the diffusion approximation for the last-buffer-first-served reentrant lines. We also study a three-station network example, and observe that the diffusion approximation may not exist, even if the proposed limiting semimartingale reflected Brownian motion (SRBM) exists.     

Affine geometry over free unitary modules

In this paper we consider systems (P,L,,), where P is an arbitrary non-empty set, L a set of subsets of p and resp. a relation on PxP resp. LxL. In successive stages adding geometrical axioms, we characterize the class of those structures (P,L, ,), which coincides — up to isomorphisms — with the class of all Affine Barbilian-Spaces.     

Arithmetic of the Modular Function j1,8

Since the genus of the modular curve X_1 (8) = _1 (8) * is zero, we find a field generator j _1,8(z) = ₃(2z)/₃(4z) (₃(z) := _n ein ^2z ) such that the function field over X ₁(8) is (j _1,8). We apply this modular function j _1,8 to the construction of some class fields over an imaginary quadratic field K, and compute the minimal polynomial of the singular value of the Hauptmodul N(j _1,8) of (j _1,8).     

Flat convergence for integral currents in metric spaces

In compact local Lipschitz neighborhood retracts in weak convergence for integral currents is equivalent to convergence with respect to the flat distance. This comes as a consequence of the deformation theorem for currents in Euclidean space. Working in the setting of metric integral currents (the theory of which was developed by Ambrosio and Kirchheim) we prove that the equivalence of weak and flat convergence remains true in the more general context of metric spaces admitting local cone type inequalities. These include in particular all Banach spaces and all CAT(κ)-spaces. As an application we obtain the existence of a minimal element in a fixed homology class and show that the weak limit of a sequence of minimizers is itself a minimizer.     

On Approximate Efficiency in Multiobjective Programming

This paper is focused on approximate ( -efficient) solutions of multiobjective mathematical programs. We introduce a new -efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these -efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different -efficiency sets. Several classical -efficiency notions are considered in order to show the concepts introduced and the results obtained.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.     

Sets with fixed congruence in a steiner system

In this paper we study particular sets of a Steiner systemS. More precisely, we study the setsA such that ¦A ¦ d modh for all lines ofS, withd andh integers satisfyingd 0,h 2.Dedicated to Professor M. Scafati Tallini on the occasion of her sixtyfifth birthday     

On problems with bounded state variables

A set of first-order necessary conditions is obtained for the general control problem of Bolza with bounded state constraints of the form (t, x)0, =1,...,m. With the solution required to satisfy the vector differential equationsx=f(t, x, u), whereu is control, an important feature of this paper is in relaxing the assumption on the rank of the matrix _x f _u generally made in attacking problems of this type. This is accomplished even though the solution may have an infinite number of intervals satisfying (t, x)=0 for various .The preparation of this paper was sponsored in part by the US Army Research Office, Grant No. DA-31-214-ARO(D)-355.     

Existence and uniqueness of solutions to two point boundary value problems for ordinary differential equations

In this paper, using the optimal control method, we deal with the following boundary value problemy + f(x, y)=0,y(0)=c,y(1)=d, under new nonresonance conditions of the form –A f _y ^/ (x, y) (x) B, where A > 0. We obtain the existence and uniqueness of solutions of the BVP (1).     

Creep of fluoroplastic in shear with application of hydrostatic pressure

Conclusions 1. It has been shown that under a deformation regime with Vxy = const, with an increase in shear deformation the effect of the action of hydrostatic pressure rises. A considerable effect of pressure on the character of the shear diagram is observed in the pressure region above 500 kgf/cm².Paper presented at the Third All-Union Conference on Polymer Mechanics in Riga, 1976.Leningrad Technological Institute of the Refrigeration Industry. Okhtinsk Scientific-Manufacturing Union Plastpolimer Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 812–818, September–October, 1977.     

Gabriel Dimension for Graded Rings

Using techniques of localization for Grothendieck categories with a family of projective generators, we show that for a graded ring R = ⊕ _σ∈G R _σ with finite support if R _e has Gabriel dimension then has Gabriel dimension. Moreover, adding some lattice results, we prove that if has Gabriel dimension then also has Gabriel dimension. This research has been supported by grant MTM2005-3227 from MEC.     

Amplitudes in Nonlocal Theories at High Energies

We obtain the upper bound for the total scattering cross section _tot(s) Cs ^–1ln ^s in the nonlocal quantum field theory of a scalar field with a bounded amplitude growth in the complex momentum p ²-space.     

Existence of exactlyn+1 simple 4-periodic solutions of the differential delay equation\dot x(t) = - f(x(t - 1))

By discussing the zeros of periodic solutions we give in this paper a criterion for the existence of exactlyn+1 simple 4-periodic solutions of the differential delay equation Supported by the Chinese National Foundation for Natural Sciences.