bluuebunny/crossref_metadata_2025 huggingface dataset:
Operator Ranges in Banach Spaces, I
Authors: Cross R. W. , Ostrovskii M. I. , Shevchik V. V.
Published: May 2007

Let X be a Banach space. A subspace L of X is called an operator range if there exists a continuous linear operator T defined on some Banach space Y and such that TY = L. If Y = X then L is called an endomorphism range. The paper investigates operator ranges under the following perspectives: (1) Existence (Section 3), (2) Inclusion (Section 4), and (3) Decomposition (Section 5).

Section 3 considers the existence in X of operator ranges satisfying certain conditions. The main result is the following: if X and Fare separable Banach spaces and T : Y → X is a continuous operator with nonclosed range, then there exists a nuclear operator R:Y→X such that T + R is injective and has nonclosed dense range (Theorem 3.2).

Section 4 seeks to determine conditions under which every nonclosed operator range in a Banach space is contained in the range of some injective endomorphism with nonclosed dense range. Theorem 4.3 contains a sufficient condition for this. Examples of spaces satisfying this condition are c0, lp (1 < p < ∞), Lq (1 < q < 2) and their quotients. In particular, this answers a question posed by W. E. Longstaff and P. Rosenthal (Integral Equations and Operator Theory 9, (1986), 820‐830.

Section 5 discusses the possibility of representing a given dense nonclosed operator range as the sum of a pair L1, L2 of operator ranges with zero intersection in the cases where (a) L1 and L2 are dense, (b) L1 and L2 are closed. The results generalize corresponding results, for endomorphisms in Hilbert space, of J. Dixmier (Bull. Soc. Math. France 77 (1949), 11‐101 and P. A. Fillmore and J. P. Williams (Adv. Math. 7 (1971), 254‐281.

A final section is devoted to open problems.
Classes of Fourier Multipliers and Besov‐Nikolskij Spaces
Authors: Dintelmann Peter
Published: May 2007

We present a discrete characterization of Besov and Triebel spaces which is used to determine various classes Fourier multipliers for these spaces. In particular, results of R. Johnson are recovered.
Nonlinear Eigenvalue Problem for p‐Laplacian in IRN
Authors: Drábek Pavel , Rother Wolfgang
Published: May 2007

The nonlinear eigenvalue problem for p‐Laplacian

is considered. We assume that 1 < p < N and that the function f is of subcritical growth with respect to the variable u. The existence and C1,α‐regularity of the weak solution is proved.
On Linear Functionals of Rational Type over H(ID)
Authors: Fournier Richard
Published: May 2007

Let H(ID) denote the set of analytic functions in the unit disk ID of the complex plane, endowed with the topology of uniform convergence on compact subsets of ID. Let Λ denote the space of continuous linear functionals over H(ID). In this paper we obtain a characterization of those λ ∈Λ such that

where B is a fixed function in H(ID). We also include a discussion of the sharpness of this characterization and an application to some extremal problem concerning Λ.
Oscillation Criteria of Comparison Type for Nonlinear Functional Differential Equations
Authors: Grace S. R.
Published: May 2007

In this paper we relate the oscillation problem of the nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= 0 and the nonlinear neutral functional differential equation (a(t) (x(t)+ p(t)x(g*(t)))'} + q(t)f (x(g(t))) = 0 to some linear second order ordinary differential equations. Recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for the nonlinear equations. Similar results for the forced nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= e(t) and the forced neutral functional differential equation (a(t) (x(t)+ mx(t — n))')' + q(t) f (x(g(t)))= e(t) are also established. The function f appeared in the above equations is not require to be monotone.
Characterization of Compact Sets by Their Dilation Volume
Authors: Rataj Jan
Published: May 2007

The uniqueness up to translation of the characterization of random compact sets in Euclidean space by their dilation volumes is shown. The unique correspondence is shown to be a homeomorphism with respect to suitable topologies. If set differences of volume zero are neglected, dilations by three‐point sets are sufficient to determine a non‐random compact set and the correspondence is again a homeomorphism with respect to vague topologies.
Bi‐invariant Integrals on GL(n) with Applications
Authors: Schindler Werner
Published: May 2007

In this paper measures and functions on GL(n) are called bi‐invariant if they are invariant under left and right multiplication of their arguments. If v is any bi‐invariant Borel measure on GL(n), then there exists a unique Borel measure v* on D + ≥(n), the set of all diagonal matrices of rank n with positive non‐increasing diagonal entries, such that

holds for each v‐integrable bi‐invariant function f:GL(n) → IR. An explicit formula for v* will be derived in case v equals the Lebesgue measure on GL(n) and the above integral formula will be applied to concrete integration problems. In particular, if v is a probability measure, then v* can be interpreted as the distribution of the singular value vector. This fact will be used to derive a stochastic version of a theorem from perturbation theory concerning the numerical computation of the polar decomposition.
Sharp Opial‐Type Inequalities Involving Higher Order Derivatives of Two Functions
Authors: Agarwal Ravi P. , Pang Peter Y. H.
Published: May 2007

In this paper we shall offer very general Opial‐type inequalities involving higher order derivatives of two functions. From these inequalities we then deduce extended and improved versions of several recent results.
Schechter Methods of Interpolation and Commutators
Authors: Carro M. J. , Cerdà J. , Milman M. , Soria J. , Carro M. J. , Cerdà J. , Soria J. , Milman M.
Published: May 2007

We study the relationship between Schechter's methods of complex interpolation and the so called commutator estimates. We obtain new commutator theorems and prove characterizations of the Domain and Range spaces associated with the corresponding quasilogarithmic operator. Our methods also provide a new approach to known results, including the higher order commutator theorems for the complex method recently obtained by R. Rochberg.
Hasse‐Arf Property and Abelian Extensions
Authors: Fesenko Ivan B.
Published: May 2007

The paper contains discussions of relations between the property of a totally ramified p‐extension of a local field to be abelian and the property of its Galois group to possess integer jumps with respect to the upper numbering (Hasse‐Arf property). It is shown that such an extension L/F is abelian if and only if for any totally ramified abelian extension E/F the extension LE/F satisfies the Hasse‐Arf property. An additional property to the Hasse‐Arf property in terms of principal units which makes the extension abelian is established as well.
Spaces of Vector‐Valued Integrable Functions and Localization of Bounded Subsets
Authors: Florencio Miguel , Mayoral Fernando , Paúl Pedro J.
Published: May 2007

We study the structure of bounded sets in the space L1{E} of absolutely integrable Lusin‐measurable functions with values in a locally convex space E. The main idea is to extend the notion of property (B) of Pietsch, defined within the context of vector‐valued sequences, to spaces of vector‐valued functions. We prove that this extension, that at first sight looks more restrictive, coincides with the original property (B) for quasicomplete spaces. Then we show that when dealing with a locally convex space, property (B) provides the link to prove the equivalence between Radon–Nikodym property (the existence of a density function for certain vector measures) and the integral representation of continuous linear operators T: L1 → E, a fact well‐known for Banach spaces. We also study the relationship between Radon–Nikodym property and the characterization of the dual of L1{E} as the space L∞{E′b}.
Regularizations of Differential‐Algebraic Equations Revisited
Authors: Hanke Michael
Published: May 2007

The present paper deals with quasilinear differential‐algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential‐algebraic equations. Using a geometric theory of singular perturbations convergence of the solutions of the regularized problems towards that of the index 2 problem is proved. The limits of the present theory are discussed and directions of future research are proposed.
Decomposing Ends of Locally Finite Graphs
Authors: Jung Heinz Adolf , Niemeyer Peter
Published: May 2007

An important invariant of translations of infinite locally finite graphs is that of a direction as introduced by Halin. This invariant gives not much information if the translation is not a proper one. A new refined concept of directions is investigated.

A double ray D of a graph X is said to be metric, if the distance metrics in D and X on V(D) are equivalent. It is called geodesic, if these metrics are equal. The translations leaving some metric double ray invariant are characterized. Using a result of Polat and Watkins, we characterize the translations leaving some geodesic double ray invariant.
The Quasiasymptotic Expansion at the Origin. Abelian‐Type Results for Laplace and Stieltjes Transforms
Authors: Nikolicacute; Danica , Pilipović Stevan
Published: May 2007

The notion of quasiasymptotic expansion at the origin of tempered distributions supported by [0, α] and the structural theorem for such distributions that have the quasiasymptotic expansion at the origin are given. As applications, the Abelian‐type results for the distributional Stieltjes and Laplace transforms are obtained.
The Weighted Discrepancies of Some Slowly Increasing Sequences
Authors: Ohkubo Yukio
Published: May 2007

In this note we give upper bounds of the weighted discrepancy of the sequence (f (n)), when f″(x) satisfies some conditions. Furthermore, by applying the generalized van der Corput's inequality, we give upper bounds of the weighted discrepancy of the sequence (f(n)), when some conditions about f (x) is satisfied, where q is any positive integer.
Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains
Authors: Parnovski L. B.
Published: May 2007

We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.
The Topology of the Real Part of a Holomorphic Function
Authors: Paunescu Laurentiu
Published: May 2007

We describe the connection between the Milnor fibre of a holomorphic function and the Milnor fibre of its real part and we derive some simple equations for manifolds appearing as real links of real parts of holomorphic functions.
Collocation Method for Singular Integral Equations on Holder Spaces
Authors: Schmid Ulrich
Published: May 2007

The classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a non‐zero index of the underlying Fredholm operator. This is done by using the structure of the kernel and a complement of the image of this operator. For the extended method we directly obtain error bounds in the norm of the weighted Holder spaces. As an illustration, some numerical results are given.
Commutation Properties of Symmetric Operators
Authors: Trapani Camillo
Published: May 2007

This relationship between the weak and strong bounded commutants of a symmetric operator S and the commutant of a generalized spectral family (in Naimark's sense) of S is studied. A characterization of the existence of self‐adjoint extensions of S via von Neumann subalgebras of the weak commutant is also given.
Grothendieck Spaces of Compact Operators
Authors: Zafarani J.
Published: May 2007

In this paper we study the Grothendieck spaces among the operator spaces Le(E'c, F). Conditions under which Le(E'c, F) contains complemented copy of c0 are given. We apply these results to spaces of the type Cb(X; F) endowed with strict topologies.
Real Interpolation and Measure of Weak Noncompactness
Authors: Aksoy A. G. , Maligranda L.
Published: May 2007

Behavior of weak measures of noncompactness under real interpolation is investigated. It is shown that “convexity type” theorems hold true for weak measures of noncompactness.
Random Walks with Stochastically Bounded Increments: Renewal Theory
Authors: Alsmeyer Gerold
Published: May 2007

Summary. This paper develops renewal theory for a rather general class of random walks SN including linear submartingales with positive drift. The basic assumption on SN is that their conditional increment distribution functions with respect to some filtration ℱℕ are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell‐type renewal theorems. In a companion paper [2], certain uniform lower and upper drift bounds for SN, describing its average growth on finite remote time intervals, have been introduced and shown to be equal in case the afore‐mentioned mean stability condition holds true. With the help of these bounds we give lower and upper estimates for H * U(B), where U denotes the renewal measure of SN, H a suitable delay distribution and B a Borel subset of IR. This is then further utilized in combination with a coupling argument to prove the principal result, namely an extension of Blackwell's renewal theorem to random walks of the previous type whose conditional increment distribution additionally contain a subsequence with a common component in a certain sense. A number of examples are also presented.
A Problem in Linear Matrix Approximation
Authors: Berens H. , Finzel M.
Published: May 2007

Let A be a normal operator in ℬ︁(H), H a complex Hilbert space, and let ℛ A = ≷ {AX ‐ XA:X ∈ ℬ︁(H)} be the commutator subspace of ℬ︁(H) associated with A. If B in ℬ︁(H) commutes with A, then B is orthogonal to ℛA with respect to the spectral norm; i.e., the null operator is an element of best approximation of B in ℛ A. This was proved by J. Anderson in 1973 and extended by P. J. Maher with respect to the Schatten p‐norm recently.

We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation of B in RA and prove that the metric projection of H onto ℛA is continuous.
Hill's Equation Systems and Infinite Determinants
Authors: Denk Robert
Published: May 2007

In this paper a method is developed to calculate the Floquet exponents of the matrix‐valued version of Hill's equation using infinite determinants. It is shown that the Floquet exponents are precisely the zeros of an infinite determinant corresponding to the differential equation. The proof of this result uses the continuity and holomorphy of the infinite determinant.
Hilbert C*‐Modules over Monotone Complete C*‐Algebras
Authors: Frank Michael
Published: May 2007

The aim of the present paper is to describe self‐duality and C*‐reflexivity of Hilbert A‐modules ℳ︁ over monotone complete C*‐algebras A by the completeness of the unit ball of ℳ︁ with respect to two types of convergence being defined, and by a structural criterion. The derived results generalize earlier results ofH. Widom [Duke Math. J. 23, 309‐324, MR 17 # 1228] and W. L. Paschke [Trans. Amer. Mat. Soc. 182, 443‐468, MR 50 # 8087, Canadian J. Math. 26, 1272‐1280, MR 57 # 10433]. For Hilbert C*‐modules over commutative AW*‐algebras the equivalence of the self‐duality property and of the Kaplansky‐Hilbert property is reproved, (cf. M. Ozawa [J. Math. Soc. Japan 36, 589‐609, MR 85 # 46068]). Especially, one derives that for a C*‐algebra A the A‐valued inner product of every Hilbert A‐module ℳ︁ can be continued to an A‐valued inner product on it's A‐dual Banach A‐module ℳ︁' turning ℳ︁' to a self‐dual Hilbert A‐module if and only if A is monotone complete (or, equivalently, additively complete) generalizing a result of M. Hamana [Internat. J. Math. 3 (1992), 185 ‐ 204]. A classification of countably generated self‐dual Hilbert A‐modules over monotone complete C*‐algebras A is established. The set of all bounded module operators End′(ℳ︁) on self‐dual Hilbert A‐modules ℳ︁ over monotone complete C*‐algebras A is proved again to be a monotone complete C*‐algebra. Applying these results a Weyl‐Berg type theorem is proved.
Pointwise Multiplication of Besov and Triebel‐Lizorkin Spaces
Authors: Johnsen Jon
Published: May 2007

It is shown that para‐multiplication applies to a certain product π(u, v) defined for appropriate u and v in 𝒴'(IRn). Boundedness of π(.,.) is investigated for the anisotropic Besov and Triebel‐Lizorkin spaces ‐ i.e., for BM,s/p,q and FM,s/p,q with s ∈ R and p and q in [0, ∞] (though p < ∞ in the F‐case) ‐ with a treatment of the generic as well as of various borderline cases.

For max (so,s,) > 0 the spaces BM,so/p,qo ⊕ BM,so/p,qo and BM,so/p,qo ⊕ BM,so/p,qo to which π(.,.) applies arc determined. For generic Bso/po,qo ⊕ Bs1/p1,q1 the receiving Fsp,q spaces are characterized.

It is proved that π(f, g) = f · g holds for functions f and g when f · g ∈L1,loc, roughly speaking. In addition, π(f, u) = fu when f ∈ 𝒪M and u ∈𝒴' .

Moreover, for an arbitrary open set Ω⊆ IRn, a product πΩ(., .) is defined by lifting to IRn. Boundedness of n on R′ is shown to carry over to πΩ is general.
Some Nonlinear Methods in Fréchet Operator Rings and Ψ*‐Algebras
Authors: Jung Joachim
Published: May 2007

Two different inverse function theorems, one of Nash‐Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo‐convex Fréchet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo‐convex Fréchet algebra with unit e and T+ : Ψ → Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation

where T‐ = IΨ‐ T, has a solution x ∈ Ψ for every y ∈ U?
On the Values of Partial Zeta Functions of Real Quadratic Fields at Nonpositive Integers
Authors: Kallies J. , Snyder C.
Published: May 2007

The authors study the partial fraction decomposition of narrow class partial zeta functions of real quadratic number fields at nonpositive integer arguments and obtain an analogue of the classical v. Staudt/Clausen Theorem. The main results follow from the study of the residues ofp‐adic zeta functions associated with ray classes of modulus (p) for all rational primesp.
Der konforme Modul schmaler Vierecke
Authors: Kühnau Reiner
Published: May 2007

Es wird eine asymptotische Formel angegeben für den konformen Modul eines Vierecks mit zwei Gegenseiten, die Parallelkurven kleinen Abstand sind.
Projective Surfaces with Class Less Than or Equal to Twice the Degree
Authors: Lanteri Antonio , Turrini Cristina
Published: May 2007

Smooth complex algebraic surfaces S ⊆ Pn of degree d and class ℳ︁ satisfying d < m ≤ 2d are classified. The result is also extended to higher dimensions.
On the Boundedness and Compactness of Nonregular Pseudo‐Differential Operators
Authors: Marschall Jurgen
Published: May 2007

We study the boundedness properties of nonregular pseudo‐differential operators and their adjoints on Triebel spaces F, 0 < p, q≦ ∞. Special attention is payed to sharp estimates. The second aim of this paper is the compactness properties of these operators on weighted and unweighted Triebel spaces F(w) where the weight w may belong to an arbitrary Muckenhoupt class A∞.
Starlikeness and Certain Class of Rational Functions
Authors: Obradović Milutin
Published: May 2007

A new criterion for starlikeness in the unit disc and an application to a certain class of rational functions are given.
On Smooth, Unramified, Étale and Flat Morphisms of Fine Logarithmic Schemes
Authors: Bauer Werner
Published: May 2007

The notion of unramified morphisms of schemes is generalized in a natural way to the category of fine logarithmic schemes. There are given several equivalent conditions for a morphism of fine log schemes to be unramified: vanishing of the differential module, all fibres to be unramified and a local structure theorem using charts of the log structures. In the main part of the paper there are shown some criterions for a morphism of fine log schemes to be smooth, fiat or étale in the sense of K. Kato. Letf : X → Y be a map of fine log schemes. Then f is smooth if and only if locally it can be factorized over an étale map into the standard log affine space over Y. The map f is étale if and only if it is flat and unramified. Further there are generalizations of the usual fibre criterions for flatness or smoothness of morphisms of schemes to the context of log schemes: Let f: X → Y be an S‐morphism of fine log schemes. Assume that X/S is flat and that the underlying maps of schemes are locally of finite presentation. Then f is flat if and only if the induced maps on the fibres fs : Xs → Ys, s → S, are flat. Finally f is smooth if and only if it is flat and the induced maps on the fibres f−1(y) → y,y → Y, are smooth.
Factorization in a Banach Algebra and the Gelfand Transform
Authors: Câmara M. C.
Published: May 2007

The Gelfand transform is used to reduce the Wiener‐Hopf factorization of a class ofn × n matrix‐valued functions to that of a scalar function. The complete factorization is obtained, including the partial indices.
On the Characterization of the Intermediate Space in Generalized Factorizations
Authors: Castro L. P. , Speck F.‐O.
Published: May 2007

The study of systems of singular integral equations of CAUCHYtype, of TOEPLITZand WIENER‐HOPFoperators leads to the question of existence and representation of generalized factorizations of matrix functions Φ in [LP(Γ, σ)]m. This yields a corresponding factorization of the basic multiplication or translation invariant operatorA=A_CA+, respectively, which can be seen as a splitting of a bounded into unbounded operators. The present paper is devoted to the study of the nature of the induced intermediate space Z = imA+=imA−1, in particular, for Γ = ℝ and Φ ε ζ[Cβ(ℝ)]m×mwhich is of special interest in certain applications. As we know, this implies detailed results about the structure and the explicit asymptotic behaviour of solutions of boundary and transmission problems near singular points with a relation also to eigenvalue problems which result from the classical series expansion approach or from the Mellin symbol calculus (see [13]).
The Neumann Laplacian on Generalized Ridged Domains
Authors: Edmunds David E. , Kauffman Robert M.
Published: May 2007

We show that for many of the bounded generalized ridged domains of Evans and Harris, all reasonable definitions of the Neumann Laplacian coincide. In particular, this shows that the lack of discreteness of the spectrum of such Laplacians is inherent, rather than an artifact of the definition.
Application of a Khintchine Inequality to Holomorphic Mappings
Authors: Floret Klaus , Matos Mário C.
Published: May 2007

After proving the Khintchine inequality for the n‐Rademacher functions of ARON and GLOBVENIK with constants independent from n ε IN, applications are given to the theory of polynomials and holomorphic functions between Banach spaces. In particular, the following result is proved: Every entire mapping from a Banach space into another one of cotype q, vanishing at the origin and of r‐dominated type at zero for some r > 0 maps unconditionally 2‐summable sequences into absolutely q‐summable sequences.
Lamé Potentials and the Stationary (m)KdV Hierarchy
Authors: Gesztesy F. , Weikard R.
Published: May 2007

A new method of constructing elliptic finite‐gap solutions of the stationary Korteweg‐de Vries (KdV) hierarchy, based on a theorem due to PICARD, is illustrated in the concrete case of the Lamé‐Ince potentials ‐s(s + 1) ρ(z), sε (ρ(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg‐de Vries (mKd V) hierarchy for the first time.
Pontryagin Duality for a Class of Locally Compact Quantum Groups
Authors: Hollevoet Jan
Published: May 2007

A class of locally compact quantum semigroups in the sense of WORONOWICZ, containing the quantized Heisenberg group, is studied. The underlying quantum space is described in terms of a crossed product. We show the existence of a universal corepresentation and a Pontryagin dual, which turns out to be a twisted crossed product. The Pontryagin duality for these quantum semigroups is investigated.
On Scales of Summability Methods
Authors: Kiesel Rüdiger
Published: May 2007

In this paper we consider generalized Nörlund methods (Nαp), α > ‐1, power series methods (Jp) and the iteration product of two such methods. A particular case is that of the Cesaro means (Cα) with corresponding power series method (A), i.e., Abel's method. We obtain generalizations of inclusion, and tauberian and convexity theorems which are well‐known for the Cesàro‐Abel case, for a rich class of methods of the above type.
Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations with Dynamic Boundary Conditions
Authors: Kirane M. , Kouachi S. , Tatar N.
Published: May 2007

In this paper the non‐existence of global solutions of two fourth‐order hyperbolic equations with dynamic boundary conditions is considered. The method of proof makes use of the generalized convexity method due to Ladyzhenskaya and Kalantarov [4].
Representation of Generalized Fractional Integrals in Terms of Laplace Transforms on Spaces Lp
Authors: Kiryakova Virginia , Raina R. K. , Saigo Megumi
Published: May 2007

In this paper the generalized fractional integration operators defined by Kiryakova [6], [7] are expressed in terms of the Laplace transform L and its inverse L−1. These decomposition results are established on Lp spaces and some examples are deduced as their special cases.
Some Special Tauberian Theorems for Fourier Type Integrals and Eigenfunction Expansions of Sturm‐Liouville Equations on the Whole Line
Authors: Levitan B. M.
Published: May 2007

We offer a new proof of a special Tauberian theorem for Fourier type integrals. This Tauberian theorem was already considered by us in the papers [1] and [2]. The idea of our initial proof was simple, but the details were complicated because we used Bochner's definition of generalized Fourier transform for functions of polynomial growth. In the present paper we work with L. Schwartz's generalization. This leads to significant simplification. The paper consists of six sections. In Section 1 we establish an integral representation of functions of polynomial growth (subjected to some Tauberian conditions), in Section 2 we prove our main Tauberian theorems (Theorems 2.1 and 2.2.), using the integral representation of Section 1, in Section 3 we study the asymptotic behavior of M. Riesz's means of functions of polynomial growth, in Sections 4 and 5 we apply our Tauberian theorems to the problem of equiconvergence of eigenfunction expansions of Sturm‐Liouville equations and expansion in ordinary Fourier integrals, and in Section 6 we compare our general equiconvergence theorems of Sections 4 and 5 with the well known theorems on eigenfunction expansions in classical orthogonal polynomials. In some sense this paper is a re‐made survey of our results obtained during the period 1953‐58. Another proof of our Tauberian theorem and some generalization can be found in the papers [3] and [4].
The Poisson Voronoi Tessellation I. A Basic Identity
Authors: Mecke Joseph , Muche Lutz
Published: May 2007

This paper gives basic relations between the stationary Poisson point process and the point process of vertices of the corresponding Voronoi tessellation in IRdand of planar sections through it. The results are based on a study of the Palm distribution of the point process of vertices. An identity is given connecting the distribution of a Poisson point process and the Palm distribution with respect to the vertices of the corresponding Voronoi tessellation. Distributional properties for the edges are discussed. Finally, identities are given for characteristics of the “typical” edge and an edge chosen at random emanating from the “typical” vertex.
Inner Derivations on σ‐C*‐Algebras
Authors: Christopher Phillips N.
Published: May 2007

We prove the following two improvements of a result of Becker. (1) If A is a pro‐C*‐algebra, then every derivation on A is approximately inner. (2) If A is a separable σ‐C*‐algebra, and if every C* quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner. We also give an example of a derivation on a separable σ‐C*‐algebra which is not inner but which induces an inner derivation on every C* quotient.
Validity and Limitation of the Newell‐Whitehead Equation
Authors: Schneider Guido
Published: May 2007

Modulation equations play an essential role in the description of systems which exhibit patterns of nearly periodic nature, e.g. in Bénard's problem. The so called Newell‐Whithead equation is derived to describe the envelope of modulated roll‐solutions in systems with two large extended or unbounded space directions. Here the validity question for the Newell‐Whitehead equation is treated, i.e., estimates between the exact solutions of the original problem and the associated approximations are given. The Newell‐Whitehead equation is a good example how important this validity question is. Although the modulation equation can formally be derived, the solutions of the original system can behave in some situations in a completely different manner than predicted by the modulation equation. This happens on a time scale which is very small compared to the natural one.
Linearized Oscillations for Differential Equations of Neutral Type
Authors: Shen Jianhua
Published: May 2007

Abstract.

Consider the nonlinear neutral delay differential equationmagnified imagewithP(t),Q(t) continuous, τ > 0, σ> 0. We obtain new sufficient conditions for the oscillation of all solutions by an associate linear equation, and thereby establish some new criteria as proposed in an earlier open problem.
Vector Fields as Derivations on Nuclear Manifolds
Authors: Thomas E. G. F.
Published: May 2007

If M is a manifold modelled over a nuclear Fréchet space, the smooth vector fields, as in the finite dimensional case, may be identified with continuous derivations in the space ζ(M) of real C∞ functions on M. This applies for instance to the loop groups and the group of diffeomorphisms of the circle: M = ζ(S1, G), M = Diff(S1).
A Note on the Galerkin Method's Stability
Authors: Titensky M. E.
Published: May 2007

Numerical stability of the Galerkin method for some class of semilinear evolution equations is studied. The stability is established in thelp(1 <p < ∞) norms. Our results are applied to the special coordinate systems. All the conditions of the stability theorems proved in this note may be readily verifiable in practice for them.
Supersoluble and Related Cofinitary Groups
Authors: Wehrfritz B. A. F.
Published: May 2007

Let D be a division ring (possibly commutative) and V an infinite‐dimensional left vector space over D. We consider irreducible subgroups G of GL(V) containing an element whose fixed‐point set in V is non‐zero but finite dimensional (over D). We then derive conclusions about cofinitary groups, an element of GL(V) being cofinitary if its fixed‐point set is finite dimensional and a subgroup G of GL(V) being cofinitary if all its non‐identity elements are confinitary. In particular we show that an irreducible cofinitary subgroup G of GL(V) is usually imprimitive if G is supersoluble and is frequently imprimitive if G is hypercyclic. The latter includes the case where G is hypercentral, which apparently is also new.
Cwikel Type Estimates in Non‐Power Ideals
Authors: Weidl Timo
Published: May 2007

The Cwikel inequality for integral operators of the type a(x)b(D) will be generalized. It will be shown that the asymptotical behavior of the singular numbers of such operators in general can be estimated by the asymptotics of classical phase space volume spanned by these symbols. Applications to non‐power symbols are given.
Saint Venant's Principle in Statical and Dynamical Problems for an Elastic Wedge and a Cone
Authors: Budaev B. V. , Morozov N. F. , Narbut M. A.
Published: May 2007

The boundary problems for an elastic wedge and a cone in statics and dynamics are investigated with special emphasis on Saint Venant's principle. The exact analytical solutions are obtained by integral transform technique and the far‐field asymptotics is obtained.
Some Properties of Minimal Splines
Authors: Demjanovich Yu. K.
Published: May 2007

S. G. Mikhlin was the first to construct systematically coordinate functions on an equidistant grid solving a system of approximate equations (called “fundamental relations”, see [5]; Goel discussed some special cases earlier in 1969; see also [1, 4, 6]). Further, the idea was developed in the case of irregular grids (which may have finite accumulation points, see [1] ).

This paper is devoted to the investigation of A‐minimal splines, introduced by the author; they include polynomial minimal splines which have been discussed earlier. Using the idea mentioned above, we give necessary and sufficient conditions for existence, uniqueness and g‐continuity of these splines. The application of these results to polynomial splines of m‐th degree on an equidistant grid leads us, in particular, to necessary and sufficient conditions for the continuity of their i‐th derivative (i = 1, ⃛, m). These conditions do not exclude discontinuities of other derivatives (e.g. of order less than i). This allows us to give a certain classification of minimal spline spaces. It turns out that the spline classes are in one‐to‐one‐correspondence with certain planes contained in a hyperplane.
The Qualocation Method for Symm's Integral Equation on a Polygon
Authors: Elschner J. , Prössdorf S. , Sloan I. H.
Published: May 2007

This paper discusses the convergence of the qualocation method for Symm's integral equation on closed polygonal boundaries in IR2. Qualocation is a Petrov‐Galerkin method in which the outer integrals are performed numerically by special quadrature rules. Before discretisation a nonlinear parametrisation of the polygon is introduced which varies more slowly than arc‐length near each corner and leads to a transformed integral equation with a regular solution. We prove that the qualocation method using smoothest splines of any order k on a uniform mesh (with respect to the new parameter) converges with optimal order O (hk). Furthermore, the method is shown to produce superconvergent approximations to linear functionals, retaining the same high convergence rates as in the case of a smooth curve.
Nonlinear programming the choice of direction by gradient projection
Authors: Zwart Philip B.
Published: May 2007

Rosen's method of Gradient Projection chooses a search direction which is not necessarily the direction of steepest ascent. However, the projection of the gradient onto a “suitably chosen subspace” does yield the direction of steepest ascent. The suitable choice is easily recognized as a result of some theorems relating gradient projection to steepest ascent. These results lead to a modification of Rosen's method. The modification improves the choice of search direction and usually yields the steepest ascent direction without solving a quadratic programming problem.
The value statement
Authors: Nightengale M. E.
Published: May 2007

Frequently there exists an insufficient amount of actual data upon which to base a decision. In this paper a method is presented whereby the subjective opinions of a group of qualified persons are utilized to quantify the relative importance of a finite number of parameters or objectives. A means of testing the consistency among the judges is given which allows the decision maker to determine the validity of the opinions gathered.

The application presented here is in the area of Multiple Incentive Contracting. Namely, a method is proposed to facilitate the answering of the question, “What is the value to the purchaser of an incremental change in the performance of a system?” Such a vehicle is not essential to the methodology proposed.
A stochastic constrained optimal replacement model
Authors: Kalman Peter J.
Published: May 2007

In this paper a stochastically constrained replacement model is formulated. This model determines a sequence of replacement dates such that the total “current account” cost of all future costs and capital expenditures over an infinite time horizon for the n initial incumbent machines is minimized subject to the constraints that an expected number of machines are in a chosen utility class at any point in time. We then indicate one possible solution method for the model.
A backward recursive technique for optimal sequential sampling plans
Authors: Wortham A. W. , Wilson E. B.
Published: May 2007

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item‐by‐item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.
Determining the most vital link in a flow network
Authors: Lubore S. H. , Ratliff H. D. , Sicilia G. T.
Published: May 2007

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.
Bayes adaptive control of two‐echelon inventory systems i: development for a special case of one‐station lower echelon and monte carlo evaluation
Authors: Zacks S. , Fennell J.
Published: May 2007

Bayes adaptive control policies are developed in the present paper for the special case of a one‐station lower echelon: a Poisson distribution of demand, whose mean is assumed to have a prior gamma distribution. The cost structure is of a common type. The ordering policy for the upper echelon, which minimizes expected cost, is replaced by a new type of policy, called Bayes prediction policy. This policy does not require tedious computations, of the sort required by dynamic programming solutions. The characteristics of the policies are studied by Monte Carlo simulation, and supplemented by further theoretical development.
A unified model for demand prediction in the context of provisining and replenishment
Authors: Haber Sheldon E. , Sitgreaves Rosedith
Published: May 2007

An improved demand prediction model is presented which incorporates features of two earlier models. The unified model pools usage data classified by repair part class and by component class. The performance of the model is evaluated in a provisioning and replenishment context and compared with that for the current procedure which employs technicians' usage estimates.
Optimal inventory policies in contagious demand models
Authors: Ravindran Arunachalam
Published: May 2007

In the past, contagious distributions have been successfully applied in bacteriology, entomology, and accident statistics. This paper applies the notion of contagious distributions in the inventory control of new products and seasonal or style goods, which have an lying “true contagion” for their demands, namely, the influence of past demands on occurrence of demands. A contagious distribution is derived by assuming a nonstationary Poisson process where the demand rate at any instant depends on the past demands to that instant. Using this contagious distribution, an inventory model is developed seasonal goods and new product lines. Optimal order policies as a function of the initial level and the review period are derived.
Termination policies for a two‐state stochastic process
Authors: Handler Gary
Published: May 2007

The purpose of this paper is to investigate and optimize policies which can be used to terminate a two‐state stochastic process with a random lifetime. Such a policy consists of a schedule of times at which termination attempts should be made. Conditions are given which reduce the difficulty of finding the optimal policy by eliminating constraints and some boundary points from consideration. Finally, a bound for the optimal policy is derived for a case where some restrictions are imposed on the model.
Computational techniques for optimizing systems with standby redundancy
Authors: Henin Claude
Published: May 2007

Three methods are used to solve the following problem: For P, a positive constant, maximize (P. Reliability‐cost) of a system with standby redundancy. The results show that a method which rounds a noninteger solution to the nearest integer solution can lead to tremendous mistakes. However, neither a well known dynamic programming algorithm nor a previously developed branch and bound technique are able to solve large size problems. The solution of problems of large dimension thus requires the use of the noninteger solution of the first method to limit the number of possible solutions when using either the dynamic programming algorithm or a modified branch and bound technique. With this assistance, the branch and bound technique is able to solve large problems in a short amount of computational time.
A note on the extension of a result on scheduling with secondary criteria
Authors: Heck Horace , Roberts Stephen
Published: May 2007

A result of Smith previously published in this journal [3], on the use of secondary criterion in scheduling problems is extended, and an example presented.
Postoptimality analysis in zero‐one programming by implicit enumeration
Authors: Roodman Gary M.
Published: May 2007

The procedures for postoptimality analysis that are so much a part of linear programming studies have no simple counterparts in an integer programming context. In the case of Balas' Additive Algorithm, however, it would appear that the capacity of the technique to facilitate certain types of postoptimality analysis has not been fully exploited. This paper proposes an extension of the additive algorithm that utilizes insights generated while solving the original problem to do subsequent analysis upon it. In particular, procedures are developed for doing limited parameter ranging and for seeking new optima in light of parameter changes.
Determining optimal growth paths in logistics operations
Authors: Srinivasan V. , Thompson G. L.
Published: May 2007

This paper considers a logistics system modelled as a transportation problem with a linear cost structure and lower bounds on supply from each origin and to each destination. We provide an algorithm for obtaining the growth path of such a system, i. e., determining the optimum shipment patterns and supply levels from origins and to destinations, when the total volume handled in the system is increased. Extensions of the procedure for the case when the costs of supplying are convex and piecewise linear and for solving transportation problems that are not in “standard form” are discussed. A procedure is provided for determining optimal plant capacities when the market requirements have prespecified growth rates. A goal programming growth model where the minimum requirements are treated as goals rather than as absolute requirements is also formulated.
A mathematical programming approach to identification and optimization of a class of unknown systems
Authors: Holloway Charles A.
Published: May 2007

There exists a class of decision problems for which: (1) models of input‐output response functions are not available in a closed‐form, functional representation; (2) informational costs associated with learning about the response function are significant. For these problems, combining identification with optimization using mathematical programming is potentially attractive. Three approaches to the identification‐optimization problem are proposed: an outer‐linearized approximation using relaxation (OLR); an inner‐linearized approximation using restriction (ILR); and a sequential combination of inner‐ and outer‐linearized subproblems (SIO). Algorithms based on each approach are developed and computational experience reported.
A comparison of the primal‐simplex and complementary pivot methods for linear programming
Authors: Ravindran Arunachalam
Published: May 2007

A comparison of the complementary pivot method of Lemke‐Howson and the more commonly used primal‐simplex method for solving linear programming problems in symmetric dual form has been made. In our tests the complementary pivot method shows a definite superiority over the simplex method both with regard to the number of iterations and computation time.
An efficient heuristic procedure for the uncapacitated warehouse location problem
Authors: Khumawala Basheer M.
Published: May 2007

This paper introduces an efficient heuristic procedure for a special class of mixed integer programming problems called the uncapacitated warehouse (plant) location problem. This procedure is derived from the branching decision rules proposed for the branch and bound algorithm by the author in an earlier paper. It can be viewed as tracing a single path of the branch and bound tree (from the initial node to the terminal node), the path being determined by the particular branching decision rule used. Unlike branch and bound the computational efficiency of this procedure is substantially less than linearly related to the number of potential warehouse locations (integer variables) in the problem. Its computational efficiency is tested on problems found in the literature.
Peak rate of occurrence of a poisson process
Authors: Alam Khursheed
Published: May 2007

Suppose that a nonhomogeneous Poisson process is observed for a length of time T, say Let λ (t) denote the mean value function of the process. It is assumed that λ (t) is first increasing then decreasing inside the interval (0, T) with peak at t = t0, say. Three methods are given for estimating to. One of these methods is nonparametric, and the other two methods are based on the standard regression technique and the maximum likelihood principle

The given resull has application in a problem of determining the azimuth of a target from the radar‐impulse data. The time series of incoming signals may be approximated by the occurrence of a nonhomogeneous Poisson process with mean value function λ (t). The azimuth of the target is reasonably determined from the direction of the axis of the radar beam at the instant to, corresponding to the peak value of λ (t).
Optimal search using two nonconcurrent sensors
Authors: Persinger Carl A.
Published: May 2007

Search for a stationary target is considered for a situation in which two sensors are available, but cannot be used simultaneously. The cost (in time) of switching from one sensor to the other is ignored, and each sensor is assumed to have perfect discrimination. For a specified class of searches an optimal allocation of search effort is obtained. In the case of a circular normal prior target location distribution, an example is presented in which one sensor is assumed to have a fixed sweep width and the other a stochastic sweep width. An optimal plan is found for this example. This plan produces an allocation of search effort which is expended in a disk by one sensor and in a bounding annulus by the other.