bluuebunny/crossref_metadata_2025 huggingface dataset:
On $\mathcal B_{p,k}$-Boundedness and Compactness of Linear Pseudo-Differential Operators
Authors: Tervo Jouko
Published: December 2016

Boundedness and compactness arguments in the Hörmander spaces

\mathcal B_{p,k}

for linear pseudo-differential operators

L(X, D)

are considered. The symbol

L(x, \xi)

of

L(X, D)

is assumed to obey appropriate temperate criteria, which guarantee that

L(X, D)

maps the Schwartz class

\mathcal S

into itself and,that the formal transpose

L’(X, D): \mathcal S \to \mathcal S

exists. A characterization for the boundedness of the operator

L’(X, D): \mathcal B_{1,kk} \tilde \to \mathcal B_{1,k}

is obtained. A sufficient condition for the boundedness of the operator

L’(X, D): \mathcal B_{p,kk} \sim \to \mathcal B_{p,k}

with

p \in [1, \infty]

is established as well. Finally, the compactness of the continuous extension of

L’(X, D): \mathcal B_{p,kk} \sim (G) \to \mathcal B_{p,k}

is studied, where

G

is an open bounded set in

\mathbb R^n

and where

\mathcal B_{p,kk} \sim (G)

is (essentially) the completion of

C_0^{\infty} (G)

with respect to the

\mathcal B_{p,kk} \sim

-norm.
Generalized Solutions of the Cauchy Problem for a Ionlinear Functional Partial Differential Equation
Authors: Turo Jan
Published: December 2016

An existence and uniqueness theorem for the generalized solution (in the sense "almost everywhere") of the Cauchy problem for a nonlinear functional partial differential equation of first order is proved.
Zur Regularität verallgemeinerter Lösungen von quasilinearen elliptischen Differentialgleichungen zweiter Ordnung in Gebieten mit Ecken
Authors: Miersemann Erich
Published: December 2016

There are studied regularity properties of a class of quasilinear elliptic equations of second order in two-dimensional domains with corners. As an application of these, there is considered the minimal surface problem.
Ein abstraktes nichtlineares Cauchy-Kowalewskaja-Theorem mit singulären Koeffizienten II
Authors: Reissig Michael
Published: December 2016

New qualitative and quantitative properties of abstract nonlinear Cauchy-Kowalewskaja problems with singular coefficients are represented. By applying the method of the Banach space scales the existence and uniqueness of the solution for a Cauchy problem of an operator equation in the scale can be shown. The Cauchy condition is given outside the singularity

t=0

. In a subscale there exists the continuous solution up to singularity.
A Differential Equation for the Positive Zeros of the Function $\alpha J_v(z) + \gamma zJ_v'(z)$
Authors: Ifantis E.K. , Siafarikas P.D.
Published: December 2016

A differential equation for any positive zero

\varrho(v)

of the function

\alpha J_v(z) + \gamma zJ_v'(z)

is found, where

J_v

is the Bessel function of the first kind of

v > -1, J_v'

is the derivative of

J_v

and

\alpha

,

\gamma

are real numbers. It is proven that:

(i) The function

\varrho(v)/(1 + v)

decreases with

v > -1

in the case

\alpha \geq 1

, and the function

\varrho(v)/(\alpha + v)

decreases with

v > -a

in the case

\alpha < 1

.

(ii) The zeros of the function

\alpha J_v (z) + zJ_v'(z)

increase with

v > -1

in the case

\alpha \geq 1

and with

v > \alpha

in the case

\alpha < 1

. The first result leads to a number of lower and upper bounds for the zeros of the function

\alpha J_v(z) + \gamma zJ_v'(z)

which complete and improve previously known bounds The second result improves a well-known result.
The Degree of Rational Approximation to Meromorphic Functions
Authors: Freund Michael
Published: December 2016

The rate of best rational approximation of a meromorphic function on a compact set is described in terms of the growth of its Nevanlinna characteristic. The results are expressed in terms of

\mathcal O

-estimates of the rate of approximation and include estimates of meromorphic functions of zero order.
Zur Anwendung des Pontrjaginschen Maximumprinzips bei distributiver Steuerung auf eine geometrische Aufgabenklasse
Authors: Klötzler Rolf
Published: December 2016

Problems of optimal control are considered in which the control appears in distributional sense. For this a generalization of Pontryagin’s maximum principle is provided and applicated on optimization problems to plane convex domains.
Zum Vergleich verschiedener Dualitätsbegriffe aus der Sicht der Steuerungstheorie
Authors: Pickenhain Sabine
Published: December 2016

Several conceptions of duality from the view-point of optimal control theory are compared. It is proved that under weak regularity assumptions the conceptions of R. T. Rockafellar [6] and J. Hersch [3] are in accordance with the conception of R. Klötzler [5], if we choose a linear statement for the admissible elements in the last conception.
General Limit Theorems with $o$-Rates and Markov Processes under Pseudo-Moment Conditions
Authors: Butzer Paul  L. , Kirschfink Heribert
Published: December 2016

Making use of the Dvoretzky extension of the Trotter-operator method, a general convergence theorem with

o

-rates for dependent, real-valued random variables satisfying a pseudo-moment condition is established. Applications are to general convergence theorems, a central limit theorem as well as a weak law of large numbers for Markov processes with discrete time parameter. Further, pseudo-moment conditions are discussed in detail and the results are compared with the theory of probability-metrics.
A Quantitative Bohman–Korovkin Theorem and its Sharpness for Riemann Integrable Functions
Authors: Mevissen H. , Nessel Rolf Joachim , van Wickeren E.
Published: December 2016

Inspired by work of Pólya (1933) on the convergence of quadrature formulas, we previously introduced a concept of sequential convergence in the space of Riemann integrable functions under which this classical space is in fact the completion of continuous functions. Discussing its consequences to approximation theory, among others we already extended the (qualitative as well as quantitative) Bohman–Korovkin theorem from continuous to Riemann integrable functions. The error bounds obtained were given in terms of the first

\tau

-modul. One purpose of this paper is to derive corresponding results, involving the second

\tau

-modul. As a consequence of our previous quantitative uniform boundedness principle it is then shown that these estimates are indeed sharp. The general results obtained are illustrated in connection with Bernstein polynomials and linear interpolating splines.
On Nonlocal Problems for Pseudoparabolic Equations
Authors: Majchrowski Marian
Published: December 2016

Three nonlocal problems for pseudoparabolic equations are considered. The method of solving of these problems is based on constructing the Riemann function for some differential operator of third order. The problems lead to respective integral equations. Sufficient conditions for existence of the solution of the nonlocal problems are given.
Pointwise nontriviality of the maximum principle in problems with phase constraints (in Russian)
Authors: Dubovitskii Avram Ya. , Dubovitskii V. A.
Published: December 2016

Some simple geometric criteria are singled out for non-vanishing of the conjugate function

\psi (\cdot)

in the maximum principle at any point of the given time interval.
Identifikation von Interferenzschichtsystemen
Authors: Kaiser Hans , Kaiser Hans-Christoph
Published: December 2016

A unified approach to methods and tendencies in the identification of layered media within the framework of systems theory is given. New results concerning the holomorphic properties of transfer coefficients and their characterization by differential equations come to bear. A complete universal method for the synthesis of optimal achromatic systems has been developed. - With regard to the reflection or transmission of electromagnetic waves stratified media act as linear transfer systems. The guiding principle in their identification has been to operate in the following two steps: the first objective in mind is to determine the system function depending on the frequency; based upon this characteristic of the system one then explores its internal structure. These conceptions have been carried out for a homogeneous halfspace and a stack of homogeneous layers of equal optical thickness. The methods are discussed with regard to the significance of measurements as well as prescribed values.
Finite-Element Methods for Singularly Perturbed Elliptic Boundary Value Problems and its Application to the Stationary Navier-Stokes Equations
Authors: Goering Herbert , Tobiska Lutz
Published: December 2016

We consider some modifications of finite-element methods for solving singularly perturbed elliptic beoundary value problems of second order where the reduced problem is of first order. Stability and convergence properties of such methods and the application to the stationary Navier-Stokes problem for high Reynolds numbers are studied.
Elliptische Randwertprobleme zweiter Ordnung in Gebieten mit einer Fehlstelle
Authors: Herwig Alfred
Published: December 2016

Solutions of boundary value problems in domains with a small hole

\Omega

, are represented by a power series of

\epsilon

. For this the solution or its normal derivative should vanish at the boundary of the hole.
On the Singular Values of Toeplitz Matrices
Authors: Widom Harold
Published: December 2016

In 1920 G. Szegö proved the basic result concerning the asymptotic distribution of the eigenvalues of selfadjoint Toeplitz matrices

T_n(f)

. An analogous result holds for the singular values in case

T_n(f)

is not necessarily selfadjoint. In this paper we present a refinement of this (a second-order result) and also determine the limiting set of the singular values, both under appropriate hypotheses in the function

f

.
Über lipschitzstetige implizite Funktionen
Authors: Langenbach Arno
Published: December 2016

A solution of the implicit function

F(x, z) + K(z)x = 0

with

K(z) \in \mathrm {Lip} (Y, X)

becomes possible if we propose

[\partial F / \partial x (x^0, z^0) + K(z^0)]^{–1} \in \mathrm {Lip} (Y, X)

.
Regularity of solutions of some problems in mathematical physics (in Russian)
Authors: Koshelev Alexander I. , Chelkak Sergey I. , Chistyakov Vladimir M.
Published: December 2016

The regularity of generalized solutions of boundary value problems for quasilinear systems of elliptic and parabolic partial differential equations is studied. Conditions are found under which the solutions and their derivatives are smooth (Hölder continuous) functions. Except for some natural demands, these conditions consist in the boundedness of dispersion in the spectrum of that matrix which determines the ellipticity of the considered operator.
A Quadrature-Based Approach to Improving the Collocation Method for Splines of Even Degree
Authors: Sloan Ian H. , Wendland Wolfgang L.
Published: December 2016

The "qualocation" method, a recently proposed quadrature-based extension of the collocation method, is here applied to a class of boundary integral equations, using an even degree spline trial space on a uniform partition. The problems handled are of the form

(L + K)u = f

where

L

is a convolutional operator with even symbol, and

K

is an operator with a greater smoothing effect than

L

. For a trial space of dimension

n

, it is shown that a certain

2n

-point quadrature rule, which is a generalization of the repeated 2-point Gauss rule, gives a stable qualocation method, and yields an order of convergence, in suitable negative norms, two powers of

h

higher than achieved by the mid-point collocation method in the recent analysis of Saranen. The treatment of the smooth perturbation covers also the earlier analysis of the odd degree spline case by Sloan.
Some Properties of Pseudo-Differential Operators with Amplitude $Q(x, y, \xi$)
Authors: Tervo Jouko
Published: December 2016

The paper considers linear pseudo-differential operators

Q

with amplitude

Q(\cdot, \cdot, \cdot) \in C^{infty} (g \times G \times \mathbb R^n

), where G is an open set in

\mathbb R^n

. A criterion, which guarantees that

Q

maps continuously

C_0^{infty} (G)

into

C^{infty} (G)

and that the continuous formal transpose

Q’ : C_0^{infty} (G) \to C^{infty}

of

Q

exists, is verified. Furthermnore, a condition, under which the extension

\mathbb Q

of

Q

from

E’(G)

to

D’(G)

is pseudolocal, is expressed. Also, the decomposition

Q = \bar {Q} + R_1

where

Q

is properly supported (and pseudolocal) and

R_1

maps

E’(G)

into

C_{infty}(G)

, is considered.
On the Semigroup Approach for the Optimal Control of Semilinear Parabolic Equations Including Distributed and Boundary Control
Authors: Tröltzsch Fredi
Published: December 2016

The concept of mild solutions and the variation of constants formula are applied to derive first-order necessary conditions for optimal control problems governed by semilinear parabolic initial-boundary value problems. An adjoint system is defined by means of an abstract integral equation, the solution of the latter being a mild solution of an adjoint parabolic equation.
Extremal inequalities in Sobolev spaces and quasiconformal mappings
Authors: Iwaniec Tadeusz
Published: December 2016

We estimate the norm of a two-dimensional Hilbert operator in $L_p-spaces. This problen leads to inequalities of the theory of Sobolev spaces. In certain cases, by using methods of the theory of quasiconformal mappings, we get best possible estimates.
On Noethericity and Mikhlin Symbols of Operators of the Type of Singular Integral Operators with Shift (in Russian)
Authors: Karlovich Yu. I. , Kravchenko V.G. , Litvinchuk G.S.
Published: December 2016

A review of general methods of investigation of the noetheriannes is given for operators being of the type of one-dimensional singular integral operators with shifts and coefficients having discontinuities of the 1st and 2nd kind.
On the optimal value function of optimal control problems
Authors: Gollan Bernhard
Published: December 2016

The optimal value of parameterized deterministic optimal control problems with state and mixed state-control constraints is studied. The main results are estimates for the effect of small variations of the parameter

p

on the optimal value

V = V(p)

. In particular, upper bounds for several directional derivatives of

V

as well as estimates for a generalized subgradient

\partial V(\cdot)

are given. These estimates are given in terms of multipliers which satisfy first or higher order necessary optimality conditions along an optimal solution of the unperturbed problem. The theory is based on the separability or nonseparability of suitable approximating cones and requires no or only very weak regularity assumptions.
The Bergman and Szegö Kernels for Separately Monogenic Functions
Authors: Constales Denis
Published: December 2016

The existence of the Bergman and Szegö kernels for separately monogenic functions in the unit ball is proved and explicit series expansions are obtained for them.
Die Struktur der Extremallösungen von linearen Differentialgleichungen $n$-ter Ordnung
Authors: Pudei Vratislav
Published: December 2016

The structure of extremal solutions of linear ordinary differential equations of order

n

on an interval

[t_0, \eta (t_0)]

is shown, where

\eta (t_0)

is the first conjugate point of

t_0

. It is also shown by it, how this structure depends on the number of linearly independent extremal solution.
Lokale Theorie des Reduktionsverfahrens für singuläre Integralgleichungen
Authors: Silbermann Bernd
Published: December 2016

Using a local principle the finite section method is studied for one-dimensional singular integral operators. In particular a principle of separation of singularities is deduced and the finite section method is studied for singular integral equations with coefficients belonging to the algebra

\overline {PC}

.
Monotonicity Properties of Oscillatory Solutions of Second Order Differential Equations
Authors: Müller-Pfeiffer Erich
Published: December 2016

It is proved in what way monotonicity properties of the coefficients of ordinary second order differential equations are transmitted to oscillatory solutions

u

of such equations. For instance, there are statements on the distances of the zeros of

u

,

u’

, and

u

and

u’

mutually.
Error Estimates in Generalized Trigonometric Hölder-Zygmund Norms
Authors: Prestin Jürgen , Prössdorf Siegfried
Published: December 2016

We consider Hölder-Zygmund spaces of

2\pi

-periodic functions

f: \mathbb R \to \mathbb C

, where the

k

-th difference with step-size

h

of the

r

-th derivative in the

L^p

- or

C

-norm is bounded by a modulus-type function

\omega (h)

. For the Fourier sum and related approximation processes we investigate error estimates in corresponding Hölder-Zygmund norms if the smoothness of

f

is given by other Hölder-Zygmund conditions. The convergence order for the general case can be formulated in a simple manner. This allows us to state also Jackson-type theorems for such Banach spaces. Moreover, we give explicit values for the constants appearing in these estimates.
Ein Fixpunktsatz für mehrdeutige konvexe Abbildungen auf der Sphäre
Authors: Beckert Herbert
Published: December 2016

The well-known fixed point theorem of Brouwer-Poincaré is generalized for upper semicontinuous multivalued mappings of the sphere

S^{n–1}

(

n

odd) on convex domains of

S^{n–1}

.
Optimal Control of a Nonlinear Singular Integral Equation Arising in Electrochemical Machining
Authors: Goebel Manfred , Oestreich Dieter
Published: December 2016

The paper is concerned with an optimal control problem for a nonlinear singular integral equation of Cauchy type. The existence of at least one optimal solution is proved and a necessary optimality condition is derived.
On the Ranges of Realizations in Distribution Spaces
Authors: Tervo Jouko
Published: December 2016

The paper deals with the closedness of ranges and the surjectivity of realizations related to linear partial differential operators

L(x,D)

.
On the Quasi-Asymptotic Expansion of the Causal Fundamental Solution of Hyperbolic Operators and Systems
Authors: Wagner Peter
Published: December 2016

Explicit formulae for the quasi-asymptotic expansion (in the sense of V.S. Vladimirov) of the causal fundamental solution of hyperbolic partial differential operators resp. systems with constant coefficients are given. The method is applied to some concrete examples.
A-Priori Estimates for the Solutions of a Class of Nonlinear Convolution Equations
Authors: Askhabov Sultan N. , Betilgiriev M.A.
Published: December 2016

We present sharp two-sided a-priori estimates for the solutions of a class of nonlinear Volterra integral equations in the cone of non-negative continuous functions. These estimates enable us to construct a complete metric space which is invariant under the nonlinear convolution operator considered here and to prove that the equation induced by this operator has a unique solution in this space as well as in the class of all non-negative continuous functions vanishing at the origin.
Domains of Attraction of Generic $\omega$-Limit Sets for Strongly Monotone Semiflows
Authors: Takác Peter
Published: December 2016

Asymptotic behavior of a strongly increasing semiflow

\Omega

in a strongly ordered metrizable topological space

X

is investigated in terms of the

\omega

-limit set

\omega (x)

of a generic point

x \in X

whose positive semiorbit

\mathcal O^+ (x)

is assumed to be relatively compact. The domain of attraction of the

\omega

-limit set of a generic order

\omega

-stable point is determined. If

X

is an open and order-convex subset of a separable strongly ordered Banach space

V

, it is proved that "almost all" points

x \in X

are order

\omega

-stable, whereas the remaining

\omega

-unstable points are contained in the union of at most countably many Lipschitz manifolds of codimension one in

V

. If

\Omega

admits a strongly positive, compact linearization about its equilibria, then

\omega (x)

is a single equilibrium for every order

\omega

-stable point

x \in X

.
On the Structure of the Solutions of the Jabotinsky Equations in Banach Spaces
Authors: Gronau Detlef
Published: December 2016

The differential-functional equations of Jabotinsky are closely related to the translation equation. They are of importance in the iteration theory. In this paper we will give an explicit representation of the solutions of each of these equations in Banach spaces.
Über eine Erweiterung des Liouvilleschen Satzes
Authors: Hoy Erich
Published: December 2016

A generalization of Liouville’s theorem is proved for a bounded function

w: \mathbb C \to \mathbb C

if, in addition,

w

behaves locally like a quasiregular function and the growth of its dilatation is restricted.
Operator Calculus for Elliptic Boundary Value Problems in Unbounded Domains
Authors: Bernstein Swanhild
Published: December 2016

The main result of the paper is the proof of the applicability of hypercomplex methods for elliptic boundary value problems in outer domains, i.e. domains, which lies outside a closed compact surface.
Zur Darstellung von Lösungen bei Systemen partieller Differentialgleichungen, insbesondere be! isolierten Singularitäten
Authors: Berglez Peter
Published: December 2016

For specific systems of elliptic partial differential equations and the associated systems of formally hyperbolic equations in complex variables the solutions can be given using certain differential operators. These operators map holomorphic functions into the set of solutions of the system. In this article we consider the relation between a solution and the holomorphic functions generating it. In particular we determine the generators of the zero solution. Finally we give a general representation theorem for the solutions defined in the neighbourhood of an isolated singularity.
Existenzsätze für einige Randsteuerprobleme bei verallgemeinerten analytischen Funktionen
Authors: Oestreich Dieter
Published: December 2016

There are considered the Riemann–Hilbert boundary control problem with analytic and generalized analytic functions, the Riemann and similar boundary control problems. Existence theorems are proved for these problems with integral cost functionals, constraints and (piecewise) Hölder-continuous coefficients in the boundary condition.
Existent einer schwachen Lösung eines eñtarteten parabolischen Rand-Anfangswertproblems zwischen schwachen Ober- und Unterlösungen
Authors: Sosna Dieter
Published: December 2016

Considering a degenerate parabolic initial-boundary-value-problem on a bounded domain which has smooth weak upper and lower solutions we proof the existence of a weak solution, being between upper and lower solutions almost everywhere.
Sequential Convergence in the Space of Absolutely Riemann Integrable Functions
Authors: Jiménez M.A. , López E. , Rückmann J.-J.
Published: December 2016

The concept of

R

-convergence in the space of usual Riemann integrable functions was introduced by Dickmeis, Mevissen, Nessel and van Wickeren in 1986. They proved that this space, provided with R-convergence, is sequentially complete and that every function in the space can be approximated by a sequence of continuous functions. They gave several applications. This paper extends that concept to the space of absolutely Riemann integrable functions and it is shown that the results mentioned above still hold there.
Extending Chains of Factorizations and Minimal Negative Signatures
Authors: Constantinescu Tiberiu , Gheondea Aurelian
Published: December 2016

We compute the minimal negative signature for a problem of extending chains of factorizations in spaces with indefinite inner product spaces. As an application, we obtain a formula for the minimal negative signature of Hermitian completions of tridiagonal partial block matrices.
General Approximation-Solvability of Nonlinear Equations Involving $\mathcal A$-regular Operators
Authors: Verma Ram U.
Published: December 2016

Here we consider a general approximation-solvability scheme involving

\mathcal A

-regular operators - a generalization of

\mathcal A

-proper operators - introduced and studied by Petryshyn [4] and further studied by Milojevic’ [3], Petryshyn [6] and others. Among significant applications, an

\mathcal A

-regular version of the Petryshyn theorem is given.
The Marcinkievicz Interpolation Theorem for Rearrangement-Invariant Function Spaces and Applications
Authors: Fehér Franziska
Published: December 2016

The interpolation theorem of J. Marcinkievicz [17] states that any sublinear operator

T

which is simultaneously of weak types (

p_1, q_1

) and (

p_2, q_2

) is also a bounded operator from the Lebesgue space

L_p(0, l), 0 < l \leq \infty

, into itself, provided

p_2 < p < p_1

. The aim of this paper is to generalize this theorem to the setting of rearrangement-invariant Banach function spaces, and thus to render the theorem available to a much larger range of applications.
On Optimality Conditions in some Control Problems for Memory Kernels in Viscoelasticity
Authors: von Wolfersdorf Lothar
Published: December 2016

The inverse problem of identifying the memory kernel in the stress-strain-relation of Boltzmann type for a rod is reduced to an optimal control problem with a quadratic cost functional in the state for the related integro-differential wave equation. For this problem necessary optimality conditions are derived and transformed into explicit form by means of suitably defined adjoint state functions.
Weakly Singular Hammerstein-Volterra Operators in Orlicz and Hölder Spaces
Authors: Appell Jürgen , Väth Martin
Published: December 2016

Acting, boundedness, and compactness conditions for nonlinear Hanimerstein- Vol terra operators are given either between two Orlicz spaces, or from an Orlicz space into a (generalized) Hölder space. Particular emphasis is put on weakly singular kernels. This leads to (local) solvability results for Hammerstein-Volterra equations of second kind.
On the Volume Infimum for Liquid Bridges
Authors: Zhou L.
Published: December 2016

We are concerned with the stable liquid bridges joining two parallel homogeneous plates in the absence of gravity following the recent work of Finn and Vogel [7]. We prove the Carter conjecture in the general case where the two contact angles can be different.
Some Classes of Essentially Maximal Operators
Authors: Tervo Jouko
Published: December 2016

Some inequalities for the complex zeros of Bessel functions and the zeros of Lommel polynomials, which improve previously known results, are presented.
Asymptotic Developments of the Solutions of the Translation Equation
Authors: Berg Lothar
Published: December 2016

For the solutions of the translation equation a special asymptotic development is considered. It is shown that the coefficients of this development can be determined by linear recursion formulas. An example illustrates the results.
Exact Difference Schemes and Difference Schemes of Arbitrary Given Degree of Accuracy for Generalized One-Dimensional Third Boundary Value Problems
Authors: Gavrilyuk I.P.
Published: December 2016

A variational problem is formulated which is a generalization of the third boundary value problem for one-dimensional equations. Conditions of existence and uniqueness of solutions are considered. The numerical approximation of arbitrary given degree of accuracy (truncated difference schemes) regarded in this paper is based on the three-point difference relations for the exact solution (exact difference scheme).
On partial differential inequalities of the first order with a retarded argument
Authors: Kamont Zdzisław , Zacharek Stanisław
Published: December 2016

This paper deals with first order partial differential inequalities of the form

(i) \: z_t(z, x) \leq f (t,x, z (t, x), z(\alpha (t, x), \beta (t, x)), z(t, x))

where

x = (x_1, \dots, x_n), z_x (t, x) = (z_{x_1} (t, x), \dots, z_{x_n} (t, x))

and

z(\alpha (t, x), \beta (t, x)) = (z(\alpha_1 (t, x), \beta_1 (t, x)), \dots, z(\alpha_m (t, x), \beta_m (t, x))).

We assume that (i) is of the Volterra type. Let

E = \{(t, x): 0 \leq t \leq a, \quad |x_i - \dot{x}_i | \leq b_i = M_i t \quad (i = 1, \dots, n)\}

and

E_0 = \{(t, x): -\tau \leq t \leq 0, \quad |x_i - \dot{x}_i | \leq b_i \quad (i = 1, \dots, n)\}.

Assume that

u,v \in C(E_0 \bigcup E, \mathbf R)

satisfy on

E

the Lipschitz condition with respect to

(t, x)

. Suppose that

u

and

v

satisfy almost everywhere on

E

the differential inequalities

u_t (t, x) \leq f(t, x, u (t, x), u(\alpha (t, x), \beta (t, x)), u_x (t, x))

v_t (t, x) \geq f(t, x, v (t, x), v(\alpha (t, x), \beta (t, x)), v_x (t, x))

and the initial inequality

u(t, x) \leq v(t, x)

on

E_0

. In the paper we prove that under certain assumptions concerning the functions

f, \alpha, \beta

, the inequality

u(t, x) \leq v(t, x)

is satisfied on

E

.
Schur Functions, Schur Parameters and Orthogonal Polynomials on the Unit Circle
Authors: Golinskii Leonid B.
Published: December 2016

Properties of Schur functions on the unit circle and asymptotic behaviour of corresponding Schur parameters are investigated. Connection between the Schur parameters and the reflection coefficients of a certain system of orthogonal polynomials on the unit circle is used.
Observations on the preceding paper of C. Hamburger: The Optimal Runner: a Control Problem with Phase Constraint
Authors: Pickenhain L.
Published: December 2016

Assuming a simple biophysical model and using the Pontryagin maximum principle, we find the optimal strategy to run a race.
Zur Konvergenz von Iterationsverfahren mit affinen Operatoren
Authors: Schott Dieter
Published: December 2016

Many well-known numerical procedures for the iterative solution of linear equations in Banach spaces have the form

x_{n+1} = \mathbf A_n \mathbf A_{n-1} \dots \mathbf A_0x_0 (n = 0, 1, 2, \dots)

with affine operators

\mathbf A_n

. If the operators

\mathbf A_n

possess common fixed points, then there often exist affine projectors

\mathbf P

with the property

\mathbf P = \mathbf A_n \mathbf P = \mathbf {PA}_n \quad (n= 0, 1,2, \dots).

In this paper some convergence theorems are proved for iteration methods having such operator sequences.
Integral and Boundary Value Problems for Nonlinear Systems of Composite Type
Authors: Lundin Leroy R. , Wen Guochun
Published: December 2016

Using the Schauder fixed point theorem we establish the solvability of an initial-boundary va-lue problem for a nonlinear first order system of composite type. The procedure depends on first establishing a priori estimates for the solutions. This investigation generalizes the results of [1,3,4].
Identifiability of the Transmissivity Coefficient in an Elliptic Boundary Value Problem
Authors: Vainikko Gennadi , Kunisch Karl
Published: December 2016

We deal with a coefficient inverse problem describing the filtration of ground water in a region

\Omega \subset R^n, n ≥ 2

. Introducing a weak formulation of the problem, discretization and regularization methods can be constructed in a natural way. These methods converge to the normal solution of the problem, i.e. to a transmissivity coefficient of a minimal

L^2 (\Omega)

-norm. Thus a question about

L^2

-identifiability (identifiability among functions of the class

L^2 (\Omega)

of the transmissivity coefficient arises. Our purpose is to describe subregions of

\Omega

where the transmissivity coefficient is really

L^2

-identifiable or even

L^1

-identifiable. Thereby we succeed introducing physically realistic conditions on the data of the problem, e.g. piecewise smooth surfaces in

\Omega

are allowed where the data of the inverse problem may have discontinuities. With some natural changes, our results about the

L^1

-identifiability extend known results about the identifiability among more smooth functions given by G. R. Richter [4], C. Chicone and J. Gerlach [1], and K. Kunisch [3].
Axially Symmetric Flow with Finite Cavities II
Authors: Brock Friedemann
Published: December 2016

An axially symmetric cavity flow of an ideal fluid is moving around an obstacle. The flow is either in a cylindrical pipe or an unbounded region and the cavity may be finite. Essentially is the assumption that the obstacle is star-like with respect to some point on the axis of symmetry. The existence of such flows was proved by the author in Part I. In the present Part lithe behaviour of the free boundaries near the end-point on the axis of symmetry (in the case of a finite cavity) and near infinity (in the case of an infinite cavity) are investigated.
On a Theorem of Rooney Concerning the Spectrum of the Singular Integral Operator
Authors: Böttcher Albrecht , Spitkovsky Ilya
Published: December 2016

The authors have recently described the spectrum and the essential spectrum of the singular in-tegral operator on spaces with general Muckenhoupt weights. In this note we show how these results imply a sharpened version of a theorem by Rooney on the spectrum of the singular integral operator on spaces with a "weakly" perturbed power weight.
Some New Classes in Topological Sequence Spaces Related to $L_r$-Spaces and an Inclusion Theorem for K(X)-Spaces
Authors: Boos Johann , Leiger T.
Published: December 2016

The aim of the present paper is to get inclusion theorems for K(X)-spaces, that is, sequence spaces over any Frchet space X endowed with a K-topology (e.g. domains of operator valued matrices). Since Kalton’s closed graph theorem is an essential tool to get inclusion theorems in the case that Xequals the set of all complex numbers and since domains of operator valued matrices are not necessarily separable FK(X)-spaces we can no longer make use of FK-space theory. Therefore, it is necessary to develop new ideas to get inclusion theorems. For this we introduce two new classes of K(X)-spaces and prove a closed graph theorem for inclusion maps. One of them is closely related to the class of

L_r

-spaces introduced by Jinghui Qiu and to the closed graph theorem of J. Qiu, the other is connected with a well-known result of K. Zeller in summability theory. As an immediate corollary of the inclusion theorem proved in this paper we get a generalization of a theorem of Mazur-Orlicz type due to the authors.
Boundary Theorems of the Gehring-Lohwater and Plessner Type for Polyanalytic Functions
Authors: Balk Mark Benevich , Tutschke Wolfgang
Published: December 2016

Using methods of the theory of generalized analytic functions, the present paper investigates the boundary behaviour of non-holomorphic functions (such as polyanalytic ones) provided the areolar derivative

\partial /\partial \bar{z}

belong to an

L_p

space,

p > 2

.
A Stochastic Nonlinear Evolution Equation
Authors: Grecksch Wilfried
Published: December 2016

A stochastic evolution equation for processes with values in two orthogonal subspaces of a Hilbert space is considered. Such types of equations arise in the study of quasistatic processes of elastic viscoplastic materials with random disturbances. Using the theory of Hilbert space valued Ito equations an existence and uniqueness theorem is proved. Finally a time discrete approximation is discussed.
On stable space dependent stationary solutions of a competition system with diffusion
Authors: de Mottoni Piero , Schiaffino A. , Tesei Alberto
Published: December 2016

A quasilinear parabolic system of two equations is considered, only one of which includes the diffusion term. The bifurcation of nonnegative stationary solutions is studied together with their stability character and their dependence on the "space" variables.
A Counterexample for $L^1$-Estimates for Parabolic Differential Equations
Authors: Kröger Pawel
Published: December 2016

We show that the Dini (1) continuity of the coefficients of a linear parabolic differential operator in non-divergence form is in some sense the weakest condition such that the solutions of the corresponding initial value problem satisfy an

L^1

-estimate;…
The Green’s Function Method for the Supported Plate Boundary Value Problem
Authors: Schot Steven H.
Published: December 2016

The deflection

u

of a thin elastic plate is governed by the biharmonic equation

\Delta^2u = 0

, where

\Delta

is the two-dimensional Laplace operator. The problem of solving this equation in the domain

D

occupied by the plate when

u

and

\Delta u

are assigned on the boundary

\delta D

is often called the supported plate boundaly value problem. Strictly speaking this terminology is not correct since

\Delta u

should be replaced by the more complicated expression for the plate’s moment

M(u)

on

\delta D

; however, when

\delta D

consists only of rectilinear segments (or when the Poisson ratio is unity)

M(u)

reduces to

\Delta u

. Here, the supported plate problem is solved by a Green’s function method, closed form solutions are obtained for the disk and the half-plane, and the supported plate Green’s functions for these domains are computed explicitly. As a check, the solutions of these boundary value problems are also derived using a modification of the Goursat-Almansi method.
Spectral Estimates for Compact Hyperbolic Space Forms and the Selberg Zeta Function for $p$-Spectra. Part I
Authors: Schuster Reinhard
Published: December 2016

We prove an asymptotic estimation for the length spectrum with certain weights for a compact hyperbolic space form. Thereby the Selberg trace formula and a Landau difference method is used.
General Sufficient Conditions for the Convexity of a Function
Authors: Zagrodny Dariusz
Published: December 2016

Sufficient conditions for a given function to be convex on a given segment, in terms of upper subderivative, are proved.
Singular Integral Equations with Monotone Nonlinearity in Complex Lebesgue Spaces
Authors: Askhabov Sultan N.
Published: December 2016

By methods of monotone operator theory, existence and uniqueness theorems are proved for some classes of nonlinear singular integral equations of Cauchy’s type involving large nonline-antics in weighted complex Lebesgue spaces and also norm estimates of solutions are obtained.
Taylor’s Expansion in a Distribution Algebra
Authors: Berg Lothar
Published: December 2016

For a certain distribution algebra it is shown that every element of the algebra possesses a value and is representable by its Taylor’s expansion. Moreover there is investigated the structure of the subalgebra of values.
Partitions of totally disconnected compact spaces (in Russian)
Authors: Vladimirov Denis  A. , Senf Peter
Published: December 2016

In the paper is studied the connection between subalgebras of a Boolean algebra and partitions of the corresponding Stone space (totally disconnected compact space). In case of extremally disconnected space it is proved that regularly embedded subalgebras correspond exactly to continuous partitions (in the sense of K. Kuratoyski). The concepts of a weight of a Boolean algebra and of a weight of a partition are studied.
Zur zeitminimalen Randsteuerung einer homogenen schwingenden Saite
Authors: Eichenauer Wolfram
Published: December 2016

In this paper the following problem is considered: A homogeneous vibrating string which is clamped at one end has to be steered into a position of permanent rest by a boundary control. Given an initial state of vibration and a bound for the norm of the control, a minimum time and a corresponding time minimal control have to be determined. This problem turns out to be equivalent to a moment problem which can be solved easily, due to its special structure. Essentially only one transcendental equation in one variable has to be solved for determining the required time and the corresponding control. Numerical results are presented at the end of the paper.
Zur lokalen Lipschitzstetigkeit der Bellmanschen Funktion für Steuerprobleme mit linearen Zustandsgleichungen
Authors: Meister Helmut
Published: December 2016

It is shown, that for qualitative control problems with linear state equations (without convexity assumptions on cost function or control domain) Bellman’s function is locally lipschitz continuous in the interior of the reachable set. An example of this type is given with non-continuous Bellman’s function on the boundary.
One-dimensional Schrödinger Operators with Ergodic Potential
Authors: Englisch Harald
Published: December 2016

In the first part of the paper the results of Luttinger and Dworin concerning the following problem of Saxon/Hutner are generalized: Which conditions guarantee that an energy value

E

lies in the resolvent set of the Hamiltonian for an alloy, presupposing that

E

lies in the resolvent set of the Hamiltonians of all pure components. Symmetric potentials play an particular role in this. In the third part the ground state energy is investigated for different types of the ergodie potential

V

. For comparison, examples with almost periodic potentials are given. E.g. Cordon’s result concerning eigenvalues for almost periodic potentials is generalized in the second part.
Singularly perturbed elliptic problems of second order with a singular line
Authors: Roos H.-G. , Tobiska Lutz
Published: December 2016

For some classes of singularly perturbed elliptic problems, in which the characteristics of the reduced problem are parallel or perpendicular to the singular line, uniform asymptotic approximations are constructed. The order of approximation depends on the behaviour of the coefficients of the reduced problem in the neighbourhood of the singular line and on the properties of the considered domain.
Eine Realisierung der Theorie der abstrakten Besov-Räume $B_q^s(A) (s > 0, 1 \leq q \leq \infty$) und der Lebesgue-Räume $H^s_{p, \mu}$ auf der Grundlage Besselscher Differentialoperatoren
Authors: Altenburg Gerd
Published: December 2016

The paper deals with the theory of abstract Besov-spaces, defined by H. Triebel, in the concrete case of weighted

L_p

-spaces on the base of Bessel-type differential operators. Also spaces of Lebesgue-type on the same base are defined and treated here. Furthermore interpolation theorems are given.
Lageabschätzung für einen Kondensator minimaler Kapazität
Authors: Kirsch Siegfried
Published: December 2016

With the help of the method of interior variation we get informations about the geometrical form and locus from that continuum, which contains

n ≥ 2

various points and has minimal generalized transfinite diameter connected with a fundamental solution for generalized Cauchy–Riemann equations.
Maximal inequalities and Fourier multipliers for spaces with mixed quasinorms. Applications
Authors: Schmeisser Hans-Jürgen
Published: December 2016

The paper concerns with maximal inequalities and Fourier multipliers for systems of entire analytic functions of exponential type belonging to mixed quasinormed spaces. As an application 4 types of spaces of functions with dominating mixed smoothness properties are introduced. Relations to classical spaces of that type (spaces of S.M. Nikol’skij, T.I. Amanov, P.I. Lizorkin) are treated. As a special case the Sobolev spaces with a dominating mixed derivative are contained.
A new high-resolution pollen sequence at Lake Van, Turkey: Insights into penultimate interglacial-glacial climate change on vegetation history
Authors: Pickarski Nadine , Litt Thomas
Published: December 2016

Abstract. A new detailed pollen and oxygen isotope record of the penultimate interglacial-glacial cycle, corresponding to the Marine Isotope Stage (MIS) 7–6 (c. 242.5–131.2 ka before present), has been generated from the "Ahlat Ridge" (AR) sediment core at Lake Van, Turkey. The presented record displays the highest temporal resolution for this interval with a mean sampling interval of ~ 540 years. Integration of all available proxies shows three intervals of effective moisture, evidenced by the predominance of forested landscapes (oak-pine steppe forest), which can be correlated with MIS 7e, 7c, and 7a. The warmest stage in terms of highest temperate tree percentages is MIS 7c, while the amplitude of MIS 7e appears to be truncated by a shift to colder/drier climatic conditions. The detailed comparison between the penultimate interglacial complex (MIS 7) to the last interglacial (Eemian, MIS 5e) and the current interglacial (Holocene, MIS 1) provides a vivid illustration of possible differences of successive climatic cycles. Intervening periods of open steppe landscape correlate with MIS 7d and 7a, favouring local erosion and detrital sedimentation. The predominance of steppe elements during MIS 7d indicates very cold/dry climatic conditions. In contrast, the occurrence of more temperate tree percentages throughout MIS 7b points to relatively mild conditions, in agreement with atmospheric CO2 concentration and oxygen isotope records. Despite the general dominance of dry/cold desert-steppe vegetation during the penultimate glacial (MIS 6), this period can be divided into two parts: an early stage (c. 193–157 ka BP) with pronounced oscillations in tree percentages, and a later stage (c. 157–131 ka BP) with lower tree percentages and subdued oscillations. The occurring vegetation pattern is analogous to the MIS 3 to MIS 2 division during the last glacial in the same sedi–159 ka BP) as described in marine pollen records, which indicates cooler but relatively wetter climate conditions during the penultimate glacial. In comparison with long European pollen records, speleothem isotope records from the Near East, and global climate parameters (e.g., insolation, atmospheric CO2 content), the new high-resolution Lake Van record presents an improved insight into regional vegetation dynamics and climate variability in the eastern Mediterranean region.
EnKF with closed-eye period – towards a consistent aggregation of information in soil hydrology
Authors: Bauser Hannes H. , Jaumann Stefan , Berg Daniel , Roth Kurt
Published: December 2016

Abstract. The representation of soil water movement exposes uncertainties in all model components. We assess the key uncertainties for the specific hydraulic situation of a 1-D soil profile with TDR (time domain reflectometry)-measured water contents. The uncertainties addressed are initial condition, soil hydraulic parameters, small-scale heterogeneity, upper boundary condition, and the local equilibrium assumption by the Richards equation. We employ an ensemble Kalman filter (EnKF) with an augmented state to represent and estimate all key uncertainties, except for the intermittent violation of the local equilibrium assumption. For the latter, we introduce a closed-eye EnKF to bridge the gap. Due to an iterative approach, the EnKF was capable of estimating soil parameters, Miller scaling factors and upper boundary condition based on TDR measurements during a single rain event. The introduced closed-eye period ensured constant parameters, suggesting that they resemble the believed true material properties. This closed-eye period improves predictions during periods when the local equilibrium assumption is met, but requires a description of the dynamics during local non-equilibrium phases to be able to predict them. Such a description remains an open challenge. Finally, for the given representation our results show the necessity of including small-scale heterogeneity. A simplified representation with Miller scaling already yielded a satisfactory description.
Regularization Destriping of Remote Sensing Imagery
Authors: Basnayake Ranil , Bollt Erik , Tufillaro Nicholas , Sun Jie , Gierach Michelle
Published: December 2016

Abstract. We illustrate the utility of variational destriping for ocean color images from both mulitspectral and hyperspectral sensors. In particular, we examine data from a filter spectrometer, the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar Partnership (NPP) orbiter, and an airborne grating spectrometer, the Jet Population Laboratory's (JPL) hyperspectral Portable Remote Imaging Spectrometer (PRISM) sensor. We solve the destriping problem using a variational regularization method by giving weights spatially to preserve the other features of the image during the destriping process. The target functional penalizes `the neighborhood of stripes' (strictly, directionally uniform features) while promoting data fidelity, and the functional is minimized by solving the Euler-Lagrange equations with an explicit finite difference scheme. We show the accuracy of our method from a benchmark data set which represents the Sea Surface Temperature off the Coast of Oregon, USA. Technical details, such as how to impose continuity across data gaps using inpainting, are also described.