bluuebunny/crossref_metadata_2025 huggingface dataset:
Accuracy of Ultrasound-Guided Intra-articular Hip Injections Performed in the Orthopedic Clinic
Authors: Balog Todd P. , Rhodehouse Blair B. , Turner Eric K. , Slevin John M. , Bush Lisabeth A. , Grassbaugh Jason A. , Marchant Bryant G.
Published: December 2016

Intra-articular hip injections have proven clinical value for both diagnostic and therapeutic purposes. Historically, these injections have been performed by radiologists using fluoroscopic guidance. This necessitates a radiology referral, delays the injection, and represents lost productivity for the orthopedist. Ultrasound-guided intra-articular hip injections have been described in the radiology literature with excellent accuracy. These injections were performed by radiologists. The purpose of this study was to determine the accuracy of ultrasound-guided hip injections performed in the orthopedic clinic by orthopedic surgeons and orthopedic physician assistants. Fifty ultrasound-guided hip injections were performed using a standard technique. Contrast was included, and an anteroposterior pelvis radiograph was obtained immediately following injection. Diagnosis, body mass index, procedure time, and visual analog scale scores were recorded. Radiographs were reviewed independently by a musculoskeletal radiologist and an orthopedic surgeon to determine intra-articular placement of the injection. A total of 50 hips were injected. There was no identifiable contrast in 2 patients, leaving 48 hips for analysis. Of these, contrast was injected intra-articularly in 46 hips for an accuracy of 96%. Average procedural time was 2.6 minutes, and the average visual analog scale score was 1.9 during the procedure. Revenue value units ranged from 1.72–2.55 for ultrasound-guided hip injections. These findings indicate ultrasound-guided intra-articular hip injections performed in the orthopedic clinic by surgeons or physician assistants are accurate, efficient, and patient-friendly. Additionally, they preserve patient continuity and maintain productivity within the orthopedic clinic. [
Orthopedics.
2017; 40(2):96–100.]
Revision Total Hip Arthroplasty Using the Cement-in-Cement Technique
Authors: Amanatullah Derek F. , Pallante Graham D. , Floccari Lorena V. , Vasileiadis George I. , Trousdale Robert T.
Published: December 2016

The cement-in-cement technique is useful in the setting of revision total hip arthroplasty (THA), especially to gain acetabular exposure, change a damaged or loose femoral component, or change the version, offset, or length of a fixed femoral component. The goal of this retrospective study was to assess the clinical and radiographic characteristics of revision THA using the cement-in- cement technique. Between 1971 and 2013, a total of 63 revision THAs used an Omnifit (Osteonics, Mahwah, New Jersey) or Exeter (Howmedica, Mahwah, New Jersey) stem and the cement-in-cement technique at the senior author's institution. Aseptic loosening (74%) was the predominant preoperative diagnosis followed by periprosthetic fracture (14%), instability (8%), and implant fracture (6%). Mean clinical follow-up was 5.5±3.8 years. The Harris Hip Score had a statistically significant increase of 18.5 points (
P
<.001) after revision THA using the cement-in-cement technique. There were 13 returns to the operating room, resulting in an overall failure rate of 21%. Eleven (18%) cases required revision THA, but only 1 (2%) revision THA was for aseptic removal of the femoral component. All other femoral implants had no evidence of component migration, cement mantel fracture, or circumferential lucent lines at final follow-up. The patients who underwent cement-in-cement revision THA at the senior author's institution had good restoration of function but a high complication rate. [
Orthopedics.
2017; 40(2):e348–e351.]
Predicción de la tasa de eliminación de material y rugosidad de la superficie de mecanizado por electroerosión de alambre de níquel utilizando la metodología de superficie de respuesta
Authors: Chinnadurai Thangam , Arungalai Vendan Subbiah
Published: December 2016

Este estudio se centra en la investigación de los efectos de los parámetros del proceso, a saber, corriente máxima (Ip), duración del impulso (Ton), duración de desconexión del impulso (Toff), presión del agua (Wp), velocidad de alimentación del alambre (WF), tensión del alambre (Wt ), servo voltaje (Sv) y ajuste de avance del servo (SFS), velocidad de eliminación de material (MRR) y rugosidad de la superficie (SR), para la fabricación de alambre de níquel por descarga eléctrica (Wire-EDM) utilizando el método “Taguchi”. Se ha adoptado la metodología superficial de respuesta (RSM) con objeto de desarrollar relaciones matemáticas entre los parámetros del proceso de corte de alambre y las variables de salida de la junta de soldadura para determinar los parámetros de potencia de la soldadura que conducen a la calidad óptima deseada de corte del alambre. Además, usando gráficas superficiales de respuesta, los efectos de interacción de los parámetros del proceso en las respuestas son analizados y discutidos. El software estadístico “Mini-tab” se utiliza para establecer el diseño y obtener las ecuaciones de regresión. Los modelos matemáticos desarrollados son probados por el método de análisis de la varianza (ANOVA) para comprobar su aptitud e idoneidad. Por último, se hace una comparación entre los resultados medidos y calculados, que están en buen acuerdo. Esto indica que los modelos desarrollados pueden predecir las respuestas con exactitud y precisión dentro de los límites de los parámetros de corte usados.
Análisis de la descomposición espinodal en aleaciones Fe-32 y 40 %at. Cr utilizando el método de campo de fases basado en las ecuaciones lineal y no lineal de Cahn y Hilliard
Authors: Soriano-Vargas Orlando , López-Hirata Víctor M. , Ávila-Dávila Erika O. , Saucedo-Muñoz Maribel L. , Cayetano-Castro Nicolás
Published: December 2016

La descomposición espinodal se estudió durante el envejecido de aleaciones Fe-Cr mediante la solución numérica de las ecuaciones diferenciales parciales lineal y no linear de Cahn y Hilliard usando el método de diferencias finito explícito. Los resultados de la simulación numérica permitieron describir apropiadamente el mecanismo, morfología y cinética de la descomposición de fases durante el envejecido isotérmico de estas aleaciones. La cinética de crecimiento de la descomposición de fases ocurrió muy lentamente durante las primeras etapas de envejecido, y se incrementó considerablemente con el tiempo de envejecido. La ecuación no lineal parece ser más apropiada para describir las primeras etapas de la descomposición espinodal que la ecuación lineal.
Estudio del desgaste de carriles en servicio y optimización de su mantenimiento
Authors: Quintana-Nicolás Amador , Preciado-Calzada Mónica
Published: December 2016

Este trabajo estudia el desgaste de los carriles a lo largo del tiempo debido al deslizamiento que ejercen las ruedas de los trenes a su paso. También estudia la influencia que tienen las elevadas cargas soportadas en la microestructura del acero de los carriles. Para ello se han analizado muestras reales de carriles con alto desgaste y otras muestras a las que se ha inducido un desgaste acelerado en laboratorio. Todos los datos experimentales se han validado a través del modelo teórico de Archard, obteniendo relaciones satisfactorias. Esta investigación puede ser aplicada en la planificación de las tareas de conservación de los carriles, optimizando los intervalos de amolado preventivo.
Síntesis de nuevos líquidos iónicos y evaluación de su rendimiento de lixiviación en la recuperación de cobre y zinc de escorias industriales de latón
Authors: Kilicarslan Sahin Ayfer , Selcen Atalay Tugba , Atbakar Muge , Ocal Nuket , Nezihi Saridede Muhlis
Published: December 2016

Los líquidos iónicos a base de imidazolio, trifluoroacetato de 1,3-dibencilimidazolio, trifluoroacetato de 1-bencil-3-etilimidazolio y trifluoroacetato de 1-bencil-3-propilimidazolio se prepararon mediante métodos sencillos, comparados con los de fuentes bibliográficas. Se caracterizaron mediante IR, NMR, GC-MS y LC-MS. Los líquidos iónicos se emplearon como agentes de lixiviación en el tratamiento de una escoria industrial de cobre y cinc para la recuperación de dichos metales. Los resultados mostraron que todos los nuevos líquidos iónicos sintetizados cumplen con las especificaciones estándar de un líquido iónico. Las tasas de recuperación de metales disminuyen con el tiempo, excepto para la disolución de zinc en trifluoroacetato de 1,3-dibencilimidazolio. El trifluoroacetato de 1,3-dibencilimidazolio, cuando se compara con otros, es un agente de lixiviación más eficaz para el tratamiento de escorias de latón. Las tasas de recuperación de metales logradas con este líquido iónico son 62,58% para el zinc y 24,95% para el cobre.
The Allostery Model of TCR Regulation
Authors: Schamel Wolfgang W. A. , Alarcon Balbino , Höfer Thomas , Minguet Susana
Published: December 2016

The activity of the αβ TCR is controlled by conformational switches. In the resting conformation, the TCR is not phosphorylated and is inactive. Binding of multivalent peptide-MHC to the TCR stabilizes the active conformation, leading to TCR signaling. These two conformations allow the TCRs to be allosterically regulated. We review recent data on heterotropic allostery where peptide-MHC and membrane cholesterol serve opposing functions as positive and negative allosteric regulators, respectively. In resting T cells cholesterol keeps TCRs in the resting conformation that otherwise would become spontaneously active. This regulation is well described by the classical Monod-Wyman-Changeux model of allostery. Moreover, the observation that TCRs assemble into nanoclusters might allow for homotropic allostery, in which individual TCRs could positively cooperate and thus enhance the sensitivity of T cell activation. This new view of TCR regulation will contribute to a better understanding of TCR functioning.
Successful treatment of refractory adult onset Still’s disease with rituximab
Authors: Belfeki N. , Smiti Khanfir M. , Said F. , Hamzaoui A. , Ben Salem T. , Ben Ghorbel I. , Lamloum M. , Houman M.H.
Published: December 2016

Adult-onset Still’s disease (AOSD) is an uncommon inflammatory condition of unknown origin. In chronic disease, joint involvement is often predominant and erosions are noted in one third of patients. Therapeutic strategies derive from observational data. Corticosteroids are usually the first-line treatment. With inadequate response to corticosteroids, methotrexate appears the best choice to control disease activity and allow for tapering of steroid use. For refractory disease, biological therapy seems the most promising. We report here the case of a 38-year-old female patient with AOSD refractory to cytotoxic agents, treated by rituximab infusion therapy with favorable outcome.
B cell autoimmunity and bone damage in rheumatoid arthritis
Authors: Bugatti S. , Bogliolo L. , Montecucco C. , Manzo A.
Published: December 2016

Rheumatoid arthritis (RA) is a chronic immune-inflammatory disease associated with significant bone damage. Pathological bone remodeling in RA is primarily driven by persistent inflammation. Indeed, pro-inflammatory cytokines stimulate the differentiation of bone-resorbing osteoclasts and, in parallel, suppress osteoblast function, resulting in net loss of bone. Abating disease activity thus remains the major goal of any treatment strategy in patients with RA. Autoantibody-positive patients, however, often show a rapidly progressive destructive course of the disease, disproportionate to the level of inflammation. The epidemiological association between RA-specific autoantibodies, in particular anti-citrullinated protein autoantibodies, and poor structural outcomes has recently found mechanistic explanation in the multiple roles that B cells play in bone remodeling. In this review, we will summarize the substantial progress that has been made in deciphering how B cells and autoantibodies negatively impact on bone in the course of RA, through both inflammation-dependent and independent mechanisms.
Theorems on polynomials in right invertible operators
Authors: Przeworska-Rolewicz Danuta
Published: December 2016

Suppose that

Q(D)

is a polynomial in a right invertible operator acting in a linear space

X

, in general, with operator coefficients. Then

Q(D) = 0

if and only if

Q(D) R^kz = 0

for all

z \in \mathrm {ker} \: D (k = 0, 1, 2, \dots)

under appropriate assumptions on

X

, the right inverse

R

of

D

and coefficients of

Q(D)

.
Fredholmness and finite section method for Toeplitz operators in $l^p (Z_+ \times Z_+)$ with piecewise continuous symbols II
Authors: Böttcher Albrecht
Published: December 2016

In this paper we prove sufficient conditions for Fredholmness of discrete Toeplitz operators with piecewise continuous symbols on the space

l^p

over the quarter-plane and for the applicability of the finite section method to such operators. The methods used here are based on a bilocalization technique and the local principle of Douglas and Krupnik. Part I of this work contained the proofs of the necessity of the corresponding conditions, the necessary definitions, and the formulation of the main results.
The Laguerre Transform of some Elementary Functions
Authors: Glaeske Hans-Jürgen , Maričev Oleg I.
Published: December 2016

This paper deals with the calculation of the generalized Laguerre transformation of a class of functions, which often appear in applications. The result is used for the derivation of the solution of an ordinary differential equation.
Zur Vollständigkeit des Systems der Eigenfunktionen irregulärer Eigenwertprobleme mit $\lambda$-abhängigen Randbedingungen
Authors: Freiling Gerhard
Published: December 2016

We show that the system of eigen- and associated functions of the eigenvalue problem

y^{(n)} + \sum \limits^{n}_{v=2} p_v (x) y^{(n-v)}) = \lambda y \quad 0 \leq x \leq 1,

U_v (y, \lambda) = 0, \quad 1 \leq v \leq n,

with irregular two-point boundary conditions depending on

\lambda

is complete in

L_2[0,1]

.
Parabolische Regularisierung einer hyperbolischen Itogleichung
Authors: Grecksch Wilfried
Published: December 2016

The solution of the first boundary value problem of a random hyperbolic equation is approximated by a method of the parabolic regularization. Considered an application of this method to the development of a maximum principle and to the existence of the

\epsilon

-optimal controls of an optimal control problem of a random hyperbolic equation.
Konforminvarianten vom Gewicht –1 elnes Zusammenhanges oder Eichfeldes
Authors: Schimming Rainer
Published: December 2016

A connection or a gauge field in a vector bundle over a riemannian manifold is introduced by means of some given Laplace-like operator. Applying new results of P. Günther and V. Wünsch we construct a sequence of conformal invariants of weight –1 for a gauge field. These are relevant e.g. in the theory of Huygens’ principle. We calculate the relative conformal invariants for some examples; especially they vanish for any instanton gauge field.
Toeplitz determinants with piecewise continuous generating function
Authors: Böttcher Albrecht
Published: December 2016

Consequent application of the theory of operator determinants and a special technique of perturbing by trace class operators allow to determine the asymptotic behavior of the Toepiitz determinants

D_n(a) = \mathrm {det} \: \{a_{j-k}\}^n_{j,k-0} (n \to \infty)

, if the generating function

a(t) = \sum^{\infty}_{k=-\infty}a_k t^k (|t| = 1)

is piecewise continuous and satisfies some natural conditions of regularity. There holds

D_n(a) \sim G^{n+1} \cdot E \cdot n^{-\sum^R_{r=1} \beta_r^2} (n \to \infty)

, where

\beta_r= \frac{1}{2 \pi i}

log

a(t_r-0)/a(t_r + 0)

, |Re

\beta_r

| < 1/2 with

t_1, \dots, t_R

being the points of discontinuity of

a(t)

; thereby the constants

G

and

B

are explicitely given.
Über Nullräume, Wertebereiche und Relationen von Operatoren, die bei instationären IterationsverIahren zur Lösung linearer Gleichungen auftreten
Authors: Schott Dieter , Peters Wolfgang
Published: December 2016

Iteration methods of the form

x_{n+1} = (I - D_nA) x_n + D_nb = P_nx_0 + B_nb

are considered to obtain solutions or generalized solutions of the linear equation

Ax = b

. Thereby the residues

r_n = b - Ax_n

satisfy the iteration procedure

r_{n+1} = (I - AD_n) r_n = Q_nr_0.

The existence of

B_{\infty} = \mathrm {lim}_{n \to \infty} B_n

already guarantees the existence of the remaining limits

P_{\infty}, Q_{\infty}, x_{\infty}

and

r_{\infty}

. Conditions are given, under which

B_{\infty}

exists and possesses certain additional properties. These conditions are expressed on the one hand by operator equations and on the other hand by relations between null spaces and ranges of operators. The results are applied to two classes of iteration methods.
Some local and nonlocal boundary value problems for hyperbolic equations (in Russian)
Authors: Aldashev S.A.
Published: December 2016

The paper deals with local and nonlocal boundary value problems for hyperbolic equations, which generalize the Darboux, Goursat and Cauchy problems. Under certain conditions on the given functions the correctness of these problems is proved, in other cases the uniqueness of the solution is proved and theorems of uniqueness of the solution in a more wide class of functions are stated. In the paper examples are given, showing the non-stability of the solution if some of the conditions on the boundary data are violated.
Riemannian Manifolds for which a Power of the Radius is $k$-harmonic
Authors: Schimming Rainer
Published: December 2016

Let

\sigma = \sigma (x, y)

denote Synge’s function of a Riemannian manifold

(M, g)

of any signature and consider the condition that some power of

\sigma

or the logarithm of

\sigma

is

k

-harmonic. Then in many, cases

(M, g)

turns out to be flat. Certain classes of non-flat manifolds can be characterized just by a condition of the aforesaid typo.
A Necessary and Sufficient Discreteness Condition for the Spectrum of a two Term Differential Operator of Higher Order
Authors: Müller-Pfeiffer Erich , Werler St.
Published: December 2016

Self-adjoint differential operators of order

2n

are considered that are associated with the expression

\mathcal A \equiv w^{-1} [(—1)^n (py^{(n)})^{(n)} + qy]

and the weighted Hilbert space

L_{2, w}(0, \infty)

. By use of discreteness conditions for the spectrum of such operators given by Kwong and Zettl a necessary and sufficient condition for the discreteness of the spectrum is established.
Vergleichende Betrachtungen zur Bestimmung des asymptotischen Verhaltens mehrdimensionaler Laplace-Gauss-Integrale
Authors: Birndt Hartmut , Richter Wolf-Dieter
Published: December 2016

The asymptotic behaviour of the Gaussian measure is investigated for some Borel sets in which one is interested in the theory of probabilities of large deviations and the distance of which from the origin tends to infinity. To that end, various methods for studying Laplace-Gauss integrals are compared. Some new assertions are illustrated by many examples.
Asymptotische Darstellungen der hypergeometrischen Funktionen für grosse Werte eines Parameters
Authors: Wagner Eberhard
Published: December 2016

Asymptotic expansions of the hypergeometric function

F(a, b, c; z)

for

|b| \to \infty

where

a, c, z

are fixed complex numbers given in well-known tables (e.g. Bateman/Erdélyi: Higher transcendental functions I. New York 1953) are incorrect. In the present paper asymptotic representations of the hypergeomctric function

F

for

a

(complex)

\to \infty

are derived where

b, c (c \neq 0, -1, -2,\dots)

and

z (z \neq 0

, |Arg

(1- z) | < \pi

are fixed complex numbers. By change of

a

and

b

appropriate asymptotic representations of

F

for

|b| \to \infty

are obtained.
A Class of Nonlinear Singular Integral and Integro-differential Equations with Hilbert Kernel
Authors: von Wolfersdorf Lothar
Published: December 2016

By means of a novel application of Schauder’s fixed point theorem, existence theorems are proved for a class of quasilinear singular integro-differential equations and a related class of nonlinear singular integral equations.
Weighted Inequalities for Vector-Valued Anisotropic Maximal Functions
Authors: Kokilashvili Vakhtang , Rákosník Jiří
Published: December 2016

The anisotropic maximal function is defined by means of one-parametric parallelepipeds instead of cubes. For vector-valued anisotropic maximal functions there are proved weak and strong type weighted inequalities. The strong type inequality is then utilised in the proof of an anisotropic weighted mixed norm maximal inequality.
Generalized Resolvents of an lsometric Operator in a Pontrjagin Space
Authors: Sorjonen Pekka
Published: December 2016

In this paper the contractive and generalized resolvents of an isometric operator in a Pontrjagin-space are studied. Especially, the domain of the operator is allowed to be degenerate. The resulting formulae are analogous to the nondegenerate case, but the values of the characterising parameter are now linear relations instead of linear operators.
On Strong Unboundedness of Symmetric Operators
Authors: Friedrich Jürgen
Published: December 2016

It will be shown that for each positive odd integer

n

there is a symmetric operator

\mathcal T

in a separable Hilbert space

\mathcal H

such that

\mathcal T, \mathcal T^3, \dots, \mathcal T^n

are unbounded from below and

\mathcal T^k \geq 0

for

k>n

.
Hypercomplex Factorization of the Helmholtz Equation
Authors: Gürlebeck Klaus
Published: December 2016

The main result of this paper is the construction of a global hypercomplex factorization of the Dirichiet problem for the Helmholtz equation. This result permits the reduction of the considered boundary value problem into two boundary value problems of first order for generalized analytic functions.
Eine Definition des Kroneckerindexes im $\mathbb R^{n+1}$ mit Hilfe der Cliffordanalysis
Authors: Habetha Klaus
Published: December 2016

An index for an

n

-dimensional closed and bounded manifold

M

in

\mathbb R^{n+1}

will be defined with the help of Clifford analysis and it will be proved, that it is an entire number in every component of the complement of

M

.
Generalized-Analytic Coverings in the Spectrum of a Uniform Algebra
Authors: Tonev Toma V.
Published: December 2016

We examine some conditions under which certain parts of a uniform algebra spectrum admit special structures so that Gelfand transforms of algebra elements are generalized-analytic functions.
On Entropy-Like Invariants for Dynamical Systems
Authors: de Paly Thomas
Published: December 2016

This paper transfers the theory of the Kolmogorov-Sinai-entropy a method which is a basic tool in the theory of the order-structure of states. The function

h(x) = —x

log

z

is replaced by arbitrary bounded, concave functions in all definitions of the entropy-theory. This procedure leads to a class of isomorphy invariants, thus generalizing the notion of dynamical entropy. The general properties of the generalized dynamical entropies are investigated and an explicit calculation of the new invariants is accomplished on some simple cases.
Boundedness of Anisotropic Pseudo-Differential Operators in Function Spaces of Besov–Hardy–Sobolev Type
Authors: Leopold Hans-Gerd
Published: December 2016

This paper is concerned with pseudo-differential operators in the anisotropic function spaces of Besov-Hardy-Sobolev type

B^{\bar s}_{p,q}

and

F^{\bar s}_{p,q}

. An anisotropie generalization of the classical Hörmander class of pseudo-differential operators is introduced and a theorem about the boundedness of these anisotropic pseudo-differential operators in associated anisotropic function spaces is proved.
Zum Begriff der Analytizität auf zusammenhängenden Iokalkompakten Gruppen
Authors: Bauch Hans F.
Published: December 2016

Several definitions of analyticity of functions on locally compact groups are introduced and tested in connection with the proprties of the Fourier coefficients on a compact solenoid. It is proved that absolute convergence of the Fourier series does not follow from analyticity and that a rapidly decreasing sequence of Fourier coefficients of a function, which is analytic on a dense subset, need not exponentially rapidly decrease. On the other hand, on compact groups functions with exponentially rapidly decreasing Fourier coefficients are analytic.
Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras
Authors: Schmüdgen Konrad
Published: December 2016

Let

\mathcal D

be a dense linear subspace of a separable Hilbert space and let

\mathcal L^+(\mathcal D)

be the maximal Op*-algebra on

\mathcal D

endowed with the uniform topology

\tau_{\mathcal D}

. Suppose

\mathcal D

is a Frechet space with respect to the graph topology of

\mathcal L^+(\mathcal D)

. Let

\mathcal C (\mathcal D)

denote the two-sided *-ideal of all operators in

\mathcal L^+(\mathcal D)

which map bounded subsets of

\mathcal D

into relatively compact subsets. We study the question of when the quotient algebra

\mathcal A (\mathcal D) \colon = \mathcal L^+(\mathcal D) / \mathcal C (\mathcal D)

, endowed with the quotient topology, has a topological realization as an Op*-algebra.
Der Satz von Cauchy–Kowalewski für hyperanalytische Funktionen
Authors: Begehr Heinrich
Published: December 2016

The theorem of Cauchy–Kowalewski is formulated for a class of hyperanalytic functions of several variables. For a nonlinear equation without a Lipschitz condition an existence theorem is given.
Solution of the Dirichlet problem in a domain with a boundary containing a rounded corner (in Russian)
Authors: Vlasov V. I. , Volkov D. B. , Prudnikov A. P.
Published: December 2016

The Dirichlet problem for the Laplace equation in a circle with a notch with rounded corner is considered; the solution is found in a form that allows differentiation of any order in the domain and at the contour of the rounded-off notch. Numerical results and their analysis are presented.
On some parabolic boundary control problems with constraints on the control and functional-constraints on the state
Authors: Tröltzsch Fredi
Published: December 2016

In this paper parabolic boundary control problems in a

n

-dimensional bounded domain are investigated, where in addition to a pointwise constraint on the control finitely many linear functional constraints on the state are given. As performance functional the

L_{\infty}

- or

L_2

-norm of the difference between the final state and a given (desired) state is used.

A generalized bang-bang-principle is proved which expresses that under natural assumptions almost everywhere (with respect to the time) either the optimal control or the corresponding state is acting on the boundary of its constraints. The assumptions are discussed by examples.
Some Recent Developments in the Theory of Nonlinear Singular Integral Equations
Authors: von Wolfersdorf Lothar
Published: December 2016

We report on some recent investigations by Soviet mathematicians and the author about nonlinear singular integral and integro-differential equations of Cauchy and Hilbert type involving large nonlinearities.
Lokale Darstellungen differenzierbarer Funktionen auf Banachräumen
Authors: Tu N.A.
Published: December 2016

Local topological properties of differentiable functions on Banach spaces are studied. It will be shown that in the neighborhood of a nondegenerate critial point

p

a certain

C^2

-function f can be written in the following form:

f(x) = \alpha (\lambda) + f(p) – \sum^q_{i=1} \alpha_i^2 + \sum^m_{i=q+1} \alpha^2_i

where

m

is the dimension of some

m

-dimensional subspace, the real numbers

\alpha_1, \dots, \alpha_m

are determined by a basis of this subspace and

\alpha (\lambda

) is given by a function

\lambda

. The dimension

m

can tend to

\infty

, while the number

q

does not change.
Starke Dualität bei verallgemeinerten Steuerproblemen
Authors: Pickenhain Sabine
Published: December 2016

In this paper a generalized parametric variational problem with restrictions on the state domain and the control is considered and its dual problem constructed. Under weak assumptions, strong duality is shown between the primary and the dual problem.
Automorphismen auf Produkten Boolescher Algebren
Authors: Senf Peter , Vladimirov Denis  A.
Published: December 2016

Two different products of Boolean algebras are considered. The Boolean product is compatible with the topological interpretation of Boolean algebras but not always convenient for the theory of Boolean algebras with measure. The product of second kind is suitable for the aim of this theory.
On the Convergence of Some Random Series
Authors: Mikosch Thomas
Published: December 2016

Let

\{ X_n \}

be a sequence of independent random elements with values in a separable Banach space,

S_n = X_1 + \cdots + X_n

and

\{a_n\}

a sequence of nonnegative numbers. There is proved a criterion for the almost sure convergence of the series

\sum a_nS_n

. The special case

a_n = n^{–\alpha}, \alpha > 0

is also studied.
Globale Existenz und Eindeutigkeit starker Lösungen für ein Gleichungssystem, das den Ladungstransport in einem Halbleiter beschreibt
Authors: Heinrich Jörg
Published: December 2016

Global existence of strong solutions is shown for a system of differential equations describing carrier transport in semiconductors which up to now has only been known to have weak solutions. At first the proof of existence is carried out for a "small" interval of the time-axis with the help of several imbedding theorems and Banach’s fixed point theorem and then is extended to an arbitrary interval. At last further smoothness properties of the solution are discussed under spezial conditions for initial and boundary values.
Über Gleichungen vom gemischt-zusammengesetzten Typ
Authors: Müller-Rettkowski Andreas
Published: December 2016

Boundary value problems for partial differential equations of the third order of mixed-composite type are studied. In the first part linear equations are investigated, in the second part nonlinear equations.
On a Class of Quasi-Linear Riemann-Hilbert Problems
Authors: Wegert Elias , von Wolfersdorf Lothar
Published: December 2016

The existence of a solution of a class of quasi-linear Riemann-Hilbert problems for a holomorphic function is proved.
Translationshomogene statistische Lösungen dér Navier–Stokesschen Gleichungen in einem dreidimensionalen Kanalgebiet
Authors: Krause Bernd
Published: December 2016

Homogeneous space-time statistical solutions of the Navier-Stokes equations in a three-dimensional channel are studied which are based on given homogeneous initial measure. The individual solution of the Navier-Stokes equations is approximated by a periodical Galerkin-ansatz which satisfies the boundary conditions at the walls of the channel. Suitable a priori estimates and an approximation of the initial measure allow the limit process and ensure the existence of homogeneous statistical solutions of the Navier-Stokes equations by Prochorov’s theorem.
A General Random Fixed Point Theorem for Upper Semicontinuous Multivalued 1-Set-Contractions
Authors: Hahn Siegfried
Published: December 2016

A random fixed point theorem of Leray-Schauder type for multivalued upper semicontinuous 1-set-contractions is proved. The domains are allowed to be random. The result generalizes several random fixed point theorems and implies a stochastic version of a fixed point theorem of Petryshyn for multivalued mappings.
Nonuniform Conditions for Periodic Solutions of Forced Liénard Systems with Distinct Delays
Authors: Conti Giuseppe , Iannacci R. , Nkashama M.N.
Published: December 2016

We use classical Leray-Schauder techniques and the coincidence degree in order to obtain the existence or periodic solutions of forced Liénard systems with distinct delays, under nonuniform conditions. The resonance and nonresonance case with respect to the eigenvalue zero are considered.
Die Grundgleichungen der inneren Elektronik - ein Evolutionsproblem im Banach-Raum
Authors: Angermann Lutz
Published: December 2016

The basic equations of inner electronics are investigated as a differential equation with special structure in a suitable Banach space. Existence, uniqueness, regularity and physical relevance of the solution are proved.
Universale Rettungskurven II
Authors: Klötzler Rolf , Pickenhain Sabine
Published: December 2016

It is proved, that the optimal live-saving line, founded in Part I under special structural assumptions, is also optimal without these assumptions.
On Certain Higher Order Riccati-Type Operator Equations with Possibly Unbounded Operator Coefficients
Authors: Mazumdar Tapas
Published: December 2016

Let

\mathcal H

and

\mathcal V^1

be complex Hilbert spaces, with

\mathcal V^1

topologically included in

\mathcal H

, and

\mathcal V^2

a complex pre-Hilbert space. There is considered the existence of a solution

X = X_Q \in \mathcal L (\mathcal V^2, \mathcal V^1)

of the operator equation

A_1XA_2 — B_1XB_2 +XDX + XEXFX = Q

in the space of (bounded or not) linear operators in

\mathcal H

under the data

A_1, B_1 \in \mathcal L (\mathcal V^1, \mathcal H), D, E, F \in \mathcal L (\mathcal V^1, \mathcal V^2); A_2, B_2: \mathcal V^2 \to \mathcal V^2

linear and

Q \in \mathcal L (\mathcal V^2, \mathcal H)

one-dimensional. Under some hypotheses, an iterative analytic metiod to arrive at the existence of such a solution is given. Two examples are given.
Über zwei spezielle inverse Probleme der Potentialtheorie
Authors: Günther Matthias
Published: December 2016

The problem to determine the shape of a solid body is treated if the density and the values of its Newtonian potential or the gradient of the latter on the surface are known. The considerations have a local character, i.e. the unknown body is situated in a neighbourhood of a known initial configuration. In the existence proofs the inverse function theorem is used as well as estimations for potentials of variable domains.
Ein Oszillationskriterum
Authors: Morgenthal Klaus
Published: December 2016

An oscillation theorem for the equation

x’(t) = \int^\infty_{\tau=0} x(t—\tau) dr (t, \tau) \;\;\; (\infty < A ≤ t < \infty)

is proved, which generalizes an earlier result of the author and a criterion of B. R. Hunt and J. A. Yorke.
Die Bevorzugung hexagonaler Strukturen bei symmetrischen Oberflächenformen magnetischer Flüssigkeiten
Authors: Quasthoff Karin
Published: December 2016

A magnetic ideal fluid under the influence of a vertical homogeneous magnetic field is considered. Over rhombic lattices with arbitrary angle equilibrium configurations of the free surface are determined. Especially, for some lattice length

l_c

the bifurcation equations are solved and over regular hexagonal lattices with lattice length

I > l_c

solutions of the bifurcation equations are given. The regular hexagonal structures, in an interval depending on physical parameters, have smallest energy.
A Class of Nonlinear Generalized Riemann-Hilbert-Poincaré Problems for Holomorphic Functions
Authors: von Wolfersdorf Lothar
Published: December 2016

By means of the theory of pseudo-monotone operators the existence of a solution of a class of nonlinear generalized Riemann-Hilbert-Poincaré problems for a holomorphic function in the unit disk is proved.
Stabilitätskriterien für Näherungsverfahren bei singulären Integralgleichungen in $L^p$
Authors: Prössdorf Siegfried , Rathsfeld A.
Published: December 2016

Approximation methods for one-dimensional singular integral equations with piecewise continuous coefficients on simple closed Liapunov curves are considered. For spline Calerkin methods and for spline and trigonometric collocation, necessary and sufficient conditions for their stability in

L^p

are given. The central idea is a general stability criterion for sequences of approximate operators with circulant structure.
Dissipativität und globale Stabilität des komplexen Lorenz-Systems
Authors: Leonov G.A. , Reitmann Volker
Published: December 2016

Using Liapunov functions it is shown that the complex Lorenz-System is dissipative and has a global asymptotic for some parameters.
On a Singular Part of an Unbounded Operator
Authors: Ôta Schôichi
Published: December 2016

The singularity of an operator in a Hilbert space is studied.
The Conditional Lindeberg–Trotter Operator in the Resolution of Limit Theorems with Rates for Dependent Random Variables. Applications to Markovian Processes
Authors: Butzer Paul  L. , Kirschfink Heribert
Published: December 2016

Making use of the properties of conditional expectations, a conditional Lindeberg–Trotter-operator is defined which extends the properties of the classical Lindeberg–Trotter operator to the case of dependent random variables. This approach enables one to establish general limit theorems equipped with little-

\mathcal o

and large-

\mathcal O

rates for sums of dependent random variables; these are applied to several versions of the central limit theorem, the weak law of large numbers, and especially to Markovian processes, not only in the case of weak convergence in distribution but partially also for strong convergence.
A Free Boundary Value Problem Modeling Thermal Oxidation of Silicon
Authors: Gröger K. , Strecker N.
Published: December 2016

Using results on evolution equations in Hilbert spaces a problem describing the diffusion of an oxidant through an oxide layer and the growth of this layer caused by the oxidation of silicon is solved. Moreover, estimates for the growth of the thickness of the oxide layer being of practical interest are given.
Bifurcation values of the parameters in a problem on forced oscillations in control systems with delays (in Russian)
Authors: Petrov D.I.
Published: December 2016

An equation describing the dynamic of systems for control with delay is considered. Using general theorems of nonlinear analysis sufficient conditions are obtained for existence of regular asymptotic point of bifurcation in the problems for forced

T

-periodic and for positive

T

-periodic solutions.
Stekloffsche Eigenwerte und konforme Abbildungen
Authors: Dittmar Bodo
Published: December 2016

New isoperimetric inequalities between Stekloff eigenvalues and function theoretic quantities in simply and multiply connected domains are derived. They sharpen on the one hand well-known isoperimetric inequalities in some cases and given on the other hand both-sided estimates for function theoretic quantities. In the simply connected case both-sided estimates for Stekloff eigenvalues are given based on a general monotonicity principle.
CIarkson's InequaIities, Besoy Spaces and Triebel–Sobolev Spaces
Authors: Cobos Fernando , Edmunds David E.
Published: December 2016

It is shown that Clarkson’s inequalities also hold in some Besov spaces

B^s_{p,q}

and Triebel–Sobolev spaces

F^s_{p,q}

.
On the Nonlinear Boltzmann Equation of the Carrier Transport in Semiconductors I: Existence and Uniqueness of Solutions
Authors: Hanke Michael
Published: December 2016

There are proved propositions on the existence and uniquenessof solutions of a steady-state, spatially homogeneous nonlinear Boltzmann equation which describes the charge carrier transport in semiconductors. In contrast to more known kinds of the Boltzmann equation (e.g. in radiation transfer theory), the form in question contains

\delta

-functions in the collision integral. Therefore, smooth functions are transformed by the collision operator into discontinuous ones in general. The precise investigation of the properties of the operators describing the Boltzmann equation leads to the construction of suitable aisisotropic Sobolev spaces, in which existence and uniqueness of solutions can be shown.
Solvability of Boundary Value Problems for the Inclusion $u_{tt} - u_{zz} \in g(t, x, u)$ via the Theory of Multi-Valued A-Proper Maps
Authors: Kaszynski Tomasz , Krawcewicz Wieslaw
Published: December 2016

The existence of a coincidence point

x

for the inclusion

Lx \in \Gamma(x)

is studied where

L: D(L) \subset E \to F

is a linear hyperbolic operator and

\Gamma : E \to 2^F

is a convex-valued map. It is shown that any such monotone demi-continuous map

\Gamma

is weakly

A

-proper. Some existence theorems for (

\ast

) are established and the reults are applicated to a boundary value problem for the inclusion

u_{tt} - u_{zz} \in g(t, x, u)

.
Necessary Optimality Conditions for Nonsmooth Problems with Operator Constraints
Authors: Scheffler H.-P. , Schirotzek W.
Published: December 2016

For nonsmooth operators, different kinds of approximations are introduced and their relationships are studied. With the aid of these approximations, F. John and Karush–Kuhn–Tucker conditions are established for optimization problems with operator inequality contraints.
Zur Interpretation von Meßergebnissen
Authors: Anger G.
Published: December 2016

In principle each applied problem in science, technology and medicine is an inverse problem. It is the only complete way of analyzing experimental results. Many parameters, such as, for example, gravity can be determined very accurately. On the other hand, there is almost a complete lack of a theory which would allow the determination of individual coefficients or the source term of a differential equation from measured data. The author’s experiences made in inverse problems of differential equations are the following: it is exceptional that an inverse problem can be uniquely solved by additional information on the boundary of a given domain. In general one can study the set of all solutions of an inveise problem as a first step. In a laboratory one can attempt to select a solution which is of interest in applications. There are relations to Cantor’s Continuum Hypothesis.
Zur Entwicklung von Randintegralgleichungen für eine Aufgabenklasse der mathematischen Physik
Authors: Gründemann H.
Published: December 2016

Based upon basic equations of continuum theory for a scope of mechanical problems a unified boundary value problem is derived. A general boundary integral solution procedure for this problem is presented. Special emphasis is taken to computational aspects of fundamental solutions.
Gleichmässige asymptotische Darstellungen für Parameterintegrale mit zwei reellen Parametern
Authors: Schell Hans-Joachim
Published: December 2016

Several asymptotic approximations, valid uniformly on certain

\alpha

-intervals, are obtained for a class of integrals depending on two real parameters s and

\alpha

, where

s

tends to

s_0

. Two cases are considered: a) the integrand has a simple maximum interior to the interval of integration, b) the interval of integration contains no stationary point. In both cases the results still hold true if the stationary point coalesces with the lower limit of integration.
Error Estimates for the Explicit Finite Difference Method Solving the Stefan Problem
Authors: Streit Uwe
Published: December 2016

The paper deals with a well-known finite difference method for solving the one-dimensional two-phase Stefan problem. Under assumptions on the data which assure a regularity

u \in W_2^{1,1} (\Omega_T) \cap L_{infty} (0, T; W_2^1 (\Omega)) \:\: \mathrm {and} \: s \in W_4^1 (0, T)

of the temperature

u

and the moving boundary

s L_2

-convergence rates

O(h)

for the approximations of

u

and

s

are derived. Additionally, a case of much weaker regularity is considered.
On Besov Spaces of Variable Order of Differentiation
Authors: Leopold Hans-Gerd
Published: December 2016

This paper is concerned with function spaces of variable order of differentiation defined on the

n

-dimensional Euclidean space. The definition of these spaces is closely connected with an appropriate class of pseudodifferential operators.
A Geometric Maximum Principle for Surfaces of Prescribed Mean Curvature in Riemannian Manifolds
Authors: Dierkes Ulrich
Published: December 2016

Let

M

be a three-dimensional Riemannian manifold and let

f

be some surface of prescribed mean curvature which is restricted to lie in some set

J \cup S \subset M

with boundary

S

of bounded mean curvature

\mathfrak H

. Assuming natural conditions, we prove that the image of

f

lies completely in

J

. An immediate consequence of this result is a sufficient condition for the existence of minimal surfaces in a set

J \subset \mathbb R^3

, the boundary

S

of which is not

\mathfrak h

-convex.
Traces of Anisotropic Sobolev Spaces with Mixed $L_p$-Norms on Hyperplanes
Authors: Malarski Mircea
Published: December 2016

We outline a new short proof of a known trace theorem for anisotropic Sobolev spices with mixed

L_p

-norms based on methods of interpolation theory.
On the Behaviour of the Distributional Stieltjes Transformation at the Origin
Authors: Pilipović Stevan
Published: December 2016

The behaviour of the distributional Stieltjes transformation at the origin 0 is investigated for distributions of

\mathcal S'_+

having appropriate quasiasymptotic behaviour at

0^+

. These new results follow by known ones for the asymptotic behaviour at

\infty

. A Tauberian-type result for the behaviour at 0 is also obtained.
Faktorisierung eines Differentialoperators unendlicher Ordnung in verallgemeinerten Ableitungen
Authors: Timofeev Alexej
Published: December 2016

The problem of factorization is solved for the differential operator, originally presented by A. F. Leontjev in 1965 and generalizing the operator by Gelfond-Leontjev.
A. Symbol Calculus for the Algebra Generated by Shift Operators
Authors: Roch Steffen , Silbermann Bernd
Published: December 2016

We describe the algebraical structure of the algebra generated by the shift operator and by one of its left-inverses and construct a symbol for the invertibility of an operator modulo the quasicommutator ideal. The correspondence between this symbol and the invertibility and Fredholmness of elements of this algebra are studied.
Über ein Bimetallproblem in der Ebene
Authors: Jentsch Lothar
Published: December 2016

Existence and uniqueness theorems for boundary-contact-problems of plane elastostatics and thermoelastostatics are given in a proper class of regularity, when the thermoelastic constants are piecewise constant and discontinuous along a straight line. The problem is reduced with the aid of the contact-tensor of elastostatics for two composite half-planes to a system of integral equations with fixed singularities. From the theory of Duduchava it follows, that the integral operator is Noetherian in the space

L_2(S)

(

S

boundary of the disc) with index zero.
The Coupling of Boundary Element and Finite Element Methods for a Nonlinear Exterior Boundary Value Problem
Authors: Gatica Gabriel N. , Hsiao George C.
Published: December 2016

This paper is concerned with an application of the coupling of the boundary element and the finite element methods to an exterior Dirichlet problem for a class of nonlinear second-order elliptic equations in divergence form. Emphasis will be placed upon the variational formulation and the mathematical foundations of the coupling procedure. In particular, sufficient conditions are given for the coefficients of the equation from which existence and uniqueness results are established by the theory of monotone operators.
Variationscharakterisierungen für gewisse quasikonforme Abbildungen
Authors: Hoy Erich
Published: December 2016

The paper deals with the construction of solutions

f

for the equation

f_{\bar z} (z) = v(z) \overline {f_z(z)}

with

v(z) = 0

in a neighbourhood of

\infty

. In the paper two variational methods are described. The first method characterizes

f

for a bounded and measurable function

v (0 \leq v(z) \leq q = \mathrm {const} < 1

. If

v

is a piecewise constant function, then there exists also a simpler characterization of

f

.
The Volume Problem for Pseudo-Riemannian Manifolds
Authors: Schimming Rainer , Matel-Kaminska Donata
Published: December 2016

We pose the volume problem for pseudo-Riemannian manifolds and present first results on it: certain geometric properties are read from the volume of small truncated light cones.