A trust-region approach with novel filter adaptive radius for system of nonlinear equations

This work introduces a version of filter technique to produce an adaptive radius and then adds it into trust-region algorithm. This method uses advantages of the functions norm’s necessary information in order to produce a smaller radius of trust-region close to the optimizer and also a larger radius of trust-region far away from the optimizer using advantages of the filter technique (Fatemi and Mahdavi-Amiri, Comput. Optim. Appl. 52(1), 239–266 2012). Under some ordinary conditions, the global convergence of the proposed approach is proved. Numerical results are also presented.     

A numerical solution of a two-dimensional IHCP

In this paper, we will first study the existence and uniqueness of the solution of a two-dimensional inverse heat conduction problem (IHCP) which is severely ill-posed, i.e., the solution does not depend continuously on the data. We propose a stable numerical approach based on the finite-difference method and the least-squares scheme to solve this problem in the presence of noisy data. We prove the convergence of the numerical solution, then to regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization 0th, 1st and 2nd method to obtain the stable numerical approximation to the solution. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method.     

On Some Properties of $c$-Frames

In this paper we discuss about $c$-frames, namely continuous frames. Since, $c$-frames are generalizations of discrete frames, we generalize some results of discrete frames to continuous version. We explain some results about relations of projections in Hilbert spaces and $c$-frames to characterize these frames. Also, we will specify (precisely) the synthesis and frame operators of Bochner integrable $c$-frames. Finally, we classify Hilbert-Schmidt operators by $c$-frames and express some new identities for Parseval $c$-frames.     

Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2?) with respect to non-homogeneous term g(x) ∈ L ₂ ^n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H _2,0 ^1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem.     

VIBRATION ANALYSIS OF A BEAM WITH EMBEDDED SHAPE MEMORY ALLOY WIRES

In this study, analytical relations for evaluating the exact solution of natural fre- quency and mode shape of beams with embedded shape memory alloy （SMA） wires are presented. Beams are modeled according to Euler-Bernoulli, Timoshenko and third order beam （Reddy） the- ories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities~ the effect of different me- chanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.     

Dual-Mode Sorption of Inorganic Acids in Polybenzimidazole (PBI) Membrane

The sorption behaviors of sulfuric, perchloric, and phosphoric acids in polybenzimidazole membranes have been investigated. The results of sorption isotherms are consistent with the general form of a dual-mode sorption isotherm. The dual-mode sorption parameters were found using a least-squares program by fitting experimental data to a dual-mode equation. Results indicate a correlation between permeant properties like acidity, size, and the affinity constant in Langmuir-mode sorption species. Moreover, the results show that the size of the permeants has the dominant effect on Henry's constant. The obtained results for , site saturation constant, in Langmuir-mode sorption in the case of perchloric and phosphoric acids, reveals that the two acid molecules interact with two N?H basic groups in the polybenzimidazole repeat units. But in the case of sulfuric acid, it is shown that sulfuric acid neutralizes some of the basic groups in the polymer by its strong second hydrogen and the obtained value for was 1.25.     

Exact Solution of Petrov Type {3,1} Metric via Time Dependent Quasi-Maxwell Equations

In this paper, we show that how to apply the time dependent quasi-Maxwell equations for exact solution of Einstein field equations in vacuum for Petrov type {3,1} metric.     

Neue Derivate der 2-Acylamino-thiophen-(und-benzo[b]thiophen-)-3-carbonsäure sowie des ([1]Benzo-)Thieno[2,3-d]-pyrimidin-4(3H)-ons

The title substances1 and2 were prepared by acylation of the corresponding ethyl 2-amino-thiophene- (or:-4,5,6,7-tetrahydro-benzo[b]thiophene)-3-carboxylates, in some cases followed by reactions introducing a basic substituent.Additionally a group of 2-aroylamino-thiophene-(or:-4,5,6,7-tetrahydro-benzo[b]thiophene)-3-carboxamides was subjected to ring closure reactions, yielding the corresponding 2-aryl-thieno[2,3-d]pyrimidin-4(3H)-ones and 2-aryl-[1]benzothieno[2,3-d]pyrimidin-4(3H)-ones (both:3).

---

---

Zum Teil unter Mitarbeit vonFerdinand Fuhrmann     

Development of a new fluorimetric bulk optode membrane based on 2,5-thiophenylbis(5-tert-butyl-1,3-benzexazole) for nickel(II) ions

A highly sensitive and selective fluorimetric optode membrane for the determination of ultra trace amounts of Ni²⁺ ions was prepared. The plasticized PVC-membrane incorporating potassium tetrakis(p-chlorophenyl)borate (KTpClPB) and 2,5-thiophenylbis(5-tert-butyl-1,3-benzexazole) (TTBB), as a highly fluorescent chromoionophore, displays a calibration response for Ni²⁺ ions over a wide concentration range of 1.0×10⁻³ to 1.0×10⁻⁸ M. It has a relatively fast response of <40 s. In addition to high stability and reproducibility, and relatively long working lifetime, the sensor possesses good selectivity for nickel ions over several common diverse ions. The fluorescence signal of the optode membrane can be easily recovered by immersion in EDTA solution. The optode was applied successfully to the determination of traces of Ni²⁺ ion in edible oil and a wastewater sample from nickel electroplating industries.