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[abridged] The class of water fountain nebulae is thought to represent the stage of the earliest onset of collimated bipolar outflows during the post-Asymptotic Giant Branch phase. They thus play a crucial role in the study of the formation of bipolar Planetary Nebulae (PNe). To date, 14 water fountain nebulae have been identified. The identification of more sources in this unique stage of stellar evolution will enable us to study the origin of bipolar PNe morphologies in more detail. We present the results of seven sources observed with the JVLA that were identified as water fountain candidates in an Effelsberg 100m telescope survey of 74 AGB and early post-AGB stars. We find that our sample of water fountain candidates displays strong variability in their 22 GHz H2O maser spectra. The JVLA observations show an extended bipolar H2O maser outflow for one source, the OH/IR star IRAS 18455+0448. This source was previously classified as a 'dying' OH/IR star based on the exponential decrease of its 1612 MHz OH maser and the lack of H2O masers. We therefore also re-observed the 1612, 1665, and 1667 MHz OH masers. We confirm that the 1612 MHz masers have not reappeared and find that the 1665/1667 MHz masers have decreased in strength by several orders of magnitude during the last decade. The OH/IR star IRAS 18455+0448 is confirmed to be a new addition to the class of water fountain nebulae. Its kinematic age is approximately 70 yr, but could be lower, depending on the distance and inclination. Previous observations indicate, with significant uncertainty, that IRAS 18455+0448 has a surprisingly low mass compared to available estimates for other water fountain nebulae. The available historical OH maser observations make IRAS 18455+0448 unique for the study of water fountain nebulae and the launch of post-AGB bipolar outflows..., Comment: 8 pages, 5 figures, accepted for publication in A&A (revised minor typos)

[abridged] The class of water fountain nebulae is thought to represent the stage of the earliest onset of collimated bipolar outflows during the post-Asymptotic Giant Branch phase. They thus play a crucial role in the study of the formation of bipolar Planetary Nebulae (PNe). To date, 14 water fountain nebulae have been identified. The identification of more sources in this unique stage of stellar evolution will enable us to study the origin of bipolar PNe morphologies in more detail. We present the results of seven sources observed with the JVLA that were identified as water fountain candidates in an Effelsberg 100m telescope survey of 74 AGB and early post-AGB stars. We find that our sample of water fountain candidates displays strong variability in their 22 GHz H2O maser spectra. The JVLA observations show an extended bipolar H2O maser outflow for one source, the OH/IR star IRAS 18455+0448. This source was previously classified as a 'dying' OH/IR star based on the exponential decrease of its 1612 MHz OH maser and the lack of H2O masers. We therefore also re-observed the 1612, 1665, and 1667 MHz OH masers. We confirm that the 1612 MHz masers have not reappeared and find that the 1665/1667 MHz masers have decreased in strength by several orders of magnitude during the last decade. The OH/IR star IRAS 18455+0448 is confirmed to be a new addition to the class of water fountain nebulae. Its kinematic age is approximately 70 yr, but could be lower, depending on the distance and inclination. Previous observations indicate, with significant uncertainty, that IRAS 18455+0448 has a surprisingly low mass compared to available estimates for other water fountain nebulae. The available historical OH maser observations make IRAS 18455+0448 unique for the study of water fountain nebulae and the launch of post-AGB bipolar outflows..., Comment: 8 pages, 5 figures, accepted for publication in A&A (revised minor typos)

We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples. © 2014 Elsevier Inc. All rights reserved.

We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples. © 2014 Elsevier Inc. All rights reserved.

We aim to detect the magnetic field and infer its properties around four AGB stars using H$_2$O maser observations. The sample we observed consists of the following sources: the semi-regular variable RT Vir and the Mira variables AP Lyn, IK Tau, and IRC+60370. We observed the 6$_{1,6}-5_{2,3}$ H$_2$O maser rotational transition, in full-polarization mode, to determine its linear and circular polarization. Based on the Zeeman effect, one can infer the properties of the magnetic field from the maser polarization analysis. We detected a total of 238 maser features, in three of the four observed sources. No masers were found toward AP Lyn. The observed masers are all located between 2.4 and 53.0 AU from the stars. Linear and circular polarization was found in 18 and 11 maser features, respectively. We more than doubled the number of AGB stars in which magnetic field has been detected from H$_2$O maser polarization, as our results confirm the presence of fields around IK Tau, RT Vir and IRC+60370. The strength of the field along the line of sight is found to be between 47 and 331 mG in the H$_2$O maser region. Extrapolating this result to the surface of the stars, assuming a toroidal field ($\propto$ r$^{-1}$), we find magnetic fields of 0.3-6.9 G on the stellar surfaces. If, instead of a toroidal field, we assume a poloidal field ($\propto$ r$^{-2}$), then the extrapolated magnetic field strength on the stellar surfaces are in the range between 2.2 and $\sim$115 G. Finally, if a dipole field ($\propto$ r$^{-3}$) is assumed, the field strength on the surface of the star is found to be between 15.8 and $\sim$1945 G. The magnetic energy of our sources is higher than the thermal and kinetic energy in the H$_2$O maser region of this class of objects. This leads us to conclude that, indeed, magnetic fields probably play an important role in shaping the outflows of evolved stars. (abridged), Comment: 15 pages, 5 figures, 7 tables. Accepted for publication in A&A

We aim to detect the magnetic field and infer its properties around four AGB stars using H$_2$O maser observations. The sample we observed consists of the following sources: the semi-regular variable RT Vir and the Mira variables AP Lyn, IK Tau, and IRC+60370. We observed the 6$_{1,6}-5_{2,3}$ H$_2$O maser rotational transition, in full-polarization mode, to determine its linear and circular polarization. Based on the Zeeman effect, one can infer the properties of the magnetic field from the maser polarization analysis. We detected a total of 238 maser features, in three of the four observed sources. No masers were found toward AP Lyn. The observed masers are all located between 2.4 and 53.0 AU from the stars. Linear and circular polarization was found in 18 and 11 maser features, respectively. We more than doubled the number of AGB stars in which magnetic field has been detected from H$_2$O maser polarization, as our results confirm the presence of fields around IK Tau, RT Vir and IRC+60370. The strength of the field along the line of sight is found to be between 47 and 331 mG in the H$_2$O maser region. Extrapolating this result to the surface of the stars, assuming a toroidal field ($\propto$ r$^{-1}$), we find magnetic fields of 0.3-6.9 G on the stellar surfaces. If, instead of a toroidal field, we assume a poloidal field ($\propto$ r$^{-2}$), then the extrapolated magnetic field strength on the stellar surfaces are in the range between 2.2 and $\sim$115 G. Finally, if a dipole field ($\propto$ r$^{-3}$) is assumed, the field strength on the surface of the star is found to be between 15.8 and $\sim$1945 G. The magnetic energy of our sources is higher than the thermal and kinetic energy in the H$_2$O maser region of this class of objects. This leads us to conclude that, indeed, magnetic fields probably play an important role in shaping the outflows of evolved stars. (abridged), Comment: 15 pages, 5 figures, 7 tables. Accepted for publication in A&A

Most of PNe are not spherical. The loss of spherical symmetry occurs somewhere between the AGB and PN phase. The cause of this change of morphology is not yet well known, but magnetic fields are one of the possible agents. Its origin remains to be determined, and potentially requires the presence of a massive companion to the AGB star. Therefore, further detections of the magnetic field around evolved stars (in particular those thought to be part of a binary system) are crucial to improve our understanding of the origin and role of magnetism on evolved stars. One such binaries is the pre-PN OH231.8, around which a magnetic field was detected in the OH maser region of the outer circumstellar envelope. We aim to detect and infer the properties of the magnetic field of this source in the water maser region. We observed the 6_{1,6}-5_{2,3} water maser rotational transition to determine its linear and circular polarization. These emissions are located within the inner regions of OH231.8 (at few tens of AU). We detected 30 water maser features, which occur in two distinct regions that are moving apart with a velocity on the sky of 2.3 mas/year. Taking into account the inclination angle of the source, this corresponds to an average separation velocity of 21 km/s. Based on the velocity gradient of the maser emission, the masers appear to be dragged along the direction of the nebula jet. Linear polarization is present in 3 of the features, and circular polarization was detected in the 2 brightest ones. We found that the strength of the magnetic field is |B_{||}|~45 mG which, when assuming a toroidal magnetic field, implies B~2.5 G on the stellar surface. The morphology of the field is not yet determined, but the high scatter found on the directions of the linear polarization vectors could indicate that the masers occur near the tangent points of a toroidal field., Comment: 7 pages, 4 figures

Most of PNe are not spherical. The loss of spherical symmetry occurs somewhere between the AGB and PN phase. The cause of this change of morphology is not yet well known, but magnetic fields are one of the possible agents. Its origin remains to be determined, and potentially requires the presence of a massive companion to the AGB star. Therefore, further detections of the magnetic field around evolved stars (in particular those thought to be part of a binary system) are crucial to improve our understanding of the origin and role of magnetism on evolved stars. One such binaries is the pre-PN OH231.8, around which a magnetic field was detected in the OH maser region of the outer circumstellar envelope. We aim to detect and infer the properties of the magnetic field of this source in the water maser region. We observed the 6_{1,6}-5_{2,3} water maser rotational transition to determine its linear and circular polarization. These emissions are located within the inner regions of OH231.8 (at few tens of AU). We detected 30 water maser features, which occur in two distinct regions that are moving apart with a velocity on the sky of 2.3 mas/year. Taking into account the inclination angle of the source, this corresponds to an average separation velocity of 21 km/s. Based on the velocity gradient of the maser emission, the masers appear to be dragged along the direction of the nebula jet. Linear polarization is present in 3 of the features, and circular polarization was detected in the 2 brightest ones. We found that the strength of the magnetic field is |B_{||}|~45 mG which, when assuming a toroidal magnetic field, implies B~2.5 G on the stellar surface. The morphology of the field is not yet determined, but the high scatter found on the directions of the linear polarization vectors could indicate that the masers occur near the tangent points of a toroidal field., Comment: 7 pages, 4 figures

SiO maser emission occurs in the extended atmosphere of evolved stars and can be studied at high angular resolution. Very long baseline interferometry (VLBI) observations of Mira variables indicate that SiO masers are significantly linearly polarized with linear polarization fraction up to 100%. However, no information is available at high angular resolution for SiO masers in higher mass loss OH/IR stars. We extend the VLBI SiO maser studies to OH/IR stars. The observations enable us to understand the SiO pumping mechanisms in higher mass loss evolved objects and compare those with Mira variables. Additionally, polarimetric observations of SiO masers help us to understand the magnetic field strength and morphology and to distinguish between conflicting polarization theories. The 43 GHz SiO maser observations of the OH/IR star OH 44.8-2.3 were performed with the VLBA in full polarization spectral line mode. Auxiliary EVLA observations were performed to allow for the absolute calibration of the polarization angle. The Zeeman splitting was measured by cross correlating the right and left circular polarization spectra as well as the S-curve fitting. Additionally, we analyzed the 1612 MHz OH maser observations of OH 44.8-2.3 from the VLA archive. The SiO masers of OH 44.8-2.2 form a ring located at ~5.4 AU around the star. The masers appear to be highly linearly polarized with fractional linear polarization up to 100%. The linear polarization vectors are consistent with a dipole field morphology in this star. We report a tentative detection of circular polarization of ~0.7% for the brightest maser feature. The magnetic field measured for this feature corresponds to 1.5\pm0.3 G. Additionally, the distribution of the 1612 MHz OH maser emission could indicate an elongated morphology., Comment: 10 pages, 6 figures, Accepted for publication in Astronomy & Astrophysics

SiO maser emission occurs in the extended atmosphere of evolved stars and can be studied at high angular resolution. Very long baseline interferometry (VLBI) observations of Mira variables indicate that SiO masers are significantly linearly polarized with linear polarization fraction up to 100%. However, no information is available at high angular resolution for SiO masers in higher mass loss OH/IR stars. We extend the VLBI SiO maser studies to OH/IR stars. The observations enable us to understand the SiO pumping mechanisms in higher mass loss evolved objects and compare those with Mira variables. Additionally, polarimetric observations of SiO masers help us to understand the magnetic field strength and morphology and to distinguish between conflicting polarization theories. The 43 GHz SiO maser observations of the OH/IR star OH 44.8-2.3 were performed with the VLBA in full polarization spectral line mode. Auxiliary EVLA observations were performed to allow for the absolute calibration of the polarization angle. The Zeeman splitting was measured by cross correlating the right and left circular polarization spectra as well as the S-curve fitting. Additionally, we analyzed the 1612 MHz OH maser observations of OH 44.8-2.3 from the VLA archive. The SiO masers of OH 44.8-2.2 form a ring located at ~5.4 AU around the star. The masers appear to be highly linearly polarized with fractional linear polarization up to 100%. The linear polarization vectors are consistent with a dipole field morphology in this star. We report a tentative detection of circular polarization of ~0.7% for the brightest maser feature. The magnetic field measured for this feature corresponds to 1.5\pm0.3 G. Additionally, the distribution of the 1612 MHz OH maser emission could indicate an elongated morphology., Comment: 10 pages, 6 figures, Accepted for publication in Astronomy & Astrophysics

A new weighted order scheme is presented for finding alternative Pareto optimal solution of multi objective linear programming problems. In developing the weighted scheme, a big M model is proposed. We establish some properties of the ordering scheme and the proposed model and show how to determine proper values of the parameter M. Illustrative examples are worked out to show the effectiveness of the proposed approach and the competitiveness of the obtained solutions as compared to the ones obtained by the weighted maxmin and the weighted aggregation methods. ©2010 IEEE.

A new weighted order scheme is presented for finding alternative Pareto optimal solution of multi objective linear programming problems. In developing the weighted scheme, a big M model is proposed. We establish some properties of the ordering scheme and the proposed model and show how to determine proper values of the parameter M. Illustrative examples are worked out to show the effectiveness of the proposed approach and the competitiveness of the obtained solutions as compared to the ones obtained by the weighted maxmin and the weighted aggregation methods. ©2010 IEEE.

The majority of the observed planetary nebulae exhibit elliptical or bipolar structures. Theoretical modeling has indicated that magnetically collimated jets may be responsible for the formation of the non-spherical planetary nebulae. The aim of this project is to measure the Zeeman splitting caused by the magnetic field in the OH and H2O maser regions occurring in the circumstellar envelope and bipolar outflow of the evolved star W43A. We report a measured magnetic field of approximately 100 micro-gauss in the OH maser region of the circumstellar envelope around W43A. The GBT observations reveal a magnetic field strength B|| of ~30 mG changing sign across the H2O masers at the tip of the red-shifted lobe of the bipolar outflow. We also find that the OH maser shell shows no sign of non-spherical expansion and that it probably has an expansion velocity that is typical for the shells of regular OH/IR stars. The GBT observations confirm that the magnetic field collimates the H2O maser jet, while the OH maser observations show that a strong large scale magnetic field is present in the envelope surrounding the W43A central star. The magnetic field in the OH maser envelope is consistent with the one extrapolated from the H2O measurements, confirming that magnetic fields play an important role in the entire circumstellar environment of W43A., Comment: 6 pages, 5 figures

The majority of the observed planetary nebulae exhibit elliptical or bipolar structures. Theoretical modeling has indicated that magnetically collimated jets may be responsible for the formation of the non-spherical planetary nebulae. The aim of this project is to measure the Zeeman splitting caused by the magnetic field in the OH and H2O maser regions occurring in the circumstellar envelope and bipolar outflow of the evolved star W43A. We report a measured magnetic field of approximately 100 micro-gauss in the OH maser region of the circumstellar envelope around W43A. The GBT observations reveal a magnetic field strength B|| of ~30 mG changing sign across the H2O masers at the tip of the red-shifted lobe of the bipolar outflow. We also find that the OH maser shell shows no sign of non-spherical expansion and that it probably has an expansion velocity that is typical for the shells of regular OH/IR stars. The GBT observations confirm that the magnetic field collimates the H2O maser jet, while the OH maser observations show that a strong large scale magnetic field is present in the envelope surrounding the W43A central star. The magnetic field in the OH maser envelope is consistent with the one extrapolated from the H2O measurements, confirming that magnetic fields play an important role in the entire circumstellar environment of W43A., Comment: 6 pages, 5 figures

We present a new model and a new approach for solving fuzzy linear programming (FLP) problems with various utilities for the satisfaction of the fuzzy constraints. The model, constructed as a multi-objective linear programming problem, provides flexibility for the decision maker (DM), and allows for the assignment of distinct weights to the constraints and the objective function. The desired solution is obtained by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and study the effect of the control parameter on the solution. We also illustrate the efficiency of the model and present three algorithms for solving the FLP problem, the first of which obtains a desired solution by solving a single crisp problem. The other two algorithms, interact with the decision maker, and compute a solution which achieves a given satisfaction level. Finally, we present an illustrative example showing that the solutions obtained are often even more satisfactory than asked for.

We present a new model and a new approach for solving fuzzy linear programming (FLP) problems with various utilities for the satisfaction of the fuzzy constraints. The model, constructed as a multi-objective linear programming problem, provides flexibility for the decision maker (DM), and allows for the assignment of distinct weights to the constraints and the objective function. The desired solution is obtained by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and study the effect of the control parameter on the solution. We also illustrate the efficiency of the model and present three algorithms for solving the FLP problem, the first of which obtains a desired solution by solving a single crisp problem. The other two algorithms, interact with the decision maker, and compute a solution which achieves a given satisfaction level. Finally, we present an illustrative example showing that the solutions obtained are often even more satisfactory than asked for.