Polyhedral Properties of RLT Relaxations of Nonconvex Quadratic Programs and Their Implications on Exact Relaxations

We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible regions of a quadratic program and its RLT relaxation. We establish various connections between recession directions, boundedness, and vertices of the two feasible regions. Using these properties, we present necessary and sufficient exactness conditions for RLT relaxations. We then give a thorough discussion of how our results can be converted into simple algorithmic procedures to construct instances of quadratic programs with exact, inexact, or unbounded RLT relaxations.Comment: Technical Report, School of Mathematics, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdo

The Black Hole in the Compact, High-dispersion Galaxy NGC 1271

Located in the Perseus cluster, NGC 1271 is an early-type galaxy with a small effective radius of 2.2 kpc and a large stellar velocity dispersion of 276 km/s for its K-band luminosity of 8.9x10^{10} L_sun. We present a mass measurement for the black hole in this compact, high-dispersion galaxy using observations from the integral field spectrograph NIFS on the Gemini North telescope assisted by laser guide star adaptive optics, large-scale integral field unit observations with PPAK at the Calar Alto Observatory, and Hubble Space Telescope WFC3 imaging observations. We are able to map out the stellar kinematics on small spatial scales, within the black hole sphere of influence, and on large scales that extend out to four times the galaxy's effective radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocity dispersion. Through the use of orbit-based stellar dynamical models, we determine that the black hole has a mass of (3.0^{+1.0}_{-1.1}) x 10^9 M_sun and the H-band stellar mass-to-light ratio is 1.40^{+0.13}_{-0.11} M_sun/L_sun (1-sigma uncertainties). NGC 1271 occupies the sparsely-populated upper end of the black hole mass distribution, but is very different from the Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are expected to host the most massive black holes. Interestingly, the black hole mass is an order of magnitude larger than expectations based on the galaxy's bulge luminosity, but is consistent with the mass predicted using the galaxy's bulge stellar velocity dispersion. More compact, high-dispersion galaxies need to be studied using high spatial resolution observations to securely determine black hole masses, as there could be systematic differences in the black hole scaling relations between these types of galaxies and the BCGs/giant ellipticals, thereby implying different pathways for black hole and galaxy growth.Comment: accepted for publication in Ap

On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, the Shor relaxation, and the relaxation resulting from their combination. We establish several structural properties of these relaxations in relation to the corresponding relaxations of StQPs without any sparsity constraints, and pay particular attention to the rank-one feasible solutions retained by these relaxations. We then utilize these relations to establish several results about the quality of the lower bounds arising from different relaxations. We also present several conditions that ensure the exactness of each relaxation.Comment: Technical Report, School of Mathematics, The University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdo

Insecticidal Activity of Lichens against the Maize Weevil, Sitophilus zeamais Motschulsky (Coleoptera: Curculionidae

Extracts of Letharia vulpina (L.) Hue and Peltigera rufescens (Weiss) Humb. lichen species and two major lichen compounds (diffractaic and usnic acids), isolated from Usnea longissima Ach., were tested against adults of the maize weevil, Sitophilus zeamais Motschulsky under laboratory conditions at various concentrations (2.5, 5, 10, 20 mg.ml-1 for extracts and 1.25, 2.5, 5, 10 mg.ml-1 for major compounds) and at 24, 48, 72, and 96 h period. Results showed that both the extracts and the secondary metabolites of U. longissima had significant insecticidal effects on adults of S. zeamais. Mortality rate was the highest at 96 h period at the treatment of maximum concentration of extracts (20 mg.ml -1) and compounds (10 mg.ml-1). The mortality rates attained 96.97, 95.96, 96.97 and 76.77% for L. vulpine, P. rufescens, diffractaic and usnic acids, respectively. No mortality was found in the control. The present results suggest that the lichen extracts and the secondary metabolites can provide a good potential for the control of S. zeamais adults

Comparative evaluation of shear bond strength of three flowable compomers on enamel of primary teeth: An in-vitro study

Background: The aim of the present study was to determine Shear bond strength (SBS) of different flowable compomers on the enamel surface of primary teeth. The null hypothesis to be tested was that none of the flowable compomer would differ significantly from the other two with respect to SBS. As a result, the tested materials that have the easiest application on child patient is preferred. Material and Methods: Sixty newly extracted non carious primary molars were selected. The buccal surface was cleaned and polished to obtain a flat enamel surface. The specimens were randomly divided into three groups of 20 teeth each, based on the flowable compomers applied, as follows: group I: Dyract Flow® (Dentsply, Konstanz, Germany); group II: Twinky Star Flow® (Voco, Cuxhaven, Germany); and group III: R&D Series Nova Compomer Flow® (Imicryl, Konya, Turkey). Results: SBS in group II (6.78± 0.45 MPa) were significantly lower than groups I and III (8.30 ± 0.29 and 8.43 ± 0.66 MPa, respectively) (P<.001). No significant difference was found between groups I and III (P<.05). Conclusions: Significant differences existed between the SBS of the groups. Therefore, the null hypothesis was rejected. Flowable compomers can provide adequate SBS with self-etching system at restoration of primary teeth. Thus, successful restorations in pediatric patients can be done in a practical way. © Medicina Oral S.L

The structural and dynamical properties of compact elliptical galaxies

Dedicated photometric and spectroscopic surveys have provided unambiguous evidence for a strong stellar mass-size evolution of galaxies within the last 10 Gyr. The likely progenitors of today's most massive galaxies are remarkably small, disky, passive and have already assembled much of their stellar mass at redshift z=2. An in-depth analysis of these objects, however, is currently not feasible due to the lack of high-quality, spatially-resolved photometric and spectroscopic data. In this paper, we present a sample of nearby compact elliptical galaxies (CEGs), which bear resemblance to the massive and quiescent galaxy population at earlier times. Hubble Space Telescope (HST) and wide-field integral field unit (IFU) data have been obtained, and are used to constrain orbit-based dynamical models and stellar population synthesis (SPS) fits, to unravel their structural and dynamical properties. We first show that our galaxies are outliers in the present-day stellar mass-size relation. They are, however, consistent with the mass-size relation of compact, massive and quiescent galaxies at redshift z=2. The compact sizes of our nearby galaxies imply high central stellar mass surface densities, which are also in agreement with the massive galaxy population at higher redshift, hinting at strong dissipational processes during their formation. Corroborating evidence for a largely passive evolution within the last 10 Gyr is provided by their orbital distribution as well as their stellar populations, which are difficult to reconcile with a very active (major) merging history. This all supports that we can use nearby CEGs as local analogues of the high-redshift, massive and quiescent galaxy population, thus providing additional constraints for models of galaxy formation and evolution.Comment: 33 pages, 27 figures and 20 tables (with most of the tables provided as online-only supporting information). Accepted for publication in MNRA

Estimation of spleen volume and surface area of the newborns’ cadaveric spleen using stereological methods

Background: The purpose of this study was to compare different techniques for the estimation of spleen volume and surface area using magnetic resonance imaging (MRI) images, ultrasonography (USG) images and cadaveric specimen, and to evaluate errors associated with volume estimation techniques based onfluid displacement.Materials and methods: Five new born cadavers, aged 39.7 ± 1.5 weeks, weighted 2.220 ± 1.056 g, were included in the present study. Three different methods were used to assess the spleen volume. The vertical section technique was applied using cycloid test probes for estimation of spleen surface area in MRI.Results: The mean ± standard deviation of spleen volumes by fluid displacement was 4.82 ± 3.85 cm3. Volumes determined by the Cavalieri’s principle using physical section and point-counting techniques were 4.45 ± 3.47 cm3 and 4.65 ± 3.75 cm3, respectively; volumes measured by USG and cadaver using ellipsoid formula were 4.70 ± 3.02 cm3 and 5.98 ± 4.58 cm3, respectively. No significant differences were found among all methods (p &gt; 0.05). The spleen surface area was calculated as a 32.3 ± 20.6 cm2 by physical sections using cadaver and also it was determined on axial, sagittal and coronal MR planes as 24.9 ± 15.2 cm2, 18.5 ± 5.92 cm2 and 24.3 ± 12.7 cm2, respectively.Conclusions: As a result, MR images allow an easy, reliable and reproducible volume and surface area estimation of normal and abnormal spleen using Cavalieri’sprinciple. We consider that our study may serve as a reference for similar studies to be conducted in future

Digital Transformation in Higher Education: Maturity and Challenges Post COVID-19

Digital transformation in higher education, especially after COVID-19 is inevitable. This research explores digital transformation maturity and challenges post COVID-19. The significance of the study does not only stem from the critical role of higher education in building the workforce and knowledge economy. This study triangulates the findings of multiple research instruments, including survey, interviews, case study, and direct observation. The research findings show a significant variance between the respondents’ perception of digital transformations maturity levels, and the core requirements of digital transformation maturity. The findings also show the lack of holistic vision, digital transformation competency, and data structure and processing as the leading challenges of digital transformation

Kırka Boraks atıklarının soda liçi

Bor, çok geniş kullanım alanları ile, insanlığın bugünkü ve gelecekteki yaşamlarında, vazgeçilmez bir endüstriyel hammadde olarak önemini gittikçe arttıracaktır. Ülkemiz bu açıdan şanslı bir konumda olup, toplam dünya bor rezervlerinin yaklaşık %60 'mı içermektedir Bu nedenlerden dolayı, bor cevherlerimizin en verimli bir şekilde üretimi ülkemiz açısından çok fazla önem arz etmektedir. Kırka boraks konsantratöründe, her yıl yaklaşık %10-12 B2O3 tenörlü 250 bin ton yaş artık oluşmakta ve bunun yanında artık göletinde de benzer tenörlü yaklaşık 4 milyon ton birikmiş katı artık bulunmaktadır. Artıkların teknolojik koşullara uygun olarak değerlendirilmesi gerekmektedir. Bu çalışmada, kırka boraks artıklarının soda liçi ile değerlendirilmesinde etken olan parametreler ayrıntılı bir şekilde araştırılmıştır. Bu amaçla, boraks artıklarının Na2C03 ve NaHCC>3 liçi; değişik sıcaklık, çözücü"miktarları, katı/sıvı oranlan ve çözeltine sürelerinde denenmiş olup, düşük çözücü oranlarında, optimal sıcaklık ve sürede başarılı sonuçlar alınmıştır. Sonuçta, seyreltik soda çözeltisi ile yapılan deneylerde, artiklardaki boraks yüksek verimle çözünmüş ve elde edilen bulgulardan yararlanılarak, tesisin mevcut çalışma koşullarına uygun optimum öneri akım şemalan geliştirilmiştir. Aynca, bu yöntemle boraks artıklarının değerlendirilmesinde, çözücü olarak tronanın kullanılması ile ülkemizde büyük bir potansiyele sahip olan trona yataklan yem bir kullanım alam bulmuş olacaktır.Boron will continue its importance in the recent world and in the future as a very well-known and necessary industrial rawmaterial with common use areas. Our country is very advantegeous in this point and contains approximately 60 % of total world reserves of boron. Thus production of boron ores is greatly significant for our country. In the Kırka Tincal Concentrator, approximately 250 000 tons wet tailings with a grade of 10 -12 % are produced and separately 4 million tons tailings with similar grade are disposed. Beneficiation from the Kırka Tincal tailings is thereby necessary. In this study, the effective parameters m soda leaching of the Kırka Tincal tailings have been investigated in detail. For this aim, Na2CC>3 and NaHCC>3 leaching of the tailings at different temperature, concentration, solid/liquid ratio and leaching time were carried out. As a conclusion, in the experiments made with aqueous soda solutions, tincal were efficiently extracted and an optimum processing plant proposal was developed. Furthermore, with use of trona in this processing method of the tailings, the great trona deposits will find a different use