Polynomial Time Algorithms in Invariant Theory for Torus Actions

An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit closure containment. These capture and relate to a variety of problems within mathematics, physics and computer science, optimization and statistics. These orbit problems extend the more basic null cone problem, whose algorithmic complexity has seen significant progress in recent years. In this paper, we initiate a study of these problems by focusing on the actions of commutative groups (namely, tori). We explain how this setting is motivated from questions in algebraic complexity, and is still rich enough to capture interesting combinatorial algorithmic problems. While the structural theory of commutative actions is well understood, no general efficient algorithms were known for the aforementioned problems. Our main results are polynomial time algorithms for all three problems. We also show how to efficiently find separating invariants for orbits, and how to compute systems of generating rational invariants for these actions (in contrast, for polynomial invariants the latter is known to be hard). Our techniques are based on a combination of fundamental results in invariant theory, linear programming, and algorithmic lattice theory

Autekologi dan Fisiologi Percambahan Centaurea kilaea Boiss. dari Turki

In this study germination requirements, plant-soil interactions and population biology of Centaurea kilaea was studied. The plant and soil samples were collected from Sofular Village (Sile District) and shore of Çatalca District (Istanbul) in Turkey by using standard methods. Methods like Scheibler, Wetdigestion, Kjeldahl and Olsen were employed for measurement of soil texture, structure and other physical and chemical characteristics (pH, total protein and electrical conductivity) using spectrophotometer, flame photometer, calcimeter and ICP. The results showed that ranges of different elements in the soil were 0.007-0.2% for N, 0.0007-0.001% for P, 0.001-0.01% for K, 0.0001-0.0002 % for Na. N, P, K and Na values in the plants were 2.17, 0.005, 0.1 and 0.006%, respectively. The data revealed that germination success of the seeds was influenced by the environmental factors such as pH, germination season and temperature.Dalam kajian ini keperluan percambahan, saling tindakan tumbuhan-tanih dan biologi populasi Centaurea kilaea telah dilakukan. Sampel tumbuhan dan tanih telah dikumpul dari Kampung Sofular (Daerah Şile) dan pantai Daerah Çatalca (Istanbul) di Turki dengan menggunakan kaedah piawai. Kaedah seperti Scheibler, Wetdigestion, Kjeldahl dan Olsen telah digunakan bagi pengukuran tekstur tanih, struktur dan sifat fizikal dan kimia lain (pH, jumlah protein dan kekonduksian elektrik) menggunakan spektrofotometer, fotometer api, kalsimeter dan ICP. Hasil menunjukkan bahawa julat unsur berbeza dalam tanih ialah 0.007-0.2% bagi N, 0.0007-0.001% bagi P, 0.001-0.01% bagi K, 0.0001-0.0002% bagi Na. N, P, K dan nilai Na dalam tumbuhan ialah masing-masing 2.17, 0.005, 0.1 dan 0.006%. Data menunjukkan kejayaan percambahan bagi biji benih telah dipengaruhi faktor persekitaran seperti pH, musim percambahan dan suhu

Stellar ages and convective cores in field main-sequence stars: first asteroseismic application to two Kepler targets

Using asteroseismic data and stellar evolution models we make the first detection of a convective core in a Kepler field main-sequence star, putting a stringent constraint on the total size of the mixed zone and showing that extra mixing beyond the formal convective boundary exists. In a slightly less massive target the presence of a convective core cannot be conclusively discarded, and thus its remaining main-sequence life time is uncertain. Our results reveal that best-fit models found solely by matching individual frequencies of oscillations corrected for surface effects do not always properly reproduce frequency combinations. Moreover, slightly different criteria to define what the best-fit model is can lead to solutions with similar global properties but very different interior structures. We argue that the use of frequency ratios is a more reliable way to obtain accurate stellar parameters, and show that our analysis in field main-sequence stars can yield an overall precision of 1.5%, 4%, and 10% in radius, mass and age, respectively. We compare our results with those obtained from global oscillation properties, and discuss the possible sources of uncertainties in asteroseismic stellar modeling where further studies are still needed.Comment: 46 pages, 10 figures, ApJ accepte

TEMPERATURE-AND DEFORMATION-DEPENDENT STRUCTURAL CHARACTERIZATION OF SEMI- CRYSTALLINE POLYMERS BY X-RAY SCATTERING

ABSTRACT The special mechanical behaviour of semi-crystalline materials is caused by the temperaturedependent interaction between the crystalline and the amorphous phase with their specific mechanical properties. Thereby, the crystalline phase has higher strength and stiffness, it fails mainly under shear stress. The amorphous phase is tough above the glass transition with steadily decreasing strength with increasing temperature. Crazing may appear during. Under the complex load between the crystallites the amorphous phase tends to cavitation if the internal strength is too low with respect to the external load. This general behaviour was investigated and presented in the past by several different groups [1-2]. Recent investigations by synchrotron x-ray scattering enabled a highly time-and strain-resolved as well as temperature dependent investigation of structural changes during deformation. While wide angle diffraction enables a detailed characterization of the crystallites with respect to their orientation and deformation small angle scattering enables information about the size of the different phases and cavitation. Therefore the SAXS patterns were processed to estimate corddistribution-functions according to the procedures developed by Stribeck for samples with fiber symmetry [3]. The behaviour of different semi-crystalline polymers will be presented and compared with the behaviour of pure amorphous materials. A special attention will be turned on the structural events with respect to the stress-strain-curve. Some micrographs confirm the structural units, which were discussed on the basis of the x-ray pattern

Solar-like oscillations in KIC11395018 and KIC11234888 from 8 months of Kepler data

We analyze the photometric short-cadence data obtained with the Kepler Mission during the first eight months of observations of two solar-type stars of spectral types G and F: KIC 11395018 and KIC 11234888 respectively, the latter having a lower signal-to-noise ratio compared to the former. We estimate global parameters of the acoustic (p) modes such as the average large and small frequency separations, the frequency of the maximum of the p-mode envelope and the average linewidth of the acoustic modes. We were able to identify and to measure 22 p-mode frequencies for the first star and 16 for the second one even though the signal-to-noise ratios of these stars are rather low. We also derive some information about the stellar rotation periods from the analyses of the low-frequency parts of the power spectral densities. A model-independent estimation of the mean density, mass and radius are obtained using the scaling laws. We emphasize the importance of continued observations for the stars with low signal-to-noise ratio for an improved characterization of the oscillation modes. Our results offer a preview of what will be possible for many stars with the long data sets obtained during the remainder of the mission.Comment: 39 pages, 9 figures. Accepted for publication in Ap

Curative Chemoradiotherapy of Primary Pancreatic Lymphoma with Vertebral Metastasis: Palliation of Persistent Biliary Stricture by Roux-en-Y Hepaticojejunostomy

Primary pancreatic lymphoma (PPL) is a rare tumor that usually presents with the clinical picture of advanced adenocarcinoma but has a much better prognosis. A 38-year-old man was referred after percutaneous transhepatic external biliary drainage for obstructive jaundice. Abdominal magnetic resonance imaging (MRI) and magnetic resonance cholangiopancreatography had revealed a 5-cm pancreatic head mass that caused biliary tract dilation. Computed tomography angiography showed that the mass encased the celiac trunk as well as the common hepatic and splenic arteries. MRI also revealed a metastatic lesion at the third lumbar vertebra. Serum carcinoembryonic antigen and carbohydrate antigen 19-9 levels were within normal range. The initial diagnosis was inoperable pancreatic adenocarcinoma; however, Tru-Cut pancreatic biopsy showed a large B cell lymphoma. After 6 sessions of chemotherapy and 21 sessions of radiotherapy, both the pancreatic mass and the vertebral metastasis had disappeared. However, he had persistent distal common bile duct stricture that could not be negotiated by either the endoscopic or percutaneous route. A Roux-en-Y hepaticojejunostomy was performed. The patient stayed alive without recurrence for 52 months after the initial diagnosis and 45 months after completion of oncologic treatment. In conclusion, a large pancreatic mass with grossly involved peripancreatic lymph nodes, without ascites, liver or splenic metastasis, should alert the clinician to the possibility of PPL. Cure is possible by chemoradiotherapy even in the presence of vertebral metastasis. Persistent stricture in the distal common bile duct may require a biliodigestive anastomosis