Matlis dual of local cohomology modules

summary:Let $(R,\mathfrak m)$ be a commutative Noetherian local ring, $\mathfrak a$ be an ideal of $R$ and $M$ a finitely generated $R$-module such that $\mathfrak a M\neq M$ and ${\rm cd}(\mathfrak a,M) - {\rm grade}(\mathfrak a,M)\leq 1$, where ${\rm cd}(\mathfrak a,M)$ is the cohomological dimension of $M$ with respect to $\mathfrak a$ and ${\rm grade}(\mathfrak a,M)$ is the $M$-grade of $\mathfrak a$. Let $D(-) := {\rm Hom}_R(-,E)$ be the Matlis dual functor, where $E := E(R/\mathfrak m)$ is the injective hull of the residue field $R/\mathfrak m$. We show that there exists the following long exact sequence \begin {eqnarray*} 0 \longrightarrow & H^{n-2}_{\mathfrak a}(D(H^{n-1}_{\mathfrak a}(M))) \longrightarrow H^{n}_{\mathfrak a}(D(H^{n}_{\mathfrak a}(M))) \longrightarrow D(M) \\ \longrightarrow & H^{n-1}_{\mathfrak a}(D(H^{n-1}_{\mathfrak a}(M))) \longrightarrow H^{n+1}_{\mathfrak a}(D(H^{n}_{\mathfrak a}(M))) \\ \longrightarrow & H^{n}_{\mathfrak a}(D(H^{n-1}_{(x_1, \ldots ,x_{n-1})}(M))) \longrightarrow H^{n}_{\mathfrak a}(D(H^{n-1}_\mathfrak (M))) \longrightarrow \ldots , \end {eqnarray*} where $n:={\rm cd}(\mathfrak a,M)$ is a non-negative integer, $x_1, \ldots ,x_{n-1}$ is a regular sequence in $\mathfrak a$ on $M$ and, for an $R$-module $L$, $H^i_{\mathfrak a}(L)$ is the $i$th local cohomology module of $L$ with respect to $\mathfrak a$

دراسة تباعد جزيئات الماء

تم في هذا البحث دراسة تباعد جزيئات الماء باستخدام التقنيات المخبرية البسيطة، إذ أن جزيئات الماء متباعدة في المحلول على الرغم من أن الروابط بينها هي روابط هيدروجينية، وتعد الرابطة الهيدروجينية أقوى أنواع الروابط بين الجزيئات، على حين تكون جزيئات الفحوم الهيدروجينية التي تربط بينها أضعف أنواع الروابط بين الجزيئات، وهي قوى فاندرفالس، غير متباعدة، والحقيقتين السابقتين تدعمهما درجات الغليان من جهة قوة الرابطة الهيدروجينية، كما يمكن من جهة أخرى اعتمادا على الكتلة الحجمية حساب الحيز الذي تشغله جزيئة غرامية واحدة، ومطابقة هذا الحجم للحسابات النظرية لحجم الجزيئة المحسوب اعتمادا على انصاف أقطار الذرات، بالنسبة لجزيئات الهكسان والهبتان نجد تقارب نتائج الحسابات السابقة، فهي مركبات جزيئاتها غير متباعدة، أما بالنسبة لجزيئة الماء فلا نجد تطابق لتباعدها، ولدفع الشك في كون جزيئة الماء أكبر حجماً من المحسوب نظرياً، أي ذات كتلة مولية أكبر من المسجل مرجعياً، حسبنا الكتلة المولية لجزيئات الماء من تجربة تجفيف بطئ جداً لمدة شهرين لملح ثيوكبريتات الصوديوم المائية، لمنع أي تفكك ممكن حدوثه عند درجات حرارة مرتفعة، مع معرفة تركيز الملح الجاف بمعايرة الملح باليود، وقد أكدت جميع النتائج صحة ما سبق من تباعد جزيئات الماء، وكان التفسير الوحيد الذي يبرر التباعد هو وجود قوى تنافر كهربائية تتوازن مع قوى التجاذب الهيدروجينية بين الجزيئات.

Surgical Technique: Second-generation Bone Marrow Stimulation via Surgical Dislocation to Treat Hip Cartilage Lesions

Background: Compared to knees, hips have more bony constraint and soft tissue coverage. Thus, repair of focal cartilage defects in hips requires more invasive and technically complex surgeries than simple arthroscopy or arthrotomy. Autologous matrix-induced chondrogenesis (AMIC) is a second-generation bone marrow stimulation technique. Improvement in Tegner, Lysholm, International Cartilage Repair Society (ICRS), and Cincinnati scores has been reported at 1 and 2years after AMIC in knees. AMIC is potentially useful to repair defects in hips, but it is unknown whether it relieves symptoms or results in a durable construct. Description of Technique: A surgical hip dislocation is used to access the defect. This is débrided to stable cartilage shoulders, necrotic bone is removed, and the lesion base is drilled. Autogenous bone graft is used for lesions with bony defects to create a level surface. Fibrin gel and a collagen membrane are placed to stabilize the superclot for fibrocartilage formation. Methods: We treated six patients with AMIC in the hip between 2009 and 2010. We obtained Oxford Hip and UCLA Activity Scores. Repair quality was assessed on 6-month postoperative MRI using the modified magnetic resonance observation of cartilage repair tissue (MOCART) system. Minimum 1-year followup data were available for four patients (range, 1-2.5years). Results: Postoperative Oxford Hip Scores ranged from 13 to 17, UCLA Activity Scores ranged from 5 to 10, and MOCART scores ranged from 55 to 75. No complications occurred. Conclusions: We describe AMIC in the hip. Although these patients had pain relief and improved function, long-term followup is necessary to assess the duration of improvement, durability of repair, and potential for arthrosis. Level of Evidence: Level IV, therapeutic study. See Instructions for Authors for a complete description of levels of evidenc

Análisis De La Percepción De La Tutoría En Los Alumnos De Primer Año De La Licenciatura En Gastronomía Del Instituto Tecnológico Superior De Escárcega

The implementation of mentoring programs in higher level institutions has brought with it a series of implications that are susceptible to be evaluated, but above all, the way in which it is applied, and is generating the expected results for each student in the course The first semester and at the same time participates in the tutoring program corresponding to the Bachelor's Degree in Gastronomy of the Instituto Tecnológico Superior de Escárcega. For this reason, the main objective of this basic research, of descriptive type, was to analyze the conceptualization of the tutoring processes that receive the students that were object of study. To achieve the objective, a questionnaire applied to the 64 tutors was used and validated using the Cronbach alpha coefficient, showing a value of 6,779, indicating that this instrument has an acceptable degree of reliability, validating its use for the collection of plotted data In the Excel 2010 program. The results indicated that 80% of the students surveyed disagree with the tutorial action processes they receive from their tutors, while only 20% reported the existence of certain tutorial activities. Therefore it should be considered in detail the assignment and personal relationship between the student and the assigned tutor, seeking the correct planning and development of the activities according to the Degree in the work plan based on the institutional program of tutoring of the Institutes Decentralized Technology

The 12-item Oxford Knee Score: cross-cultural adaptation into German and assessment of its psychometric properties in patients with osteoarthritis of the knee

SummaryObjectiveTo cross-culturally adapt and validate the Oxford Knee Score (OKS) for use in German-speaking patients with osteoarthritis of the knee.MethodsAfter the cross-cultural adaptation (OKS-D), the following metric properties of the questionnaire were assessed in 100 consecutive patients (mean age 66.5 years, 61 women) undergoing total knee replacement: feasibility (percentage of fully completed questionnaires), reliability (Intraclass Correlation Coefficients [ICC] and Bland and Altman's limits of agreement), and construct validity (correlation with the Western Ontario and McMaster Universities Index [WOMAC], Knee Society Score [KSS], Activities of Daily Living Scale [ADLS], and Short Form 12 [SF-12]), floor and ceiling effects, and internal consistency (Cronbach's Alpha, CA).ResultsWe received 91.9% fully completed questionnaires. Reliability of the OKS-D was excellent (ICC 0.91). Bland and Altman's limits of agreement revealed no significant bias (−0.2) and a random error of 6.2. Correlation coefficients with the other questionnaires ranged from −0.22 (SF-12 Mental Component Scale [MCS]) to −0.77 (ADLS). We observed no floor or ceiling effects. The CA was 0.83.ConclusionsThe German version of the OKS is a reliable and valid measure for the self-assessment of pain and function in German-speaking patients with osteoarthritis of the knee

Experimental–computational study of carbon nanotube effects on mitochondrial respiration: in silico nano-QSPR machine learning models based on new Raman spectra transform with Markov–Shannon entropy invariants

[Abstract] The study of selective toxicity of carbon nanotubes (CNTs) on mitochondria (CNT-mitotoxicity) is of major interest for future biomedical applications. In the current work, the mitochondrial oxygen consumption (E3) is measured under three experimental conditions by exposure to pristine and oxidized CNTs (hydroxylated and carboxylated). Respiratory functional assays showed that the information on the CNT Raman spectroscopy could be useful to predict structural parameters of mitotoxicity induced by CNTs. The in vitro functional assays show that the mitochondrial oxidative phosphorylation by ATP-synthase (or state V3 of respiration) was not perturbed in isolated rat-liver mitochondria. For the first time a star graph (SG) transform of the CNT Raman spectra is proposed in order to obtain the raw information for a nano-QSPR model. Box–Jenkins and perturbation theory operators are used for the SG Shannon entropies. A modified RRegrs methodology is employed to test four regression methods such as multiple linear regression (LM), partial least squares regression (PLS), neural networks regression (NN), and random forest (RF). RF provides the best models to predict the mitochondrial oxygen consumption in the presence of specific CNTs with R2 of 0.998–0.999 and RMSE of 0.0068–0.0133 (training and test subsets). This work is aimed at demonstrating that the SG transform of Raman spectra is useful to encode CNT information, similarly to the SG transform of the blood proteome spectra in cancer or electroencephalograms in epilepsy and also as a prospective chemoinformatics tool for nanorisk assessmentXunta de Galicia; GRC2014/049Xunta de Galicia; R2014/03

Caracterización Físico-Química Y Organoléptica De Un Licor A Base De Piñuela

La piñuela es una baya agridulce y jugosa, su pulpa es de color blanco. En la península de Yucatán, la población maya la conoce con distintos nombres, sin embargo, también ha sido registrado para al menos 13 estados del país. Esta especie crece en las regiones tropicales de ambos litorales en México, así como en Centroamérica y las islas del Caribe, presentando mayor abundancia en la zona costera y en la selva baja caducifolia. Los usos que se le da a la piñuela son diversos (ornamental, medicinal, fines alimenticios, decorativos y ceremonial). Por lo anterior, el objetivo de la presente investigación fue elaboración y caracterización de un licor del fruto de la piñuela (Bromelia pinguin L) de forma artesanal en el municipio de Escárcega, Campeche. Para el logro de la investigación se hizo la recolección del fruto en localidades rurales del municipio de Candelaria, las cuales fueron trasladas a las instalaciones del Instituto Tecnológico Superior de Escárcega para la elaboración del licor, en donde después de tres meses se procedió a la evaluación de aceptabilidad ante un panel semientrenado. Los resultados indican que presenta una alta concentración de alcohol (31). Los panelistas valoraron el licor de piñuela satisfactoriamente (más del 80%). Como conclusión del estudio es importante considerar a este fruto como parte de un crecimiento en la industria alimentaria de la región, ya que por sus características naturales se le considera como un fuerte producto potencial para ser aprovechado por la comunidad local. The piñuela is a bittersweet and juicy berry, its pulp is white in color. In the Yucatan Peninsula, the Mayan population knows it by different names, however, it has also been recorded for at least 13 states in the country. This species grows in the tropical regions of both coasts in Mexico, as well as in Central America and the Caribbean islands, presenting greater abundance in the coastal zone and in the low deciduous forest. Piñuelas are used for a variety of purposes (ornamental, medicinal, food, decorative, and ceremonial). Therefore, the objective of this research was to elaborate and characterize a liqueur made from the fruit of the piñuela (Bromelia pinguin L) in an artisanal way in the municipality of Escárcega, Campeche. For the achievement of the research, the fruit was collected in rural localities of the municipality of Candelaria, which were transferred to the facilities of the Instituto Tecnológico Superior de Escárcega for the elaboration of the liquor, where after three months the evaluation of acceptability was made before a semi-trained panel. The results indicate that it has a high alcohol concentration (31). The panelists rated the piñuela liqueur satisfactorily (more than 80%). As a conclusion of the study, it is important to consider this fruit as part of a growing food industry in the region, since its natural characteristics make it a strong potential product to be exploited by the local community

Intake of fruits, vegetables, folic acid and related nutrients and risk of breast cancer in postmenopausal women

OBJECTIVE: To determine the role of fruit and vegetable consumption and dietary intake of folic acid and related nutrients such as methionine, cysteine and alcohol in the aetiology of breast cancer. DESIGN: Population based case-control study. SETTING: Part of the European Community Multicentre Study on Antioxidants, Myocardial Infarction, and Cancer of the Breast (EURAMIC) in Berlin, Germany. SUBJECTS: As part of the EURAMIC study, dietary intake data were collected in 43 postmenopausal women diagnosed with breast cancer between 1991 and 1992 in Berlin, Germany, and compared to 106 population-based controls. RESULTS: Odds ratios (ORs) adjusted for major risk factors of breast cancer but not for total energy intake showed a non-significant inverse association between a high intake of vegetables (OR=0.76, 95% CI=0.48-1.20) and fruits (OR=0.74, 95% CI=0.48-1.15) and breast cancer. Once results were adjusted for total energy intake the associations became much weaker (vegetables: R=0.86, 95% CI=0.51-1.46; fruits: OR=0.82, 95% CI=0.51-1.32). For all nutrients, the effect of energy adjustment was more profound and the inverse associations disappeared when results were adjusted for energy intake (total folate-not energy adjusted: OR = 0.79, 95% CI=0.51-1.21; energy adjusted: OR=1.14, 95% CI=0.73-1.79; folate equivalents-not energy adjusted: OR=0.81, 95% CI=0.53-1.23; energy adjusted: OR=1.16, 95% CI=0.78-1.74; methionine-not energy adjusted: OR=0.60, 95% CI=0.35-1.03; energy adjusted: OR=1.29, 95% CI=0.76-2.19; cysteine-not energy adjusted: OR=0.52, 95% CI=0.29-0.94; energy adjusted: OR=1.22, 95% CI=0.75-1.97). Alcohol intake was inversely associated with breast cancer in a non-significant way, possibly due to the relatively low alcohol intake of the study population. CONCLUSIONS: The results of this study do not provide firm evidence that a high intake of fruits and vegetables, folic acid, methionine or cysteine reduces the risk of getting breast cancer

Mechanical Stimulation Increases Knee Meniscus Gene RNA-level Expression in Adipose-derived Stromal Cells

Background: Efforts have been made to engineer knee meniscus tissue for injury repair, yet most attempts have been unsuccessful. Creating a cell source that resembles the complex, heterogeneous phenotype of the meniscus cell remains difficult. Stem cell differentiation has been investigated, mainly using bone marrow mesenchymal cells and biochemical means for differentiation, resulting in no solution. Mechanical stimulation has been investigated to an extent with no conclusion. Here, we explore the potential for and effectiveness of mechanical stimulation to induce the meniscal phenotype in adipose-derived stromal cells. Methods: Human adipose-derived stromal cells were chosen for their fibrogenic nature and conduciveness for chondrogenesis. Biochemical and mechanical stimulation were investigated. Biochemical stimulation included fibrogenic and chondrogenic media. For mechanical stimulation, a custom-built device was used to apply constant, cyclical, uniaxial strain for up to 6 hours. Strain and frequency varied. Results: Under biochemical stimulation, both fibrogenic (collagen I, versican) and chondrogenic (collagen II, Sox9, aggrecan) genes were expressed by cells exposed to either fibrogenic or chondrogenic biochemical factors. Mechanical strain was found to preferentially promote fibrogenesis over chondrogenesis, confirming that tensile strain is an effective fibrogenic cue. Three hours at 10% strain and 1 Hz in chondrogenic media resulted in the highest expression of fibrochondrogenic genes. Although mechanical stimulation did not seem to affect protein level expression, biochemical means did affect protein level presence of collagen fibers. Conclusion: Mechanical stimulation can be a useful differentiation tool for mechanoresponsive cell types as long as biochemical factors are also integrated