When is the super socle of C(X) prime?

[EN] Let SCF(X) denote the ideal of C(X) consisting of functions which are zero everywhere except on a countable number of points of X. It is generalization of the socle of C(X) denoted by CF(X). Using this concept we extend some of the basic results concerning CF(X) to SCF(X). In particular, we characterize the spaces X such that SCF(X) is a prime ideal in C(X) (note, CF(X) is never a prime ideal in C(X)). This may be considered as an advantage of SCF(X) over C(X). We are also interested in characterizing topological spaces X such that Cc(X) =R+SCF(X), where Cc(X) denotes the subring of C(X) consisting of functions with countable image.The authors would like to thank professor O. A. S. Karamzadeh for introducing the concept of super socle of C(X) and for his helpful suggestions. The authors are also indebted to the well-informed, meticulous referee for reading the article carefully and giving valuable and constructive comments.Ghasemzadeh, S.; Namdari, M. (2019). When is the super socle of C(X) prime?. Applied General Topology. 20(1):231-236. https://doi.org/10.4995/agt.2019.10731SWORD231236201F. Azarpanah, Algebraic properties of some compact spaces, Real Anal. Exchange 25 (2000), 317-328.F. Azarpanah, Essential ideals in C(X), Period. Math. Hungar. 31 (1995), 105-112. https://doi.org/10.1007/BF01876485F. Azarpanah, Intersection of essential ideals in C(X), Proc. Amer. Math. Soc. 125 (1997), 2149-2154. https://doi.org/10.1090/S0002-9939-97-04086-0F. Azarpanah and O. A. S. Karamzadeh, Algebric characterization of some disconnected spaces, Italian. J. Pure Appl. Math. 12 (2002), 155-168.F. Azarpanah, O. A. S. Karamzadeh and S. Rahmati, C(X) vs. C(X) modulo its socle, Coll. Math. 3 (2008), 315-336. https://doi.org/10.4064/cm111-2-9T. Dube, Contracting the socle in ring of continuous functions, Rend. Semin. Mat. Univ. Padova 123 (2010), 37-53. https://doi.org/10.4171/RSMUP/123-2R. Engelking, General Topology, Heldermann Verlag Berlin, 1989.A. A. Estaji and O. A. S. karamzadeh, On C(X) modulo its socle, Comm. Algebra 13 (2003),1561-1571. https://doi.org/10.1081/AGB-120018497M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, C(X) versus its functionally countable subalgebra, Bull. Iranian Math. Soc. 45 (2019), 173-187. https://doi.org/10.1007/s41980-018-0124-8M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova 129 (2013), 47-70. https://doi.org/10.4171/RSMUP/129-4S. Ghasemzadeh, O. A. S. Karamzadeh and M. Namdari, The super socle of the ring of continuous functions, Math. Slovaca 67 (2017), 1001-1010. https://doi.org/10.1515/ms-2017-0028L. Gillman and M. Jerison, Rings of continuous functions, Springer-Verlag, 1976.O. A. S. Karamzadeh, M. Motamedi and S. M. Shahrtash, On rings with a unique proper essential right ideal, Fund. Math. 183 (2004), 229-244. https://doi.org/10.4064/fm183-3-3O. A. S. Karamzadeh and M. Rostami, On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93 (1985), 179-184. https://doi.org/10.1090/s0002-9939-1985-0766552-9O. A. S. Karamzadeh, M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol. 16, no. 2 (2015), 183-207. https://doi.org/10.4995/agt.2015.3445S. Mehran and M. Namdari, The λ-super socle of the ring of continuous functions, Categ. General Alg. Struct. Appl. 6 (2017), 37-50.M. Namdari and M. A. Siavoshi, A note on discrete c-embedded subspaces, Mathematica Slovaca, to appear. https://doi.org/10.1515/ms-2017-023

On the essentiality and primeness of λ-super socle of C(X)

Spaces X for which the annihilator of Sλ(X), the λ-super socle of C(X) (i.e., the set of elements of C(X) that cardinality of their cozerosets are less than λ, where λ is a regular cardinal number such that λ≤|X|) is generated by an idempotent are characterized. This enables us to find a topological property equivalent to essentiality of Sλ(X). It is proved that every prime ideal in C(X) containing Sλ(X) is essential and it is an intersection of free prime ideals. Primeness of Sλ(X) is characterized via a fixed maximal ideal of C(X)

Economically optimal cutting cycle in a beech forest, Iranian Caspian Forests

The aim of this study was to determine the optimal cutting cycle in an uneven-aged beech forest in the North of Iran. First of all, a logistic growth model was determined for an uneven aged forest. Then, the stumpage price was predicted via an autoregressive model. The average stumpage price of beech was derived from actual timber, round wood, fire and pulpwood prices at road side minus the variable harvesting costs. Price and growth models were used in order to determine the optimal cutting cycle under different rates of interest and setup costs. The Faustmann’s model was used for optimal cutting cycle. The results indicated that the optimal cutting cycle will decrease if the rate of interest increased. The results also indicated that if the setup costs increase, the optimal cutting cycle will also increase

Lithium-ion battery prognostics through reinforcement learning based on entropy measures

Lithium-ion is a progressive battery technology that has vastly been used in different electrical systems. Failure in the battery can lead to failure in the entire system where the battery is embedded and cause irreversible damage. To avoid the probable damages, research is actively conducted, and data-driven methods are proposed based on prognostics and health management (PHM) systems. PHM can use multiple time-scale data and stored information from battery capacities over cycles to determine the battery state of health (SOH) and its remaining useful life (RUL). This results in battery safety, stability, reliability, and longer lifetime. In this paper, we propose different data-driven approaches to battery prognostics that rely on: Long Short-Term Memory (LSTM), Autoregressive Integrated Moving Average (ARIMA) and Reinforcement Learning (RL) based on the Permutation Entropy of battery voltage sequences at each cycle since they take into account the vital information from the past data and result in high accuracy

Effectiveness of Lesson Study on Teachers Professional Skills in Hamadan Province Exceptional Education

The purpose of this study was to determine the effectiveness of the lesson study on professional skills in Hamadan province Exceptional Education Teachers’. Research method was ex-post facto. The population was all of exceptional teachers’ in Hamadan Province in 2013-2014 academic year. Through stratified random sampling method, 320 teachers were selected as sample. Data gathering tools included questionnaires of providing learning opportunities, interest in increasing knowledge and job skills, class organization and management, and observation forms included applying learning theories, use of teaching aids and education supplies, use of correct methods of assessment, encourage students to work in groups and test of familiar with theories of learning. Results showed that lesson study groups and other have significant differences in variables of providing learning opportunities (t=2.23;

A survey on some risk factors and evaluation of their impacts on streptococcosis incidence in rainbow trout farms in Fars province

Streptococcosis is an infectious bacterial disease that causes huge economic losses in cold water aquaculture industry. Disease outbreak was experienced in some of provinces farms in recent years. Fars Province, has produced 7,000 tons of cold-water fish. According to Streptococcosis report in 1381 from the province and Proceedings have been performed during 10 years against disease and also economic losses impact of disease on rainbow trout production, risk assessment of Streptococcosis conducted on the plan. In this study, of 586 sick fish (have symptoms) studied 230 fish (39.24%) Streptococcus and (26.62%) gram negative bacteria were isolated. Of 754 healthy grower fish and fry (with no clinical signs) 10 fish or fry (1.32%)infected with streptococcus and 60 fish or fry(7.95%) infected with gram negative bacteria (Yersinia ruckeri, Pseudomonas, entrobacteriaceae). According to biochemical tests and molecular examinations, isolated Streptococcuus iniae and Streptococcus sp. Furthermore some physical and chemical parameters measured and aerobic bacteria of selected farm water counted. These factors effects on disease incidence and changes were evaluated by applying logistic regression

Variability of the pullout strength of cancellous bone screws with cement augmentation

Background Orthopaedic surgeons often face clinical situations where improved screw holding power in cancellous bone is needed. Injectable calcium phosphate cements are one option to enhance fixation. Methods Paired screw pullout tests were undertaken in which human cadaver bone was augmented with calcium phosphate cement. A finite element model was used to investigate sensitivity to screw positional placement. Findings Statistical analysis of the data concluded that the pullout strength was generally increased by cement augmentation in the in vitro human cadaver tests. However, when comparing the individual paired samples there were surprising results with lower strength than anticipated after augmentation, in apparent contradiction to the generally expected conclusion. Investigation using the finite element model showed that these strength reductions could be accounted for by small screw positional changes. A change of 0.5 mm might result in predicted pullout force changes of up to 28%. Interpretation Small changes in screw position might lead to significant changes in pullout strength sufficient to explain the lower than expected individual pullout values in augmented cancellous bone. Consequently whilst the addition of cement at a position of low strength would increase the pullout strength at that point, it might not reach the pullout strength of the un-augmented paired test site. However, the overall effect of cement augmentation produces a significant improvement at whatever point in the bone the screw is placed. The use of polymeric bone-substitute materials for tests may not reveal the natural variation encountered in tests using real bone structures.Dr V. Stadelmann (AOR, Davos, Switzerland) and Mr. M. Behrens (Stryker, Selzach, Switzerland). Professor Procter and Dr Arnoldi were employed by Stryker Trauma. Dr Bennani's PhD studies at Brunel University were funded by Stryker Trauma AG

Bloodstream and endovascular infections due to Abiotrophia defectiva and Granulicatella species

BACKGROUND: Abiotrophia and Granulicatella species, previously referred to as nutritionally variant streptococci (NVS), are significant causative agents of endocarditis and bacteraemia. In this study, we reviewed the clinical manifestations of infections due to A. defectiva and Granulicatella species that occurred at our institution between 1998 and 2004. METHODS: The analysis included all strains of NVS that were isolated from blood cultures or vascular graft specimens. All strains were identified by 16S rRNA sequence analysis. Patients' medical charts were reviewed for each case of infection. RESULTS: Eleven strains of NVS were isolated during the 6-year period. Identification of the strains by 16S rRNA showed 2 genogroups: Abiotrophia defectiva (3) and Granulicatella adiacens (6) or "para-adiacens" (2). The three A. defectiva strains were isolated from immunocompetent patients with endovascular infections, whereas 7 of 8 Granulicatella spp. strains were isolated from immunosuppressed patients, mainly febrile neutropenic patients. We report the first case of "G. para-adiacens" bacteraemia in the setting of febrile neutropenia. CONCLUSION: We propose that Granulicatella spp. be considered as a possible agent of bacteraemia in neutropenic patients

Sonographic evaluation of the shoulder in asymptomatic elderly subjects with diabetes

<p>Abstract</p> <p>Background</p> <p>The prevalence of rotator cuff tears increases with age and several studies have shown that diabetes is associated with symptomatic shoulder pathologies. Aim of our research was to evaluate the prevalence of shoulder lesions in a population of asymptomatic elderly subjects, normal and with non insulin - dependent diabetes mellitus.</p> <p>Methods</p> <p>The study was performed on 48 subjects with diabetes and 32 controls (mean age: 71.5 ± 4.8 and 70.7 ± 4.5, respectively), who did not complain shoulder pain or dysfunction. An ultrasound examination was performed on both shoulders according to a standard protocol, utilizing multiplanar scans.</p> <p>Results</p> <p>Tendons thickness was greater in diabetics than in controls (Supraspinatus Tendon: 6.2 ± 0.09 mm <it>vs </it>5.2 ± 0.7 mm, p < 0.001; Biceps Tendon: 4 ± 0.8 mm <it>vs </it>3.2 ± 0.4 mm, p < 0.001). Sonographic appearances of degenerative features in the rotator cuff and biceps were more frequently observed in diabetics (Supraspinatus Tendon: 42.7% <it>vs </it>20.3%, p < 0.003; Biceps Tendon: 27% <it>vs </it>7.8%, p < 0.002).</p> <p>Subjects with diabetes exhibited more tears in the Supraspinatus Tendon (Minor tears: 15 (15.8%) <it>vs </it>2 (3.1%), p < 0.03; Major tears: 15 (15.8%) <it>vs </it>5 (7.8%), p = ns), but not in the long head of Biceps. More effusions in subacromial bursa were observed in diabetics (23.9% <it>vs </it>10.9%, p < 0.03) as well as tenosynovitis in biceps tendon (33.3% <it>vs </it>10.9%, p < 0.001).</p> <p>In both groups, pathological findings were prevalent on the dominant side, but no difference related to duration of diabetes was found.</p> <p>Conclusions</p> <p>Our results suggest that age - related rotator cuff tendon degenerative changes are more common in diabetics.</p> <p>Ultrasound is an useful tool for discovering in pre - symptomatic stages the subjects that may undergo shoulder symptomatic pathologies.</p

Whole Transcriptome-Based Skin Virome Profiling in Typical Epidermodysplasia Verruciformis Reveals α-, β-, and γ-HPV Infections

HPVs are DNA viruses include approximately 450 types that are classified into 5 genera (α-, β-, γ-, μ-, and ν-HPV). The γ- and β-HPVs are present in low copy numbers in healthy individuals; however, in patients with an inborn error of immunity, certain species of β-HPVs can cause epidermodysplasia verruciformis (EV), manifesting as recalcitrant cutaneous warts and skin cancer. EV presents as either typical or atypical. Manifestations of typical EV are limited to the skin and are caused by abnormal keratinocyte-intrinsic immunity to β-HPVs due to pathogenic sequence variants in TMC6, TMC8, or CIB1. We applied a transcriptome-based computational pipeline, VirPy, to RNA extracted from normal-appearing skin and wart samples of patients with typical EV to explore the viral and human genetic determinants. In 26 patients, 9 distinct biallelic mutations were detected in TMC6, TMC8, and CIB1, 7 of which are previously unreported to our knowledge. Additionally, 20 different HPV species, including 3 α-HPVs, 16 β-HPVs, and 1 γ-HPV, were detected, 8 of which are reported here for the first time to our knowledge in patients with EV (β-HPV-37, -47, -80, -151, and -159; α-HPV-2 and -57; and γ-HPV-128). This study expands the TMC6, TMC8, and CIB1 sequence variant spectrum and implicates new HPV subtypes in the pathogenesis of typical EV