On invariant subspaces of collectively compact sets of linear operators

Bir Banach uzayı üzerinde tanımlı sınırlı doğrusal operatörünün aşikar olmayan (yani ve ten farklı) kapalı (hiper)değişmez altuzaya sahip olup olmaması, ‘değişmez altuzay problemi’ olarak bilinir. Burada in bir altuzayının operatörü altında değişmez kalması, hiperdeğişmez kalması ise ile değişmeli her operatör altında değişmez kalmasıdır. Tek bir operatörü yerine bu operatörlerin bir ailesi göz önüne alındığında, nin altında (hiper)değişmez kalması, ailesine ait her operatör altında (hiper)değişmez olmasıdır. in kapalı birim yuvarını göstermek üzere, kümesi önkompakt ise ailesine birlikte kompakt denir. Bu çalışmada doğrusal operatörlerin birlikte kompakt ailelerinin (hiper)değişmez altuzayları araştırılmaktadır. Kompakt operatörlerin önkompakt ailesi birlikte kompaktır ancak bunun tersi her zaman doğru değildir. Kompakt operatörlerin önkompakt aileleri için bilinen bazı değişmez altuzay sonuçları, birlikte kompakt operatör ailelerine genişletilmektedir. Bunu yaparken, Rota-Strang spektral yarıçapı, Berger-Wang spektral yarıçapı ve deki sıfırdan farklı bir elemanı için yerel spektral yarıçapı kullanılmaktadır. Ayrıca  daki birlikte kompakt ailesinin, Berger-Wang formülünü sağladığı gösterilmektedir; burada, X in altuzaylarının tam zincirini ve, daki tüm altuzayları değişmez bırakan operatörlerin kümesini göstermektedir. Anahtar kelimeler: Değişmez altuzay, birlikte kompakt kümeler, ortak spektral yarıçap.Given a Banach space and a bounded linear operator, may or may not have a closed subspace, other than and, which is left invariant under, that is,. This work is concerned with this problem which is commonly known as the invariant subspace problem. However, instead of taking a single operator, we consider a family of linear bounded operators on infinite dimensional Banach spaces which are tied together with a strong compactness condition, known as collective compactness and we look for a common invariant subspace of elements of. A family of operators is called collectively compact if the closure of the closed unit ball of is compact under the action of. That is, is compact in. Using well-known techniques, we generalize invariant subspace results which are proven for precompact families of compact operators to collectively compact families of operators. In doing so, we use joint spectral radius, Berger-Wang spectral radius of and the local joint spectral radius for a non-zero in. A common technique to show that a multiplicative semigroup generated by has a common invariant subspace is to show that has a non-zero semigroup ideal which has a non-trivial closed invariant subspace. Employing this technique and introducing a semigroup ideal in the multiplicative semigroup, we show that if is collectively compact and then has an invariant subspace. Another results in this direction are the ones which yield a common invariant subspace for a collectively compact family of operators if for some non-zero in. If, on the other hand, is collectively compact and, then we show that has a common invariant subspace. Another case where collectively compact family has a common invariant subspace is when and is not bounded. In the final part of the work, we consider a complete chain of closed subspaces of and show that if is a collectively compact family in then we have. Here, denotes the set of operators that leave all the subspaces in invariant and denotes the set of all operators satisfying for any gap in and all. As a result of this, we relate the joint spectral radius to Ringrose?s diagonal numbers for triangularizable collectively compact sets of operators: The arbitrary complete chains of invariant subspaces for collectively compact sets of operators are then considered, and the joint spectral radius is compared with joint spectral radii of sets induced by in the quotient spaces corresponding to the gaps of the chain. So we first show that that if is a collectively family in and, then there exists only a finite number of gaps of the chain  such that. And by using this result we obtain that if is a collectively family in, then we have. We finally show that the Berger-Wang formula holds for a collectively compact family in where is a complete chain of subspaces.  Keywords: Invariant subspace, collectively compact set, joint spectral radius

First record of Eisenia andrei (Bouche, 1972) (Clitellata : Megadrili) from natural habitat in Turkey

Bu çalışmada Antalya Kent ormanından toplanan topraksolucanı örnekleri incelenmiş ve bu inceleme sonucu örneklerin Eisenia andrei (Bouche, 1972) olduğu görülmüştür. E. andrei pek çok özelliğiyle E. fetida türüne benzer ve tüm dünyada vermikompost çalışmalarında yaygın olarak kullanılır. Bu kayıt, türün vermikültür ve vermikompost alanları dışında Türkiye’de doğal ortamdaki ilk kaydıdır.In this study, earthworm samples collected from Kent Ormanı in Antalya Province were examined and at the end of the identification, it has been seen that samples were Eisenia andrei (Bouche, 1972). E. andrei resembles to E. fetida in terms of many features and it is used in vermicompost studies all over the world. Except vermiculture and vermicompost areas, it is the first record of this species from natural habitat in Turkey

Paroxysmal Supraventricular Tachycardia in an Infant with Hand, Foot, and Mouth Disease

An 11-month-old male infant was admitted to our hospital with fever, fussiness, poor feeding, vomiting, and tachypnea for two days prior. Physical examination revealed sporadic papules and vesicles occurring on his hands, feet, face, and perianal mucosa. Enterovirus 71 was identified from both throat swab and vesicle fluid using virus isolation techniques. The patient's heart rate fluctuated in a very narrow range from 180~210/beats/min regardless of his physiologic state. An electrocardiogram showed P-waves buried within or occurring just after regular, narrow, QRS complexes. The patient was diagnosed as having hand, foot, and mouth disease in combination with paroxysmal supraventricular tachycardia (PSVT). The child recovered well with symptomatic treatment, including intravenous administration of acyclovir, glucocorticoids, immunoglobulin, adenosine, and sotalol. PSVT was terminated within 36 hours of hospitalization. The skin lesions became crusted on the third day, and then proceeded to heal spontaneously. Here we report on this unusual case and review the associated literature

Sensitization to Aeroallergens in Korean Children: A Population-based Study in 2010

We performed this study to assess the prevalence of sensitization to aeroallergens and to analyze the difference between prevalence rates according to children's ages and residential areas. In this nationwide cross-sectional study, first grade students of 45 elementary schools and 40 middle schools were randomly selected, and skin prick tests were performed for 18 inhalant allergens between October and November 2010. Of 7,829 analyzed subjects, 3,753 (47.9%) were sensitized to at least one aeroallergen. Sensitization to Dermatophagoides farinae was found to be the most prevalent in elementary schoolchildren (32.4%), followed by Dermatophagoides pteronyssinus, Tyrophagus putrescentiae, Japanese hop, and oak. In middle schoolchildren, D. pteronyssinus yielded the highest prevalence (42.7%), followed by D. farinae, T. putrescentiae, Japanese hop, and cat. In middle schoolchildren, the sensitization rate to aeroallergens in metropolitan, urban, and rural areas was 57.2%, 54.3%, and 49.8%, respectively (P = 0.019). In this age group, the sensitization rate in low, middle, high, and very high income groups was 53.8%, 51.8%, 59.0%, and 59.6%, respectively (P = 0.002). In conclusion, the sensitization rate is 47.9% and house dust mite is the most prevalent allergen in the pediatric population in Korea. The rate is higher in metropolitan areas and the highest income group than in rural areas and low income groups

Promjena prirodne vegetacije u vremenskom razdoblju na kosinama nasipa šumskih cesta i njeni učinci na smanjenje erozije

During the construction of forest roads, slopes become more susceptible to erosion as they remain bare due to soil excavation and felling of trees along the road route. In Türkiye, studies are carried out to prevent erosion and maintain slope stability, and it is known that these studies are quite costly. In this study, analyses were made on three forest roads built less than a year ago, 5 years ago and 10 years ago from the forest road network located at the same aspect and level, and the aim was to determine whether these costs were needed. Soil samples were taken from the fill slopes of these roads and the degree of covering of the plants was determined by using the grid method on the images taken with the drone. Analyses of organic matter, texture, stony ratio, and pH-EC determination were made on these soil samples. The vegetation cover of the fill slope surfaces was determined as 93% for the 10-year-old road, 80% for the 5-year-old road and 0% for the newly built road. According to the ABAG method (which is a simulation of the USLE model converted to the metric system and adapted to European conditions), the annual soil loss amount for the 10-year-old forest road was 1.59 tons/ha/years, for the 5-year-old forest road it was 1.75 tons/ha/years and, finally, for the newly built forest road, this value was 15.52 tons/ha/years. Considering that most of the soil loss occurs in the first years, the amount of soil loss determined on the 5-year-old forest road is at an acceptable level according to the erosion values that occur in natural areas. For this reason, considering that the fill slopes are naturally covered with vegetation, it has been determined that there is no need for costly stabilization process in the fill slopes in this study areaTijekom izgradnje šumskih prometnica kosine postaju podložnije eroziji budući da ostaju gole zbog iskopavanja tla i sječe stabala uz trasu ceste. U Turskoj se provode studije za sprječavanje erozije i održavanje stabilnosti kosina, a poznato je da su te studije prilično skupe. U ovom istraživanju analizirane su tri šumske ceste izgrađene prije manje od godinu dana, prije 5 godina i prije 10 godina iz mreže šumskih cesta koje se nalaze na istom položaju i razini te se istraživanjem željelo utvrditi jesu li ti troškovi potrebni. Uzeti su uzorci tla s kosina nasipa prometnica te je metodom rešetke na snimkama snimljenim dronom određen stupanj vegetacijske pokrivenosti. Na uzorcima tla napravljene su analize organske tvari, teksture, omjera kamenja te je određen pH-EC. Za desetogodišnju cestu utvrđena je vegetacijska pokrivenost površina nasipa od 93 %, za petogodišnju cestu 80 % i za novoizgrađenu cestu 0 %. Prema ABAG metodi (koja je simulacija USLE modela pretvorena u metrički sustav i prilagođena europskim uvjetima), godišnji iznos gubitka tla za desetogodišnju šumsku cestu iznosi 1,59 tona/ha godišnje, za petogodišnju šumsku cesta 1,75 tona/ha godišnje te za novoizgrađenu šumsku cestu 15,52 tona/ha godišnje. S obzirom na to da do većine gubitka tla dolazi u prvim godinama, količina gubitka tla utvrđena na 5 godina staroj šumskoj cesti na odgovarajućoj je razini prema erozijskim vrijednostima koje se javljaju u prirodnim područjima. Iz tog razloga, s obzirom da su padine nasipa prirodno prekrivene vegetacijom, utvrđeno je da nema potrebe za skupim procesom stabilizacije padina nasipa na ovom području istraživanja

Evaluation of risk factors in patients diagnosed as bronchial asthma

PubMed: 16540064Bronchial asthma is a public health problem with gradually increasing importance, affecting more than 100 million individuals worldwide and found independently of the level of development of the country. Factors related to lifestyle and the environment form the basis for the increase in the prevalence of the disease. Aim: To evaluate our patients being followed-up with a diagnosis of bronchial asthma at the Allergy Clinic for risk factors and to determine their sociodemographic characteristics Material and Method: The risk factors of 3025 patients followed-up with a diagnosis of bronchial asthma at the Allergy Clinic of the Ministry of Health, Ankara Diskapi Children's Diseases Training and Research Hospital between January 1995 and March 2000 were evaluated retrospectively. Results: A high percentage of our patients suffered from both asthma and allergic rhinitis and 45% of our asthmatic patients had allergic rhinitis while 93.5% of those with allergic rhinitis were also asthmatic. Asthma was more common in males and those born in the summer months. 57.6% of the patients had a history of atopy. Passive smoking was observed at a high rate and cigarette smoke was the most important factor increasing the symptoms. The symptoms increased during the winter. 92.8% of the patients lived in the city. The average Ig E level was high and 60.9% of the patients were atopic on the skin prick test. Results: Asthma seems to be an important health problem in our country. Recognizing the risk factors is important for the diagnosis and prevention of the disease

New earthworm records (Clitellata: Lumbricidae) from Bulgaria since 2012

Valchovski, Hristo, Misirlioğlu, Mete, Stojanović, Mirjana (2018): New earthworm records (Clitellata: Lumbricidae) from Bulgaria since 2012. Zootaxa 4496 (1): 173-174, DOI: https://doi.org/10.11646/zootaxa.4496.1.1

Distribution of non-lumbricid earthworms (Clitellata: Acanthodrilidae, Criodrilidae, Megascolecidae and Ocnerodrilidae) on the Balkans and Anatolia with first record of Amynthas morrisi (Beddard, 1892) from Turkey

Misirlioğlu, İbrahim Mete, Stojanović, Mirjana (2018): Distribution of non-lumbricid earthworms (Clitellata: Acanthodrilidae, Criodrilidae, Megascolecidae and Ocnerodrilidae) on the Balkans and Anatolia with first record of Amynthas morrisi (Beddard, 1892) from Turkey. Zootaxa 4496 (1): 197-205, DOI: https://doi.org/10.11646/zootaxa.4496.1.1