Tauberian theorems for regularly generated sequences

Klasik Tauber teorisinin temel amac.lar³ndan biri, Abel'in gerek ko»sulu yada genelle»stirilmesi olarak bilinen limitin varl³~g³ndan ve sal³n³m davran³»slar³n³ kon- trol eden ko»sullar ile ³raksakl³~g³ kontrol edilebilen dizilerin yak³nsakl³~g³na ula»s³lma s³d³r. Bu ko»sullara Tauber ko»sullar³ ve bu tip teoremlere Tauber teoremleri denir. Stanojevi¶c taraf³ndan tan³mlanan tamsay³ mertebeli kontrol modÄulolar ile klasik Tauber teoremleri incelenecektir. Tauber, bir dizinin klasik kontrol modÄulosu s³f³r dizisi ise Abel'in gerek ko»sulundan dizinin yak³nsakl³~g³na ula»s³ld³~g³na gÄostermi»stir. Littlewood, Tauber'in ko»sulundan daha zay³f olan dizinin klasik kontrol modÄulosu nun s³n³rl³l³~g³ ile de~gi»stirebilece~gini gÄostermi»stir. Sonra Schmidt yava»s sal³n³ml³ dizileri tan³tm³»s ve genelle»stirilmi»s Littlewood teoremi olarak bilinen daha genel teoremi ispatlam³»st³r. Dik, Karamata'n³n temel toreminden yararlanarak ve Stano- jevi¶c taraf³ndan tan³t³lan dÄuzenli olarak Äuretilen dizi kavram³n³ kullanarak Abel limitleme metodu ic.in yeni Tauber tipi teoremler elde etmi»s ve klasik Tauber tipi teoremleri genelle»stirmi»stir. Dik ve C. anak dÄuzenli olarak Äuretilen dizi kavram³ yard³m³yla Abel limitleme metodu ic.in klasik ve klasik olmayan yeni Tauber tipi teoremler ispatlam³»st³r. C. anak ve Dik verilen bir dizinin Äuretec.lerinin yada geri farklar³n³n yava»s sal³n³ml³ olmas³ durumunda dizinin hangi ko»sullar alt³nda yak³nsak yada altdizisel yak³nsak oldu~gu ara»st³rm³»st³r. One of the main objectives of the classical Tauberian theory is to recover con- vergence of sequences, whose divergence is manageable, out of the existence of certain limits which is known as Abel's necessary condition or its generalizations, and certain additional conditions that control the oscillatory behavior. These conditions are called Tauberian conditions and this type of theorems are called Tauberian theorems. In terms of the control modulo of oscillatory behavior of integer order, introduced by Stanojevi¶c, we now summarize the classical results. Tauber proved that if the classical control modulo of a sequence is a null sequence, then one obtains convergence of sequence out of its Abel's necessary condition. Littlewood showed that Tauber's condition can be replaced by the boundedness of the classical control modulo of a sequence. Later Schmidt introduced the slowly oscillating sequences and proved the more general theorem, which is known as the generalized Littlewood theorem. Using Karamata's Hauptsatz and employing the concept of regularly generated sequences introduced by Stanojevi¶c, Dik ob- tained new Tauberian theorems and generalized classical Tauberian theorems for Abel limitable method. Dik ve C. anak proved classical and nonclassical Taube- rian theorems for Abel limitable method by the concept of regularly generated sequences. C. anak ve Dik investigated under which conditions sequences converges or converges subsquentially, provided that its generator sequence or sequence of its backword di®erences is slowly oscillating

Statistical Analysis of Chemical Admixtures Usage for Concrete: A Survey of Eskisehir city, Turkey

AbstractNowadays, the concrete admixtures are widely used in the construction projects. The main types of chemical admixtures can be summarized as plasticizers, accelerating/retarding agents, air entraining agents, waterproofing additives and others such as corrosion inhibitors and colouring agents etc. The benefits derived from the use of chemical admixtures include improved durability, strength, chemical resistance, colouring, reduction in water and cement requirement and enhanced working properties of concrete. Turkey is one of the major consumers in developing countries regarding chemical admixtures. Therefore, this study set out to determine general utilization and consciousness about admixtures through a survey in Eskisehir, Turkey. The survey was performed by 153 construction professionals. The questions about reasons for preference of admixtures, types of preferred admixtures and dosage, beneficial and adverse effects of admixtures, impacts on cost and judicious use of admixtures are included in the survey. A number of statistical analyses are carried out using SPSS on data obtained. According to results, chemical admixtures are used over 70% of the total annual concrete production. The initial expectation of the participants in the use of the admixtures is to improve the properties of the fresh concrete. Additionally, the most preferred admixtures are plasticizers. The ensuing types of admixtures are agents affecting the setting time of concrete. Although the participants’ interest to using chemical admixtures is very remarkable, the awareness on this subject is very deficient. The similar studies can be suggested to apply more comprehensively. Professionals, at any level in the construction sector, need to be informed about the accurate consumption of these agents in order to avoid inappropriate results

ON ABEL CONVERGENT SERIES OF FUNCTIONS

In this paper, we are concerned with Abel uniform convergence and Abel pointwise convergence of series of real functions where a series of functions Σ fn is called Abel uniformly convergent to a function f if for each " > 0 there is a _ > 0 such that jfx(t) 􀀀 f(t)j < " for 1 􀀀 _ < x < 1 and 8t 2 X, and a series of functions Σ fn is called Abel pointwisely convergent to f if for each t 2 X and 8" > 0 there is a _("; t) such that for 1 􀀀 _ < x < 1 jfx(t) 􀀀 f(t)j < "

A Rare Hand Pain Cause, Schwannoma with Median Nerve Localisation

Schwannoma is a firm, properly limited, encapsulated, and slow-growing benign tumor of nerve sheaths. It can be seen at all ages, most commonly between the ages of 20 and 50 years and the ratio of female to male is 2:1. It is most commonly seen in the head and neck, but 20% of Schwannomas arise from the peripheral nerves. Peripheral nerve Schwannomas can easily be misdiagnosed as nerve entrapment syndromes because their symptoms overlap most of the times. Symptoms occur by pressing on the mass or on the surrounding tissues. There is no medical treatment of Schwannomas, but the treatment is total excision of the mass. In this case report, a 64-year-old male patient with a Schwannoma of the median nerve in the left forearm, who was misdiagnosed and misoperated as carpal tunnel syndrome, is reported

Pregnancy and Lactation-Associated Osteoporosis

Osteoporosis in pregnancy and during lactation period is a rare clinical problem with unknown etiology and pathophysiology. Pregnancy and lactation may have significant impact on bone loss and this may result in osteoporosis and related fractures. The symptoms often occur during the first pregnancy and usually do not recur. Secondary causes of osteoporosis that may cause back pain and fractures during pregnancy should be taught in differential diagnosis. Still no guidelines exist about the accurate treatment of this rarely seen osteoporosis type, this means each case must be evaluated on an individual basis in order to decide for a treatment plan. In this case report, a 25-year-old woman, complaining of severe back pain after twenty days of giving birth, is reported

Response of durum wheat seedlings to salinity

Salinity is an important source of abiotic stress, limiting crop performance in most arid and semi-arid areas of the world. This research was conducted to determine the effects of salinity on physiological parameters of durum wheat (Triticum durum Desf.) genotypes. The research was conducted in the tissue culture laboratory at the Agriculture Faculty of Dicle University. The study consisted of one durum wheat commercial cultivar, five local cultivars and four advanced genotypes. There were three replications in a split-plot experimental design. Genotypes were germinated in four NaCl concentrations (0, 50, 100, 150 mM) in plastic boxes. There were statistically assured significant differences among the genotypes for all salt concentrations and all observed parameters (coleoptile length, seedling length, root length, seedling fresh weight, root fresh weight, seedling dry weight, root dry weight, germination rate and seedling vigor). There was significant decrease in all examined parameters depending on the increase of salt concentration. The ‘Sorgul’ genotype was most tolerant to salinity, in terms of root length and root dry weight, whereas ‘Altintoprak 98’ was most tolerant as measured by the impact of salinity on coleoptile length, seedling fresh weight, germination rate and seedling vigour. The ‘Beyaziye’ genotype was the most sensitive to salinity-induced stress. The results from this study demonstrated differences among durum wheat genotypes for seedling parameters measured in the presence of salinity stress. © 2015, Notulae Botanicae Horti Agrobotanici Cluj-Napoca. All Rights Reserved

Serebral Palsili Pediatrik Hastalarda Femoral Anteversiyon ve Femur Boyun-Şaft Açılarının Değerlendirilmesi ve Literatürün Tekrar Değerlendirilmesi

Amaç: Serebral palsi (SP), gelişimini tamamlamamış beyin hasarı sonucu oluşan kronik, sensorimotor bir hastalıktır. Bu çalışmada pediatrik SP’li hastalarda femoral anteversiyon (FA) ve femur boyun-şaft (FNS) açılarını değerlendirdik ve sağlıklı popülasyon ve hasta grubunun kendi içinde tutulum alt tiplerine ve Kaba Motor Fonksiyonel Sınıflandırma Sistemi’ne (GMFCS) göre bir fark olup olmadığını araştırdık. Gereç ve Yöntem: Spastik SP tanısı alan ve cerrahi uygulanan 30 hasta (20 kadın, 10 erkek; ortalama yaş 10 yıl 8 ay; dağılım 4-14 yıl) geriye dönük olarak değerlendirildi. Çalışmada 30 hastanın 51 kalçası incelendi. Otuz hastanın 11’i kuadriplejik, 10’u diplejik ve dokuzu hemiplejikti. GMFCS’ye göre II. düzeyde dokuz, III. düzeyde sekiz, IV. düzeyde altı ve düzey V’te yedi hasta bulunmaktaydı. Hasta ve kontrol grubunun bilgisayarlı tomografi görüntüleri hastanenin radyolojik dosyalarından değerlendirildi. Tüm hastaların FA ve FNS açıları ölçüldü ve elde edilen değerler karşılaştırıldı. Bulgular: FNS açısı (p<0,05) ve FA açısı (p<0,05) hasta grubunda kontrol grubuna göre anlamlı olarak daha büyüktü. Kuadriplejik hastalarda FNS açısı (p<0,05) ve FA açısı (p<0,05) diplejik ve hemiplejik gruba göre anlamlı olarak daha büyüktü. FNS açısı (p<0,05) ve FA açısı (p<0,05), GMFCS seviye IV/V hastalarında, GMFCS seviye II/III hastalarına göre anlamlı olarak daha büyüktü. Sonuç: Kalçaya etki eden bazı kaslarda spastisite ve buna bağlı olarak kas gücünde dengesizlik nedeniyle SP’de normal popülasyona göre FA ve FNS açıları artar. Kuadriplejiklerde açılar diplejiklere ve hemiplejiklere göre belirgin olarak daha yüksektir, GMFCS seviye IV/V, GMFCS II/III’e göre daha yüksek açı değerlerine sahiptir

In Which Conditions is Conservative Tratment Likely to Fail in Humeral Shaft Fractures? A Retrospective Analysis of 67 Patients

Aim:Humeral shaft fractures are one of the most common fractures of the upper extremity. Most humeral shaft fractures can be treated conservatively, but in some cases, surgical treatment is required. In this study, the characteristics of patients who needed surgical intervention due to unsuccessful conservative treatment and inability to achieve union were investigated.Materials and Methods:Data of 67 patients [female (n=41) and male (n=26)] in whom conservative treatment was initiated due to humeral shaft fracture were evaluated retrospectively. The data of the patients in whom treatment had to be switched to surgery during the follow-up period were analyzed. Age, gender, trauma type, fracture site and vitamin D levels on the day of the fracture were noted.Results:At the end of 54 (42-77) days, the treatment was switched to surgery due to nonunion in 14 patients. All of these patients were female, over the age of 60 years, and the humeral fractures in these patients were in the middle third of the humerus. The mean 25(OH) vitamin D [25(OH) D] level of these patients was 14 mg/dL (4-22 mg/dL).Conclusion:It is concluded that the conservative treatment is prone to fail if humeral shaft fracture is a proximal oblique or a mid-shaft one, if the patient is over the age of 60 years and female, and if 25(OH)D level of the patient is low

Design and Implementation 4-Bit Quaternary MVL Arithmetic and Logic Unit

In the recent years, there were major importance to Multiple Valued Logic (MVL), where the most common reasons for considering the implementation of MVL circuits better then binary valued circuits are that reducing wiring congestion as compared to binary circuits, using a single conductor to transmit three or more discrete voltage or current values allows for greater information content per wire and the circuit cost models would be more economical. Therefore, in this paper the MVL concepts have been used to design 4-bit quaternary MVL Arithmetic and Logic Unit, which is considered a basic unit of a MVL microprocessor. It is the "heart" of a microprocessor and we could say that everything else in the microprocessor is there to support the ALU. The proposed Arithmetic and Logic Unit will do the operations as Addition, Subtraction, Maximum, Minimum and Invert. Simulation Program with Integrated Circuit Emphasis (SPICE) tool in Cadence simulator used in simulation the proposed Arithmetic and Logic Unit. The simulation results tells that the design is more efficient compared with the binary ALU and the circuit will be less area and less number of transistors