Approximation of functions of two variables by certain linear positive operators

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an $r$th order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.Comment: 13 page

APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator

On Bivariate Meyer-König and Zeller Operators

WOS: 000338514500025This work relates to bivariate Meyer-Konig and Zeller operators, M-n,M- n is an element of N which are not a tensor product setting. We show the monotonicity of the sequence of operators for n under convexity, moreover we study the property of monotonicity in the sense of Li [9]. Finally, we provide an rth order generalization M-n([r]) of M-n and also study approximation of M-n([r])

Batch and continuous removal of heavy metals from industrial effluents using microbial consortia

Bio-removal of heavy metals, using microbial biomass, increasingly attracting scientific attention due to their significant role in purification of different types of wastewaters making it reusable. Heavy metals were reported to have a significant hazardous effect on human health, and while the conventional methods of removal were found to be insufficient; microbial biosorption was found to be the most suitable alternative. In this work, an immobilized microbial consortium was generated using Statistical Design of Experiment (DOE) as a robust method to screen the efficiency of the microbial isolates in heavy metal removal process. This is the first report of applying Statistical DOE to screen the efficacy of microbial isolates to remove heavy metals instead of screening normal variables. A mixture of bacterial biomass and fungal spores was used both in batch and continuous modes to remove Chromium and Iron ions from industrial effluents. Bakery yeast was applied as a positive control, and all the obtained biosorbent isolates showed more significant efficiency in heavy metal removal. In batch mode, the immobilized biomass was enclosed in a hanged tea bag-like cellulose membrane to facilitate the separation of the biosorbent from the treated solutions, which is one of the main challenges in applying microbial biosorption at large scale. The continuous flow removal was performed using fixed bed mini-bioreactor, and the process was optimized in terms of pH (6) and flow rates (1 ml/min) using Response Surface Methodology. The most potential biosorbent microbes were identified and characterized. The generated microbial consortia and process succeeded in the total removal of Chromium ions and more than half of Iron ions both from standard solutions and industrial effluents

SINGLE CENTER EXPERIENCE: RETROSPECTIVE ANALYSIS OF FOLLICULER LYMPHOMA

Amaç: Folliküler lenfoma, ikinci en sık görülen lenfoma türü olup, bütün non hodgkinlenfomaların %20-25'ini, yavaş seyirli (indolen) lenfomaların ise %70'ini oluşturur.Ortalama yaşam beklentisi yaklaşık 10 yıldır. Fakat beklenen yaşam süresi monoklonalantikorların keşfi ile uzamıştır.Yöntemler: Bu çalışmada, folliküler lenfomalı 28 hastanın klinikopatolojik özellikleri,tedavi modaliteleri ve yanıt oranları retrospektif olarak değerlendirilmiştir.Bulgular: Hastaların %39,3'ünde B semptomları ve %35,7'sinde kemik iliği tutulumumevcuttu. FLIPI skorlarına göre hastaların %37,5'i düşük, %21,4'ü orta ve %39,3'ü iseyüksek risk grubundaydı. Hastaların %32,1'i hastalığın erken evrelerinde idi.Hastaların %46,4'inde evre 1 ve %14,3'ünde evre 3 patolojik hastalık mevcuttu. %78,6hasta kemoterapi almıştı ve en çok kullanılan rejim de CVP (%53,6) idi. %14,3 hastadaradyoterapi uygulanmış ve hastaların %7,1' i tedavisiz izlenmişti. 9 hastada rituksimabilk sırada kullanılmış, 5 hastada ise ilk nükste kemoterapi ile birlikte uygulanmıştı. İlksıra kemoterapi sonrası; toplam remisyon oranı %74 olmakla birlikte hastaların%46,4'ünde tam yanıt, %25'inde ise kısmi yanıt gözlendi. Ortanca izlem süresi 32,8 ay(5-101 ay) ve ortanca hastalıksız sağ kalım 22,5 aydı (1-67 ay).Sonuç: Çalışmamızın sonuçları doğrultusunda, folliküler lenfomada başlangıçtedavisinde rituksimablı kemoterapi rejimleri ve remisyon sağlanan olgularda idamerituksimab tedavisinin akılcı bir hasta yönetimi olduğunu düşünmekteyiz. Objectıve: Follicular lymphoma is the second most common lymphoma comprising20-25% of all non hodgkin lymphomas and 70% of low grade lymphomas.Mediansurvival is around 10 years but survival rates were improved since the discovery ofmonoclonal antibodies.Methods: In this study, the clinicopathological features, the treatment modalities andthe response rates of 28 patients with follicular lymphoma were retrospectivelyanalyzed.Results: 39.3% of patients had b symptoms and the bone marrow involvement rate was35.7%. FLIPI scores; 35.7% of patients were in low risk group, 21.4% were in intermedi ate risk group and 39.3% were in high risk group. 32.1% of patiens were in early stagesof disease. 46.4% of patients had grade 1 and 14.3% had grade 3 pathologicdisease.78.6% of patients were treated with chemotherapy and the leading regimenwas CVP (53.6%) 14.3% of patients were treated with radiotherapy and 7.1% of patientswere followed without treatment.9 patients had rituximab as a firstline therapy and 5patients had rituximab after first relapse with adjunct to the chemotherapy. 4 patientshad rituximab as a maintanence therapy after remission. After firstline chemotherapy,with a total remission rate of 71.4,46.4% of patients had complete remission and 25%had partial remission.Median follow up time was 32.8 months (5-101 months) andmedian disease free survival was 22.5 months (1-67 months).Conclusion: We may conclude that the combination of rituximab with the firstlinetherapies and maintanence of rituximab after the first response is a rational way ofmanagement of follicular lymphoma with regard to the analysis of data obtained fromthis study

Feasibility studies for the measurement of time-like proton electromagnetic form factors from p¯ p→ μ+μ- at P ¯ ANDA at FAIR

This paper reports on Monte Carlo simulation results for future measurements of the moduli of time-like proton electromagnetic form factors, | GE| and | GM| , using the p¯ p→ μ+μ- reaction at P ¯ ANDA (FAIR). The electromagnetic form factors are fundamental quantities parameterizing the electric and magnetic structure of hadrons. This work estimates the statistical and total accuracy with which the form factors can be measured at P ¯ ANDA , using an analysis of simulated data within the PandaRoot software framework. The most crucial background channel is p¯ p→ π+π-, due to the very similar behavior of muons and pions in the detector. The suppression factors are evaluated for this and all other relevant background channels at different values of antiproton beam momentum. The signal/background separation is based on a multivariate analysis, using the Boosted Decision Trees method. An expected background subtraction is included in this study, based on realistic angular distributions of the background contribution. Systematic uncertainties are considered and the relative total uncertainties of the form factor measurements are presented

PANDA Phase One - PANDA collaboration

The Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany, provides unique possibilities for a new generation of hadron-, nuclear- and atomic physics experiments. The future antiProton ANnihilations at DArmstadt (PANDA or P¯ANDA) experiment at FAIR will offer a broad physics programme, covering different aspects of the strong interaction. Understanding the latter in the non-perturbative regime remains one of the greatest challenges in contemporary physics. The antiproton–nucleon interaction studied with PANDA provides crucial tests in this area. Furthermore, the high-intensity, low-energy domain of PANDA allows for searches for physics beyond the Standard Model, e.g. through high precision symmetry tests. This paper takes into account a staged approach for the detector setup and for the delivered luminosity from the accelerator. The available detector setup at the time of the delivery of the first antiproton beams in the HESR storage ring is referred to as the Phase One setup. The physics programme that is achievable during Phase One is outlined in this paper

SOME PROPERTIES OF THE MULTIVARIATE SZAZS OPERATORS

WOS: 000303430700001In this work some properties of multivariate Szazs operators are considered. We prove that the Szazs operators preserve some properties of the function of modulus of continuity, Lipschitz condition, and a kind of monotonicity

ON APPROXIMATION PROPERTIES OF TWO VARIABLES OF MODIFIED KANTOROVICH-TYPE OPERATORS

WOS: 000463698900015In the present paper, we introduce certain modification of Szasz-Mirakyan-Kantorovich-type operators in polynomial weighted spaces of continuous functions of two variables. Then we research some approximation properties of these operators. We give some inequalities for the operators by means of the weighted modulus of continuity and also obtain a Voronovskaya-type theorem. Furthermore, in the paper we show that our operators give better degree of approximation of functions belonging to weighted spaces than classical Szasz-Mirakyan operators.Scientific Research Project Coordination Unit(BAP) in Kirikkale University [2015/7]This paper is supported by the Scientific Research Project Coordination Unit(BAP) in Kirikkale University(Grant code: 2015/7)